# Uncertainty Analysis of Phytoplankton Dynamics in Coastal Waters Proefschrift

Uncertainty Analysis of Phytoplankton Dynamics in Coastal Waters Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus prof. ir. K. C. A. M. Luyben, voorzitter van het College voor Promoties, in het openbaar te verdedigen op woensdag 25 November 2015 om 12.30 uur door Lixia Niu Master of Science in Hydrology and Water Resources Engineering Hohai University, China geboren te Puyang, China This dissertation has been approved by the promotors: Prof. drs. ir. J.K. Vrijling Prof. dr. ir. P.H.A.J.M. van Gelder Composition of the doctoral committee: Rector Magnificus voorzitter Prof. drs. ir. J.K. Vrijling Technische Universiteit Delft, promotor Prof. dr. ir. P.H.A.J.M. van Gelder Technische Universiteit Delft, promotor Independent members: Prof. dr. ir. Z.B. Wang Technische Universiteit Delft Prof. ir. T. Vellinga Technische Universiteit Delft Dr. Y.Q. Guan Hohai University Dr. F.J. Los Deltares Dr. F. Heinis Heinis Waterbeheer en Ecologie Substitute member: Prof. dr. D.P. Solomatine Technische Universiteit Delft/UNESCO-IHE Institute for Water Education, reservelid This work was financially supported by the China Scholarship Council (CSC). Printed by Ipskamp Drukkers ISBN 978-94-6259-955-0 c 2015 by Lixia Niu Copyright All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or machanical, including photocopying, recording or by any information storage and retrieval system, without the prior permission of the author. Author email: [email protected]; [email protected] Summary There is an increasing concern about the interactions between phytoplankton and coastal ecosystems, especially on the negative effects from coastal eutrophication and phytoplankton blooms. As the key indicator of the coastal ecosystem, phytoplankton plays an important role in the whole impact-effect chain. Primary production by phytoplankton forms the basic link in the food-chain. A lot of effort has been paid to the investigation of phytoplankton dynamics on the basis of literature surveys, field observations, and model predictions, providing a better understanding of the coastal ecosystem. In this thesis, the significance of phytoplankton is stressed and no discussion is given to zooplankton. Phytoplankton dynamics (i.e. growth, loss, grazing, biomass, bloom) is closely related to environmental variables, such as light intensity, temperature, nutrients, suspended matter, wind profiles, and tidal currents. In chapter 2, factor analysis is developed to characterize the contributions of the environmental variables to the phytoplankton biomass (in terms of chlorophyll a), determined by the 10-year’s historical record from 2000 through 2009 in the case study of the Frisian Inlet. In this thesis we focus on three elements of phytoplankton dynamics: phytoplankton growth, phytoplankton biomass, and phytoplankton blooms. Based on the specific properties of the case zones, the Frisian Inlet and the Jiangsu coast, different focuses are taken. Field measurement of phytoplankton dynamics is expensive, thus we use mathematical models as the useful and convenient tool to perform the investigation. The BLOOM II model and the phytoplankton model are introduced to investigate the annual variation of the phytoplankton biomass in coastal waters (chapter 3, chapter 4, and chapter 5). The reliability of the parameter estimation largely determines the confidence of the model output. The estimate function of the phytoplankton growth rate is controlled by the variables of temperature, light intensity and nutrients, separately or comprehensively. The phytoplankton needs light to grow through the photosynthesis process, whereas the light intensity is attenuated due to the absorption by chlorophyll a, salinity, organic matter, turbid water, and background extinction. Phytoplankton consumes nutrients, in turn, phytoplankton releases nutrients back to the water bodies ii Summary iii through its death and the subsequent decay. In this research the growth rate is estimated with the effects of light intensity and ambient water temperature. The loss rate and the grazing rate are simplified as constants in the models, but actually are varied with the environmental variables. Moreover, the role of the vertical mixing process on the phytoplankton is significant, controlling the vertical distributions of the phytoplankton biomass and affecting the availability of light intensity and nutrients. Although a vertical phytoplankton model is discussed in chapter 4 and chapter 5, reducing the three-dimensional model to a onedimensional model, the vertical mixing rate involved in both cases is processed with the Delft3D model. In this context, the estimation of the vertical mixing rate increases the applicability of the phytoplankton model. Chapter 4 discusses the effect of the vertical turbulent diffusivity on the variation of the phytoplankton biomass, driven by the physical and chemical conditions. Chapter 5 performs a similar study of the vertical mixing rate as described in chapter 4, but now only driven by the physical condition, as well as one driver (vertical stability threshold) of the occurrence of the phytoplankton blooms. The model prediction is always accompanied with the simplification, overestimating or underestimating the actual status, named as original value ± uncertainty. Thus, uncertainty analysis is required to be integrated with the model output. The uncertainty arising from the model output is focused, only a short discussion is given to the uncertainty arising from the input. The Bootstrap method and the Bayesian Markov Chain Monte Carlo simulation are approached to give insight in the model prediction with a characterization of uncertainty analysis. Samenvatting Er is toenemende bezorgdheid over de interactie van het fytoplankton en het ecosysteem van de kust, met name met betrekking tot de negatieve effecten van eutrofiëring van de kustwateren en de algenbloei van fytoplankton. Als de belangrijkste indicator van het kust-ecosysteem, speelt de fytoplankton een belangrijke rol in de hele oorzaakeffectketen. De primaire productie van fytoplankton vormt de basis in de voedselketen. Veel aandacht is besteed aan het onderzoek van de dynamiek van fytoplankton in de literatuur, veldwaarnemingen en modelvoorspellingen, om tot een beter begrip van het kust-ecosysteem te komen. In dit proefschrift wordt de betekenis van het fytoplankton in de voedselketen benadrukt; zoöplankton wordt in dit proefschrift verder niet besproken. De dynamiek van het fytoplankton (zoals groei, vermindering, grazen, biomassa, celgrootte, bloei) is nauw verbonden met de variabelen die zich voordoen in de natuur-lijke omgeving, zoals lichtintensiteit, temperatuur, voedingsstoffen, zwevende sedimenten, wind profielen en getijdenstromingen. In hoofdstuk 2 wordt een factoranalyse ontwikkeld om de bijdragen van de omgevingsvariabelen te karakteriseren en om de drij-vende krachten te onderscheiden, bepaald door de gegevens uit de 10-jarige historische record van 2000 tot en met 2009, in een case studie van de Friese Inlaat. Drie aspecten van dynamiek van het fytoplankton, namelijk de groei van fytoplankton, de fytoplankton biomassa en de bloei van fytoplankton, zijn de focus van dit onderzoek. Veldmetingen van de fytoplankton dynamiek zijn kostbaar, daarom is gekozen voor het gebruik van wiskundige modellen als instrument voor de uitvoering van het onderzoek. Het BLOOM II-model en het fytoplankton model worden toegepast om de jaarlijkse variaties van de fytoplankton biomassa in de kustwateren te onderzoeken (hoofdstuk 3, hoofdstuk 4, en hoofdstuk 5). De betrouwbaarheid van de schatting van de variabelen is grotendeels bepalend voor het vertrouwen in de output van het model. De betrouwbaarheid van de bepaling van de groei van het fytoplankton op jaarbasis wordt gecontroleerd door de variabelen van temperatuur, lichtintensiteit en voedingsstoffen, afzonderlijk of geheel omvattend. Fytoplankton heeft licht nodig voor het groeiproces door middel van fotosynthese, terwijl de lichtintensiteit wordt verzwakt als gevolg van iv Samenvatting v de absorptie door de chlorofyl a, het zoutgehalte, het gehalte aan organische stof, het troebele water en het uitsterven van de achtergrond. De fytoplankton verbruikt voedingsstoffen, maar de fytoplankton geeft ook weer voedingsstoffen terug aan het water door afsterving en het daaropvolgende verval. Het verlies en de begrazing van het fytoplankton zijn in het model vereenvoudigd, maar zijn in werkelijkheid meer gevarieerd onder invloed van de omgevingsvariabelen. De rol van het verticale vermengingsproces van fytoplankton is aanzienlijk, deze is namelijk van invloed op de verticale distributies van de fytoplankton biomassa en heeft gevolgen voor de aanwezigheid van lichtintensiteit en voedingsstoffen. Hoewel in hoofdstuk 4 en hoofdstuk 5 een verticaal model van fytoplankton wordt besproken waarin het driedimensionale model van fytoplankton wordt gereduceerd tot een eendimensionaal model, wordt de mate van verticale vermenging in beide gevallen ontleend aan het Delft3D model. In deze context draagt een betrouwbare schatting van de verticale vermengingsgraad toe aan the toepasbaarheid van het fytoplankton model. In hoofdstuk 4 wordt het effect van de verticale turbulente op de variatie van de fytoplankton biomassa, gedreven door de getijde stromingen en de wind profielen, besproken. In hoofdstuk 5 wordt dezelfde studie van de mate van verticale vermenging, zoals beschreven in hoofdstuk 4, uitgevoerd, maar nu gedreven door de fysieke condities, zowel als een aanjager (de verticale stabiliteitsdrempel) van de waarschijnlijkheid van fytoplankton bloei. De voorspelling van het model gaat gepaard met de vereenvoudiging, overschatting of onderschatting van de werkelijke situatie, genoemd oorspronkelijke waarde ± onzekerheid. Dus, de onzekerheidsanalyse dient geı̈ntegreerd te worden met de output van het model. De onzekerheid die voortvloeit uit de output van het model is de focus, er wordt slechts een korte bespreking van onzekerheid als gevolg van de input van het model gegeven. De Bootstrap methode en de Bayesian Markov Chain Monte Carlo (BMCMC) simulatie zijn ontwikkeld om inzicht te geven in de voorspellingen van het model, met een karakterisering van de onzekerheidsanalyse. Contents Summary ii Samenvatting iv Contents vi List of Figures ix List of Tables xiv Abbreviations xv Symbols xvi 1 Introduction 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Phytoplankton dynamics . . . . . . . . . . . . . 1.1.2 Mathematical models of phytoplankton dynamics 1.1.3 Uncertainty of phytoplankton dynamics . . . . . 1.1.4 Description of the study areas . . . . . . . . . . . 1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Phytoplankton dynamics in response to the environmental factors 2.1 Test case one: Statistical analysis of the phytoplankton biomass in the Wadden Sea near Lauwersoog (NL) . . . . . . . . . . . . . . . . . . . . . 2.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Data information in 10-year time period from 2000 through 2009 at Lauwersoog station . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Factor analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Test case two: Estimate of the phytoplankton growth rate in the coastal waters of Lianyungang (CN) . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Data information at Lianyungang station . . . . . . . . . . . . . 2.2.3 Estimate function of the phytoplankton growth rate . . . . . . . 2.2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Application of the BLOOM II model vi . . . . . . . 1 1 1 3 4 5 6 8 11 . 11 . 11 . 12 . 12 . 14 . . . . . 23 23 23 24 26 29 Contents 3.1 3.2 vii Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Description of the BLOOM II model . . . . . . . . . 3.2.2 Bayesian Markov Chain Monte Carlo (BMCMC) . . 3.2.3 Cost-function . . . . . . . . . . . . . . . . . . . . . . BLOOM II model set-up at the Frisian Inlet . . . . . . . . . 3.3.1 Hydrodynamic characteristics and ecological factors 3.3.2 Model scenarios . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Observational analysis of the driving forces . . . . . 3.4.2 BLOOM II model output . . . . . . . . . . . . . . . 3.4.3 BMCMC simulation . . . . . . . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 30 30 30 32 32 32 33 34 34 35 37 40 4 A vertical model study of phytoplankton dynamics 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Phytoplankton model . . . . . . . . . . . . . . . . . . . . . 4.3 Case study of the Frisian Inlet . . . . . . . . . . . . . . . . 4.3.1 Observational analysis . . . . . . . . . . . . . . . . . 4.3.2 Parameter estimation . . . . . . . . . . . . . . . . . 4.3.3 Validation of the phytoplankton model . . . . . . . . 4.3.4 Vertical distributions of the phytoplankton biomass 4.3.5 Depth-averaged phytoplankton biomass . . . . . . . 4.3.6 Uncertainty analysis . . . . . . . . . . . . . . . . . . 4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 43 44 46 46 48 49 51 54 55 57 . . . . . . . . . . . . . . . . . 59 59 60 60 61 62 64 65 67 67 68 70 71 73 74 77 78 81 3.3 3.4 3.5 5 Physical limitation of phytoplankton bloom development 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Phytoplankton model . . . . . . . . . . . . . . . . . . . . . 5.2.1 Vertical stability theory . . . . . . . . . . . . . . . . 5.2.2 Critical depth . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Parameter estimation . . . . . . . . . . . . . . . . . 5.2.4 Skill assessment . . . . . . . . . . . . . . . . . . . . . 5.2.5 Bloom forecast . . . . . . . . . . . . . . . . . . . . . 5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Statistical analysis of the monitored data . . . . . . 5.3.2 Specific growth rate and net growth rate . . . . . . . 5.3.3 Validation of the phytoplankton model . . . . . . . . 5.3.4 Vertical distributions of the phytoplankton biomass 5.3.5 Depth-averaged phytoplankton biomass . . . . . . . 5.3.6 Vertical stability threshold . . . . . . . . . . . . . . 5.3.7 Critical depth and mixed layer depth . . . . . . . . . 5.3.8 Phytoplankton bloom . . . . . . . . . . . . . . . . . 5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions and future work 83 6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Contents viii 6.1.1 6.2 Statistical analysis of the phytoplankton biomass in the environmental variables . . . . . . . . . . . . . . 6.1.2 Validation of the mathematical models . . . . . . . . 6.1.3 Application of the mathematical models . . . . . . . 6.1.4 Uncertainty analysis of phytoplankton dynamics . . Suggestions for future work . . . . . . . . . . . . . . . . . . A BLOOM II model A.1 Nutrient cycling . . . . . . . . A.2 Light attenuation . . . . . . . A.3 Growth and mortality . . . . A.4 Reaeration of dissolve oxygen A.5 Competition between species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . response to . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 85 85 86 86 . . . . . 89 89 91 91 91 91 B Factor analysis 93 B.1 Principal Component Analysis (PCA) . . . . . . . . . . . . . . . . . . . . 93 B.2 Maximum Likelihood (ML) . . . . . . . . . . . . . . . . . . . . . . . . . . 95 B.3 Unweighted Least Squares (ULS) . . . . . . . . . . . . . . . . . . . . . . . 96 C Critical depth D Commonly used probability D.1 Normal distribution . . . D.2 Lognormal distribution . . D.3 Gamma distribution . . . D.4 Weibull distribution . . . 97 distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E Statistical properties of random variables E.1 Mean, median, and quartiles . . . . . . . . E.2 Variance and standard deviation . . . . . E.3 Skewness coefficient and kurtosis . . . . . E.4 Covariance and correlation coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 99 99 100 101 . . . . . . . . . . . . 102 . 102 . 103 . 103 . 104 Bibliography 105 Glossary 121 Acknowledgements 123 Curriculum Vitae 125 List of Figures 1.1 1.2 1.3 1.4 1.5 2.1 2.2 2.3 2.4 2.5 2.6 Contribution of the environmental variables to phytoplankton dynamics in coastal waters. The variation of the zooplankton is influenced, directly or indirectly, by the phytoplankton variability. In this thesis the research is focused on the significance of the phytoplankton, and the zooplankton remains outside the scope of the current thesis. . . . . . . . . . . . . . . Case area of the Frisian Inlet and surrounding water zones. A: Lauwersoog station; B: Huibertgat station; C: Harlingen station. . . . . . . . . . . . Case area of the Jiangsu coastal zone (from north to south, the red stars indicate Lianyungang station, Dafeng station, Yangkou station, and the north branch of the Yangtze River estuary, respectively). . . . . . . . . . Phytoplankton abundance at the Dafeng estuary in 2006 . . . . . . . . . Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Observed variations in the Wadden Sea near Lauwersoog (2000-2009) . . Historical analysis of phytoplankton biomass (in terms of chlorophyll a, expressed in mg m−3 ) in the Wadden Sea near Lauwersoog, determined by the dataset from 2000 through 2009. A: frequency distribution, presented as histogram; B: goodness-of-fit test using a probability model (Gamma distribution, x-axis indicates the observed cumulative probability and yaxis indicates the expected cumulative probability, κ means the shape parameter of Gamma distribution and ν means the rate parameter) . . Seasonal dynamics of phytoplankton biomass (in terms of chlorophyll a) and physical-chemical conditions in the Wadden Sea near Lauwersoog (2000-2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Target diagram for the first two rotated component/factor loading matrix from three extraction methods, determined by the 2000-2009 dataset in the Wadden Sea near Lauwersoog (x-axis: first component; y-axis: second component) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Target diagram for the first two rotated component/factor score matrix from three extraction methods, determined by the 2000-2009 dataset in the Wadden Sea near Lauwersoog (x-axis: first component; y-axis: second component) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time series variations of the associated variables (I, T , Chla, P ) at Lianyungang station, monitored either weekly or biweekly over the year of 2006. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x . 2 . 6 . 7 . 7 . 10 . 13 . 16 . 17 . 22 . 23 . 24 List of Figures xi 2.7 Estimate of the phytoplankton growth rate, expressed in day −1 . In which, graph A denotes the comparison of the specific growth rate between the photosynthetic light curve and Smith’s function; graph B denotes the variations of the specific growth rate and the net growth rate over the year of 2006 in the Lianyungang coastal waters. The red dashed line indicates a balance of k = 0. . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.1 Observed driving forces used in the model, (A )Wind profile (speed: m s−1 , direction: degree), (B) I and T , (C) Annually variations of nutrients (mg l−1 ), (D) salinity (SPU) and SP M (g m−3 ). The sources of Figs of A and B are from the KNMI database, accessible through www.knmi.nl; Figs of C and D are from the DONAR database, at Lauwersoog station, accessible through http://live.waterbase.nl/waterbase_wns. cfm?taal=en. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Graphical comparisons between the model results and the observations over the year of 1992 at Lauwersoog station. In which, the blue smooth lines indicate the model results, and the red scatters indicate the observations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The first two graphs indicate the frequency distributions of secchi depth and chlorophyll a. The third graph indicates the secchi depth against chlorophyll a, using a non-linear function (R2 = 0.7113) . . . . . . . . . Cumulative density function (CDF, log scale) of chlorophyll a in response to nutrient availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . Density of chlorophyll a in the BMCMC simulation, expressed in mg m−3 . In which, x denotes the modelled chlorophyll a; y denotes the prediction with uncertainty analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . Gelman-Rubin convergence statistics in the BMCMC model. The green line indicates the normalized width of the central 80% interval of the pooled runs; the blue line indicates the average width of 80% intervals within the individual runs; the red line indicates the ratio of the green line to the blue line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trace plots of the predicted chlorophyll a, expressed in mg m−3 . . . . . 3.2 3.3 3.4 3.5 3.6 3.7 4.1 4.2 4.3 4.4 A function fits well with the observations ( Iz /I0 > 1%) of light attenuation coefficient (Kd ) and euphotic depth (Ze ) at the Frisian Inlet. The light attenuation coefficient is caused by the phytoplankton growth and SP M at Lauwersoog station (high turbidity, table 4.2), but only by the phytoplankton growth at Huibertgat station. . . . . . . . . . . . . . . . Component loadings in rotated space by the principal component analysis. In which, x-axis indicates the first component, and y-axis indicates the second component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Annual variations of the specific growth rate ( the black smooth line ) and the net growth rate ( k1: Lauwersoog station; k2: Huibertgat station), expressed in day −1 . The specific growth rate has a big potential range, varying from 0.38 day −1 to 1.87 day −1 . The net growth rate varies from -0.25 day −1 to 0.25 day −1 at Lauwersoog station, while -0.14 day −1 to 0.12 day −1 at Huibertgat station. . . . . . . . . . . . . . . . . . . . . . . Graphical comparisons of chlorophyll a, salinity and nutrients between the Delft3D model output and the observations in 2009 at Huibertgat station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 . 36 . 37 . 39 . 40 . 40 . 41 . 48 . 48 . 49 . 50 List of Figures 4.5 4.6 4.7 4.8 5.1 5.2 5.3 5.4 5.5 5.6 Estimate of the vertical turbulent diffusivity (Ez ) with the Delft3D model at the Frisian Inlet, driven by the physical-chemical conditions and expressed in m2 s−1 . This factor is influenced by the tidal currents and the wind profile, mixing with the mass transport. The appropriate range of the vertical turbulent diffusivity can promote the phytoplankton growth (Margalef [1978]; Huisman et al. [1999]). . . . . . . . . . . . . . . . . . Graphical comparisons between model outputs (Delft3D model and vertical phytoplankton model) and monitored phytoplankton biomass in 2009 at the Frisian Inlet, expressed in g m−3 . . . . . . . . . . . . . . . . . . . Gelman-Rubin convergence statistics. x denotes the model output; y denotes the prediction with uncertainty analysis. The normalized width of the central 80% interval of the pooled runs is green, the average width of the 80% intervals within the individual runs is blue, and their ratio R0 is red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trace plots of the phytoplankton biomass at the Frisian Inlet, expressed in g m−3 . Graph A displays the model output of the phytoplankton biomass at Lauwersoog station. Graph B displays the prediction with uncertainty analysis at Lauwersoog station. A1 and B1 are to zoom out the iterations of the prediction. Graph C displays the prediction with uncertainty analysis at Huibertgat station. . . . . . . . . . . . . . . . . . Graphical comparisons of the water level between the model results (the red smooth line) and the observations (the blue markers) at Dafeng station (A) and Yangkou station (B) in the Jiangsu coastal zone, expressed in m. Most of the model results are consistent with the observations. . . . . . A logarithm function fits with the observations of suspended sediment (expressed in kg m−3 ) and turbidity (expressed in m−1 ) in the coastal waters of Jiangsu (R2 = 0.8261 ) . . . . . . . . . . . . . . . . . . . . . . Vertical distribution of the observed suspended sediment over the water depth in September at four stations (x-: sediment concentration, expressed in kg m−3 ; y-: water depth, expressed in m). . . . . . . . . . . . Work-flow of the bloom forecast from the physical limitation in the Jiangsu coastal waters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time series variations of the specific growth rate µ (the black smooth line) and the net growth rate k (the red dash line) at four stations along the Jiangsu coastal zone (A: Lianyungang, B: Dafeng, C:Yangkou, D: the north branch of the Yangtze River estuary), both expressed in day −1 . The specific growth rate is estimated from the combined effects of temperature and available light intensity, while the net growth rate is derived from the increase of the phytoplankton biomass with respect to time interval (8day or biweekly). The area-averaged patterns of light intensity (the blue smooth line, expressed in Einstein m−2 day −1 ) and water temperature (the purple smooth line, expressed in 0 C) are presented in the first graph (A). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Graphical comparisons of the modelled phytoplankton biomass and the monitored data in the Jiangsu coastal zone (A: Lianyungang station; B: Dafeng station; C: Yangkou station; D: the north branch of the Yangtze River estuary), determined by the samples over the year of 2006 at the surface layer. The red smooth lines indicate the model output and the blue markers indicate the monitored data, expressed in g m−3 . . . . . . xii . 51 . 51 . 55 . 56 . 62 . 63 . 64 . 66 . 69 . 71 List of Figures Annual distributions of the phytoplankton biomass for the different water depths over the year of 2006 in the Jiangsu coastal waters, expressed in g m−3 . In this graph, A, B, C and D denote the annual variations of the phytoplankton biomass for the water depths of 2m, 5m, 10m and 20m, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8 Boxplot of the depth-averaged phytoplankton biomass in the Jiangsu coastal waters. In which, the middle black line indicates the median, the shaded region stating the middle 50%. The lines extending out of the shaded region are the top and bottom 25% of the data and the horizontal lines at the top/bottom of the boxplot are the minimum and maximum values (non-extreme). One case is classified as the extreme value at Lianyungang station (2.76 g m−3 ). . . . . . . . . . . . . . . . . . . . . . 5.9 Good-of-fit test using the probability distribution models of Weibull and Normal, determined by the depth-averaged phytoplankton biomass over the year of 2006 in the Jiangsu coastal waters. In which, x-axis indicates the cumulative probability of the model output and y-axis indicates the cumulative probability of the predictions with the random effects. λ: shape parameter for Weibull distribution, γ: scale parameter for Weibull distribution. µ: mean value for Normal distribution, σ: standard deviation for Normal distribution. A: Lianyungang station (Weibull distribution); B: Dafeng station (Normal distribution); C: Yangkou station (Normal distribution); D: the north branch of the Yangtze River estuary (Weibull distribution). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10 Vertical stability threshold (the blue smooth line) and the vertical turbulent diffusivity (the red smooth line) at four stations (A: Lianyungang; B: Dafeng; C: Yangkou; D: the north branch of the Yangtze River estuary), expressed in m2 s−1 . The purple rectangles mark the moments that the vertical turbulent diffusivity is within the vertical stability threshold. . . 5.11 Time series variation of the critical depth (the blue smooth line) and the mixed layer depth (the red smooth line) over the year of 2006 at four stations (A: Lianyungang; B: Dafeng; C: Yangkou; D: the north branch of the Yangtze River estuary), expressed in m. The mixed layer depth starts to be shallower in March. The purple rectangles mark the moments that the mixed layer depth is shallower than the critical depth, corresponding to a higher phytoplankton density. . . . . . . . . . . . . . . . . . . . . . 5.12 Comparisons of the predicted blooms (the blue column) and the observations (the red arrow ) in the Jiangsu coastal zone (A: Lianyungang; B: Dafeng; C: Yangkou; D: the north branch of the Yangtze River estuary). The red arrow at Lianyungang station indicates the timing of the bloom occurrence, 2nd to 7th October, while the other two red arrows at the north branch of the Yangtze River estuary indicate the timings of 14th May and 4th August, respectively. . . . . . . . . . . . . . . . . . . . . . xiii 5.7 . 73 . 75 . 76 . 77 . 79 . 80 A.1 Ecological processes in BLOOM II (after Los et al. [2008]) . . . . . . . . . 90 List of Tables 2.1 2.2 2.3 2.4 2.5 2.6 Statistics of chlorophyll a in the Wadden Sea near Lauwersoog (2000-2009, n=187), expressed in mg m−3 . . . . . . . . . . . . . . . . . . . . . . . . Correlation matrix between the variables (187 samples for each variable) in the Wadden Sea near Lauwersoog, the Netherlands . . . . . . . . . . Calculation results of the Kaiser-Meyer-Olkin Measure of Sampling Adequacy and the Bartlett’s Test of Sphericity over the 10-year’s chlorophyll a record from 2000 through 2009 in the Wadden Sea near Lauwersoog . Eigenvalues and total variance explained by the factor analysis (PCA, ULS and ML) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary of the commonly used estimate of the specific growth rate . . Model summary of regression analysis for the specific growth rate and the net growth rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 . 19 . 20 . 21 . 24 . 27 3.1 3.2 3.3 Correlation matrix of chlorophyll a and other driving forces . . . . . . . . 34 Cost-function results of ten programs at the Frisian Inlet . . . . . . . . . . 35 Chlorophyll a in response to nutrient reduction (Dr: decrease rate) . . . . 38 4.1 4.2 4.3 Sinking rate and the components of the loss term considered in the model Statistics of the observed variables over the year of 2009 . . . . . . . . . . Statistical analysis of the model output for the different water depths (z=0m, 2m, 5m, 10m and 20m) over the year of 2009 at Lauwersoog station, expressed in g m−3 . . . . . . . . . . . . . . . . . . . . . . . . . . Statistical analysis of the annual cycles of the phytoplankton biomass for the different water depths (z=0m, 2m, 5m, 10m and 20m) over the year of 2009 at Huibertgat station, expressed in g m−3 . . . . . . . . . . . . . . Statistical analysis of the depth-averaged phytoplankton biomass at the Frisian Inlet over the year of 2009, expressed in g m−3 . . . . . . . . . . . Node statistics of the depth-averaged phytoplankton biomass in the BMCMC simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 4.5 4.6 5.1 5.2 5.3 5.4 Statistical analysis of the monitored samples in 2006 at four stations along the Jiangsu coast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Correlation matrix between the phytoplankton biomass and the physical conditions in 2006 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Skill assessment of the vertical phytoplankton model at four stations along the Jiangsu coast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Statistical analysis of the depth-averaged phytoplankton biomass in the Jiangsu coastal waters over the year of 2006 . . . . . . . . . . . . . . . . xiv 46 47 52 53 54 56 . 67 . 68 . 71 . 75 Abbreviations BMCMC Bayesian Markov Chain Monte Carlo BOD5 Biochemical Oxygen Demand CDF Cumulative Density Function Chla Chlorophyll a CI Confidence Interval DIN Dissolved Inorganic Nitrogen DO Dissolved Oxygen I Light Intensity KMO Kaiser- Meyer- Olkin measure of sampling adequacy ML Maximum Likelihood MLD Mixed Layer Depth N H4 Ammonium N O3 Nitrate NPZ Nutrient-Phytoplankton-Zooplankton PCA Principal Component Analysis PDF Probability Density Function P O4 Phosphorus RMSE Root Mean Square Error Si Dissolved Silicate SOA State Oceanic Administration people’s republic of China SPM Suspended Paticulate Matter T Temperature TN Total Nitrogen TP Total Phosphorus ULS Unweighted Least Squares xv Symbols c constant coefficient (default value 0.5) [-] C concentration of the state variable g m−3 C0 phytoplankton production at the surface layer g m−3 COV (M, D) covariance between predictions and observations [-] Cx normalized deviation between model results and observations Dx,t obervations Eh , Ez horizontal and vertical turbulent diffusivities m2 s−1 f plant metabolic loss day −1 g grazing rate by zooplankton day −1 Icr compensation light intensity Einstein m−2 day −1 or W m−2 I0 light intensity at the surface layer Einstein m−2 day −1 or W m−2 Iz light intensity at the water depth z Einstein m−2 day −1 or W m−2 k net growth rate day −1 K1/2 light intensity associated with half of Einstein m−2 day −1 the maximum photosynthetic rate or W m−2 Kbg background turbidity m−1 Kd light attenuation coefficient m−1 l loss rate of the phytoplankton day −1 L0 phytoplankton loss at the surface layer day −1 Mx,t model results p significance level xvi Symbols xvii P phytoplankton biomass g m−3 P0 photosynthetic rate Einstein m−2 day −1 or W m−2 PH depth-averaged phytoplankton biomass g m−3 at Huibertgat station PL depth-averaged phytoplankton biomass g m−3 at Lauwersoog station Pmax maximum photosynthetic rate Einstein m−2 day −1 or W m−2 r or R correlation coefficient r0 respiration rate day −1 s mortality rate of phytoplankton day −1 sdD standard deviation of the observations sdM standard deviation of the model results µ specific growth rate day −1 µmax maximum growth rate day −1 ux , uy , uz velocities in the x-, y- and z-direction m s−1 us sinking velocity m s−1 z water depth m Z zooplankton biomass g m−3 Zcr critical depth m Chapter 1 Introduction 1.1 1.1.1 Background Phytoplankton dynamics The coastal ecosystem is facing a big challenge caused by the effects of anthropogenic activities and coastal development (Kennedy et al. [2002]; Conley et al. [2002]; Andersen [2006]). As a critical indicator of the coastal ecosystem, phytoplankton plays an important role in the whole impact-effect chain and is responsible for most of primary production. In the open ocean, the phytoplankton accounts for 80% of the marine production (Martin et al. [1987]). The coastal environment is favorable for the phytoplankton as well. The investigation of phytoplankton dynamics has provided useful insights and a better understanding of the coastal ecosystem (Cloern [1996]; Pedersen and Borum [1996]; Edelvang et al. [2005]; Fu et al. [2009]; Godrijan et al. [2013]). Phytoplankton dynamics (i.e. growth, loss, grazing, biomass, bloom) varies with the characteristics of the environmental variables in the water column (Pedersen and Borum [1996]; Recknagel et al. [2006]; Taylor and Ferrari [2011]). The associated environmental variables are divided into three categories: physical condition, chemical condition and biological condition, displayed in figure 1.1. Take the physical condition as an example to illustrate the relation to phytoplankton dynamics: temperature and light intensity are closely related with the phytoplankton growth (Eppley [1972]; Smith [1980]; Geider et al. [1998]; Örnólfsdóttir et al. [2004]); a change of salinity has an effect on the phytoplankton 1 Chapter 1. Introduction 2 Figure 1.1: Contribution of the environmental variables to phytoplankton dynamics in coastal waters. The variation of the zooplankton is influenced, directly or indirectly, by the phytoplankton variability. In this thesis the research is focused on the significance of the phytoplankton, and the zooplankton remains outside the scope of the current thesis. community (Schmidt [1999]; Lionard et al. [2005]); wind stress and tidal currents affect the turbulent mixing rate determining the vertical distributions of the phytoplankton biomass (Serra et al. [2007]; Wong et al. [2007]; Woernle et al. [2014]), and affecting the species composition due to the effects on the availability of light intensity and nutrients (Ferris and Christian [1991]); suspended sediment absorbs and scatters light intensity, implying that phytoplankton is limited by light availability in the high turbidity zone (Wild-Allen et al. [2002]). Of all the environmental variables, phytoplankton dynamics is mainly refined by the limitations of light and nutrient availability (Eilers and Peeters [1988]; Boyer et al. [2009]). Light intensity Phytoplankton needs sunlight for the photosynthesis, which is averaged through the mixed layer zone. Light intensity over the water depth follows the Lambert-Beer’s Law (Dennison et al. [1993]; Devlin et al. [2008]), declining exponentially with the extinction coefficient. The extinction is the sum of inorganic suspended particulate matter, organic matter, chlorophyll a, salinity and background extinction. In temperate regions, light limitation happens in winter although sufficient nutrients are available. Nutrients Chapter 1. Introduction 3 Nutrient enrichment (eutrophication) becomes a societal issue due to the increased inputs into the coastal zone and as a consequence of the phytoplankton blooms (Cloern [1999]; Andersen [2006]; Howarth and Marino [2006]). The main sources of the coastal eutrophication are the use of fertilizers in agriculture, the presence of livestock, wastewater, urban runoff, and the load of the river flow. The coastal ecosystem stores and cycles the nutrients. The nutrient fluxes in the phytoplankton processes are described in figure A.1 (Appendix A). Three major nutrients (nitrogen, phosphorus, and silicon) are often considered as the limiting factors for phytoplankton, as well with light intensity. Nitrogen is an essential component of the light-sensitive pigments like chlorophyll a. In aquatic systems nitrogen is available as ammonium and nitrate. Compared with nitrogen, phosphorus is less sensitive to phytoplankton cells. Silicon is essential to only one phytoplankton group, diatoms, and is available as dissolved silicate. The earlier work on the estimate function of the phytoplankton growth rate is related to the nutrients, using Michaelis-Menten kinetics to explain the uptake rate by the algal cells (Caperon [1967]; Dugdale [1967]). Diverse studies have found that nitrogen, phosphorus, or both of them control the phytoplankton growth (Haney and Jackson [1996]; Flynn and Fasham [1997]; Geider et al. [1998]; Cloern [1999]; Geider and La Roche [2002]; Smith [2003]; Örnólfsdóttir et al. [2004]; Davey et al. [2008]), the phytoplankton biomass (Cloern [2001]; Fennel [2003]; Blauw and Los [2004]; Niu et al. [2015b]; Niu et al. [2015a]; Niu et al. [2015c]), and the phytoplankton community (Mei et al. [2009]; Jin et al. [2013]). 1.1.2 Mathematical models of phytoplankton dynamics Investigating the variations of phytoplankton dynamics could effectively elucidate the role of the coast in the biogeochemical cycling (Longhurst et al. [1995]). The behaviours of phytoplankton dynamics and the associated environmental variables can be adequately modelled with the ecological models in a site-specific station or in a broad application of the coastal and transitional water systems. A relatively large number of models has been managed as software for simulating the ecological processes ( i.e. nutrient cycles, transport of substances, phytoplankton biomass, primary production), examples include BLOOM II/GEM (Hydraulics [1991]; Hydraulics [2003]), ERSEM (Baretta Chapter 1. Introduction 4 et al. [1995]), NORWECOM (Skogen [1993]), COHERENS (Luyten et al. [1999]), and MIKE 3 (DHI [2000]). Moreover, the mathematical phytoplankton models are also convenient to analyze the phytoplankton processes. Generally, the characteristics of phytoplankton dynamics are coupled with a physical model (i.e. NPZ model with the advection-diffusion equation), considering the physical-chemical-biological interactions (Riley [1949]; Evans and Parslow [1985]; Franks [1997]; Franks [2002]; Murray and Parslow [1999]). With the simplifications, researchers reduce the three-dimensional phytoplankton model to a onedimensional form to get a practical solution (Riley [1949]; Evans and Parslow [1985]; Wong et al. [2007]; Taylor and Ferrari [2011]). 1.1.3 Uncertainty of phytoplankton dynamics When there are two or more environmental variables, there may be a variety of relationships between them. In the presence of uncertainty, the relationships are not unique. Given the values of one variable, there is a range of possible values of other variables. The relationships between the object and the associated variables thus require a probabilistic analysis (Chapman [1961]; Vrijling et al. [1998]; Van Gelder [2000]; Portielje et al. [2000]; Shukla et al. [2006]; Ang and Tang [2007]; Govaert [2009]). The classic modelling approaches are based on the steady status with some simplifying assumptions, but the actual processes are not deterministic with respect to uncertainty. The uncertainties cannot be avoided in any of the analyses. For example, we stress the significance of the phytoplankton in this thesis, whereas the grazing rate of the zooplankton is considered as a constant value. The grazing process of the zooplankton, however, is sensitive to the phytoplankton growth, varying with the environmental factors (Steele and Henderson [1992]; Haney and Jackson [1996]). Therefore, the simplification of the model is accompanied with an overestimate or an underestimate of the real status. To give insight in the model output, uncertainty analysis is required. In principle, uncertainty refers to a lack of knowledge, including parameter uncertainty (measurement errors, sampling errors, experimental errors, systematic errors), model uncertainty (due to the simplification of the real problems, mis-design of the model Chapter 1. Introduction 5 structure, model misuse), and scenario uncertainty (descriptive errors, aggregation errors, errors in the professional judgment, incomplete analysis). Tung et al. [2005] give the definition of uncertainty as following: “Uncertainty is attributed to the lack of perfect information concerning the phenomena, processes, and data involved in problem definition and resolution. Uncertainty could simply be defined as the occurrence of events that are beyond one’s control (Mays and Tung [1992]). In practical all engineering designs and operations, decisions are frequently made under uncertainty. As such, the reliability and safety of engineering projects are closely related to the level of uncertainty involved.” 1.1.4 Description of the study areas Frisian Inlet (the Netherlands) The Frisian Inlet, as one of the case studies, is a part of the Dutch Wadden Sea located in the north of the Netherlands, with two barrier islands of Ameland (the west one) and Schiermonikoog (the east one), displayed in figure 1.2. The Frisian islands seperate the Wadden Sea from the North Sea. A large supra tidal shoal in the centre divides the inlet into two smaller ones. Three representative stations are marked out, Lauwersoog station (A), Huibertgat station (B), and Harlingen station (C). The water environment in this area is favourable for the phytoplankton (Van Beusekom et al. [2012]). In this thesis, the Frisian Inlet is addressed to three major studies. The first study is to investigate the responses of phytoplankton biomass to environmental factors, determined in the 10-year time period from 2000 through 2009 (chapter 2). The second study focuses on the application of the BLOOM II model to predict the variation of the phytoplankton biomass (in terms of chlorophyll a), determined by the dataset in 1992 (chapter 3). The third study is to develop another convenient modelling approach, a vertical phytoplankton model, to investigate the vertical distributions of the phytoplankton biomass, determined by the dataset in 2009 (chapter 4). Jiangsu coast (China) The Jiangsu coast is bounded by the Shandong Peninsula and is the shore of the Yellow Sea, shown in figure 1.3. In 2006, according to the historical record of the State Oceanic Administration People’s Republic of China (SOA, http://www.soa.gov.cn/ Chapter 1. Introduction 6 Figure 1.2: Case area of the Frisian Inlet and surrounding water zones. A: Lauwersoog station; B: Huibertgat station; C: Harlingen station. zwgk/hygb/), the water was seriously polluted from the Guanhe estuary to the north branch of the Yangtze River estuary. The main pollutants are inorganic nitrogen, phosphate and oil. The average inorganic nitrogen in the Jiangsu coastal waters is 0.32 mg l−1 , and the average phosphate is 0.14 mg l−1 . The total nitrogen ranges from 0.051 mg l−1 to 1.102 mg l−1 , and the total phosphorus ranges from 0.014 mg l−1 to 0.282 mg l−1 . The ambient water environment provides a favourable living condition for the phytoplankton. Figure 1.4 presents the phytoplankton abundance in 2006 at the Dafeng estuary. The Radial Sand Ridges area locates in the south of the Jiangsu coast, with a complicated topography and a high suspended sediment concentration. The water masses are dominated by the Yangtze River diluted water, the Taiwan warm current and the Yellow Sea coastal water. This case study is approached to the application of the vertical phytoplankton model, and to investigate the occurrence of the phytoplankton blooms, determined by the dataset in 2006 (chapter 5). 1.2 Objectives This research explores the following questions: 1) How does the long-term phytoplankton biomass (in terms of chlorophyll a) respond to the physical-chemical factors (light intensity, salinity, water temperature, suspended matter, and nutrients)? Which estimate function of the phytoplankton growth is applicable? (chapter 2) 2) How is the annual variation of the phytoplankton biomass (in terms of chlorophyll a) Chapter 1. Introduction 7 Figure 1.3: Case area of the Jiangsu coastal zone (from north to south, the red stars indicate Lianyungang station, Dafeng station, Yangkou station, and the north branch of the Yangtze River estuary, respectively). Figure 1.4: Phytoplankton abundance at the Dafeng estuary in 2006 in a specific year of 1992? How will be the response of the phytoplankton biomass (in terms of chlorophyll a) to nutrient availability? How can we give insight in the predictions with an integration of uncertainty analysis? (chapter 3) 3) How can we investigate the annual variation of the phytoplankton biomass from physical-chemical properties in a specific year of 2009? How will the predictions fluctuate subject to uncertainty? (chapter 4) Chapter 1. Introduction 8 4) How will the physical limitation contribute to the phytoplankton biomass in a specific year of 2006? How can we investigate the bloom development from the physical properties? (chapter 5) Accordingly, the methods are introduced to solve the questions: 1) Boxplot analysis and factor analysis are convenient and flexible to process the longterm data; a reliable estimate function of the phytoplankton growth rate is developed, combined the effects of temperature and light intensity. 2) Bloom II model is able to produce the reliable prediction of chlorophyll a; Bayesian Markov Chain Monte Carlo simulation is used to give insight in the prediction with uncertainty. 3) A vertical phytoplankton model is developed, with the well-known simplifications, combined the analyses of Delft3D model; to give a reliable interval of the predictions, the BMCMC simulation is approached. 4) The application of the vertical phytoplankton model is performed to investigate the phytoplankton variability in coastal waters, and to extend the model application to investigate the bloom development. These questions are motivated by issues across a range of spatial and temporal scales. The objectives of this research are described below: 1) To investigate the responses of phytoplankton dynamics to the environmental factors and to characterize the significant and non-significant factors; 2) To predict the variation of the phytoplankton biomass (in terms of chlorophyll a); 3) To give insight in the vertical patterns of the phytoplankton biomass; 4) To investigate the phytoplankton bloom development from the physical properties; 5) To give insight in the model output with an integration of uncertainty analysis. 1.3 Outline of the thesis Three elements of phytoplankton dynamics are concentrated in this thesis: phytoplankton growth, phytoplankton biomass, and phytoplankton blooms. The outline of this thesis is illustrated in figure 1.5. In chapter 1, the general descriptions of phytoplankton dynamics are introduced. Chapter 1. Introduction 9 In chapter 2, the responses of phytoplankton dynamics to the environmental factors are discussed, emphasizing on the phytoplankton biomass (in terms of chlorophyll a) and the growth rate. Within this chapter, two case studies are presented, Lauwersoog station (NL) located in the north of the Dutch coast and Lianyungang station (CN) located in the north of the Jiangsu coast. For the case study of Lauwersoog station, the research aims to find out to what extent the phytoplankton biomass (in terms of chlorophyll a) responds to the environmental variables, characterizing the driving forces using factor analysis. For the case study of Lianyungang station, the research introduces a combined estimate function of the phytoplankton growth rate, incorporating the temperaturegrowth function with the photosynthetic light curve. In chapter 3, the ecological model of BLOOM II is applied to predict the variation of the phytoplankton biomass (in terms of chlorophyll a) in a case of the Frisian Inlet (NL). This study is determined by the dataset in 1992. Particular attention has been paid to the phytoplankton biomass (in terms of chlorophyll a) in response to nutrient availability. Considering the uncertainty arising from the model itself, the reliable prediction of the phytoplankton biomass is derived within the 95% confidence interval using the Bayesian Markov Chain Monte Carlo (BMCMC) simulation. In chapter 4, a vertical phytoplankton model is developed to investigate the vertical distributions of the phytoplankton biomass in the case of the Frisian Inlet. This study is determined by the dataset in 2009. To stress the uncertainty arising from the model itself, the BMCMC simulation is applied to give insight in the model output. In chapter 5, the extended application of the vertical phytoplankton model is performed to the Jiangsu coastal waters. Skill assessment is introduced to validate the reliability of the phytoplankton model. Additionally, the physical limitation of the phytoplankton bloom is discussed: vertical stability threshold and critical depth. The vertical stability threshold is captured from the condition of k > 0; the critical depth is derived from the concept of the compensation light intensity, a widely used condition to distinguish the occurrence of the bloom event. In chapter 6, various issues about phytoplankton dynamics are discussed and the suggestions for future work are elaborated. Figure 1.5: Outline of the thesis Chapter 2 Phytoplankton dynamics in response to the environmental factors 2.1 Test case one: Statistical analysis of the phytoplankton biomass in the Wadden Sea near Lauwersoog (NL) 2.1.1 Introduction Various research has completely accepted that chlorophyll a is a reliable measure of phytoplankton biomass (Voros and Padisak [1991]; Scharler and Baird [2003]; Ramı́rez et al. [2005]; Boyer et al. [2009]). Chlorophyll a, varying substantially from place to place and from time to time, has been explained as a consequence of many environmental factors, like nutrients (Margalef [1978]; Reckhow [1993]; Recknagel et al. [2006]; Paytan and McLaughlin [2007]; Struyf et al. [2010]; Jin et al. [2013]) and light intensity (Hunter and Laws [1981]; Huisman and Weissing [1994]; Moore [2009]). A multivariate analysis is needed to characterize the effects of the environmental factors to the phytoplankton biomass. There are several commonly used paths to complete the multivariate analysis, including structural analysis (Bölter et al. [1980]; Paudel and Montagna [2014]), factor analysis (Kaiser [1960]; Chau and Muttil [2007]), principal component analysis (Pedersen and Borum [1996]; Schlüter et al. [2008]; Friedrichs et al. [2009]; Primpas et al. [2010]; 11 Chapter 2. Phytoplankton dynamics in response to the environmental factors 12 Marić et al. [2012]), artificial neural network analysis (Recknagel et al. [2006]), and data mining analysis (Su et al. [2013]). This study, using the factor analysis, aims to find out to what extent the phytoplankton biomass (in terms of chlorophyll a) responds to the environmental factors in the Wadden Sea near Lauwersoog, determined in the 10-year time period dataset from 2000 through 2009. The study area of Lauwersoog station, located in the north of the Netherlands, is a part of the Frisian Inlet, shown in figure 1.2 (symbol A). The main objectives are described below: 1) to give insight in the seasonal dynamics of the phytoplankton biomass; 2) to investigate the response of phytoplankton biomass to the physical-chemical factors (light intensity, salinity, nitrate, ammonium, phosphorus, silicate, total nitrogen, total phosphorus, suspended matter, and ambient water temperature); and 3) to characterize the driving factors to the phytoplankton biomass without much loss of information. 2.1.2 Data information in 10-year time period from 2000 through 2009 at Lauwersoog station The monitoring programme has been carried out by Rijkswaterstaat (NL), and the observations are stored in the main database of DONAR, accessible through http: //live.waterbase.nl/waterbase_wns.cfm?taal=en. Eleven variables (chlorophyll a, Chla, mg m−3 ; light intensity, I, Einstein m−2 day −1 ; salinity, P SU ; nitrate, N O3 , mg l−1 ; ammonia, N H4 , mg l−1 ; dissolved phosphorus, P O4 , mg l−1 ; dissolved silicate, Si, mg l−1 ; total nitrogen, T N , mg l−1 ; total phosphorus, T P , mg l−1 ; suspended matter, SP M , g m−3 ; water temperature, T , 0 C), monitored either biweekly or monthly, are collected for the 10-year time period from 2000 through 2009. Figure 2.1 plots the long term observations (2000-2009) of the associated variables in the Wadden Sea near Lauwersoog (NL). 2.1.3 Factor analysis Factor analysis is a useful tool to reduce the overlapping information and to investigate the relationships between the coastal ecosystem and the environmental factors. It is often used in the data dimension-reduction to identify a small set of variables that represent most of the variance (Shukla et al. [2006]; Chau and Muttil [2007]; Friedrichs Chapter 2. Phytoplankton dynamics in response to the environmental factors 13 Figure 2.1: Observed variations in the Wadden Sea near Lauwersoog (2000-2009) et al. [2009]). Data analysis often includes a large number of observations, and some may be unnecessary. From the factor analysis, the dominant variables could be extracted. Factor analysis is totally dependent on correlation or covariance matrix between variables. But 90% of the factor analysis is meant to use the correlation matrix, as is applied in this study. Concerning the properties of the variables, they are divided into common variables and dependent variables in the correlation matrix. Herein, the phytoplankton biomass is set as a dependent variable, while others are set as common variables. Two Chapter 2. Phytoplankton dynamics in response to the environmental factors 14 types of outputs are generated, eigenvalues and fixed number of factors. The widely used is the eigenvalues. The eigenvalue analysis determines the number of the extracted components/factors. In general, it is required to satisfy the criterion of eigenvalue > 1.0. Three extraction methods are introduced to perform the factor analysis: Principal Component Analysis (PCA), Maximum Likelihood (ML), and Unweighted Least Squares (ULS). It is noted that the principal component analysis could be used independently or comprehensively in the data analysis. Principal component analysis, as the basic extraction method, aims to find a linear combination of variables in a relatively simple way. Factor analysis is conducted using the statistical package IBM SPSS Statistics 20, accessible through http://www-01.ibm.com/support/docview.wss?uid= swg24029274. The detailed information of three extraction methods is described in Appendix B. To obtain a clear pattern of the factor loadings, we can rotate the axes in any direction without any changes. There are many different types of rotations that can be applied after the initial extraction of components/factors. In this study, an orthogonal rotation method, Varimax with Kaiser normalization, is preferred to determine what the components represent. 2.1.4 Discussion Statistics of phytoplankton biomass Summarizing the historical dataset (2000-2009) in the Wadden Sea near Lauwersoog, the statistics of the phytoplankton biomass (in terms of chlorophyll a) are shown in table 2.1. The values of chlorophyll a vary around 15.13 ± 11.85 mg m−3 . Most of chlorophyll a are concentrated at a range of [0, 20], accounting for 75% of all values, followed by the ranges of [20, 40] and [40, 70] mg m−3 . The values larger than 60 mg m−3 occur in the spring of 2003 and 2006. Fast phytoplankton growth usually appears in spring and in autumn with the favorable living conditions. The skewness of the dataset is 1.53, indicating that chlorophyll a has a long right tail. The frequency distribution is asymmetric, with some distant values in a positive direction from the center, displayed in figure 2.2A, corresponding well with the positive skewness. A Gamma model is fitted well by the observations, with a shape parameter of 1.63 mgm−3 and a rate parameter Chapter 2. Phytoplankton dynamics in response to the environmental factors 15 of 9.26 mgm−3 , shown in figure 2.2B. The positive skewness also states that the mean value (15.13 mgm−3 ) is at the right of the median value (12.40 mgm−3 ). Table 2.1: Statistics of chlorophyll a in the Wadden Sea near Lauwersoog (2000-2009, n=187), expressed in mg m−3 Bootstrap Statistic Mean Median Std. Deviation Variance Skewness 25 50 Percentiles 75 95 15.13 12.40 11.85 140.47 1.53 6.18 12.40 20.00 37.92 Bias Std. Error -0.02 -0.20 -0.05 -0.27 -0.05 0.04 -0.20 0.32 0.32 0.86 1.00 0.94 22.19 0.25 0.52 1.00 1.50 2.62 95% Confidence Interval Lower Upper 13.44 16.90 10.20 14.20 9.97 13.54 99.42 183.32 0.96 1.94 5.12 7.30 10.20 14.20 18.20 24.20 33.77 44.40 The Bootstrap method, based on 1000 random samples, is introduced to investigate the properties of chlorophyll a with a 95% confidence interval (table 2.1). In practice, there are two ways to express the degree of uncertainty of a statistical quantity, namely standard error and confidence interval. Similar to the standard deviation of a variable, the standard error measures the standard deviation of an estimated statistical quantity from a sample. On the other hand, the confidence interval of an estimated quantity is an interval that has a specified probability (confidence) to include the true values. Within the 95% confidence interval, the expected mean value varies from 13.44 to 16.90 mg m−3 , with a bias of -0.02 mg m−3 and a standard error of 0.86 mg m−3 , and the expected standard deviation varies from 9.97 to 13.54 mg m−3 , with a bias of -0.05 mg m−3 and a standard error of 0.94 mg m−3 . 75% of all expected values are less than 24.20 mg m−3 , while the observed values are less than 20.00 mg m−3 , accordingly. Seasonal dynamics of phytoplankton biomass and environmental variables In this section, the spatial variations in physical-chemical factors and phytoplankton biomass (in terms of chlorophyll a) are discussed, depicted in figure 2.3. The boxplot is a graphical display of the data. In which, the middle black line indicates the median, the shaded region stating the middle 50%. The lines extending out of the shaded region are the top and bottom 25% of data and the horizontal lines at the top/bottom of the boxplot are the minimum and maximum values. Chapter 2. Phytoplankton dynamics in response to the environmental factors 16 Figure 2.2: Historical analysis of phytoplankton biomass (in terms of chlorophyll a, expressed in mg m−3 ) in the Wadden Sea near Lauwersoog, determined by the dataset from 2000 through 2009. A: frequency distribution, presented as histogram; B: goodness-of-fit test using a probability model (Gamma distribution, x-axis indicates the observed cumulative probability and y-axis indicates the expected cumulative probability, κ means the shape parameter of Gamma distribution and ν means the rate parameter) Ammonium varies from 0.002 mg l−1 to 0.485 mg l−1 , with a mean value of 0.16 mg l−1 and a standard deviation of 0.123 mg l−1 . The maximum ammonium values appear in August and September, and the minimum values appear in April, June and July. Nitrate varies from 0.005 mg l−1 to 1.83 mg l−1 , with a mean value of 0.292 mg l−1 and a standard deviation of 0.373 mg l−1 . The maximum nitrate values appear in March and the minimum values appear in summer (from June to August) and autumn (from September to November). Compared with other nutrients, the order of phosphorus is much lower. Phosphorus ranges from 0.005 mg l−1 to 0.167 mg l−1 , with a mean value of 0.051 mg l−1 and a standard deviation of 0.031 mg l−1 . The maximum phosphorus values appear in July, August and September, and the minimum values appear in April. Small difference is found in salinity, ranging from 22.55 PSU to 32.82 PSU, with a mean value of 28.75 PSU and a standard deviation of 1.95 PSU. The maximum salinity values are found in June, July and September, and the minimum values are found in March and December. Water temperature and light intensity show obvious seasonal variations, varying from 2.5 0 C to 21.7 0 C and from 6.37 W m−2 to 337.04 W m−2 , respectively. The maximum temperature and light intensity appear in summer. Chlorophyll a shows a significant difference, ranging from 0.86 mg m−3 to 65 mg m−3 . The maximum chlorophyll a values appear in April and July, and the minimum values appear in winter. Chapter 2. Phytoplankton dynamics in response to the environmental factors 17 Figure 2.3: Seasonal dynamics of phytoplankton biomass (in terms of chlorophyll a) and physical-chemical conditions in the Wadden Sea near Lauwersoog (2000-2009) Extreme values and boxplot analysis are related with each other. In this study, four extreme values are found in ammonium, two extreme values are found in nitrate, three extreme values are found in phosphorus, one extreme value is found in silicate, one extreme value is found in salinity, four extreme values are found in suspended matter, and one extreme value is found in chlorophyll a. Response of phytoplankton biomass to environmental variables Chapter 2. Phytoplankton dynamics in response to the environmental factors 18 As known that light intensity and nutrients contribute much to the phytoplankton. Figure 2.3 also simply presents the relationship between phytoplankton and environmental factors. The patterns of nutrients inversely follow the variation of chlorophyll a due to the uptake of nutrients by the phytoplankton. The maximum chlorophyll a is found in April, while lower nutrients are found at that time. In this section, the response of phytoplankton biomass to the effects of environmental variables is discussed, separately and comprehensively. Some variables are significant to the phytoplankton and some are non-significant. From a comprehensive view, the regression analysis shows a good result (ANOVA). Two thirds of the variance (r2 = 0.684, F = 15.358, p < 0.01) in chlorophyll a is explained. If we focus on the separate contribution of each variable, the correlation matrix is derived, shown in table 2.2. Chlorophyll a is strongly and significantly correlated with the variables of silicate, ammonium, and light intensity, and is moderately correlated with the variables of salinity, nitrate, and temperature. Additionally, temperature is correlated with salinity, nitrate, phosphorus, silicate and total nitrogen. I T SP M Si P O4 N O3 N H4 Salinity Variables Chla r = 0.333 p < 0.001 r = −0.481 p < 0.001 r = −0.433 p < 0.001 r = 0.124 p = 0.046 r = −0.585 p < 0.001 r = −0.074 p = 0.157 r = 0.375 p < 0.001 r = 0.497 p < 0.001 r = −0.140 p = 0.028 r = −0.753 p < 0.001 r = 0.313 p < 0.001 r = −0.552 p < 0.001 r = −0.237 p < 0.001 r = 0.569 p < 0.001 r = 0.260 p < 0.001 Salinity N O3 P O4 r = 0.107 p = 0.073 r = 0.227 r = −0.345 p < 0.001 p < 0.001 r = 0.657 r = 0.649 r = 0.107 p < 0.001 p < 0.001 p = 0.073 r = 0.068 r = 0.305 r = −0.234 p = 0.178 p < 0.001 p < 0.001 r = −0.065 r − 0.721 r = 0.656 p = 0.189 p < 0.001 p < 0.001 r = −0.456 r = −0.348 r = 0.250 p < 0.001 p < 0.001 p = 0.002 r indicates the correlation coefficient p indicates the significance level N H4 r = 0.306 p < 0.001 r = −0.411 p < 0.001 r = −0.510 p < 0.001 Si r = −0.296 p < 0.001 r = −0.337 p < 0.001 SP M r = 0.449 p < 0.001 T Table 2.2: Correlation matrix between the variables (187 samples for each variable) in the Wadden Sea near Lauwersoog, the Netherlands Chapter 2. Phytoplankton dynamics in response to the environmental factors 19 Chapter 2. Phytoplankton dynamics in response to the environmental factors 20 Factor analysis Factor analysis is performed to reduce the redundancy information from a set of correlated variables and to represent them with a smaller number of variables. Prior to the application of factor analysis, the reliability of the factor analysis for this dataset should be characterized with the Kaiser-Meyer-Olkin measure of sampling adequacy (KMO) and the Bartlett’s test. A higher KMO (asymptotic to 1.0) and a lower significance (< 0.05) indicate a higher confidence in the factor analysis. The results of the reliability analysis (KMO=0.75, p < 0.01) demonstrate that factor analysis is feasible in this dataset (Chau and Muttil [2007]), displayed in table 2.3. Table 2.3: Calculation results of the Kaiser-Meyer-Olkin Measure of Sampling Adequacy and the Bartlett’s Test of Sphericity over the 10-year’s chlorophyll a record from 2000 through 2009 in the Wadden Sea near Lauwersoog Kaiser-Meyer-Olkin Measure of Sampling Adequacy Chi-Square Bartlettis Test of Sphericity Degree of freedom Significance level 0.726 89.074 33 < 0.001 The total variance explained by factor analysis is presented in table 2.4. Eleven original components/ factors are derived, which is relative to the number of the original variables. Concerning the criterion of eigenvalue > 1.0, the first three components/factors contribute much to this solution and form the extraction, accounting for 69.89%, 61.02% and 61.22% of the total variance using PCA, ML and ULS, respectively. PCA forms the basis of the factor analysis, and is mainly used to extract the dominant components. Compared with the proportion of the total variance by PCA, a decrease appears when using the other two extraction methods. The eigenvalues are also different using ML and ULS from those when using PCA. From the component loadings by PCA, the first three components should be explored. However, from the factor loadings by ULS and ML, the eigenvalues of the third component are not satisfied with the criterion, so only the first two components are required to be investigated. 1 2 3 4 5 6 7 8 9 10 11 Component Initial Total 4.157 2.509 1.022 0.876 0.724 0.455 0.401 0.354 0.266 0.143 0.092 Eigenvalues % of Variance 37.788 22.808 9.295 7.967 6.579 4.139 3.649 3.222 2.421 1.298 0.834 Cumulative % 37.788 60.596 69.891 77.858 84.437 88.576 92.225 95.447 97.868 99.166 100.000 Extraction Sums of Squared Loadings by PCA Total % of Variance 4.157 37.788 2.509 22.808 1.022 9.295 Extraction Sums of Squared Loadings by ULS Total % of Variance 3.883 35.302 2.138 19.437 0.713 6.484 Extraction Sums of Squared Loadings by ML Total % of Variance 3.611 32.826 2.295 20.868 0.806 7.326 Table 2.4: Eigenvalues and total variance explained by the factor analysis (PCA, ULS and ML) Chapter 2. Phytoplankton dynamics in response to the environmental factors 21 Chapter 2. Phytoplankton dynamics in response to the environmental factors 22 Figure 2.4: Target diagram for the first two rotated component/factor loading matrix from three extraction methods, determined by the 2000-2009 dataset in the Wadden Sea near Lauwersoog (x-axis: first component; y-axis: second component) The components vary within the standard range of [-1.0, +1.0]. The closer is to the boundary value, the higher contribution is to the phytoplankton biomass, negatively or positively. In figure 2.4, the target diagrams for the first two rotated component/factor loadings from three extraction methods are displayed. From the basic extraction method of PCA, the first component, with an eigenvalue of 4.157, explains 37.8% of the total variance. In the unrotated space, it is mainly driven by the variables of N O3 (-0.852) and T (0.815), while N O3 denotes a high negative contribution. In the rotated space (Varimax with Kaiser normalization), it is mainly driven by the variable of N O3 (-0.887). The second component, with an eigenvalue of 2.509, accounting for 22.8% of the total variance, is dominated by the variable of N H4 (0.763 in the unrotated space and 0.860 in the rotated space). From the extraction method of ULS, the first factor, with an eigenvalue of 3.883, explains 35.3% of the total variance. The driving variable is N O3 (0.881). The second factor, with an eigenvalue of 2.138, accounting for 19.4% of the total variance, is dominated by the variable of N H4 (0.797). From the extraction method of ML, the first factor, with an eigenvalue of 3.611, explains 32.8% of the total variance. It is driven by the variable of N O3 (0.903). The second factor, with an eigenvalue of 2.295, accounting for 20.9% of the total variance, is dominated by the variable of N H4 (0.838). Furthermore, the rotated component/factor score matrix is depicted in figure 2.5. This factor weight matrix is used to compute the factor scores. The contributions of the driving variables in this solution from three extraction methods correspond well with the rotated component/factor loading matrix in figure 2.4, although some changes appear in other variables. Chapter 2. Phytoplankton dynamics in response to the environmental factors 23 Figure 2.5: Target diagram for the first two rotated component/factor score matrix from three extraction methods, determined by the 2000-2009 dataset in the Wadden Sea near Lauwersoog (x-axis: first component; y-axis: second component) 2.2 Test case two: Estimate of the phytoplankton growth rate in the coastal waters of Lianyungang (CN) 2.2.1 Introduction The commonly used estimate function of the phytoplankton growth rate is often linked with environmental variables, like nutrients (Flynn and Fasham [1997]; Geider et al. [1998]; Geider and La Roche [2002]; Örnólfsdóttir et al. [2004]; Davey et al. [2008]), temperature (Eppley [1966]; Eppley [1972]; Ratkowsky et al. [1982]; Thomann and Mueller [1987]; Bissinger et al. [2008]; Sal and López-Urrutia [2011]), light intensity (Smith [1980]), and also salinity and meteorological forcing (Marić et al. [2012]). This case, the Lianyungang station, is located in the northeast of Jiangsu Province, China (figure 1.3). The area is a pool of the frequent blooms, with a rapid growth rate in spring and autumn (SOA: State Oceanic Administration People’s Republic of China, accessing through http://www.soa.gov.cn/zwgk/hygb/). This research aims to explore a simplified estimate function of the phytoplankton growth rate, incorporating the temperature-growth function into the photosynthetic light curve. 2.2.2 Data information at Lianyungang station Data information of the associated variables used in this study is derived from the NASA data (accessible through http://oceancolor.gsfc.nasa.gov/cms/), processed Chapter 2. Phytoplankton dynamics in response to the environmental factors 24 Figure 2.6: Time series variations of the associated variables (I, T , Chla, P ) at Lianyungang station, monitored either weekly or biweekly over the year of 2006. with the SeaDAS 7.0. Figure 2.6 displays the annual variations of the variables (I, T , Chla, P ) over the year of 2006 in the Lianyungang coastal waters. Temperature and light intensity show seasonal variations. The maximum temperature, up to 27 0 C, appears in August, while the peak moment of the light intensity appears in June. Chlorophyll a varies from 0.63 mg m−3 to 5.64 mg m−3 , with a mean value of 3.10 mg m−3 and a standard deviation of 1.03 mg m−3 . The maximum chlorophyll a appears on 15th April. From the values of the chlorophyll a and the phytoplankton biomass (figure 2.6), we can distinguish that a rapid phytoplankton growth occurs in April. The frequently used estimate functions of the phytoplankton growth rate are summarized in table 2.5. In which, r0 indicates growth rate constant, b0 indicates the regression coefficient, and T0 indicates a reference temperature (20 0 C). Table 2.5: Summary of the commonly used estimate of the specific growth rate Function µ= Reference C/Chla+∆C/Chla C/Chla 0.0633T 0.59e 1 ∆t log2 µmax = 0.0631T µ √max = 00.81e r0 = b (T − T0 ) µ = µmax (1.066)T −20 C µ = (0.0868 Chla I −1 + 100.230−0.0275T )−1 2.2.3 Eppley [1972] Eppley [1972] Bissinger et al. [2008] Ratkowsky et al. [1982] Thomann and Mueller [1987] Smith [1980] Estimate function of the phytoplankton growth rate The simplest photosynthetic light curve is described as (Steele [1962]): Chapter 2. Phytoplankton dynamics in response to the environmental factors P0 = Pmax I K1/2 +I 25 (2.1) The simple transformation of the light curve to the specific growth function is described after Huisman et al. [1999], stating that the ratio of P0 Pmax is asymptotic to the ratio of µ µmax . Substituting the µmax after Eppley [1972] into the light curve, the specific growth rate is derived as (K1/2 = 30): I µ = 0.59e0.0633T I+30 (2.2) Additionally, the light intensity over the water depth follows the Lambert-Beer’s Law, written as: Iz = I0 exp(−Kd z) (2.3) This law has been validated by the measurements after Liu et al. [2012] in the Subei Bank along the Jiangsu coast. When the growth rate is balanced by the loss rate, the compensation light intensity Icr is captured from the equation of µ − l = 0, written as: Icr = 1 0.65exp(0.0633T )−0.03 (2.4) Another important indicator, the net growth rate of the phytoplankton, is introduced (Schnoor and Di Toro [1980]; Behrenfeld [2010]), defined as an increase of the phytoplankton biomass with respect to the time interval: k = ln[P (z, t2 )/P (z, t1 )]/(t2 − t1 ) (2.5) Chapter 2. Phytoplankton dynamics in response to the environmental factors 26 Figure 2.7: Estimate of the phytoplankton growth rate, expressed in day −1 . In which, graph A denotes the comparison of the specific growth rate between the photosynthetic light curve and Smith’s function; graph B denotes the variations of the specific growth rate and the net growth rate over the year of 2006 in the Lianyungang coastal waters. The red dashed line indicates a balance of k = 0. k is a comprehensive coefficient caused by the phytoplankton growth, mortality, respiration, sinking and predation. When k = 0 is satisfied, there is no net growth or loss from the previous time. Our concern is the condition of k > 0. 2.2.4 Discussion Most of the data information is confined to the surface layer. The estimate function of the specific growth rate is obtained from equation (2.2). Compared with the estimate of Smith’s function, there is no big difference between these two estimates, displayed in figure 2.7 (A). The maximum specific growth rate is around 2.0 day −1 , corresponding well with the view of Jorgensen [1979] and Arhonditsis and Brett [2005]. The specific growth rate also shows a seasonal variation, following the trends of I and T . But k shows a totally different fluctuation, presented in figure 2.7 (B). When the values of k are around 0, there is a balance stating that there is no net production or destruction from the previous time. Positive k values however reveal the relative increase of the phytoplankton biomass. It is noted that the variation of µ is small relative to k. The concept of the compensation light intensity is the minimum demand of the light intensity to support the phytoplankton growth. The euphotic depth Ze is defined as a special zone in the water column. A lower Icr corresponds to a deeper Ze. In the analysis of the phytoplankton growth rate, the associated variables are not only I and T , but also the ratio of C/Chla, Chla, P , Kd , and Ze. The effects of the variables Chapter 2. Phytoplankton dynamics in response to the environmental factors 27 on µ and k are analyzed using regression analysis, displayed in table 2.6. When all variables are considered, the correlation coefficient r reaches the maximum, 0.975 for µ and 0.716 for k. The effects on µ are larger than that on k. The variables of I and T contribute much to the specific growth rate , but little to the net growth rate k. Table 2.6: Model summary of regression analysis for the specific growth rate and the net growth rate Model 1 2 3 4 5 6 7 Dependent variable: µ R R2 Adjusted R2 a 0.891 0.794 0.788 0.920b 0.846 0.837 0.936c 0.875 0.864 0.967d 0.936 0.927 0.968e 0.937 0.926 0.973f 0.948 0.937 0.975g 0.95 0.937 Std. Error 0.227 0.199 0.182 0.133 0.134 0.124 0.123 dependent variable: k R R2 Adjusted R2 a 0.031 0.001 -0.028 0.089b 0.008 -0.052 0.064c 0.409 0.354 0.707d 0.5 0.436 0.708e 0.501 0.417 0.716f 0.513 0.412 0.716g 0.513 0.391 Std. Error 0.078 0.078 0.061 0.057 0.058 0.058 0.06 a. Predictors: (Constant), T b. Predictors: (Constant), T , I c. Predictors: (Constant), T , I, Chla d. Predictors: (Constant), T , I, Chla, P e. Predictors: (Constant), T , I, Chla, P , Kd f. Predictors: (Constant), T , I, Chla, P , Kd , Ze g. Predictors: (Constant), T , I, Chla, P , Kd , Ze, C/Chla With the regreesion analysis, µ is significantly correlated with T , and is moderately correlated with I, Ze, and C/Chla. The relationships between or among the variables of Kd , Ze, and I can be explained by the Lambert-Beer’s Law. With respect to uncertainty, the Bootstrap method is introduced to describe the random effects. Within the 95% confidence interval, the correlation coefficient between µ and T varies at a range of [0.812, 0.948], while [0.376, 0.810] between µ and I, [0.056, 0.544] between µ and Ze, [-0.754, -0.411] between µ and C/Chla. Chapter 3 Application of the BLOOM II model 3.1 Introduction Concepts to describe the dynamics of phytoplankton in coastal waters are related to the effects of environmental variables, which has been discussed in chapter 2. In general, the field measurement of the phytoplankton biomass is time consuming and an expensive work. The most common issue is only a limited number of observations to explain the phytoplankton processes. The better approach is to fully analyze the limited observations and to interrogate the possible estimates of the ecological factors. Thus, there is an increasing demand of the operational tools that provide quick and inexpensive paths to investigate the phytoplankton. The BLOOM II model (one module of the Delft3D modelling suite), applied in this study, reveals the importance of coupling the hydro-sediment model with the ecological model, leading to a more realistic estimate of the phytoplankton biomass (Hydraulics [1991]; Hydraulics [2003]; Los et al. [2008]; Los [2009]). The present study is performed to the case of the Frisian Inlet, location map shown in figure 1.2. The investigation of the phytoplankton biomass here is in terms of chlorophyll a. One objective is to predict the annual variation of the phytoplankton biomass and to pay attention to the phytoplankton biomass in response to nutrient availability, determined by the dataset in 1992. Researchers have proposed the relevant studies. Franks [1997], 29 Chapter 3. Application of the BLOOM II model 30 and Kishi and Ikeda [1986] describe the coupled physical-biological or physical-chemicalbiological equations which imply the Monod-like responses of the phytoplankton to the changes of the nutrient concentrations. Villars et al. [1996] develop a model study to assess the reference conditions and the responses to the nutrient loadings in the Dutch coastal waters. Blauw and Los [2004] perform the research on the responses of the phytoplankton to the nutrient reductions in the Dutch coastal waters. The second objective of this study is to give insight in the model prediction subject to uncertainty, given that little research on uncertainty analysis of the phytoplankton biomass has been carried out in this area. 3.2 3.2.1 Methodology Description of the BLOOM II model BLOOM II is a multi-species ecological model, based on an optimization technique, which distributes the available resources in terms of nutrients and light intensity among the algae types (Los and Brinkman [1988]; Hydraulics [1991]; Hydraulics [2003]; Los and Wijsman [2007]; Los et al. [2008]; Los [2009]). It combines water movement and sediment fluxes. BLOOM II characterizes the species such as marine diatoms, green algae, flagellates, phaeocystis, cyanobacteria and dinoflagellates. The species have different resource demands and ecological properties. According to the classical theories, the yield of each species will be limited by only one factor at a time. Algal species living in the water column (phytoplankton) and sediment can be contained with their specific eco-physiological characteristics. The BLOOM II model can be applied in any water body to simulate the phytoplankton processes in the water column (detailed information is shown in Appendix A). 3.2.2 Bayesian Markov Chain Monte Carlo (BMCMC) In ecological modelling, a large amount of information on the ecological factors will be needed. The information requires us to translate the real-world into valuable information. There are two types of information: non-deterministic (probabilistic) and deterministic. The deterministic method simplifies the actual problems and tries to Chapter 3. Application of the BLOOM II model 31 find a shortcut which will underestimate or overestimate the observations, while the probabilistic method provides much more reliable information because it considers the uncertainty of the natural variations or models. It is possible to take these uncertainties into account in a probabilistic approach, whereas the deterministic approach always takes a safe assumption as a beginning. In this case, we distinguish the influences of the (uncertain) factors and processes on the final results including the uncertainty of model inputs using the Bootstrap method and the uncertainty of the model output using the BMCMC simulation. Three situations need to be discerned in the BLOOM II model application: abundant data, only few data, or no data. The common case is the second, few but insufficient data, and hence the need is to incorporate the model results with the observations. Stressing the uncertainty of the model results, the Bayesian theory is proposed. We could estimate the parameters on the basis of the posterior distribution of the Bayesian inference. With a Bayesian approach, our understanding of the likelihood is described by a probability density function. The Bayesian theorem is composed of three parts: prior distribution, likelihood function and posterior distribution. The function is defined as: π1 (y|x) = R f (x|y)π0 (y) f (x|y)π0 (y)dy (3.1) Where x is the known parameter, y is the unknown parameter of interest, π0 (y) is the prior distribution, f (x|y) is the likelihood function, and π1 (y|x) is the posterior distribution. The BMCMC simulation is a general purpose technique for generating fair samples from a probability in a high-dimensional space, using random numbers drawn from a uniform probability in a certain range. Two popular BMCMC algorithms are the Gibbs sampler and the Metropolis-Hastings algorithm. Bayesian inference using Gibbs sampling has been widely applied since the mid-1990s. The BMCMC simulation is a useful tool to develop a full description of the uncertainty (Kuczera [1999]; Oakley and Hagan [2004]; Reis and Stedinger [2005]; Kelly and Smith [2009]). Chapter 3. Application of the BLOOM II model 3.2.3 32 Cost-function Undoubtedly, it is necessary before we apply the model to question: to what extent the phytoplankton biomass can be predicted with the BLOOM II model in this case? Thus, a model validation is performed. The paths for validation are conducted by graphically presenting the model output versus the observations, or the results from previous model exercises and then visually assessing the comparisons. One method called ‘costfunction’ is a mathematical function which provides a means of comparing the data from two different sources (Los et al. [2008]; Los [2009]; Blauw et al. [2009]). During the ASMO eutrophication modelling workshop different cost functions are put forward (Villars et al. [1996]). The use of cost-function is defined as: r= P |Mx,t −Dx,t |/12 sdM COV (M,D) sdM ×sdD Cx = × (1 − c) + c(1 − r) (3.2) The cost-function is classified as four standard levels: very good, good, reasonable and poor, the values defining as [0, 1], [1, 2], [2, 3], and [3, ∞] respectively. 3.3 BLOOM II model set-up at the Frisian Inlet 3.3.1 Hydrodynamic characteristics and ecological factors The BLOOM II model is based on the hydrodynamic characteristics, the variations of which directly or indirectly influencing the distributions of the phytoplankton biomass. A refined curvilinear grid with 85 × 77 cells is generated in this case. For the vertical dimension, the water column is subdivided into 10 layers, 4.0%, 5.9%, 8.7%, 12.7%, 18.7%, 18.7%, 12.7%, 8.7%, 5.9%, and 4.0% (Los et al. [2008]), using a sigma-coordinated approach (Stelling and van Kester [1994]). In the BLOOM II model, three layers are integrated: the surface three integrated as the surface layer, the bottom three integrated as the bottom layer, and the middle four integrated as the middle layer. Two west boundaries, two north boundaries, and two east boundaries are set. Chapter 3. Application of the BLOOM II model 33 Figure 3.1: Observed driving forces used in the model, (A )Wind profile (speed: m s−1 , direction: degree), (B) I and T , (C) Annually variations of nutrients (mg l−1 ), (D) salinity (SPU) and SP M (g m−3 ). The sources of Figs of A and B are from the KNMI database, accessible through www.knmi.nl; Figs of C and D are from the DONAR database, at Lauwersoog station, accessible through http: //live.waterbase.nl/waterbase_wns.cfm?taal=en. Figure 3.1 displays the observed driving forces (wind profile, T , I, salinity, SP M and nutrients) in 1992. In this case, wind profile, T , and I are set as the model domain conditions, while other factors are set as the boundary inputs. I and T show seasonal variations, and the peak moments appear in the summer days. The maximum DIN (N O3 + N H4 ) reaches 1.0 mg l−1 in winter while the target of DIN in the Wadden Sea and Wadden coast is defined as 0.46 mg l−1 by the WFD (European Water Framework Directive) and 0.42 mg l−1 by the OSPAR commission. Although extensive data have been collected, most of the data are confined to the surface water layer. 3.3.2 Model scenarios The BLOOM II model aims to identify the phytoplankton processes, including light attenuation, nutrient distribution, phytoplankton growth, and transport of the substances. Chapter 3. Application of the BLOOM II model 34 Three layers are integrated in the model: surface layer, middle layer and bottom layer. Regarding the limiting factors (nutrient and light) of the phytoplankton, three phenotypes (energy type, nitrogen type and phosphorus type) are considered within the BLOOM II model (Hydraulics [1991]). In this case, our concern is to investigate the annual variation of the phytoplankton biomass, specifically the response to nutrient availability, N-reduction (10%, 20%, 30%, 50%, 70%, and 90%), P-reduction (10%, 20%, 30%, 50%, 70%, and 90%), and both Nand P-reduction (10%, 30%, 50%, 70%, and 90%). The reference simulation is under 0% of the nutrient reduction. Specific extinction coefficients and the stoichiometric ratios of algal types used in the BLOOM II model are referred to after Los [2009]. 3.4 3.4.1 Results Observational analysis of the driving forces Figure 3.1 has shown the variations of the major driving forces measured either biweekly or monthly. The random effects of these factors on the phytoplankton biomass are derived using the Bootstrap method, displayed in table 3.1. In chapter 2, the correlation analysis between chlorophyll a and other driving forces has been discussed, determined by the 10-year dataset from 2000 through 2009. Herein, the similar results are derived, determined by the dataset in 1992. In this study, chlorophyll a is strongly and significantly correlated with Si and N H4 , and moderately correlated with the variables of N O3 , T , I, and P O4 . We should pay more attention to these factors in further analysis. Note that 500 random samples are integrated into the Bootstrap calculation for each factor, deriving the estimate within the 95% confidence interval. Table 3.1: Correlation matrix of chlorophyll a and other driving forces Chla Pearson Correlation (r) Sig. (2-tailed) (p) Bias Std. Error Bootstrap Lower 95% CI Upper I 0.479 0.038 0.013 0.142 0.186 0.758 N H4 -0.714 0.001 -0.009 0.108 -0.877 -0.453 salinity 0.371 0.118 -0.021 0.232 -0.248 0.697 N O3 -0.523 0.022 -0.017 0.194 -0.850 -0.132 P O4 0.440 0.060 -0.003 0.191 -0.068 0.720 Si -0.732 0.000 0.004 0.103 -0.892 -0.507 SP M -0.273 0.259 0.009 0.209 -0.630 0.176 T 0.502 0.028 -0.180 0.210 0.015 0.800 Chapter 3. Application of the BLOOM II model 35 Table 3.2: Cost-function results of ten programs at the Frisian Inlet programme salinity SP M N O3 N H4 P O4 Si BOD5 DO Kd Chla 3.4.2 Harlingen 1.0426 0.0389 0.4203 0.5788 0.7482 3.3355 1.3808 1.0470 0.9275 1.0234 Lauwersoog 0.5637 0.4222 0.7997 0.5060 0.3720 0.4705 0.7040 0.7786 1.0536 0.5736 Huibertgat 1.1106 0.2859 0.3016 0.4493 0.6185 0.2599 0.2222 0.2659 0.9917 1.7746 BLOOM II model output Model validation The more reliable model produces a better prediction of the phytoplankton biomass. Table 3.2 presents the cost-function results of ten programs (salinity, SP M , N O3 , N H4 , P O4 , Si, BOD5 , DO, Kd , and chlorophyll a) at three stations: Lauwersoog, Huibertgat, and Harlingen. It is concluded that 96.9% of the validation results have a good agreement, while only 3.1% are classified as poor. Compared with the values at Harlingen station and Huibertgat station, the model has a higher reliability at Lauwersoog station. We also can have a graphical view of the comparisons between the model results and the observations at Lauwersoog station, displayed in figure 3.2. The following discussion is explored at Lauwersoog station. Analysis of the predicted environmental factors As the phytoplankton biomass is strongly influenced by light intensity and light penetrates into the water column until self-shading occurs, the water property has a close relationship with Kd (Modenutti et al. [2000]; Devlin et al. [2008]). A higher turbidity corresponds to a higher Kd value. A linear relation between the predicted (R2 > 0.8) or the observed (R2 > 0.4) SP M and Kd exists which coincides well with the report by Devlin et al. [2008]. Secchi depth, closely related to the water turbidity in the water column, is another reliable water quality indicator (Lee et al. [2007]) and is used in the physical and biological modelling as a measure of the light penetration into the water body, inversely related Chapter 3. Application of the BLOOM II model 36 Figure 3.2: Graphical comparisons between the model results and the observations over the year of 1992 at Lauwersoog station. In which, the blue smooth lines indicate the model results, and the red scatters indicate the observations. to the phytoplankton biomass. The relationships between I, Kd , and secchi depth can be explained by the Lambert-Beer’s Law. Chlorophyll a shows a large fluctuation during the whole year, with higher concentrations in spring and summer, and lower in winter. Light limitation often occurs in the winter days. In addition, the high turbidity increases the light limitation in this case until the light intensity is too low to support the phytoplankton growth. Figure 3.3 shows the frequency distributions of two ecological factors (secchi depth and chlorophyll a) and a logarithmic relationship between them (R2 = 0.7113). Chlorophyll a is fitted with a Gamma distribution, with a shape parameter of 1.605 mg m−3 and a scale parameter of 0.281 mg m−3 . In order to better understand the ecological processes, it is necessary to have some basic understanding of the limiting factors of the phytoplankton growth. Only one limiting factor exists at a time so there is the need to know how the limiting factors vary in time and space. Light is the main limiting factor all year round especially in winter or in the higher turbidity zones. Phytoplankton biomass in response to nutrient availability Chapter 3. Application of the BLOOM II model 37 Figure 3.3: The first two graphs indicate the frequency distributions of secchi depth and chlorophyll a. The third graph indicates the secchi depth against chlorophyll a, using a non-linear function (R2 = 0.7113) As could be expected the nutrient concentrations decrease with nutrient reduction scenarios and so do the responses of chlorophyll a to a decrease of nutrients (table 3.3). If all other settings remain unchanged, chlorophyll a immediately decreases when the nutrient reduction occurs, but with a strong decrease rate at first and then tending to be relatively steady. Changes in chlorophyll a are assessed by comparing nutrient reduction results with the reference data. The maximum mean value (µ = 4.932 mg m−3 , σ = 4.063 mg m−3 ) happens at the N-90% scenario, while the minimum value (µ = 4.272 mg m−3 , σ = 4.137 mg m−3 ) is under both N- and P-90% scenario whereas there are small differences with the values of N-10%, N-50%, N-70%, and P-70%. Compared with the P-reduction (Dr: 17.4%-21.3%), the decrease rate of the N-reduction is relatively lower in this area (Dr: 16.8%-19.2%) and so phosphorus is the sensitive parameter to the phytoplankton species while the effects of chlorophyll a with both nutrient reductions are significant (Dr: 21.7%-28.0%). Figure 3.4 illustrates the cumulative distribution functions of chlorophyll a response curve to the nutrient reductions. There are four pairs of probabilistic analysis: the reference scenario, the N-reduction scenario, the P-reduction scenario, both N- and Preduction scenario. 3.4.3 BMCMC simulation There is much information on the phytoplankton biomass given by the BLOOM II model although the general approximation of chlorophyll a (overestimate or underestimate) is Chapter 3. Application of the BLOOM II model 38 Table 3.3: Chlorophyll a in response to nutrient reduction (Dr: decrease rate) Scenario Reference N-10% N-20% N-30% N-50% N-70% N-90% P-10% P-20% P-30% P-50% P-70% P-90% Both-10% Both-30% Both-50% Both-70% Both-90% M ean (mg m−3 ) 5.932 4.885 4.790 4.900 4.882 4.847 4.932 4.665 4.665 4.897 4.665 4.879 4.897 4.644 4.592 4.556 4.484 4.272 SD (mg m−3 ) 4.450 4.021 3.955 4.030 4.022 4.024 4.063 4.071 4.071 4.033 4.071 4.022 4.033 4.064 4.053 4.077 4.130 4.137 M aximum (mg m−3 ) 18.442 16.054 15.923 15.981 16.011 16.000 16.000 16.000 16.123 16.123 16.123 15.746 15.659 15.896 15.941 15.924 15.923 15.903 Dr 0.0% 17.6% 19.2% 17.4% 17.7% 18.3% 16.8% 21.3% 21.3% 17.4% 21.3% 17.7% 17.4% 21.7% 22.6% 23.2% 24.4% 28.0% not very asymptotic to the actual data with respect to uncertainty. In this study, the uncertainty of the modelled chlorophyll a is approached using the BMCMC simulation, giving insight in the model output of the phytoplankton biomass. Bugs (Bayesian Inference Using Gibbs Sampling) is used to perform the simulation. Two Markov chains in parallel and 8000 random samples are proposed for the uncertainty analysis. The BMCMC statistics include the mean value, the standard deviation, the Monte Carlo standard error, and the 95% confidence interval. Figure 3.5 shows the probability distribution functions of the variables. Within the 95% confidence interval, the modelled chlorophyll a varies from 1.57 mg m−3 to 10.11 mg m−3 , with a Monte Carlo error 0.04 mg m−3 ; the prediction with uncertainty analysis varies from 0.18 mg m−3 to 19.82 mg m−3 , with a Monte Carlo error 0.19 mg m−3 . The Markov Chain Monte Carlo methods are convenient and flexible, but compare with other simpler methods, they involve two difficulties: running the Markov chains for a sufficiently long time for convergence, and having sufficient simulation draws for a suitably exact inference. Figure 3.6 displays the Gelman-Rubin convergence statistic, as introduced by Gelman and Rubin [1992] and modified by Brooks and Gelman [1998]. The Gelman-Rubin test is based on two chains and on a comparison of the within and between chain variances for variables. The normalized width of the central 80% interval Chapter 3. Application of the BLOOM II model 39 Figure 3.4: Cumulative density function (CDF, log scale) of chlorophyll a in response to nutrient availability of the pooled runs is green, the average width of 80% intervals within the individual runs is blue, and their ratio R0 is red; the convergence of R0 should be approximately 1. The complete trace plots of the predicted chlorophyll a of chain 1:2 are shown in figure 3.7, with 5000 random samples. They all fluctuate around a Gamma distribution, with µ = 5.956 mg m−3 and σ = 5.242 mg m−3 . Chapter 3. Application of the BLOOM II model 40 Figure 3.5: Density of chlorophyll a in the BMCMC simulation, expressed in mg m−3 . In which, x denotes the modelled chlorophyll a; y denotes the prediction with uncertainty analysis. Figure 3.6: Gelman-Rubin convergence statistics in the BMCMC model. The green line indicates the normalized width of the central 80% interval of the pooled runs; the blue line indicates the average width of 80% intervals within the individual runs; the red line indicates the ratio of the green line to the blue line. 3.5 Discussion The present study introduces the ecological model of BLOOM II which could be applied in any water system to predict the annual variation of chlorophyll a. It is a useful instrument for the coastal ecosystem management. Chapter 3. Application of the BLOOM II model 41 Figure 3.7: Trace plots of the predicted chlorophyll a, expressed in mg m−3 The applicability analysis of the BLOOM II model is conducted using a ‘cost-function’ which has been applied for a station specific to the Dutch coast (Villars et al. [1996]; Radach and Moll [2006]; Los et al. [2008]; Los [2009]; Blauw et al. [2009]). Ten programs are involved in the validation (salinity, SP M , N O3 , N H4 , P O4 , Si, BOD5 , DO, Kd , and chlorophyll a). A smaller cost-function value indicates a better fit of the model results with the observations. Phytoplankton biomass in response to nutrient availability is distinguished by the variations of chlorophyll a. In view of the target of the nutrients defined by the OSPAR Commission and the European Water Framework Directive (WFD), this work is especially valuable where different responses are derived with different nutrient reduction scenarios. The BMCMC simulation is to give insight in the prediction of the phytoplankton biomass, which is subject to the uncertainty. The observed chlorophyll a concentrations vary from 1.82 mg m−3 to 28.9 mg m−3 , and the modelled values vary from 0.23 mg m−3 to 18.44 mg m−3 (figure 3.2 and figure 3.3), while the predictions with uncertainty vary from 0.18 mg m−3 to 19.82 mg m−3 within the 95% confidence interval and the maximum prediction reaches 30 mg m−3 (figure 3.7). Chlorophyll a is an important estimate of the phytoplankton biomass, however, the relationship between them, linearly or non-linearly, is not fixed but site-specific (Voros and Padisak [1991]; Felip and Catalan [2000]; Huot et al. [2007]). Therefore, the study of chlorophyll a cannot completely investigate the coastal ecosystem but also the study of phytoplankton. Chapter 4 A vertical model study of phytoplankton dynamics 4.1 Introduction The role of phytoplankton to a coastal ecosystem is significant and more attention has been paid to the interactions. Truscott [1995] examines the phytoplankton population in response to the environmental forcing. Franks [1997] describes the coupled physicalbiological equations to examine the occurrence of the harmful algal blooms. Schmidt [1999] demonstrates the importance of the phytoplankton biomass as a key indicator of the coastal ecosystem in the western branch of the Oder-estuary. Boyer et al. [2009] discuss the nutrient limitation of the phytoplankton bloom in the Florida Bay ecosystem. Mei et al. [2009] assess how light and nutrients alter the growth rate of the phytoplankton species. Since the BLOOM II model has been applied to investigate chlorophyll a in chapter 3, problems are still accompanied. The BLOOM II model has a higher resouce demands, including nutrients, light intensity, and species composition. The reliability of the phytoplankton biomass is hardly to be guaranteed wth the BLOOM II model when the ecological property of each species is unknown, especially when we are lack of nutrient information. As such, the mathematical phytoplankton models become available to investigate the phytoplankton. Evans and Parslow [1985] present a model to explain the 43 Chapter 4. A vertical model study of phytoplankton dynamics 44 annual cycle of the phytoplankton population. Skogen et al. [1995] use a coupled threedimensional physical-chemical-biological ocean model to study the primary production. Chen et al. [1997] apply the coupled physical-biological model to study the influence of the physical forces on the shelf ecosystem. Edwards and Brindley [1996] develop the plankton model to examine the sensitivities to model complexity and to parameter values. Franks [2002] reviews the N P Z models, including the construction, coupling to a physical model, and the application in oceanography. In this study, another convenient modelling approach, phytoplankton model, is introduced to investigate the vertical distributions of the phytoplankton biomass, reducing the three-dimensional model to a one-dimensional model (in the vertical direction). With the well-known simplification of the model, the predictions over a certain area and a certain time have a large uncertainty. Stressing the uncertainty arising from the model results, the BMCMC simulation is approached to give insight in the model output within the 95% confidence interval. 4.2 Phytoplankton model In the general form, the characteristics of phytoplankton dynamics are coupled with a physical model (advection-diffusion equation), written as: ∂C ∂t 2 2 2 ∂C ∂C ∂ C ∂ C ∂ C + ux ∂C ∂x + uy ∂y + (uz + us ) ∂z = Eh ( ∂x2 + ∂y 2 ) + Ez ∂z 2 + P hytoplankton dynamics (4.1) Further, phytoplankton dynamics has been described by researchers (Steele and Henderson [1992]; Edwards [2001]; Franks [2002]; Tian et al. [2005]) in the form of dP dt =µ×P −g×Z −l×P dZ dt = γg × Z − l0 × Z (4.2) In which, γ indicates the assimilation rate and l0 indicates the loss rate of the zooplankton. Chapter 4. A vertical model study of phytoplankton dynamics 45 Stressing the significance of the phytoplankton in the vertical direction, the vertical phytoplankton model follows the mathematical form of ∂P ∂t 2 − Ez ∂∂zP2 + (uz + us ) ∂P ∂z = (µ − l)P (4.3) In the coastal ecosystem, the water column is divided into three layers: surface layer, euphotic layer and non-euphotic layer. The non-euphotic layer contains available nutrients but few living algae due to little light intensity. An important notion of the euphotic zone (Ze), sufficient light intensity existing to support the phytoplankton growth, is to distinguish the dominated activity of the growth or the death (Margalef [1978], Morel and Berthon [1989]; Claustre and Marty [1995]; Aarup [2002]; Lee et al. [2007]). The vertical model study is available to grasp the features of the phytoplankton (Riley [1949]; Schnoor and Di Toro [1980]; Evans and Parslow [1985]; Franks [1997]; Wong et al. [2007]; Taylor and Ferrari [2011]). The asymptotic solution P (z, t) = f (z)ekt of equation (4.3) is provided by Di Toro [1974]. The form of f (z) is written as: √ √ √ f (z) = Aeaz (asin λz + λcos λz) (z < Ze) a = (uz + us )/2Ez λ = [µ − (k + l)]/Ez − (uz + us )2 /4Ez2 (4.4) (4.5) (4.6) Where A is a constant defined by the initial condition, and k is the net growth rate of the phytoplankton, written as k = ln[P (z, t2 )/P (z, t1 )]/(t2 − t1 ) (Schnoor and Di Toro [1980]; Cloern [1991]; Cloern [1996]; Behrenfeld [2010]). In this case, the estimate of k is derived from the function of k = ln(Chla2 /Chla1 )/(t2 − t1 ). To explore the practical solution of the vertical phytoplankton model (equation 4.3), the transfer functions need to be investigated: Ez , uz , us , µ, and l. In which, us and l are referred to as constants, displayed in table 4.1. The vertical mixing process Ez can be performed with the Delft3D model which has been validated in this area and Chapter 4. A vertical model study of phytoplankton dynamics 46 the neighbouring zones (Los [2009]; Blauw et al. [2009]; Niu and Van Gelder [2013]; Niu et al. [2015b]; Niu et al. [2015a]). Table 4.1: Sinking rate and the components of the loss term considered in the model Parameters Sinking velocity Mortality rate of phytoplankton Respiration rate Plant metabolic loss Symbol us s r0 f Value [3E-6,3E-5] 0.07 0.06 0.07 Unit m s−1 day −1 day −1 day −1 Source Skogen et al. [1995] Blauw et al. [2009]; Los [2009] Blauw et al. [2009] Evans and Parslow [1985] *l = s + r0 + f 4.3 Case study of the Frisian Inlet Huibertgat station and Lauwersoog station are selected as proxies to conduct the analysis. Seven variables (Chla, N O3 , N H4 , P O4 , Si, SP M , and salinity) over the year of 2009, measured either biweekly or monthly, are collected from the DON AR database, accessible through http://live.waterbase.nl/waterbase_wns.cfm?taal=en. Another three variables of I, T , and wind profile (speed and direction), measured daily, are collected from the KN M I database, accessible through www.knmi.nl. Note that the variables of T , I, and wind profile are set as domain parameters, while the others are site-specific. In addition, the monitored data of euphotic depth (Ze) and area-averaged phytoplankton biomass are derived from the N ASA data, processed with the SeaDAS 7.0. 4.3.1 Observational analysis The statistics of the variables over the year of 2009 is shown in table 4.2, including the minimum value (Min), the maximum value (Max), the mean value and the standard deviation (SD). At Lauwersoog station, chlorophyll a fluctuates around a big interval, 0.64-87.89 mg m−3 , with the mean value of 26.92 mg m−3 and the standard deviation of 25.1 mg m−3 . The minimum chlorophyll a appeared on 18th May and the maximum appeared on 17th April. The dissolved nitrate ranges from 0.01 mg l−1 to 0.53 mg l−1 , while 0.005-0.520 mg l−1 for ammonium, 0.013-0.14 mg l−1 for phosphorus and 0.03-1.42 mg l−1 for silicate. Most of the ratios of N/P are lower than the optimal condition of 16:1 (Brzezinski [2004]), which indicates a nitrogen deficiency relative to the phosphorus. Chapter 4. A vertical model study of phytoplankton dynamics 47 The nutrients show a similar pattern at two stations, increasing in winter but decreasing quickly in spring. Table 4.2: Statistics of the observed variables over the year of 2009 Variables Chla (mg m−3 ) I (W m−2 ) T (0 C) N O3 (mg l−1 ) N H4 (mg l−1 ) P O4 (mg l−1 ) Si (mg l−1 ) N/P ([−]) SP M (g m−3 ) Salinity (PSU) Wind speed (m s−1 ) Lauwersoog station Min Max Mean 0.64 87.89 26.92 4.51 354.63 123.5 2.1 19.8 11.27 0.01 0.53 0.15 0.005 0.52 0.147 0.013 0.14 0.051 0.03 1.42 0.47 0.22 21.6 7.41 27 390 105 25.9 31.7 29.56 0.2 13.1 5.38 SD 25.1 97.3 5.59 0.16 0.16 0.03 0.4 6.8 77.3 1.81 2.55 Huibertgat station Min Max Mean 1.11 124 12.07 4.51 354.63 123.5 2.1 19.8 11.27 0.01 0.72 0.19 0.005 0.3 0.08 0.008 0.043 0.021 0.01 0.9 0.28 1.35 51.43 14.1 3.6 37 17.6 27.4 31.9 30.2 0.2 13.1 5.38 SD 25.67 97.3 5.59 0.2 0.08 0.01 0.27 14.28 8.79 1.35 2.55 At Huibertgat station, chlorophyll a varies from 1.11 mg m−3 to 124 mg m−3 , with the mean value of 12.07 mg m−3 and the standard deviation of 25.67 mg m−3 . The minimum appeared on 20th February and the maximum appeared on 20th April. The concentrations of the nutrients are lower than that at Lauwersoog station. It is to infer that the phosphorus limits the phytoplankton growth from November to March because the ratios of N/P are larger than the optimal condition during that time period. In the light of the definition of the euphotic depth, the condition of Iz /I0 > 1% should be satisfied (Margalef [1978]; Morel and Berthon [1989]; Claustre and Marty [1995]; Aarup [2002]; Lee et al. [2007]). Accordingly, few light penetrates into the non-euphotic zone, stating that the death is the main activity. In this case, the Lambert-Beer’s law has been validated with the observations (R2 = 0.8959), displayed in figure 4.1. Moreover, the principal component analysis (PCA) is applied to discuss the relationship between the phytoplankton biomass (in terms of chlorophyll a) and the environmental variables, and to characterize the representative variables that represent most of the variance. The first three components are required to be extracted according to the criterion of eigenvalue > 1.0, accounting for 77.836% of the total variance. The components vary within the standard range of [-1, +1]. The closer is to the boundary, the more contribution is to this solution. The first two rotated component loadings are displayed in figure 4.2. The first component, with an eigenvalue of 3.801, explains 38.013% of the total variance, driven by the variable of light intensity (-0.918). The second component, with Chapter 4. A vertical model study of phytoplankton dynamics 48 Figure 4.1: A function fits well with the observations ( Iz /I0 > 1%) of light attenuation coefficient (Kd ) and euphotic depth (Ze ) at the Frisian Inlet. The light attenuation coefficient is caused by the phytoplankton growth and SP M at Lauwersoog station (high turbidity, table 4.2), but only by the phytoplankton growth at Huibertgat station. Figure 4.2: Component loadings in rotated space by the principal component analysis. In which, x-axis indicates the first component, and y-axis indicates the second component an eigenvalue of 2.586, explains 25.864% of the total variance, driven by the variable of salinity (0.911). Therefore, of all the variables, light intensity and salinity contribute much to the phytoplankton biomass (in terms of chlorophyll a). 4.3.2 Parameter estimation Estimate of the growth rate In figure 4.3, the specific growth rate µ of the phytoplankton presents a seasonal variation over the year of 2009 (the black smooth line). Normally, the maximum value of the specific growth rate is around 2.0 day −1 in coastal waters (Arhonditsis and Brett [2005]). In this case, the maximum specific growth rate is 1.87 day −1 appeared on 18th August Chapter 4. A vertical model study of phytoplankton dynamics 49 Figure 4.3: Annual variations of the specific growth rate ( the black smooth line ) and the net growth rate ( k1: Lauwersoog station; k2: Huibertgat station), expressed in day −1 . The specific growth rate has a big potential range, varying from 0.38 day −1 to 1.87 day −1 . The net growth rate varies from -0.25 day −1 to 0.25 day −1 at Lauwersoog station, while -0.14 day −1 to 0.12 day −1 at Huibertgat station. and the minimum is 0.38 day −1 appeared on 6th March. The net growth rate k of the phytoplankton shows a completely different trend. The positive values of the net growth rate indicate the increased phytoplankton biomass from the previous time interval. Estimate of the vertical turbulent diffusivity The estimate of the vertical turbulent diffusivity is derived from the Delft3D model which has been validated in this case (Niu and Van Gelder [2013]; Niu et al. [2015a]; Niu et al. [2015b]). Graphical comparisons between Delft3D model results and observations over the year of 2009 are depicted in figure 4.4 (Niu et al. [2015a]). Figure 4.5 presents the estimated vertical turbulent diffusivity at the Frisian Inlet. In view of the specific demand, the phytoplankton species can be distinguished by the classification of Margalef (1978): the order of vertical turbulent diffusivity and nutrient availability. The order of the vertical turbulent diffusivity is 10−4 at Lauwersoog station, while 10−3 at Huibertgat station. Therefore, dinoflagellates and diatoms are equally significant at Lauwersoog station, while only diatoms are predominant at Huibertgat station. 4.3.3 Validation of the phytoplankton model The graphical comparisons between the model output and the monitored phytoplankton biomass are displayed in figure 4.6. All of the values are confined near the surface layer in the area-averaged scale. The Delft3D model can reproduce the reliable levels Chapter 4. A vertical model study of phytoplankton dynamics 50 Figure 4.4: Graphical comparisons of chlorophyll a, salinity and nutrients between the Delft3D model output and the observations in 2009 at Huibertgat station of chlorophyll a (figure 4.4) but only 40% agreement of the phytoplankton biomass when the properties of the species are unknown, while the vertical phytoplankton model reproduces 70% agreement. The vertical phytoplankton model is applicable in this case. The modelled phytoplankton biomass varies from 0.145 g m−3 to 1.105 g m−3 , with the mean value of 0.44 g m−3 and the standard deviation of 0.30 g m−3 . The monitored phytoplankton biomass varies from 0.17 g m−3 to 1.40 g m−3 , with the mean value of 0.57 g m−3 and the standard deviation of 0.26 g m−3 . The common disadvantage of Chapter 4. A vertical model study of phytoplankton dynamics 51 Figure 4.5: Estimate of the vertical turbulent diffusivity (Ez ) with the Delft3D model at the Frisian Inlet, driven by the physical-chemical conditions and expressed in m2 s−1 . This factor is influenced by the tidal currents and the wind profile, mixing with the mass transport. The appropriate range of the vertical turbulent diffusivity can promote the phytoplankton growth (Margalef [1978]; Huisman et al. [1999]). Figure 4.6: Graphical comparisons between model outputs (Delft3D model and vertical phytoplankton model) and monitored phytoplankton biomass in 2009 at the Frisian Inlet, expressed in g m−3 . chlorophyll a and phytoplankton here is that they both indicate the characteristics of all the species. 4.3.4 Vertical distributions of the phytoplankton biomass In this section, the general patterns of the phytoplankton biomass over water depth are illustrated. Table 4.3 reveals the statistical analysis of the model output for the different water depths (z=0m, 2m, 5m, 10m, and 20m) at Lauwersoog station, and gives insight in the prediction with uncertainty analysis using the Bootstrap method. At the surface layer, the phytoplankton biomass, ranging from 0.014 g m−3 to 2.29 g m−3 , fits with chlorophyll a by a power function (P = 31.43Chla0.67 , R2 = 0.50). In the early June, Chapter 4. A vertical model study of phytoplankton dynamics 52 chlorophyll a rises sharply from 0.64 mg m−3 to 80.27 mg m−3 in the course of weeks, so does the pattern of the phytoplankton biomass increasing from 0.01 g m−3 to 1.90 g m−3 . Higher values of the phytoplankton biomass appear in the months of March, April, July and September. Nutrients (N O3 , N H4 , P O4 , Si) show specific properties over the year. The lower values of the nutrients are in the months of May and August, accompanied with the rapid growth of the phytoplankton. Light intensity becomes limiting in winter, that constrains the phytoplankton growth regardless of sufficient nutrients (figure 4.4). Normally, the sharp decrease of nutrients happens during or before the bloom event and the followed increasing process indicates the end of the bloom event. Table 4.3: Statistical analysis of the model output for the different water depths (z=0m, 2m, 5m, 10m and 20m) over the year of 2009 at Lauwersoog station, expressed in g m−3 Bootstrapa Lauwersoog Statistic 95% CI Lower Upper Mean 0.291 0.003 0.066 0.179 0.438 P(2) SD 0.294 -0.014 0.074 0.131 0.405 Skewness 1.803 -0.315 0.709 -0.190 2.719 Mean 0.452 0.006 0.130 0.240 0.729 P(5) SD 0.573 -0.039 0.185 0.172 0.847 Skewness 2.549 -0.497 0.771 0.571 3.675 Mean 0.390 0.007 0.134 0.172 0.691 P(10) SD 0.604 -0.036 0.178 0.190 0.871 Skewness 2.405 -0.242 0.717 0.923 3.696 Mean 0.569 0.009 0.128 0.348 0.851 P(20) SD 0.578 -0.024 0.134 0.258 0.791 Skewness 1.747 -0.216 0.555 0.550 2.831 a: unless otherwise noted, bootstrap results are based on 1000 bootstrap samples *the object of the 95% CI in the bootstrap method is the estimate, like mean value, standard deviation, and skewness. Bias Std. Error For the water depth of 2m at Lauwersoog station, the phytoplankton biomass shows a relative small fluctuation, with the mean value of 0.291 g m−3 and the standard deviation of 0.294 g m−3 . The maximum value is 1.11 g m−3 appeared on 2nd July. Higher values are concentrated in the months of March and July. Considering the uncertainty arising from the model, the mean value varies at a range of [0.178, 0.438] g m−3 within the 95% CI. The positive skewness (1.803) indicates a long right tail in the distribution. The values follow a Gamma distribution, with a shape parameter of 0.978 g m−3 and a scale parameter of 3.361 g m−3 . Chapter 4. A vertical model study of phytoplankton dynamics 53 For the water depth of 5m at Lauwersoog station, the phytoplankton biomass varies from 0.013 g m−3 to 2.406 g m−3 , with the mean value of 0.452 g m−3 and the standard deviation of 0.573 g m−3 . The maximum value occurred on 19th March. Take the uncertainty into account, the mean value fluctuates at a range of [0.240, 0.729] g m−3 within the 95% CI. For the water depth of 10m, the maximum value is 2.331 g m−3 appeared on 19th March, the same day as the depth of 5m. The average phytoplankton biomass is 0.390 g m−3 , varying at a range of [0.172, 0.691] g m−3 within the 95% CI. For the water depth of 20m, the phytoplankton biomass varies from 0.007 g m−3 to 2.260 g m−3 , with the mean value of 0.569 g m−3 . 80% of the values are less than 1.0 g m−3 . Table 4.4 presents the statistical analysis of the model output for the different water depths (z=0m, 2m, 5m, 10m and 20m) at Huibertgat station. The values are smaller than that at Lauwersoog station. At the surface layer, the phytoplankton biomass, varying from 0.03 g m−3 to 0.96 g m−3 , fits with chlorophyll a by a logarithmic function (P = 0.2ln(Chla) − 0.05, R2 = 0.70)). In April, although chlorophyll a and the phytoplankton biomass all reach the peak values, the nutrients are decreasing sharply from 1.63 mg l−1 to 0.22 mg l−1 . Table 4.4: Statistical analysis of the annual cycles of the phytoplankton biomass for the different water depths (z=0m, 2m, 5m, 10m and 20m) over the year of 2009 at Huibertgat station, expressed in g m−3 . Bootstrapa Huibertgat Statistic 95% CI Lower Upper Mean 0.215 0.000 0.576 0.105 0.338 P(2) SD 0.263 -0.011 0.049 0.144 0.337 Skewness 1.411 -0.012 0.586 0.411 2.823 Mean 0.179 0.001 0.040 0.106 0.259 P(5) SD 0.182 -0.008 0.035 0.099 0.234 Skewness 1.427 -0.047 0.537 0.489 2.596 Mean 0.163 0.002 0.039 0.088 0.245 P(10) SD 0.182 -0.007 0.037 0.076 0.230 Skewness 1.565 -0.006 0.624 0.471 3.102 Mean 0.138 0.000 0.030 0.085 0.198 P(20) SD 0.139 -0.006 0.026 0.079 0.177 Skewness 1.394 -0.054 0.534 0.474 2.554 a: unless otherwise noted, bootstrap results are based on 1000 bootstrap samples Bias Std. Error For the water depth of 2m at Huibertgat station, the mean value of the phytoplankton biomass is 0.215 g m−3 , varying at a range of [0.105, 0.338] g m−3 within the 95% CI. Chapter 4. A vertical model study of phytoplankton dynamics 54 The maximum value of 0.678 g m−3 occurred on 20th March, while the minimum of 0.012 g m−3 appeared on 19th May. For the water depth of 5m, the phytoplankton biomass varies from 0.014 g m−3 to 0.648 g m−3 , with the mean value of 0.178 g m−3 and the standard deviation of 0.182 g m−3 . The maximum value appeared on 2nd September and the minimum appeared on 16th September. The model output for the water depth of 10m is similar to the water depth of 5m. For the water depth of 20m, the phytoplankton biomass varies from 0.008 g m−3 to 0.497 g m−3 , with the mean value of 0.138 g m−3 and the standard deviation of 0.139 g m−3 . 4.3.5 Depth-averaged phytoplankton biomass In this section, the depth-averaged phytoplankton biomass at the Frisian Inlet is discussed, shown in table 4.5. At Lauwersoog station, the phytoplankton biomass fluctuates at a range of [0.009, 1.902] g m−3 . The mean value is 0.459 g m−3 , varying from 0.284 g m−3 to 0.695 g m−3 within the 95% CI. The phytoplankton biomass follows a Gamma distribution, with a shape parameter of 0.936 g m−3 and a scale parameter of 2.037 g m−3 . At Huibertgat station, the phytoplankton biomass fluctuates at a range of [0.019, 0.663] g m−3 . The average phytoplankton biomass is 0.197 g m−3 , varying from 0.123 g m−3 to 0.238 g m−3 within the 95% CI. The values also follow a Gamma distribution, with the shape parameter of 1.099 g m−3 and the scale parameter of 5.573 g m−3 . Table 4.5: Statistical analysis of the depth-averaged phytoplankton biomass at the Frisian Inlet over the year of 2009, expressed in g m−3 Bootstrapa Depth-averaged Statistic 95% CI Lower Upper Mean 0.459 0.007 0.106 0.284 0.695 0.475 -0.024 0.124 0.163 0.668 PL SD Skewness 2.053 -0.208 0.651 0.642 3.317 Mean 0.197 0.001 0.041 0.123 0.280 0.188 -0.008 0.034 0.103 0.238 PH SD Skewness 1.285 -0.059 0.512 0.344 2.422 a: unless otherwise noted, bootstrap results are based on 1000 bootstrap samples PL : the depth-averaged phytoplankton biomass at Lauwersoog station; PH : the depth-averaged phytoplankton biomass at Huibertgat station; Bias Std. Error Chapter 4. A vertical model study of phytoplankton dynamics 55 Figure 4.7: Gelman-Rubin convergence statistics. x denotes the model output; y denotes the prediction with uncertainty analysis. The normalized width of the central 80% interval of the pooled runs is green, the average width of the 80% intervals within the individual runs is blue, and their ratio R0 is red. 4.3.6 Uncertainty analysis Prior to the approaching of the BMCMC simulation in this case, the convergence is needed to be tested. Figure 4.7 displays the widely used Gelman-Rubin convergence statistics. Two chains are designed, and 2000 random samples are distributed to each chain. As described in chapter 3, the rule of the convergence is to keep the red line tended to 1. The BMCMC simulation is reliable in this case. We stress the uncertainty of the model and perform the BMCMC simulation to give insight in the prediction with uncertainty analysis. Table 4.6 shows the important BMCMC statistics, including the mean value, the standard deviation, the Monte Carlo standard error (MC error) and the 95% CI. Compared with the 95% CIs in the BMCMC simulation and the Bootstrap method, we find out that there is a big difference between the values. Worth to point out that the object of the 95% CI in the Bootstrap method is for the estimates (like the mean value, the standard deviation, the skewness), while the object in the BMCMC simulation is for the whole dataset. Therefore, the 95% CI in the two methods has a different meaning. At Lauwersoog station, the modelled phytoplankton biomass varies from 0.010 g m−3 to 1.721 g m−3 within the 95% CI, with a MC error of 0.007 g m−3 ; the prediction with uncertainty analysis varies from 0.006 g m−3 to 1.526 g m−3 , with a MC error of 0.004 g m−3 . At Huibertgat station, the modelled phytoplankton biomass varies from 0.011 g m−3 to 0.677 g m−3 within the 95% CI, with a MC error of 0.002 g m−3 ; the prediction with uncertainty analysis varies from 0.008 g m−3 to 0.708 g m−3 , with a MC error of 0.001 g m−3 . Figure 4.8 shows Chapter 4. A vertical model study of phytoplankton dynamics 56 Figure 4.8: Trace plots of the phytoplankton biomass at the Frisian Inlet, expressed in g m−3 . Graph A displays the model output of the phytoplankton biomass at Lauwersoog station. Graph B displays the prediction with uncertainty analysis at Lauwersoog station. A1 and B1 are to zoom out the iterations of the prediction. Graph C displays the prediction with uncertainty analysis at Huibertgat station. the completely trace plots of the model output with uncertainty analysis, based on 4000 samples. Table 4.6: Node statistics of the depth-averaged phytoplankton biomass in the BMCMC simulation Node Mean x 0.459 Lauwersoog y 0.332 x 0.200 Huibertgat y 0.198 *the object of the 95% CI in SD MC error 2.5% 0.475 0.007 0.010 0.308 0.004 0.006 0.188 0.002 0.011 0.116 0.001 0.008 the BMCMC simulation is Median 0.299 0.116 0.145 0.157 the whole 97.5% 1.721 1.526 0.677 0.708 dataset Chapter 4. A vertical model study of phytoplankton dynamics 4.4 57 Discussion In this case, there is a low vertical mixing rate due to the semi-enclosed inlet position. The slow exchange between the tidal inlet and the North Sea also increases the water residence time, which promotes the phytoplankton growth. The vertical mixing process, playing an important role in the investigation of phytoplankton dynamics, is performed with the Delft3D model. Comparing the model output with the monitored phytoplankton biomass, the application of the vertical phytoplankton model in this case is reliable. Higher values of the phytoplankton biomass appear in spring and in autumn, followed by the rapid reduction of the nutrients. The phytoplankton biomass at Lauwersoog station is higher than that at Huibertgat station. One reason is closely related to the concentration of the nutrients (figure 4.4). Another reason is that water exchange with the North Sea or the Wadden Sea is slower at Lauwersoog station, so longer residence time encourages the phytoplankton growth (figure 4.5). The model output of the phytoplankton biomass are non-deterministic, which is subject to the uncertainty. In this case, we stress the uncertainty arising from the model results. The BMCMC simulation, as a useful tool to fully describe the uncertainty, is proposed to give insight in the prediction with an integration of uncertainty analysis, fluctuating at a reliable range within the 95% CI. Chapter 5 Physical limitation of phytoplankton bloom development 5.1 Introduction The notion of the phytoplankton bloom is in the forefront of the coastal ecosystem in the Chinese marginal seas, and has been better understood since 2000 (Tang et al. [2003]; Tang et al. [2006a]; Tang et al. [2006b]; Son et al. [2012]; Jin et al. [2013]). Phytoplankton bloom events are often visible and caused by population explosions in the course of days to weeks, the pigments of water colours showing the characteristics of the phytoplankton species (Smayda [1997]; Allen et al. [2008]; Allen and Wolfe [2013]). The major causes of the blooms are eutrophication (nutrient enrichment), an unbalanced ratio of N/P , and a favourable living environment. Phytoplankton blooms have become a common issue in coastal waters, frequently occurring in spring and in autumn, as well as occasionally in winter (Allen and Wolfe [2013]). The bloom events are thought to be globally increasing and have turned out to be a great threat to the coastal ecosystem, especially the socalled harmful algal blooms (Falkowski et al. [1991]; Van Dolah [2000]; Anderson et al. [2002]). Although most of the blooms are not poisonous, they can block the sunshine penetration into the water column and consume large amounts of oxygen, which can threaten the marine life. Therefore, it is necessary to be aware of the phytoplankton 59 Chapter 5. Physical limitation of phytoplankton bloom development 60 bloom development in coastal waters. Within the course of a year, the bloom events follow an annual cycle, accompanied with the cycles of phytoplankton and zooplankton (Evans and Parslow [1985]; Steele and Henderson [1992]; Behrenfeld [2010]). This study proposes the modelling approach, as described in chapter 4, to give insight in the phytoplankton variability and to extend the application to investigate the bloom development. The trigger of the phytoplankton blooms is not a single factor. Critical factors contribute much to the occurrence of the bloom events, like light availability (Sverdrup [1953]; Huisman et al. [1999]), nutrient availability (Margalef [1978]; Jamart et al. [1979]; Wong et al. [2007]; Jin et al. [2013]), vertical mixing rate (Margalef [1978]; Huisman et al. [1999]; Wong et al. [2007]; Taylor and Ferrari [2011]) and meteorological forcing (Henson et al. [2006]; Taylor and Ferrari [2011]). A case study of the Jiangsu coastal waters is performed. The physical-ecological samples in the Jiangsu coastal waters are derived from two sources: the NASA monitoring data (the Ocean Color web, accessible through http://oceancolor.gsfc.nasa.gov/cms/) and in situ observations. Suppose in this case the nutrients are saturated. Seven variables are extracted from the NASA data, including chlorophyll a, ambient water temperature, light intensity, light attenuation coefficient, euphotic depth, mixed-layer depth, and phytoplankton biomass. Five variables are taken from in situ observations, including salinity, wind stress, suspended sediment, water turbidity, and water level. 5.2 Phytoplankton model The phytoplankton model is described as the same form as equation 4.3: ∂P ∂t 2 − Ez ∂∂zP2 + (uz + us ) ∂P ∂z = (µ − l)P 5.2.1 (5.1) Vertical stability theory We assume that no mass crosses the air-water interface, so the eigenvalue condition of the vertical phytoplankton model requires the initial condition of C(z, 0) = 0 to be satisfied. Then we can derive the function of f (z) = 0. Chapter 5. Physical limitation of phytoplankton bloom development 61 So, √ √ √ asin λz + λcos λz = 0, (0 < z < Ze) (5.2) Then, √ √ tan λz = − aλ (5.3) In the non-euphotic zone, the water environment is unfavourable for the phytoplankton species, mostly the species die off due to little light penetration into this layer. Given insight in the asymptotic solution, P (z, t) = f (z)ekt , attention should be paid to the transfer functions: k , µ, l, uz , us , and Ez . Reliability of the parameter estimation largely determines the applicability of the model. In which, the functions of l and us are referred to as constants ( l = 0.05 after Wei et al. [2004]; the order of us is 10−6 after Blauw et al. [2009] and Skogen et al. [1995]). Estimates of vertical turbulent diffusivity and phytoplankton growth rate are equally significant in the phytoplankton model. The vertical mixing process is performed with the Delft3D model which has been validated in this area (He et al. [2015]). Figure 5.1 plots the graphical comparisons of the water level between the model results and the observations at Dafeng station and Yangkou station, from 6th September to 14th September in 2006. To incorporate the ratio of (uz + us )/Ez into equation (5.3), the asymptotic function √ of tan λZe ≈ 0 is obtained. Following this derivation, when the condition of k > 0 is satisfied, we can get the lower boundary of the vertical turbulent diffusivity, Ez > (uz +us )2 /4(µ−l), which corresponds to the view of Riley [1949]. Consider the reciprocal √ transformation of equation (5.3), cot λZe = − √aλ , then the upper boundary of the vertical turbulent diffusivity can be derived, Ez < 4(µ − l)Ze2 /π 2 . 5.2.2 Critical depth The critical depth concept is commonly used as one critical condition to distinguish the phytoplankton blooms from the physical properties (Sverdrup [1953]; Platt et al. Chapter 5. Physical limitation of phytoplankton bloom development 62 Figure 5.1: Graphical comparisons of the water level between the model results (the red smooth line) and the observations (the blue markers) at Dafeng station (A) and Yangkou station (B) in the Jiangsu coastal zone, expressed in m. Most of the model results are consistent with the observations. [1991]; Huisman et al. [1999]; Schloss et al. [2002]; Taylor and Ferrari [2011]). When the mixed layer depth (M LD) is shallower, the light condition for the phytoplankton growth will be favourable, so the density of the phytoplankton will increase. When the density reaches a critical level, the bloom events will be initiated. The critical density corresponds to a critical depth. From the concept of the compensation light intensity, a simplified estimate of the critical depth is introduced (Sverdrup [1953]; Huisman et al. [1999]), written as Zcr = ln(I/Icr )/Kbg . Additionally, Siegel et al. [2002] define the critical depth as a function of Zcr = ln(C0 /L0 )/Kd , C0 and L0 indicating the production and the loss at the surface layer. We can see that Siegel’s view is related to Huisman’s report. In this case, the values of M LD are extracted from the Ocean Productivity of the NASA data (accessible through http://www.science.oregonstate.edu/ocean.productivity/ index.php), processed by the SeaDAS (http://seadas.gsfc.nasa.gov/). 5.2.3 Parameter estimation Specific growth rate Chapter 5. Physical limitation of phytoplankton bloom development 63 Figure 5.2: A logarithm function fits with the observations of suspended sediment (expressed in kg m−3 ) and turbidity (expressed in m−1 ) in the coastal waters of Jiangsu (R2 = 0.8261 ) The estimate function of the specific growth rate has been discussed in chapter 2. There is no big difference between the Smith’s estimate and the simplified estimate on the basis of temperature-function with the light curve. Smith’s curve is selected as the estimate of the growth rate in this study, integrating the effect of the ratio of carbon/chlorophyll a (C/Chla) into the phytoplankton growth. Estimate of turbidity The Jiangsu coastal waters with high turbidity block the sunlight penetration into the water column. A relationship between the turbidity and the suspended sediment has been investigated (Lewis [1996]; Holliday et al. [2003]). A logarithmic function fits with the observations of suspended sediment and turbidity in the Jiangsu coastal zone (R2 = 0.8261), shown in figure 5.2. The samples of the suspended sediment are separately monitored at spring tide and neap tide. The vertical distributions of the suspended sediment are displayed in figure 5.3. The variations of the suspended sediment show specific characteristics at four stations. The highest suspended sediment is found at Dafeng station, 2.5 kg m−3 . Estimates of the water turbidity vary at the ranges of [1.0, 1.5] m−1 , [0.143, 1.256] m−1 , [0.323, 2.06] m−1 , and [0.53, 1.90] m−1 at Lianyungang station, Dafeng station, Yangkou station and the north branch of the Yangtze River estuary, respectively. Chapter 5. Physical limitation of phytoplankton bloom development 64 Figure 5.3: Vertical distribution of the observed suspended sediment over the water depth in September at four stations (x-: sediment concentration, expressed in kg m−3 ; y-: water depth, expressed in m). 5.2.4 Skill assessment In order to get the practical solution of the phytoplankton model, the estimates of the key parameters have to be captured. The quality of the estimates determines the reliability of the model output. To make sure getting relatively better model output, we should test the applicability of the phytoplankton model in this case. Skill assessment measures the difference between the model results and the observations. The Root Mean Square Error (RMSE), summed over data points, provides a reliable comparison of the models. In principle, the form of RMSE is defined as: RM SE = ( N1 PN i=1 ∆ 2 ) 12 (5.4) The use of ∆ is defined as: ∆ = Pm − Pd (5.5) Chapter 5. Physical limitation of phytoplankton bloom development 65 In which, Pm is the modelled phytoplankton biomass, Pd is the monitored data. The bias provides a measure of the mean values, defined as: Bias = Pm − Pd (5.6) If Bias < 0, Pm is underestimating Pd ; if Bias > 0, Pm is overestimating Pd . The unbiased RMSE (RMSE’) is defined as: RM SE 02 = RM SE 2 − Bias2 (5.7) Normalized Bias (Bias*) by standard deviation (σd ): Bias∗ = Bias/σd (5.8) And the normalized RMSE’ (RMSE’*) is defined as: RM SE 0 ∗ = RM SE 0 Pdmax −Pdmin (5.9) Equations (5.6-5.9), Pm and Pd indicate the mean value of the model output and the monitored data; σd indicates the standard deviation of the monitored data; Bias* states the normalized Bias; RMSE’ states the unbiased root mean square error; RMSE’* states the normalized unbiased root mean square error. If the values of Bias* and RMSE’* are out of the standard range [-1, 1], the model results are less reliable. 5.2.5 Bloom forecast This research is intended to investigate the physical limitation of the bloom development in the coastal waters of Jiangsu. Critical factors mentioned above contribute much to the trigger of the blooms, but only the physical control is concentrated in this case. Chapter 5. Physical limitation of phytoplankton bloom development 66 Figure 5.4: Work-flow of the bloom forecast from the physical limitation in the Jiangsu coastal waters The vertical stability theory has been discussed under the condition of k > 0 over the water depth, which is closely related to the specific growth rate, the loss rate and the euphotic zone depth. Several transfer functions need to be investigated. Our concern is on the descriptions of the vertical turbulent diffusivity, the specific growth rate and the net growth rate. The vertical stability provides a favourable living condition for the phytoplankton, while the shallower mixed layer depth promotes the accumulation of the phytoplankton density in the water volume. The work-flow of the bloom forecast is depicted in figure 5.4. Chapter 5. Physical limitation of phytoplankton bloom development 5.3 5.3.1 67 Results Statistical analysis of the monitored data The statistical analysis of the associated variables is displayed in table 5.1, including Chla (mg m−3 ) , T (0 C), I (Einstein m−2 day −1 ), Ze (m), Kd (day −1 ), and P (g m−3 ). Note that all the samples are confined at the surface layer, monitored either 8-day or biweekly. Table 5.1: Statistical analysis of the monitored samples in 2006 at four stations along the Jiangsu coast Chla P Kd I Ze T Mean SD Min Max Mean SD Min Max Mean SD Min Max Mean SD Min Max Mean SD Min Max Mean SD Min Max Lianyungang 3.10 1.03 0.63 5.64 0.54 0.45 0.11 2.63 0.23 0.06 0.09 0.38 30.85 10.99 10.72 50.08 17.34 7.96 5.61 39.51 15.1 8.1 4.0 26.2 Dafeng 3.91 0.46 3.30 5.20 0.37 0.02 0.32 0.41 0.27 0.03 0.24 0.35 30.06 11.31 10.78 49.88 7.44 2.89 3.17 15.61 16.5 8.0 5.3 28.4 Yangkou 3.68 1.20 2.45 7.79 0.34 0.04 0.28 0.45 0.26 0.08 0.19 0.53 30.41 11.84 6.85 54.39 7.49 2.73 3.46 14.10 17.0 7.8 6.3 28.3 North branch of the Yangtze River estuary 5.50 5.29 3.24 25.71 0.38 0.06 0.33 0.58 0.41 0.48 0.23 2.25 30.94 12.12 7.11 55.40 6.11 2.23 3.00 11.69 17.3 7.8 6.3 28.6 The annual variations of the two seasonal variables, light intensity and water temperature, show a small difference at four stations. In other words, these two variables can be set as domain parameters. An extreme value of chlorophyll a (25.71 mg m−3 ) appeared on 4th August at the north branch of the Yangtze River estuary, while the maximum phytoplankton biomass (2.63 g m−3 ) appeared on 30th April at Lianyungang station. Significant correlations (R = 0.74−0.90) are established between phytoplankton biomass and chlorophyll a in this case, described as P = AeBChla (P = 0.1166e0.4291Chla and R2 = 0.5458 at Lianyungang station, P = 0.2238e0.1193Chla and R2 = 0.6047 Chapter 5. Physical limitation of phytoplankton bloom development 68 at Dafeng station, P = 0.2527e0.0768Chla and R2 = 0.8139 at Yangkou station, and P = 0.3268e0.0241Chla and R2 = 0.7154 at the north branch of the Yangtze River estuary). Accordingly, the coefficients of A and B also follow a non-linear function (B = 2.2547e−13.61A , R2 = 0.9933). Another important variable of euphotic depth Ze, ranging from 5.61 m to 39.51 m at Lianyungang station, is higher than that at other three stations. Within the layer of Ze, sufficient light intensity exists to support the phytoplankton growth. Light is one of the limiting factors for the phytoplankton, especially in winter. Light attenuation coefficient Kd has a close link with Ze, which can be explained by the Lambert-Beer’s law (Sverdrup [1953]; Huisman et al. [1999]; Devlin et al. [2008]). This law has been validated by the observations in the Jiangsu coastal zone (y = 900.96e1.333x and R2 = 0.9307, in which, y indicates the incident light intensity; x indicates the water depth), and the data sources are after Liu et al. [2012]. In table 5.2, the correlation matrix between the phytoplankton biomass and the physical conditions is discussed. Considering the random effects, the Bootstrap method is applied to derive the reliable range of the correlation coefficient within the 95% confidence interval. The phytoplankton biomass is significantly correlated with T , Kd , and Ze. Table 5.2: Correlation matrix between the phytoplankton biomass and the physical conditions in 2006 I Kd Ze T Pearson Correlation (r) 0.284 0.591** -0.630** 0.706** Sig. (2-tailed) (p) 0.104 0.000 0.000 0.000 Bias -0.004 -0.012 -0.004 -0.001 P Std. Error 0.152 0.113 0.073 0.077 Bootstrapa Lower 0.008 0.307 -0.752 0.555 95% CI Upper 0.587 0.758 -0.472 0.845 **. Correlation is significant at the 0.01 level (2-tailed); a. Unless otherwise noted, bootstrap results are based on 500 bootstrap samples; r: Correlation coefficient; p: Significant level; Note: The object of the bootstrap is the estimate of Pearson Correlation. 5.3.2 Specific growth rate and net growth rate A general function of the specific growth rate is used in this study, integrating the temperature-function into the light curve. In figure 5.5, the specific growth rate µ shows Chapter 5. Physical limitation of phytoplankton bloom development 69 Figure 5.5: Time series variations of the specific growth rate µ (the black smooth line) and the net growth rate k (the red dash line) at four stations along the Jiangsu coastal zone (A: Lianyungang, B: Dafeng, C:Yangkou, D: the north branch of the Yangtze River estuary), both expressed in day −1 . The specific growth rate is estimated from the combined effects of temperature and available light intensity, while the net growth rate is derived from the increase of the phytoplankton biomass with respect to time interval (8-day or biweekly). The area-averaged patterns of light intensity (the blue smooth line, expressed in Einstein m−2 day −1 ) and water temperature (the purple smooth line, expressed in 0 C) are presented in the first graph (A). a seasonal variation, fluctuating with light intensity and temperature. The patterns of the specific growth rate at four stations are similar. The values continually increase in winter and peak in the summer days, and then gradually decrease until winter. But at Lianyungang station, an abnormal situation happens, the specific growth rate µ decreasing sharply after the maximum value (figure 5.5A). The abnormal process is probably caused by the special variation of light intensity, reducing sharply from 34 to 20 Einstein m−2 day −1 during that time period. In this case, the maximum growth rate is 3.17 day −1 appeared on 4th August at the north branch of the Yangtze River estuary (figure 5.5D). The relative temperature and light intensity are all very high, 28.6 0 C and 52.89 Einstein m−2 day −1 , respectively. The followed maximum value is 2.67 day −1 appeared at Yangkou station (figure 5.5C), with a high temperature of 28.3 0 C and sufficient light intensity of 54.39 Einstein m−2 day −1 . Chapter 5. Physical limitation of phytoplankton bloom development 70 Compared with the variation of the specific growth rate, the net growth rate presents a totally different pattern both in spatial and temporal dimensions. The positive values of the net growth rate state that the phytoplankton production is higher than the loss with respect to time interval. Furthermore, the bloom events may be triggered when the sharp increase of the net growth rate happens, like the day of 4th August both at Yangkou station and the north branch of the Yangtze River estuary (figure 5.5C and figure 5.5D). Although the phytoplankton species have a large growth potential (µ=0.37-2.08 day −1 , 0.55-2.34 day −1 , 0.67-2.67 day −1 , and 0.63-3.17 day −1 at Lianyungang station, Dafeng station, Yangkou station, and the north branch of the Yangtze River estuary, respectively), the net growth rate k varies within ±0.1 day −1 , ±0.015 day −1 , ±0.03 day −1 , and ±0.06 day −1 over the 8-day interval at four stations along the Jiangsu coast accordingly. When the values of k fluctuate around 0, there is no obvious increase or loss of production during that time period. 5.3.3 Validation of the phytoplankton model To test the applicability of the phytoplankton model in this case, skill assessment is performed to compare the model output with the monitored data, displayed in table 5.3. Figure 5.6 presents the graphical comparisons. At Lianyungang station, the monitored phytoplankton biomass varies around 0.54±0.45 g m−3 , while the modelled phytoplankton biomass varies around 0.48 ± 0.55 g m−3 . At Dafeng station, the monitored data varies around 0.37 ± 0.02 g m−3 , while the modelled data varies around 0.37±0.10 g m−3 . At Yangkou station, the monitored phytoplankton biomass varies around 0.34 ± 0.03 g m−3 , while the modelled phytoplankton biomass varies around 0.31 ± 0.07 g m−3 . At the north branch of the Yangtze River estuary, the monitored phytoplankton biomass varies around 0.38 ± 0.07 g m−3 , while the modelled phytoplankton biomass varies around 0.34 ± 0.11 g m−3 . The index of RM SE denotes the difference between the model output and the monitored data. The modelled phytoplankton biomass underestimates the monitored data (Bias < 0) at Lianyungang, Yangkou, and the north branch of the Yangtze River estuary, while the modelled values overestimate the monitored data at Dafeng station (Bias > 0). The normalized Bias and unbiased RM SE are used to characterize the skill assessment, 90% being inside the Chapter 5. Physical limitation of phytoplankton bloom development 71 Figure 5.6: Graphical comparisons of the modelled phytoplankton biomass and the monitored data in the Jiangsu coastal zone (A: Lianyungang station; B: Dafeng station; C: Yangkou station; D: the north branch of the Yangtze River estuary), determined by the samples over the year of 2006 at the surface layer. The red smooth lines indicate the model output and the blue markers indicate the monitored data, expressed in g m−3 . standard range of [-1, 1]. It is concluded that the vertical phytoplankton model is able to reproduce reliable predictions of the phytoplankton biomass in this case. Table 5.3: Skill assessment of the vertical phytoplankton model at four stations along the Jiangsu coast Lianyungang Dafeng Yangkou North branch of the Yangtze River estuary 5.3.4 Pd 0.54 0.37 0.34 0.38 Pm 0.48 0.37 0.31 0.34 σd 0.45 0.02 0.03 0.07 Bias -0.06 0.00 -0.03 -0.03 Bias* -0.14 0.17 -0.88 -0.51 RMSE 0.59 0.09 0.07 0.09 RMSE’ 0.59 0.09 0.06 0.08 RMSE’* 0.23 1.06 0.38 0.32 Vertical distributions of the phytoplankton biomass To investigate the vertical distributions of the phytoplankton biomass, the phytoplankton model is developed over the water depth, shown in figure 5.7. In spring, the phytoplankton biomass is higher at Lianyungang station than that at other three stations. A decrease of the phytoplankton biomass corresponds to a deeper water depth, excluding the case of Yangkou station. Chapter 5. Physical limitation of phytoplankton bloom development 72 Figure 5.7A displays the annual variation of the phytoplankton biomass for the water depth of 2m in the Jiangsu coastal waters. At Lianyungang station, the minimum value is 0.01 g m−3 , appeared on 30th April. And the maximum is 3.07 g m−3 , appeared on 14th April. Higher values are in spring and in autumn. The average value is 0.36 g m−3 and the standard deviation is 0.51 g m−3 . At Dafeng station, the annual fluctuation is relatively steady, with the mean value of 0.28 g m−3 and the standard deviation of 0.15 g m−3 . The minimum value is 0.03 g m−3 , appeared on 10th February. And the maximum is 0.57 g m−3 , appeared on 26th July. At Yangkou station, the phytoplankton biomass varies at a range of [0.01, 0.28] g m−3 . The minimum appeared on 19th August and the maximum appeared on 4th August. At the north branch of the Yangtze River estuary, the phytoplankton biomass varies around 0.21 ± 0.16 g m−3 . Higher values appear in August. Figure 5.7B displays the annual cycle of the phytoplankton biomass for the water depth of 5m. Similar to the water depth of 2m, the phytoplankton biomass varies with a big difference at Lianyungang station, ranging from 0.02 g m−3 to 3.34 g m−3 . At Dafeng station, the phytoplankton biomass varies at a range of [0.03, 0.57] g m−3 , with the mean value of 0.27 g m−3 and the standard deviation of 0.14 g m−3 . While at Yangkou station and the north branch of the Yangtze River estuary, the values of the phytoplankton biomass are relatively smaller, varying at the ranges of [0.02, 0.35] g m−3 and [0.002, 0.51] g m−3 , respectively. Figure 5.7C displays the annual variation of the phytoplankton biomass for the water depth of 10m. At Lianyungang station, the phytoplankton biomass varies at a range of [0.005, 2.95] g m−3 , with the mean value of 0.41 g m−3 and the standard deviation of 0.53 g m−3 . The minimum appeared on 6th May and the maximum appeared on the same day as other water depths. Higher values appear in the months of April, May and July. The phytoplankton biomass fluctuates with 0.26 ± 0.13 g m−3 , 0.15 ± 0.11 g m−3 , and 0.22 ± 0.18 g m−3 at Dafeng station, Yangkou station and the north branch of the Yangtze River estuary, respectively. Figure 5.7D shows the time series variation of the phytoplankton biomass for the water depth of 20m. At Lianyungang station, the minimum value appeared on 1st July. The values become smaller with the deeper water depth. At Dafeng station, the phytoplankton biomass varies at a range of [0.007, 0.57] g m−3 , with the mean value of Chapter 5. Physical limitation of phytoplankton bloom development 73 Figure 5.7: Annual distributions of the phytoplankton biomass for the different water depths over the year of 2006 in the Jiangsu coastal waters, expressed in g m−3 . In this graph, A, B, C and D denote the annual variations of the phytoplankton biomass for the water depths of 2m, 5m, 10m and 20m, respectively. 0.26 g m−3 and the standard deviation of 0.15 g m−3 . At Yangkou station, the values become higher with the deeper water. The phytoplankton biomass ranges from 0.01 g m−3 to 0.50 g m−3 , with the mean value of 0.22 g m−3 and the standard deviation of 0.14 g m−3 . At the north branch of the Yangtze River estuary, the phytoplankton biomass ranges from 0.002 g m−3 to 0.47 g m−3 , with the mean value of 0.27 g m−3 and the standard deviation of 0.13 g m−3 . 5.3.5 Depth-averaged phytoplankton biomass In this section, the annual variation of the depth-averaged phytoplankton biomass in the Jiangsu coastal waters is discussed, shown in table 5.4. At Lianyungang station, the depth-averaged phytoplankton biomass varies at a range of [0.05, 2.76] g m−3 , with the mean value of 0.49 g m−3 and the standard deviation of 0.71 g m−3 . At Dafeng station, the depth-averaged phytoplankton biomass varies around 0.28 ± 0.09 g m−3 , Chapter 5. Physical limitation of phytoplankton bloom development 74 while 0.20 ± 0.06 g m−3 and 0.28 ± 0.09 g m−3 at Yangkou station and the north branch of the Yangtze River estuary, respectively. In order to get a practical solution of the phytoplankton model, we have simplified the real problems. With respect to the random effects, the Bootstrap method is used to derive the 95% confidence interval of the estimate, shown in table 5.4. At Lianyungang station, the mean value varies from 0.23 g m−3 to 0.91 g m−3 within the 95% confidence interval, with a bias of -0.007 g m−3 . At Dafeng station, the mean value varies from 0.23 g m−3 to 0.33 g m−3 within the 95% confidence interval, with a bias of -0.001 g m−3 . At Yangkou station, the mean value varies from 0.17 g m−3 to 0.23 g m−3 within the 95% confidence interval, with a bias of 0.001 g m−3 and a standard error of 0.015 g m−3 . At the north branch of the Yangtze River estuary, the mean value varies from 0.23 g m−3 to 0.33 g m−3 within the 95% confidence interval. From the index of skewness, the distributions of the depth-averaged phytoplankton biomass have a long right tail at Lianyungang station (3.091) and at the north branch of the Yangtze River estuary (1.866), deviating largely from the centre. The potential extreme values of the phytoplankton biomass may appear at these two stations resulting from the boxplot analysis, shown in figure 5.8. The open dots indicate the higher values of the phytoplankton biomass (non-extreme), and the black star indicates the extreme value. The probability distribution model of Weibull is explored to perform the goodof-fit test at Lianyungang station and at the north branch of the Yangtze River estuary, presented as figure 5.9A and figure 5.9D, respectively. The values of skewness are relatively smaller at Dafeng station (0.054) and Yangkou station (0.639), revealing that the symmetric distribution can fit with the data. Figure 5.9B and figure 5.9C display the good-of-fit test of Normal distribution at these two stations. 5.3.6 Vertical stability threshold As mentioned above, there is a suitable range of the vertical turbulent diffusivity for the phytoplankton, which promotes the growth. When the vertical turbulent diffusivity is outside that boundary, the phytoplankton biomass will show a negative increase. The vertical stability is determined by the condition of k > 0, depending on the specific growth rate, the loss rate and the euphotic zone depth, shown in figure 5.10 (the blue Chapter 5. Physical limitation of phytoplankton bloom development 75 Table 5.4: Statistical analysis of the depth-averaged phytoplankton biomass in the Jiangsu coastal waters over the year of 2006 Bootstrapa Statistic Lianyungang Dafeng Yangkou North branch of the Yangtze River estuary Statistic Mean Std. Deviation Skewness Mean Std. Deviation Skewness Mean Std. Deviation Skewness Mean Std. Deviation Skewness 0.496 0.712 3.091 0.279 0.095 0.054 0.197 0.059 0.639 0.280 0.097 1.866 Bias Std. Error -0.007 -0.132 -1.114 -0.001 -0.005 -0.088 0.001 -0.004 -0.190 0.001 -0.009 -0.479 0.194 0.330 1.031 0.025 0.014 0.466 0.015 0.010 0.563 0.027 0.029 0.690 95% CI Lower 0.232 0.110 -0.090 0.230 0.060 -0.992 0.169 0.035 -0.747 0.236 0.037 0.071 Upper 0.911 1.102 3.470 0.331 0.118 0.998 0.229 0.075 1.643 0.336 0.140 2.776 a: Unless otherwise noted, bootstrap results are based on 500 bootstrap samples; Note: the object of the bootstrap method is the estimate of the mean vaue, the standard deviation, and the skewness. Figure 5.8: Boxplot of the depth-averaged phytoplankton biomass in the Jiangsu coastal waters. In which, the middle black line indicates the median, the shaded region stating the middle 50%. The lines extending out of the shaded region are the top and bottom 25% of the data and the horizontal lines at the top/bottom of the boxplot are the minimum and maximum values (non-extreme). One case is classified as the extreme value at Lianyungang station (2.76 g m−3 ). smooth line). In winter, the smaller values of the euphotic depth and the specific growth rate reduce the vertical stability threshold. The vertical mixing process can influence the vertical distributions of the phytoplankton biomass, driven by the effects of the hydrodynamics. The strong turbulence appears in winter. The average estimate of the vertical turbulent diffusivity is 9.99 ± 2.78 cm2 s−1 in the Jiangsu coastal zone (8.07 ± 3.64 cm2 s−1 at Lianyungang station, 7.21 ± 2.70 cm2 s−1 at Dafeng station, 14.40 ± 8.00 cm2 s−1 at Yangkou station, 10.3 ± 4.13 cm2 s−1 Chapter 5. Physical limitation of phytoplankton bloom development 76 Figure 5.9: Good-of-fit test using the probability distribution models of Weibull and Normal, determined by the depth-averaged phytoplankton biomass over the year of 2006 in the Jiangsu coastal waters. In which, x-axis indicates the cumulative probability of the model output and y-axis indicates the cumulative probability of the predictions with the random effects. λ: shape parameter for Weibull distribution, γ: scale parameter for Weibull distribution. µ: mean value for Normal distribution, σ: standard deviation for Normal distribution. A: Lianyungang station (Weibull distribution); B: Dafeng station (Normal distribution); C: Yangkou station (Normal distribution); D: the north branch of the Yangtze River estuary (Weibull distribution). at the north branch of the Yangtze River estuary). The order of the vertical turbulent diffusivity coincides with the report after Su et al. [2013]. By the classification of Margalef [1978], diatoms are the dominant species in this zone. From the condition of the vertical turbulent diffusivity within the threshold (the purple rectangles in figure 5.10), the phytoplankton bloom events potentially occur in the months of March, May, August and October at Lianyungang station, while in the months of April, June and August at Dafeng station, in the months of June and August at Yangkou station, and in the months of May and August at the north branch of the Yangtze River estuary. Chapter 5. Physical limitation of phytoplankton bloom development 77 Figure 5.10: Vertical stability threshold (the blue smooth line) and the vertical turbulent diffusivity (the red smooth line) at four stations (A: Lianyungang; B: Dafeng; C: Yangkou; D: the north branch of the Yangtze River estuary), expressed in m2 s−1 . The purple rectangles mark the moments that the vertical turbulent diffusivity is within the vertical stability threshold. 5.3.7 Critical depth and mixed layer depth Regardless of the concepts of the critical depth, the euphotic depth or the mixed layer depth, all have a link with light availability, following the Lambert-Beer’s Law. To be exact, the critical depth varies with the compensation light intensity derived from a balanced interface of µ − l = 0. One frequently used condition of characterizing the blooms is to compare the mixed layer depth with the critical depth. The mixed layer depth is the layer between the water surface and a depth, where there is little variation in temperature, salinity and phytoplankton density over the water depth. Similar with the vertical turbulent diffusivity, the mixed layer depth mostly depends on the stability of water and the effects of wind stress and tidal currents. When the mixed layer depth is shallower than the critical depth, the light intensity will be more favourable for photosynthesis. On the contrary, Chapter 5. Physical limitation of phytoplankton bloom development 78 when the mixed layer depth is deeper than the critical depth, the phytoplankton growth will be limited by light intensity despite sufficient nutrients may be available. In figure 5.11, the critical depth varies with a similar trend but with different ranges at four stations, [8.58, 16.15]m at Lianyungang station, [5.84, 12.01]m at Dafeng station, [7.55, 18.07]m at Yangkou station, and [8.92, 14.89]m at the north branch of the Yangtze River estuary. The average critical depth is 12.32m, 9.21m, 13.67m and 12.13m at Lianyungang, Dafeng, Yangkou and the north branch of the Yangtze River estuary, respectively. The minimum critical depth appeared on 19th January at Lianyungang station, while it appeared on 2nd February at Dafeng station, on 4th August at Yangkou station and on 17th November at the north branch of the Yangtze River estuary. The maximum critical depth appeared on 27th June, while on 20th August at Dafeng station, on 8th June at Yangkou station and on 8th October at the north branch of the Yangtze River estuary. Compared with other three stations, the critical depth at Dafeng station shows a relatively stable state over the year of 2006. All of the mixed layer depths are less than 50m in the Jiangsu coastal waters. The deeper mixed layer depth occurs in winter and in the early spring, which may be caused by the wind stress and the weak stratification. The mixed layer depth ranges from 10.69m to 40m at Lianyungang station, while 10.81-50m at Dafeng station, 10.79-50m at Yangkou station, and 10.93-50m at the north branch of the Yangtze River estuary. The shallowest mixed layer depth appeared on 21st August at four stations. From the condition of the mixed layer depth being shallower than the critical depth (the purple rectangles in figure 5.11), the phytoplankton bloom events probably happen in the months of May, July, September and October at Lianyungang station, while in August at Dafeng station, from May to October at Yangkou station and in the months of May, August and October at the north branch of the Yangtze River estuary. 5.3.8 Phytoplankton bloom The phytoplankton bloom events have been predicted based on the discussion of the physical limitation, shown in figure 5.12 (the blue column); the observed bloom events are also shown (the red arrow). Chapter 5. Physical limitation of phytoplankton bloom development 79 Figure 5.11: Time series variation of the critical depth (the blue smooth line) and the mixed layer depth (the red smooth line) over the year of 2006 at four stations (A: Lianyungang; B: Dafeng; C: Yangkou; D: the north branch of the Yangtze River estuary), expressed in m. The mixed layer depth starts to be shallower in March. The purple rectangles mark the moments that the mixed layer depth is shallower than the critical depth, corresponding to a higher phytoplankton density. At Lianyungang station (figure 5.12A), the predicted timings of the phytoplankton bloom events are from 23rd May to 25th May, 26th July to 12th August, and 30th September to 7th October, while the observed bloom event occurs on 2nd October till 8th October, which is mainly caused by Eucampia zodiacus Ehrenberg and Gymnodinium catenatum, covering an area of 600 km2 (the observed information from SOA, accessible through http://www.soa.gov.cn/zwgk/hygb/). At Dafeng station (figure 5.12B), the phytoplankton bloom event happens from 10th August till 18th August. At Yangkou station (figure 5.12C), the predictions of the bloom events happen from 4th June to 17th June and 4th August to 13th August. While no observed data is collected at Dafeng and Yangkou station. At the north branch of the Yangtze River estuary (figure 5.12D), the predicted bloom events appear from 8th May to 23rd May and 2nd August to 18th August, while the observed blooms occur on 14th May and 4th August. Unfortunately, we don’t have much in situ information on the small scale bloom events, Chapter 5. Physical limitation of phytoplankton bloom development 80 Figure 5.12: Comparisons of the predicted blooms (the blue column) and the observations (the red arrow ) in the Jiangsu coastal zone (A: Lianyungang; B: Dafeng; C: Yangkou; D: the north branch of the Yangtze River estuary). The red arrow at Lianyungang station indicates the timing of the bloom occurrence, 2nd to 7th October, while the other two red arrows at the north branch of the Yangtze River estuary indicate the timings of 14th May and 4th August, respectively. only having collected the large scale blooms which cover an area more than 100 km2 . Most likely, more smaller blooms have occurred around the observed timings. From the comparisons of the predictions and the limited observations, the physical control of the blooms is applicable in this case. As is already known, chlorophyll a can be a measure of the phytoplankton biomass. Researchers also have found out that critical chlorophyll a or critical phytoplankton concentrations can be the condition to distinguish the bloom events (Xuan et al. [2011]). In this case, for chlorophyll a, when the bloom events occur, the values vary from 3.01 to 4.01 mg m−3 at Lianyungang station, while 3.56-3.74 mg m−3 at Dafeng station, 3.37-7.79 mg m−3 at Yangkou station and 6.59-27.51 mg m−3 at the north branch of the Yangtze River estuary. For the phytoplankton biomass, when the blooms occur, the values vary from 0.32 to 0.37 g m−3 at Lianyungang station, while 0.33-0.36 g m−3 at Dafeng station, 0.30-0.44 g m−3 at Yangkou station and 0.49-0.58 g m−3 at the north branch of the Yangtze River estuary. Therefore, we can simply conclude that chlorophyll a should be larger than 3 mg m−3 or the phytoplankton biomass should be larger than 0.3 g m−3 when the phytoplankton bloom events occur. Chapter 5. Physical limitation of phytoplankton bloom development 5.4 81 Discussion The investigation of the phytoplankton has provided useful insights in the coastal ecosystem. The typical subject regarding phytoplankton is the bloom development. The trigger of the blooms is not a single event but is linked with environmental factors. This study develops a vertical phytoplankton model and extends the application to investigate the blooms from the physical properties. Due to the semi-enclosed location, the Jiangsu coastal waters have a slow exchange with other water systems. In other words, the horizontal effects are less sensitive to the phytoplankton. Among all the transfer functions, our concern is on the descriptions of specific growth rate and vertical turbulent diffusivity. Only when the condition of k > 0 is satisfied, the phytoplankton blooms may occur. The vertical stability threshold is obtained from the asymptotic transformation of the trigonometric functions, [(uz + us )2 /4(µ − l) , 4(µ − l)Ze2 /π 2 ], which corresponds with the view of other researchers (Riley [1949]; Wong et al. [2007]). The vertical mixing process is driven by the effects of tidal currents and wind stress, performed with the Delft3D model. From the concept of the compensation light intensity, the critical depth is introduced after Sverdrup [1953] and Huisman et al. [1999]. When the mixed layer depth is shallower than the critical depth, the phytoplankton density will increase rapidly, which may trigger the bloom events (figure 5.11). It is noted that a combination of environmental factors will improve the application of the phytoplankton model. However, more field samples are required. In this study, only the physical control of the bloom development is stressed, but no consideration is given to the chemical conditions (like nutrient availability, DO, COD and BOD5 ), especially nutrient availability. In future work, we will further research these issues. Chapter 6 Conclusions and future work Phytoplankton is recognized as a basic component of the coastal ecosystem. Primary production by phytoplankton forms the first link in the food chain. The interactions between the phytoplankton and the water properties are concerned. Shallow water zones (i.e. coasts, lakes, and estuaries) are the hot spots for the phytoplankton owing to sufficient nutrients originating from the lands and the oceans (Schmidt [1999]; Cloern et al. [2014]). The studies of the phytoplankton have frequently been proposed (Cloern [1996]; Edelvang et al. [2005]; Godrijan et al. [2013]). Within the course of a year, the features of phytoplankton dynamics will move forward to a steady state (Evans and Parslow [1985]; Steele and Henderson [1992]; Behrenfeld [2010]). The annual cycles of phytoplankton dynamics are driven by the cycles of the physical characteristics in coastal waters. We stress the significance of the phytoplankton in this thesis without the discussions of the zooplankton or the higher level species. To capture the key point of this thesis is to completely understand the interrelations between chlorophyll a, phytoplankton, and coastal ecosystems. The relationship between phytoplankton and coastal ecosystems has been explained above. Chlorophyll a is a reliable estimate of phytoplankton, so the investigation of phytoplankton is often explained by the study of chlorophyll a. However, the relation between chlorophyll a and phytoplankton is not fixed but site-specific. It is not acceptable to give a better vision in the coastal ecosystem only through the research of chlorophyll a but also phytoplankton. In this thesis, different focuses are taken in the four body chapters (chapter 2 to chapter 5). Chapter 2 investigates the response of chlorophyll a to the environmental factors 83 Chapter 6. Conclusions and future work 84 (temperature, salinity, suspended particulate matter, nutrients, and light intensity) from 2000 through 2009, and characterizes the significant factors. Chapter 3 discusses the annual variation of chlorophyll a over the year of 1992, with a case study of the Frisian Inlet, and the attention is also paid to the response of chlorophyll a to the environmental factors. Chapter 4 describes the vertical distributions of phytoplankton biomass over the year of 2009. Chapter 5 discusses the annual variation of the phytoplankton biomass and investigates the bloom development from the physical properties over the year of 2006, with a case study of the Jiangsu coast. This section concludes the main study, and gives a few recommendations and future directions. 6.1 6.1.1 Conclusions Statistical analysis of the phytoplankton biomass in response to the environmental variables In chapter 2, the factor analysis is developed to reduce the redundant information from a set of correlated variables and to represent with a smaller set of variables in a case of Lauwersoog station (NL), determined by the 10-year’s historical dataset from 2000 through 2009. Summarizing the historical dataset of the chlorophyll a (187 samples), 75% of the values fluctuate at a range of [0, 20] mg m−3 , and a Gamma model fits well by the observations (k = 1.63 , ν = 0.11) (figure 2.2). From a comprehensive view, two thirds of the total variance in the phytoplankton biomass can be explained by the physical-chemical conditions. The phytoplankton biomass is positively correlated with the physical conditions (salinity, light intensity, and temperature), and is negatively correlated with the nutrients (ammonium, nitrate, and silicate). Factor analysis identifies the driving variables from a set of correlated variables to the phytoplankton biomass. The first two components/factors are concerned in the analysis. Of all the variables, dissolved nitrate is characterized as the driving variable in the first rotated component/factor (-0.887 by PCA, 0.881 by ULS, and 0.903 by ML), and ammonium is the driving variable in the second rotated component/factor (0.860 by PCA, 0.797 by ULS, and 0.838 by ML). Moreover, nitrate is higher correlated with Chapter 6. Conclusions and future work 85 other variables than ammonium, accounting for 37.8%, 35.3%, and 32.8% of the total variance by PCA, ULS, and ML, respectively (figure 2.5 and figure 2.6). 6.1.2 Validation of the mathematical models In chapter 3, prior to the application of the BLOOM II model, the validation is performed using the graphical comparisons and a cost-function as proposed in ASMO eutrophication modelling workshop. 96.9% of all the comparisons are classified as in good agreement, while only 3.1% as in poor (table 3.2). In chapter 4, the graphical comparisons of the model output and the monitored phytoplankton biomass are displayed (figure 4.4), demonstrating that the phytoplankton model can produce reliable predictions of the phytoplankton biomass in this case. In chapter 5, skill assessment is introduced to discuss the reliability of the phytoplankton model. The normalized Bias and unbiased RMSE, 90% being inside the standard range of [-1, 1], indicate that the phytoplankton model is applicable in the Jiangsu coastal waters (table 5.3). 6.1.3 Application of the mathematical models In chapter 3, the ecological model of BLOOM II is applied to the Frisian Inlet to investigate the dynamics of chlorophyll a. Attention is paid to the response of chlorophyll a to nutrient availability, including N-reduction, P-reduction and both N-and P-reduction (table 3.3). The effect from both N- and P-reduction scenario is larger than that from N-only and P-only reduction scenarios. In chapter 4, a vertical phytoplankton model is developed. This study aims to better understand the vertical distributions of the phytoplankton biomass. Higher values of the phytoplankton biomass appear in spring and autumn, followed by the rapid reduction of the nutrients (figure 4.5). In chapter 5, the extended application of the vertical phytoplankton model is apllied to the Jiangsu coastal waters, emphasizing on the phytoplankton biomass and the phytoplankton blooms from the physical properties. Normally, the occurrence of the bloom event is triggered by the critical conditions. Our concern is focused on the physical Chapter 6. Conclusions and future work 86 limitation, vertical stability threshold and critical depth. At Lianyungang station, the predicted timings of the phytoplankton bloom events are from 23rd May to 25th May, 26th July to 12th August, and 30th September to 7th October, while the observed bloom event occurs on 2nd October till 8th October. At Dafeng station, the phytoplankton bloom event happens on 10th August till 18th August. At Yangkou station, the bloom events happen from 4th June to 17th June and 4th August to 13th August. While no observed data is collected at Dafeng and Yangkou station. At the north branch of the Yangtze River estuary, the predicted bloom events appear from 8th May to 23rd May and 2nd August to 18th August, while the observed blooms occur on 14th May and 4th August (figure 5.12). 6.1.4 Uncertainty analysis of phytoplankton dynamics The simplfiication of the models is accompanied with uncertainty, which cannot be avoided in any of analyses. To get insight in the model prediction, uncertainty analysis is required. The Bayesian Markov Chain Monte Carlo simulation, a full description of uncertainty, is approached to perform uncertainty analysis, processed with WinBugs. Prior to the application, the commonly used Gelman-Rubin convergence test is explored. The prediction varies at a range within the 95% confidence interval, with a small Monte Carlo error. The Bootstrap method is also used in the study to get the 95% confidence interval of the estimate. 6.2 Suggestions for future work Possible future directions for this research extend to four categories. Firstly, testing of the models in other cases may result in a broad reflection. Meanwhile, we may in the future introduce other widely used models applied to coastal waters, like SMS (Surface Water Modelling System, accessible through http://www. scientificsoftwaregroup.com/pages/detailed_description.php?products_id=119) and MIKE (accessible through http://www.mikepoweredbydhi.com/). Secondly, more field samples should be collected to improve the models. For the BLOOM II model (in chapter 3), the physical and chemical factors are observed, but the effects Chapter 6. Conclusions and future work 87 of the biological features also should be studied, like species composition, cell size, and predation. For the phytoplankton model (in chapter 5), only the physical condition is considered, other chemical-biological factors should still be measured. The common weakness of the BLOOM II model and the phytoplankton model is that chlorophyll a or the phytoplankton biomass indicates all the species due to the unknown properties of the species. The specific properties of the species should be distinguished, like diatoms, flagellate, dinoflagellate, and phaeocystis. Thirdly, a comprehensive understanding of the impact-effect chain of the coastal ecosystem is required. In this thesis, only the significance of the phytoplankton is stressed. The interactions between the phytoplankton and the zooplankton, even the fish and the benthic organisms, need to be investigated in future analysis. Fourthly, it is valuable to link the phytoplankton model to the bloom forecasting system. One subject of phytoplankton dynamics concerns the bloom development, but is only briefly discussed in chapter 5. Although most of the blooms are not poisonous, the phytoplankton blooms would block the light intensity penetration into the water and affect the marine life. The impacts of these blooms show up in many ways: water is seriously polluted; human health is placed at risk; coastal ecosystems are destroyed; marine life is dying; and overall, economic loss is immense. To reduce the impacts of the bloom events, it is required to regulate the phytoplankton bloom dynamics. A bloom event is defined as a sharp increase of the phytoplankton population within a short time period. The problem is that there is no officially recognized threshold level of the increased population to define a bloom. Researchers have developed the trigger conditions of the blooms, like critical nutrients, critical depth, and vertical stability threshold. In this thesis, the theories of vertical stability threshold and critical depth are discussed. Phytoplankton blooms result from a complex interaction between the environmental variables (hydrographic, meteorological, biological and chemical conditions), of which only a few can be controlled. Without essential nutrients, principally nitrates and phosphates, algae will usually not reach the bloom proportions. The need of the nutrient reduction measures has been recognized as essential for controlling the blooms. We should pay much more attention to these issues in future work. To manipulate bloom events is a combined work, all the associated actors should involve and cooperate with each other. Chapter 6. Conclusions and future work 88 • Government The role of the government is to draft the practical measures to control the wastewater which include a large amount of nutrients. • Public On the one hand, the public should reduce the use of fertilizers in agriculture. On the other hand, the public are responsible for informing the relevant departments when they encounter abnormal water colours. • Industry The role of the industry is to comply with the emission standards of the sewage and to control the water quality. • Scientific researchers The role of the scientific researchers is to provide accurate and timely information on the prediction of the bloom events, finding out the main causes and offering reasonable suggestions. Appendix A BLOOM II model BLOOM II model could be applied in fresh water, transitional water or coastal water to calculate the growth of algae species and transport of substances in the water column. The objective is to maximize the total biomass concentration of phytoplankton species at equilibrium in a certain time period given a set of environmental conditions. The following ecological processes are concentrated: Phytoplankton processes: growth and mortality; Attenuation of light; Decomposition of particulate organic matter in water and sediment; Reaeration of oxygen; Nitrification and denitrification of nitrogen; Settling; Burial; Competition processes: grazing, excretion and respiration. Figure A.1 considers the physical-chemical-biological interactions, and the mathematical formulations required are described after Blauw et al. [2009]. A.1 Nutrient cycling Nutrient (N, P, and Si) is one of the main limiting factors for the phytoplankton species. The nutrient cycle has three major pools: dissolved inorganic nutrients, living organic 89 Appendix A. BLOOM II model 90 Figure A.1: Ecological processes in BLOOM II (after Los et al. [2008]) matter and dead organic matter. Dissolved inorganic nutrients are uptake by primary producers. A number of nutrients are released as dissolved inorganic nutrients within the processes which are called autolysis by the mortality of algae, mineralisation by detritus and nitrification by algae. Some are released from the respiration by the algae. Processes for nitrogen are denitrification (N2 ) and nitrification. Nitrate (N O3− ) is subjected to denitrification in anaerobic zones of the water system: the sediment and deep water in stratified water systems. The microbial process reduces nitrate into elementary nitrogen, which may escape from water system as nitrogen gas. The opposite process is possible by means of the fixation of nitrogen into ammonium by algae. Living organisms require phosphorus for energy transfer within the cell, for several enzyme systems, and as ingredients of DNA and RNA (Ishige et al. [2003]). In the water column, all phosphorus forms are transformed to more bio-available forms at various rates dependent on microbial actions and environmental conditions. In the sediment layer, phosphorus affects the concentration in the water column when it occurs P-release from the sediment (Nurnberg [1988]; Sas [1989]). Appendix A. BLOOM II model 91 Silicon is only available for phytoplankton in the form of dissolved silicate which just exists in diatoms. A.2 Light attenuation The energy constraint concerns the energy obtained from light intensity. It is expressed as the maximal extinction by phytoplankton when the light intensity is reduced to a level where the growth rate equals to the respiration rate. Extinction is modelled as an exponential decrease of light intensity with water depth according to the LambertBeer formula. The total extinction coefficient is the sum of the extinction by inorganic suspended particulate matter, organic matter, chlorophyll a, salinity and background extinction. Primary production is strongly influenced by light intensity. A.3 Growth and mortality The growth of phytoplankton has been concerned many years ago (Goldman et al. [1979]; Eppley [1981]; Stockner and Antia [1986]). The researchers also explored the relationships between growth rate and cell size (Banse [1976]), nutrient (Skogen et al. [1995]; Los et al. [2008]), temperature (Goldman and Carpenter [1974]) and light (Langdon [1988]). A.4 Reaeration of dissolve oxygen Algae can produce and consume oxygen. The process of reaeration of oxygen is to exchange the oxygen with atmosphere and this activity can result in the gain or loss of oxygen in the water column (Hydraulics [2003]). A.5 Competition between species Two (or more) plants may influence each other by means of competition and coexistence. Different species of vegetation compete for nutrients, space, light etc. For vegetation the competition is mostly governed by local processes, but for animals the competition takes Appendix A. BLOOM II model 92 place over larger domains. In a model this process often implemented as a formulation limited by the interaction of a relatively small number of computational segments in space and time. Appendix B Factor analysis B.1 Principal Component Analysis (PCA) Let X be the (n,p) matrix of observations xi,j , for i = 1, 2, ..., n, j = 1, 2, ..., p. x ... x1p 11 X = ... ... xn1 ... xnp Where xij is the value of individual i for variable j which is defined with a vector of n components (x1j , ..., xnj )0 . In the same way, an individual i is identified to a vector xi of p components with (xi1 , ..., xip )0 . Let x be the vector of arithmetic means of each of the p variables, x = (x1 , ..., xp )0 Where xj = Pn i=1 pi xij 93 Appendix B. Factor analysis 94 However, it can be useful for some applications to use weight pi varying from one individual to another as grouped data. These weights, which are positive numbers summing to 1, can be viewed as frequencies and are stored in a diagonal matrix of size n, Dp = p1 ... pn The method consists of projecting the data cloud in order to minimize the shrinkage of the distances which are inherent to the projection. This is equivalent to choosing the projection space F which maximizes the criterion: Pn Pn i=1 2 j=1 pi pj d (i, j) Where, d(i, j) indicates the distance between two individual xi and xj . One dimension subspace is defined by a unit vector u = (u1 , ..., up )0 . The projection, P or coordinate ci , is defined by ci = pj=1 xij uj = Xu . It is a linear combination of the original variables. The variance is then: V ar(c) = Pn i pi c2i = c0 Dp c = u0 X 0 Dp Xu The solution of this quadratic maximization problem is the eigenvector u1 associated with the largest eigenvalue ω1 . We then search for the vector u2 orthogonal to u1 . Similarly, it is shown that u2 is the eigenvector associated with the second largest eigenvalue ω2 . Vectors uj are called principal factors. They contain the coefficients to be applied to the original variables in the linear combination c = Xu. Principal components are artificial variables defined by principal factors cj = Xuj . Appendix B. Factor analysis B.2 95 Maximum Likelihood (ML) This method determines the values of parameters of a distribution model that maximizes the likelihood of the sample data. The maximum solutions are obtained by minimizing F = tr[(ΛΛ0 + Ψ2 )−1 R] − log|(ΛΛ0 + Ψ2 )−1 R| − p Where, Λ is the factor loading matrix, Ψ2 is the diagonal matrix of variances. Firstly, the conditional minimum of F for a given y is found. This gives the function f (Ψ) , which is minimized using the Newton-Raphson procedure. Let xs be the column vector including the logarithm of the diagonal elements of y at the sth iteration, then xs+1 = xs − ds In which, ds is the solution to the system of linear equations, Hs ds = hs and Hs = ∂ 2 f (Ψ) ∂xi ∂xj hs is the column vector. The starting point x1 is, x1j = log[(1 − m/2p)/rij ] Where m is the number of factors and rij is the j th diagonal element of R−1 . Appendix B. Factor analysis 96 The function of f (Ψ) can be expressed in terms of the eigenvalues ω1 ≤ ω2 ≤ ... ≤ ωp . That is, f (Ψ) = B.3 Pp k=m+1 (logωk + ωk−1 − 1) Unweighted Least Squares (ULS) The same basic theory is used in ULS as in ML, except the form of function f (Ψ). f (Ψ) = Pp k=m+1 (wk −1)2 2 Appendix C Critical depth This concept is introduced after Sverdrup [1953], and is referred to after Huisman et al. [1999] here. Consider a well-mixed water column. Let ω denote the phytoplankton population density, with dimension being number of phytoplankton per unit volume. The growth rate of the phytoplankton population depends on the balance between production and loss: dω dt = 1 H RH 0 p[I(z)]ωdz − Lω where p[I] is the specific rate of production as an increasing function of light intensity, I(z) is the light intensity as a decreasing function of depth, H is the total depth of the water column, and L is the loss rate imposed by dilution. The light intensity, I, decreases with depth according to Lambert-Beer’s law: I(z) = Iin e−(Kd ωz+Kbg z) Where Iin is the incident light intensity, Kd is the specific light attenuation coefficient of the phytoplankton, and Kbg is the total background turbidity due to non-phytoplankton components. The light intensity at the bottom of the water column, Iout , is given by Iout = I(H). 97 Appendix C. Critical depth 98 Combining the two equations mentioned above gives the following dynamical system (Huisman and Weissing [1994]; Weissing and Huisman [1994]; see also Bannister [1974]): dω dt = Kd ω 1 H Kd ω+Kbg R Iin p[I)] Iout Kd I dI − Lω Iout = Iin e−(Kd ωz+Kbg z) This model predicts that there is a critical value of Iout which we have called the critical light intensity, at which the phytoplankton population should remain stationary. Because the critical light intensity is independent of mixing depth, the population density at steady state should be inversely proportional to mixing depth: ω∗ = 1 Kd H ln(Iin /Iout ∗) − Kbg Kd Where Iout ∗ is the critical light intensity, and ω∗ indicates that ω is evaluated at steady state. Then we can get the critical depth (ω∗ = 0): z∗ = ln(Iin /Iout ∗) Kbg Appendix D Commonly used probability distributions D.1 Normal distribution The best known and most widely used probability distribution is undoubtedly the normal distribution (Gaussian distribution). Its PDF for a continuous random variable X, is given by fX (x) = √1 exp[− 1 ( x−µ )2 ] 2 σ σ 2π −∞ < x < ∞ Where, µ and σ indicate the mean and standard deviation of X , respectively. It is well known that the normal distribution is bell-shaped and symmetrical with respect to the mean µ. Therefore, the skewness coefficient of a normal random variable is zero. D.2 Lognormal distribution The lognormal distribution is also a popular probability distribution for positively valued random variables. Its PDF for a random variable X is defined as: 99 Appendix D. Commonly used probability distributions fX (x) = 1 2 √ exp[− 12 ( lnx−η ς ) ] ςx 2π Where, η = E(lnX) and ς = 100 x>0 p V ar(lnX) indicate the mean and standard deviation of lnX , respectively. Lognormal random variables are closely related to normal random variables by a transform Y = ln(X). D.3 Gamma distribution The Gamma distribution is a versatile continuous distribution associated with a positivevalued random variable. The Gamma distribution for a random variable X has the following PDF, fX (x) = ν(νx)κ−1 Γ(κ) exp(−νx) x>0 In which, ν and κ are the rate parameter and shape parameter of Gamma distribution, respectively, and Γ(κ) is the Gamma function defined as: Γ(κ) = R∞ 0 xκ−1 ex dx κ>1 The mean and variance of Gamma distribution are, µX = κ ν and 2 = σX κ ν2 Appendix D. Commonly used probability distributions D.4 101 Weibull distribution The Weibull distribution for a random variable X is defined as: fX (x) = λγ ( λx )γ−1 exp[−( λx )γ ] x>0 In which, γ and λ indicate the scale parameter and shape parameter of Weibull distribution, respectively. Appendix E Statistical properties of random variables E.1 Mean, median, and quartiles The central tendency of a random variable is the so-called mean µX , which is the first order moment. µX = E(X) = R∞ −∞ xfX (x)dx The median of a random variable is the value that splits the distribution into two equal halves. Mathematically, the median of a continuous random variable satisfies the following equation. FX (xmd ) = R xmd −∞ fX (x)dx = 0.5 Therefore, the median is the 50th percentile of a random variable X. A quantity xp satisfies 102 Appendix E. Statistical properties of random variables 103 p = P (X 6 xp ) = FX (xp ) E.2 Variance and standard deviation The variance is the second order central moment, defined as V ar[X] = σx2 = E[(X − µX )2 ] = R∞ −∞ (x − µX )2 fX (x)dx The positive squared root of variance is the standard deviation, which is often used as the measure of the degree of uncertainty. E.3 Skewness coefficient and kurtosis Another property of a random variable is the symmetry or asymmetry of its PDF or PMF, and the associated degree of asymmetry. Skewness is the third central moment, γx = E(X − µX )3 = P xi (xi − µX )3 PX (xi ) for discrete X and γx = E(X − µX )3 = R∞ −∞ (xi − µX )3 PX (xi ) for continuous X If γx = 0, the distribution is symmetric about its mean value µX ; if γx > 0, the distribution has a long tail to the right; if γx < 0, the distribution has a long tail to the left. A convenient dimensionless measure of the degree of asymmetry can be defined as θ= γx σ3 Appendix E. 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Glossary Coastal ecosystems Coastal ecosystems are regions of remarkable biological productivity and high accessibility, involving the interactions between all elements of flora and fauna and the physical environment, storing and cycling nutrients, filtering pollutants from inland freshwater systems, and helping to protect shorelines from erosion and storms. Coastal eutrophication Coastal eutrophication is formed by excess nutrients in the water column. It can cause serious problems in the coastal zone through disturbance of ecological balances and fisheries, and through interference with recreational activities and quality of life. Eutrophication is the result of an anthropogenically induced alteration of the global nitrogen cycle, and just like climate change, should be regarded as a ”global change”. Eutrophication is usually treated scientifically and in terms of management as a local and regional phenomenon. Phytoplankton Phytoplankton are microscopic floating photosynthetic organisms in aquatic environments, both freshwater and seawater. In seawater, the most common types of phytoplankton are diatoms and dinoflagellates. In the oceans, they are responsible for most of the primary production (photosynthesis). Since they need sunlight in order to photosynthesize, they are found only in the upper, sunlit layers of the water. When excessive nutrients are present, there may be excessive blooms of phytoplankton, which when they die and sink to the bottom, may use up much of the oxygen in the deeper water and create a hypoxic layer. Euphotic depth 121 Glossary 122 Euphotic zone depth reflects the depth where only 1% of the surface photosynthetic available radiation remains. It is a measure of water clarity, which is not only a quality index of an ecosystem but also an important property for primary production (Behrenfeld and Falkowski [1997]; Sathyendranath and Platt [1989]) and heat transfer (Chang [2004]; Kara et al. [2005]) in the upper layer water. Mixed layer depth The mixed-layer is the layer between the ocean surface and a depth usually ranging between 25 and 200m, where the density is about the same as at the surface. The mixed-layer owes its existence to the mixing initiated by waves and turbulence caused by the wind stress on the sea surface. The penetration of mixing to a certain depth (the mixed-layer depth) mostly depends on the stability of the sea water and on the incoming energy from the wind. The more stable is the surface water, the less mixing occurs, and the shallower is the mixed-layer. Many important processes occur within the mixed-layer, whether physical (e.g. direct wind-forcing of the ocean circulation), chemical (e.g. dissolution of incoming CO2 from the atmosphere), or biological (e.g. phytoplankton production). Acknowledgements I would like to express my sincere gratitude to the people who made this doctoral dissertation possible. First and foremost, I would like to thank my promotors: Professor Han Vrijling and Professor Pieter van Gelder. Many thanks are addressed to them. It is my great honour to be one of their PhD students. Prof. Vrijling, thank you for your inspiring advice and excellent guidance. My PhD study has become so much more enjoyable and inspiring by your sparkling ideas and valuable suggestions. Thanks for your time and patience in reading almost all the materials needed in our meetings. You cannot imagine how happy I was when I heard your compliment about my work and my English writing. I have not only learnt from your experience in the scientific research, but also from your attitude and wise conclusions in life. Prof. Van Gelder, you are always encouraging. I have been extremely lucky to be supervised by you who cares so much about my work. Thank you very much for putting faith in my topic and always standing by me. Thanks for everything you have done for me. I have benefitted greatly from your patient supervision and continuous encouragement. Special thanks are addressed to Professor Changkuan Zhang. You are a very kind man and have contributed much to my study. You have always helped me when I was in a trouble. Thanks for the constructive advice in improving my research. Many thanks are also addressed to Associate Professor Yiqing Guan and Professor Danrong Zhang. Thanks for your valuable suggestions regarding the study and my future career. I would like to thank Professor Bas Jonkman and Professor Marcel Stive for their efforts in making the Chinese students feel at home, celebrating the Chinese New Year with us. Thanks are extended to Ms. Mariette van Tilburg who offered me great help in correcting the writing and in translating the propositions and the summary of the dissertation. It has been a very good experience to co-organize the PhD peer group with you. Assistance provided by our secretaries, Ms. Judith Schooneveld, Ms. Agnes Groenestein, and Ms. Inge van Rooij, is greatly appreciated. Thanks for arranging everything during my PhD. I would like to thank Cees Timmers and Franca Post in CICAT for arranging a convenient and comfortable life for me in the Netherlands. I would like to thank my officemates: Mehdi, Wenhao, Flora, Nils, and Defne. It has been a good time to share the office with you. 123 Acknowledgements 124 The China Scholarship Council (CSC) is acknowledged for the financial support for this study. My committee members are gratefully acknowledged for their constructive comments, which have been really important and helpful in improving the thesis. Thanks also go to the people I met in the Netherlands, colleagues and friends, who have made my life colourful and interesting. I would like to keep you all in my memory. Last but not the least, I would like to express my deep gratitude to my family. Thanks for always believing in me and encouraging me to do my best. Lixia Niu October 2015 in Delft Curriculum Vitae Personal Information Name Telephone E-mail Date of Birth Nationality Lixia Niu +31(0)684601091 [email protected]; [email protected] 15-10-1985 Chinese Education 2011.9-2015.11 2008.9-2011.6 2004.9-2008.6 University Department Section Topic Degree University Department Section Topic Degree University Department Section Degree Delft University of Technology Hydraulic Engineering Hydraulic Structures and Flood Risk Uncertainty Analysis of Phytoplankton Dynamics in Coastal Waters PhD Hohai University Hydrology and Water Resources Ecological Water Environment Flow and Water Quality Simulation of Shallow Lakes MSc North China University of Water Resources and Electric Power Water Resources Engineering Management Bachelor Conference Papers Yiqing Guan, Lixia Niu*, Danrong Zhang, Xiaoshuai Lv, and Li Wei, 2011. Flow and water quality simulation of Tongxiang Reservoir. The 4th International Conference on Bioinformatics and Biomedical Engineering, 2048-2052. Zhaoyue Tai, Yiqing Guan, Lixia Niu, Danrong Zhang, Mingjuan Zu, 2011. The effects of eco-environmental water demand on the power generation benefit of qinshan hydropower station. Proceedings of the 2011 IEEE International Conference on waste recycling, Ecology and Environment, 613-617. 125 Curriculum Vitae 126 Niu L *, and van Gelder P.H.A.J.M., 2013. Probabilistic analysis of sand transport behaviour at the Frisian Inlet (NL) under storm events. Proceedings of the 35th IAHR world congress, 1-10. Niu, L.*, Van Gelder, P.H.A.J.M., Zhang, C., Guan, Y. and Vrijling, J.K., 2015. Statistical analysis of phytoplankton biomass in the coastal waters of Lauwersoog (NL). Proceedings of the 36th IAHR World Congress, 1-6. Journal Publications Niu L.*, Yiqing Guan, Handong Ge, Danrong Zhang, Dongmei Xia, 2011. Effect of eco-environmental water demand on electricity benefit of Qinshan Hydropower Station. Water Resources Protection, 27, 29-33. Niu, L.*, Van Gelder, P.H.A.J.M., Guan, Y., Zhang, C. and Vrijling, J.K., 2015. Probabilistic analysis of phytoplankton biomass at the Frisian Inlet (NL). Estuarine, Coastal and Shelf Science, 155, 29-37. Niu, L.*, Van Gelder, P.H.A.J.M., Guan, Y. and Vrijling, J.K., 2015. Uncertainty analysis and modelling of phytoplankton dynamics in coastal waters. Environment Protection and Sustainable Development, 1(4), 193-202. Niu, L.*, Van Gelder, P.H.A.J.M., Zhang, C., Guan, Y. and Vrijling, J.K., 2015. Statistical analysis of phytoplankton biomass in coastal waters: case study of the Wadden Sea near Lauwersoog (the Netherlands) from 2000 through 2009. Ecological Informatics, 30, 12-19. Niu, L.*, Van Gelder, P.H.A.J.M., Zhang, C., Guan, Y. and Vrijling, J.K., 2015. Physical control of phytoplankton bloom development in the coastal waters of Jiangsu (China). Ecological Modelling (Accepted). DOI: 10.1016/j.ecolmodel.2015.10.008. Niu, L.*, Van Gelder, P.H.A.J.M., and Vrijling, J.K., 2015. Physical limitation of phytoplankton dynamics in coastal waters. Journal of Coastal Research (Accepted).

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