Uncertainty Analysis of Phytoplankton Dynamics in Coastal Waters Proefschrift

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 . . . . . . . . . . . . . . . . . . . .
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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
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Contents
3.1
3.2
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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6 Conclusions and future work
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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
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response to
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B Factor analysis
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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
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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 . . .
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Bibliography
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Glossary
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Acknowledgements
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Curriculum Vitae
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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. Statistical properties of random variables
104
Kurtosis is a measure of the peakedness of the underlying distribution. It is the fourth
central moment of a random variable.
κx = E(X − µX )4 =
P
xi (xi
− µX )4 PX (xi )
for discrete X
and
κx = E(X − µX )4 =
E.4
R∞
−∞ (xi
− µX )4 PX (xi )
for continuous X
Covariance and correlation coefficient
When there are two dependent random variables, there may be a relationship between
them. The correlation coefficient is defined by the covariance to standard deviations of
the two random variables.
ρx,y = Corr(X, Y ) =
Cov(X,Y )
σx σy
Where Cov(X, Y ) is the covariance defined as
Cov(X, Y ) = E[(X − µX )(Y − µY )] = E(XY ) − µX µY
ρx,y , a dimensionless number, ranges between -1.0 and +1.0.
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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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