Flood Frequency Analyses for New Brunswick Rivers Aucoin, F., D. Caissie, N. El-Jabi and N. Turkkan Department of Fisheries and Oceans Gulf Region Oceans and Science Branch Diadromous Fish Section P.O. Box 5030, Moncton, NB, E1C 9B6 2011 Canadian Technical Report of Fisheries and Aquatic Sciences 2920 Canadian Technical Report of Fisheries and Aquatic Sciences Technical reports contain scientific and technical information that contributes to existing knowledge but which is not normally appropriate for primary literature. Technical reports are directed primarily toward a worldwide audience and have an international distribution. No restriction is placed on subject matter and the series reflects the broad interests and policies of Fisheries and Oceans, namely, fisheries and aquatic sciences. Technical reports may be cited as full publications. The correct citation appears above the abstract of each report. 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Les demandes de rapports seront satisfaites par l'établissement auteur dont le nom figure sur la couverture et la page du titre. Les numéros 1 à 456 de cette série ont été publiés à titre de Rapports techniques de l'Office des recherches sur les pêcheries du Canada. Les numéros 457 à 714 sont parus à titre de Rapports techniques de la Direction générale de la recherche et du développe-ment, Service des pêches et de la mer, ministère de l'Environnement. Les numéros 715 à 924 ont été publiés à titre de Rapports techniques du Service des pêches et de la mer, ministère des Pêches et de l'Environnement. Le nom actuel de la série a été établi lors de la parution du numéro 925. Canadian Technical Report of Fisheries and Aquatic Sciences 2920 2011 Flood Frequency Analyses for New Brunswick Rivers by François Aucoin1, Daniel Caissie2, Nassir El-Jabi1 and Noyan Turkkan1 Department of Fisheries and Oceans Gulf Region, Oceans and Science Branch Diadromous Fish Section P.O. Box 5030, Moncton, NB, E1C 9B6 1. Université de Moncton, Moncton, NB, E1A 3E9 2. Fisheries and Oceans Canada, Moncton, NB, E1C 9B6 ii © Her Majesty the Queen in Right of Canada, 2011. Cat. No. Fs. 97-6/2920E ISSN 0706-6457 (Printed version) Cat. No. F597/2920E-PDF ISNN 1488-5379 (on-line verson) Correct citation for this publication: Aucoin, F., D. Caissie, N. El-Jabi and N. Turkkan. 2011. Flood frequency analyses for New Brunswick rivers. Can. Tech. Rep. Fish. Aquat. Sci. 2920: xi + 77p. iii Warning: Neither the organizations named in this Technical Report, nor any person acting on behalf of any of them assume any liability for the misuse or misunderstanding of the information presented in this study. The user is expected to make the final evaluation of the appropriateness of the technique and the accuracy of the data and calculations in his or her own set of circumstances. Avertissement: Les organisations énumérées dans ce rapport technique ou toute personne agissant en leurs noms déclinent toute responsabilité pour le mauvais emploi ou la mauvaise interprétation des renseignements contenus dans cette étude. Il incombe aux utilisateurs d’évaluer la pertinence des techniques et l’exactitude des données et calculs dans les circonstances qui s’appliquent. iv TABLE OF CONTENTS Table of Contents ............................................................................................................iv List of Tables....................................................................................................................v List of Figures .................................................................................................................vi Abstract ...........................................................................................................................ix Résumé .............................................................................................................................x 1.0 Introduction ................................................................................................................1 2.0 Material and Methods.................................................................................................3 2.1 Data and Study Region...............................................................................3 2.2 Single Station Flood Frequency Analysis ..................................................4 2.2.1 Probability Density Functions .............................................................4 2.2.2 Parameter Estimation...........................................................................6 2.2.3 Goodness-of-Fit and Model Selection.................................................7 2.2.4 Recurrence Intervals............................................................................9 2.3 Regional Regression Equations................................................................10 2.4 Index Flood Method .................................................................................11 2.4.1 Averaging Approach .........................................................................11 2.4.2 Pooling Approach..............................................................................13 2.5 Daily to Instantaneous Flows ...................................................................15 3.0 Results and Discussion .............................................................................................16 3.1 Single Station Flood Frequency Analyses................................................16 3.2 Regional Flood Frequency Analyses........................................................18 3.2.1 Regression Method............................................................................18 3.2.2 Index Flood Method ..........................................................................19 3.4 Instantaneous Flows and Envelope Curves ..............................................21 4.0 Summary and Conclusions .......................................................................................24 5.0 Acknowledgements ..................................................................................................26 6.0 References ................................................................................................................26 Appendix A ....................................................................................................................44 Appendix B.....................................................................................................................73 v LIST OF TABLES 1. Analyzed hydrometric stations for the flood frequency analysis ............... 29 2. Summary of physiographic and climatic characteristics for selected hydrometric stations (data from report by Environment Canada and New Brunswick Department of Municipal Affairs and Environment, 1987)........................................................................................................... 30 Results of single station flood frequency analyses using the 3parameter Lognormal (LN3) distribution ................................................... 31 Results of single station flood frequency analyses using the Generalized Extreme Value (GEV) distribution ........................................ 32 Parameters for the 3 parameter lognormal distribution (single station analysis), the Anderson-Darling (AD) statistic and the negative loglikelihood (NLL) value............................................................................... 33 Parameters for the Generalized Extreme Value distribution function (single station analysis), the Anderson-Darling (AD) statistic and negative log-likelihood (NLL) value .......................................................... 34 7. Regional regression coefficient estimates and R2 (GEV distribution) ....... 35 8. Regional flood indices using the index flood method in New Brunswick (values in parentheses represent the coefficients of variation (Cv, %)) ....................................................................................... 36 Results of mean and maximum QP/QD ratio and associated variability (Cv, %) for analyzed hydrometric stations................................................. 37 3. 4. 5. 6. 9. vi LIST OF FIGURES 1. Location of selected hydrometric stations (56 stations) ............................. 38 2. Flood frequency analysis for Narrows Mountain Brook (NB), station 01AL004. .................................................................................................... 39 Relation between the Anderson-Darling (AD) statistics obtained from the 3-parameter Lognormal (LN3) and the Generalized Extreme Value (GEV) distributions. ................................................................................... 40 Estimated 100-year flood (daily discharge) as a function of drainage area (km2) for all 56 hydrometric stations (GEV and LN3). Regional regression line for both the present study (QD100 = 1.58 A0.842) and the EC & NB study (1987; QD100 = 1.33 A0.855) are presented ................ 41 Ratio of instantaneous peak flow to daily flow (QP/QD) for the 54 analyzed hydrometric stations (see Table 9 for more details). ................... 42 Envelope curve of the present study for instantaneous flows (m3/s) in relation to those of previous studies. Data points represent the maximum instantaneous discharge (highest recorded flow) for each station in NB. .............................................................................................. 43 Flood frequency analysis for a) Saint John River at Fort Kent and b) St Francis River............................................................................................... 45 Flood frequency analysis for a) Saint John River at Grand Falls and b) Green River................................................................................................. 46 Flood frequency analysis for a) Limestone River and b) Aroostook River ........................................................................................................... 47 Flood frequency analysis for a) Mamozekel River and b) Saint John River near East Florenceville ..................................................................... 48 Flood frequency analysis for a) Meduxnekeag River and b) Big Presque Isle Stream .................................................................................... 49 Flood frequency analysis for a) Becaguimec Stream and b) Cold Stream......................................................................................................... 50 Flood frequency analysis for a) Shogomoc Stream and b) Saint John River below Mactaquac .............................................................................. 51 3. 4. 5. 6. A.1. A.2. A.3. A.4. A.5. A.6. A.7. vii A.8. Flood frequency analysis for a) Middle Branch Nashwaaksis Stream and b) Nackawic River ............................................................................... 52 Flood frequency analysis for a) Eel River and b) Nashwaak River ........... 53 A.10. Flood frequency analysis for a) Hayden Brook and b) Narrows Mountain Brook.......................................................................................... 54 A.11. Flood frequency analysis for a) North Branch Oromocto River and b) Castaway Brook.......................................................................................... 55 A.12. Flood frequency analysis for a) Salmon River and b) Canaan River ......... 56 A.13. Flood frequency analysis for a) Kennebecasis River and b) Nerepis River ........................................................................................................... 57 A.14. Flood frequency analysis for a) Lepreau River and b) Magaguadavic River ........................................................................................................... 58 A.15. Flood frequency analysis for a) Dennis Stream and b) Bocabec River...... 59 A.16. Flood frequency analysis for a) Restigouche River and b) Upsalquitch River ........................................................................................................... 60 A.17. Flood frequency analysis for a) Tetagouche River and b) Jacquet River... 61 A.18. Flood frequency analysis for a) Eel River and b) Restigouche River ........ 62 A.19. Flood frequency analysis for a) Nepisiquit River and b) Bass River ......... 63 A.20. Flood frequency analysis for a) Rivière Caraquet and b) Big Tracadie River ........................................................................................................... 64 A.21. Flood frequency analysis for a) Southwest Miramichi River and b) Renous River .............................................................................................. 65 A.22. Flood frequency analysis for a) Barnaby River and b) Little Southwest Miramichi River ......................................................................................... 66 A.23. Flood frequency analysis for a) Northwest Miramichi River and b) Kouchibouguac River ................................................................................. 67 A.24. Flood frequency analysis for a) Coal Branch River and b) Petitcodiac River ........................................................................................................... 68 A.9. viii A.25. Flood frequency analysis for a) Turtle Creek and b) Palmer’s Creek ........ 69 A.26. Flood frequency analysis for a) Ratcliffe Brook and b) Point Wolfe River ........................................................................................................... 70 A.27. Flood frequency analysis for a) Upper Salmon River and b) Rivière Matapedia, QC............................................................................................ 71 A.28. Flood frequency analysis for a) Kelley River, NS, and b) Rivière Nouvelle au Pont, QC ................................................................................. 72 B.1. B.2. B.3. B.4. Estimated 2-year flood (daily discharge) as a function of drainage area (km2) for all 56 hydrometric stations (GEV and LN3). Regional regression line for both the present study and the EC & NB study (1987) are presented ................................................................................... 74 Estimated 10-year flood (daily discharge) as a function of drainage area (km2) for all 56 hydrometric stations (GEV and LN3). Regional regression line for both the present study and the EC & NB study (1987) are presented ................................................................................... 75 Estimated 20-year flood (daily discharge) as a function of drainage area (km2) for all 56 hydrometric stations (GEV and LN3). Regional regression line for both the present study and the EC & NB study (1987) are presented ................................................................................... 76 Estimated 50-year flood (daily discharge) as a function of drainage area (km2) for all 56 hydrometric stations (GEV and LN3). Regional regression line for both the present study and the EC & NB study (1987) are presented ................................................................................... 77 ix ABSTRACT Aucoin, F., D. Caissie, N. El-Jabi and N. Turkkan. 2011. Flood frequency analyses for New Brunswick rivers. Can. Tech. Rep. Fish. Aquat. Sci. 2920: xi + 77p. A flood frequency analysis was carried out in the present study to determine the characteristics of high flow events in New Brunswick. High flow events are a key component in river engineering, for the design and risk assessment of various projects. For many practical situations, at-site historical flood data are available, such that extreme flood events can be estimated (or predicted) with reasonable accuracy. However, for many other situations (e.g., ungauged basins) flood estimates are required at locations where no historical data are available. When this arises, regional flood frequency analysis may be considered as a viable means to approximate at-site flood characteristics by exploiting the information available at neighbouring sites. In the past, some studies have been dedicated to the analysis of floods across the Province of New Brunswick (e.g. Environment Canada and New Brunswick Department of Municipal Affairs and Environment, 1987). Since new data are available, the goal of the present study was to update those flood frequency analyses previously analysed. As such, results presented in this document will better reflect our current state of knowledge regarding the high flow regimes throughout the province. Single stations analyses were carried out for 56 hydrometric stations located in the New Brunswick watershed and one station in Nova Scotia. A regional flood frequency analysis was also carried out using both regression equations and the index flood approach. In general, the results of the present study are consistent with those from early studies, although it can be seen that updating the flood information resulted, for many stations, in an improvement of flood estimates. x RÉSUMÉ Aucoin, F., D. Caissie, N. El-Jabi and N. Turkkan. 2011. Flood frequency analyses for New Brunswick rivers. Can. Tech. Rep. Fish. Aquat. Sci. 2920: xi + 77p. Dans la présente étude, une analyse fréquentielle des crues a été réalisée en vue de déterminer les caractéristiques d'événements de crues au Nouveau-Brunswick. Dans le cadre de projets en ingénierie fluviale, l’étude des débits de crues constitue un élément clé, autant du point de vue de la conception que de celui de l'évaluation du risque. Pour de nombreuses situations pratiques, des données historiques de débits sont disponibles au niveau des sites d’intérêt, de sorte que les débits extrêmes peuvent être estimés (ou prédits) avec précision raisonnable. Cependant, dans beaucoup d'autres scénarios (p. ex., bassins non jaugés), l’on souhaite faire l’estimation des crues où aucune information n’est disponible. Lorsque ce problème se pose, l’analyse régionale fréquentielle constitue une alternative viable, laquelle suggère que l’estimation des caractéristiques des crues au niveau du site d'intérêt soit basée sur l’information disponible au niveau des sites jaugés voisins. Dans le passé, quelques études ont été consacrées à l’analyse fréquentielle des crues pour la province du Nouveau-Brunswick (par exemple, Environment Canada and New Brunswick Department of Municipal Affairs and Environment, 1987). Puisque de nouvelles données sont maintenant disponibles, l'objectif de la présente étude était de mettre à jour l’analyse fréquentielle des crues. Les résultats présentés dans ce document visent donc à mieux refléter l’état actuel des connaissances à propos du régime des débits de crues au niveau de la province. Dans cette étude, des analyses ont été réalisées pour 56 stations hydrométriques situées dans la province. En plus des 56 stations analysées, une analyse régionale xi fréquentielle des crues a été effectuée en utilisant des équations de régression et l'approche d’indice de crues. En général, les résultats ici présentés sont compatibles avec ceux des études précédentes. Cependant, il est possible d’observer que l'actualisation de l’information concernant les crues a entraîné, pour de nombreuses stations à travers la province, de nettes améliorations en ce qui concerne l'estimation des crues. 1.0 Introduction The understanding of floods plays a key role in many hydrological studies, especially in the design of hydraulics structures such as dams, culverts, bridges and others. The estimation of floods is also important in the evaluation of flood risk, particularly in areas in close proximity of flood plains. Extreme hydrological events are not only important in the design of water resource projects but also for fish habitat and in the management of fisheries resources. In New Brunswick there have been a number of studies dealing with floods and regional flood frequency analyses. For instance, a study was carried out by Montreal Engineering Co. Ltd, (1969), where high flows were estimated for many stations across the Maritime Provinces. Another study dealing with high flows in New Brunswick was carried out by Acres Consulting Services Ltd. (1977). That study corresponded to one of the most extensive analysis of floods within the province: it included a flood frequency analysis for each station, regional floods equations, and flood risk maps for a number of communities within the province. A flood study in NB was also carried out in 1987 (Environment Canada and New Brunswick Department of Municipal Affairs and Environment, 1987). The latter study depicted regional equations as well as envelope curves for the estimation of floods. More recently, a study by Caissie and Robichaud (2009) looked at many aspects of the flow regime within the Maritime Provinces including mean flow, flow duration, as well as high and low flows. The present document focuses on updating information related to floods in the province of New Brunswick. Here, both single station analyses and regional flood equations are presented. Arguably, there are two main approaches when it comes to flood estimation. The first, often referred to as the block maxima approach (BM), consists in modeling only the most extreme observation of each year, i.e., the annual maxima. Due to its simplicity, the latter corresponds to the most commonly encountered method in practice. The BM approach can get around the high correlation of daily discharge time 2 series by considering only the highest observed value each year. As such, these annual maxima will approximately behave as realizations of independent random variables. Then, under the assumption of the data being stationary through time, simple frequency distribution functions can be fitted to the maxima in order to yield estimates of the frequency of events. Although the BM approach is simpler to apply, it has the disadvantage of being somewhat “wasteful” in data, especially in situations that deal with short data series (e.g., less than 20 years). A way around this problem is to use the “threshold models” approach, also commonly referred to as peak over threshold (POT) method. The POT method considers only observations that fall above a specific threshold, a level that is selected to reflect only extremes events (e.g., floods). The POT approach allows for more observations (or data) and is especially valuable for shorter time series. The main difficulty in implementing the method lies in the selection of the threshold level: if the level is set too high, only few observations will be retained for further analysis; if the level is set too low, the retained observations will tend to be serially correlated, thus violating the independence assumption. Some theoretical arguments suggest the exclusive use of certain distributions when dealing with extreme data. For this reason, both the BM and POT approaches remain the object of extensive research in the statistical literature. For example, without knowing the “parent distribution” of the raw data, it can be shown that, under certain conditions, extreme data will converge to some explicitly known limiting distributions. For the BM approach, the limiting distribution can be shown to belong to the generalized extreme value (GEV) family of distributions, whereas, for the POT approach, the limiting distribution can be shown to belong to the generalized Pareto (GP) family of distributions (Coles, 2001; Salvadori et al., 2007). 3 All previous flood studies for New Brunswick have used the annual maxima (BM) approach. Since the goal of the present study was to update this information, the BM approach was used. More precisely, the study focused on flood characteristics at 56 hydrometric stations across the province, and the analyzed flow characteristics included the single station frequency analyses and regional flood analyses (regression equations and index flood) to calculate floods for ungauged basins. 2.0 Material and Methods 2.1 Data and Study Region The hydrological analysis was carried out using historical data from 56 hydrometric stations of which 53 are located in New Brunswick. In order to enhance the quality of the regional frequency analysis, three stations located outside the province of New Brunswick were also included: two stations located in Quebec and one station located in Nova Scotia. All data used in this study were collected from the HYDAT database up to 2005 (Environment Canada, 2007) and the Environment Canada web site for 2006-2008. Data extracted included extreme values, i.e., annual maximum daily discharges and instantaneous discharge. The 56 stations are plotted on a map of New Brunswick (Figure 1) and some of their relevant characteristics are presented in Table 1. Similar to previous studies (e.g., Environment Canada and New Brunswick Department of Municipal Affairs and Environment, 1987) some stations are affected by flow regulation and identified by (Reg) in Table 1. However, these stations were nevertheless included in the analysis as it was felt that the degree of regulation would not impact much on the regional flood frequency equations. The number of years of record varies between 11 and 92 with a mean value of 39 years. The smallest drainage basin corresponds to Narrows Mountain Brook at 3.89 km2 whereas the largest 4 river corresponds to the Saint John River below Mactaquac at 39900 km2. Moreover, a summary of the physiographic and climatic characteristics for the selected hydrometric stations is provided in Table 2 (data coming from, Environment Canada and New Brunswick Department of Municipal Affairs and Environment, 1987). 2.2 Single Station Flood Frequency Analysis A frequency analysis was carried for each station to estimate floods of different recurrence intervals. The maximum daily discharge by year was extracted from the HYDAT database and fitted to two distributions, namely the 3-parameter lognormal (LN3) and the generalized extreme value (GEV) distributions. The main motivation for considering LN3 stemmed from the fact that it was previously used with good success to describe floods in New Brunswick (Environment Canada and New Brunswick Department of Municipal Affairs and Environment, 1987). However, although the LN3 has been extensively used for describing extreme events in the past, the GEV distribution has gained in popularity over the years due to its theoretical properties. The extreme value theory suggests that distribution of extreme events, such as annual daily discharge maxima (under certain conditions, asymptotically), will most likely converge in probability toward a distribution belonging to the family of GEV distributions (Coles, 2001). 2.2.1 Probability Density Functions The probability density function (PDF) of LN3 is given by: f ( x) = ⎧ − [ln( x − λ ) − μ ]2 ⎫ 1 exp⎨ ⎬ 2σ 2 2π σ ( x − λ ) ⎩ ⎭ (1) defined for λ < x < ∞; and where μ ∈ R is the shape parameter, σ > 0 is the scale 5 parameter, and λ ∈ R is the threshold parameter. In hydrology, the cumulative distribution function (CDF) is most often used to represent flows of different recurrence intervals. For LN3, the CDF is given by: x F ( x) = ∫ λ ⎧⎪ [ ln(t − λ ) − μ ]2 ⎫⎪ 1 exp ⎨− ⎬ dt 2 2 σ 2πσ (t − λ ) ⎩⎪ ⎭⎪ (2) with parameters defined in equation (1). For GEV, the PDF is given by: 1 ⎡ ⎛ x − μ ' ⎞⎤ 1+ ξ ⎜ f ( x) = ⎟⎥ ⎢ σ'⎣ ⎝ σ ' ⎠⎦ − (1/ ξ +1) −1/ ξ ⎧⎪ ⎡ ⎛ x − μ ' ⎞ ⎤ ⎫⎪ exp ⎨ − ⎢1 + ξ ⎜ ⎟⎥ ⎬ ⎝ σ ' ⎠ ⎦ ⎭⎪ ⎪⎩ ⎣ (3) defined for 1 + ξ ( x − μ ') / σ ' > 0; and where σ’ > 0 is the scale parameter, μ ′ ∈ R is the location parameter, and ξ ∈ R is the shape parameter. The CDF for the GEV is given by the following equation: −1/ ξ ⎧⎪ ⎡ ⎛ x − μ ' ⎞ ⎤ ⎫⎪ F ( x) = exp ⎨− ⎢1 + ξ ⎜ ⎟⎥ ⎬ ⎝ σ ' ⎠ ⎦ ⎭⎪ ⎩⎪ ⎣ (4) with parameters defined in equation (3). Note that, for simplicity, x , f ( x) , and F ( x) are used here for both LN3 and GEV; however they are different for each distribution. 6 2.2.2 Parameter Estimation The method of maximum likelihood was used for estimating the parameters for v both LN3 and GEV. More formally, let x = ( x1 , x2 ,..., xn ) ' denote a vector of n observations, whose PDF is believed to be f ( xi | θ ) , for i = 1, 2,..., n , and where θ corresponds to a vector of unknown parameters. For example, θ would correspond to v θ = (ξ , σ ', μ ') ' for the GEV distribution. Under the assumption that x corresponds to a v realization of the random vector X = ( X 1 , X 2 ,..., X n ) , where the X i ’s are independent and identically distributed, the likelihood function can be defined as the joint probability function of the n observations conditionally on the unknown vector of parameters; that is n v L(θ | x ) = ∏ f ( xi | θ ) = f ( x1 | θ ) * f ( x2 | θ ) *...* f ( xn | θ ) (5) i =1 The method of maximum likelihood consists in finding the value of θ for which (5) is at a maximum, or, equivalently, in finding θ for which the log-likelihood function (LL) is at a maximum. n n v LL(θ | x ) = ln ∏ f ( xi | θ ) = ∑ ln f ( xi | θ ) i =1 (6) i =1 In other words, the idea consists in finding the parameter values θˆ that are the most v likely for the observed sample x under the chosen distribution function. Note that some optimization algorithms will only allow the search of minima. When this is the case, minimizing the negative-log-likelihood function (NLL) will be equivalent to maximizing the LL. The estimation of unknown parameters using this method almost always requires the use of iterative procedures. In the present study, the statistical freeware R (2009) was used for all computations pertaining to parameter estimation. 7 2.2.3 Goodness-of-Fit and Model Selection Usually, once the unknown parameters have been estimated for distinct distributions, there is an interest in 1) assessing the quality of the fitted models, as well as 2) determining which model fits the data best using selected criteria. As such, three diagnostic tools were used, namely, the quantile-quantile plot or (Q-Q plot), the NLL value, and the Anderson-Darling (AD) statistic (Anderson and Darling, 1952). 2.2.3.1 Q-Q Plot The Q-Q plot is a visual assessment tool that plots the sorted observations (that represent the maximum annual daily discharges) against their respective cumulative frequencies. The cumulative frequency, denoted here by h , was plotted graphically using the Weibull plotting position formula (Chow et al., 1988): h= m n +1 (7) where m refers to the rank of the annual maximum daily discharge in increasing order, and n is the number of years of record. Given h , the position on the x axis was determined using the Gumbel reduced variable Y: Y = −ln ( − ln ( h ) ) (8) The above transformation is usually used for plotting flood data due to the logarithmic nature of such events. This type of a plotting transformation is referred to as plotting data on a Gumbel paper. The fitted lines for several distribution functions can also be plotted in order to discriminate between the relative performances of each 8 model. When both distributions fit the data reasonably well, descriptive criteria (as described below) can be used to discriminate between distributions. 2.2.3.2 Negative Log-likelihood Value The NLL value, which corresponds to the value at which the negative-loglikelihood function is minimized, can be used as a means for discriminating between distributions. For example, the distribution that yields the smallest NLL value will be regarded, based on this criterion, as the most probable (or “likely to be”) for the observed sample. 2.2.3.3 Anderson-Darling Statistic In addition to the NLL value and the visual Q-Q plot, the AD statistic was also used as a means of discriminating between the fitted distributions. The AD statistic can be found under several different forms across the statistical literature, and only the most v popular form is described here. Let Z = ( Z1 , Z 2 ,..., Z n ) denote a random vector defined such that Z i = Z (i ) , where X (1) ≤ X (2) ≤ ... ≤ X ( n ) are the order statistics for the random v vector X , whose notation was presented previously. The AD statistic, often referred to as A2 , can thus be defined as: n A2 = − n − ∑ i =1 2i − 1 ⎡ln F ( Z i ) − ln {1 − F ( Z n +1−i )}⎤⎦ n ⎣ (9) In this case, the notation Fˆ ( Z i ) is used instead of F ( Z i ) , since the latter is not fully specified (the parameters must be estimated). 9 An important feature of the AD version presented in equation (9) is that it gives more weight to the observations in the tails of the distribution than to those in the center of the distribution. Incidentally, inferences for values located in the tails are usually of interest when fitting distribution function (e.g., high flood events). Furthermore, the reference distribution of A2 can be studied (using either simulations or asymptotic results), and p-values can be calculated, i.e., Pr[ A2 ≤ a 2 ] , where a 2 is a realization of A2 . Generally a smaller A2 represents a better fit; however, without knowing the reference distribution of A2 , it is usually difficult to have a definition of a “small” value (since the reference distribution will be different for varying assumptions, parametric model, parameter values, the sample size, etc.). That said, AD may also be put to good use when considered as a “relative” measure of the goodness-of-fit between different distributions. More information pertaining to the AD statistic can be found in D’Agostino and Stephens (1986). 2.2.4 Recurrence Intervals The relation between the CDF, i.e., F ( x) , and the recurrence interval (T, in years) used in flood hydrology, is given by the equation: F ( x) = 1 − 1 T (10) where T-year flood denoted by QD-T, such that QD-T = 1/ [1 − F ( x)] . For example, in the present study, the following values of T were considered: T = 2,10, 20, 50,100 years. 10 2.3 Regional Regression Equations Characteristics of floods differ from one drainage basin to another and results of single station analysis are only applicable to the specific gauged streams or those streams near hydrometric stations. As many water resource projects are undertaken for ungauged basins, there is a requirement for the development of regional equations. In a previous study (Environment Canada and New Brunswick Department of Municipal Affairs and Environment, 1987) the province was divided into 5 different regions. This tends to limit the applicability of regional equations in terms of sample size and drainage size for each region. As such, the present study considers the province as one region. The main idea behind regional regression analysis is to establish a relationship between floods and physiographic parameters describing the basin. With the discharge as the dependent variable and the physiographic factors as independent variable(s) (in this case the area of the drainage basin and precipitation), linear regressions of the following types can be entertained: QT = a ( DA)b1 or QT = a ( DA)b1 ( MAP )b 2 (11) where a, b1, and b2 are regression parameters; DA and MAP are used in reference to the “drainage area” (in km²) and the “mean annual precipitation” (in mm), respectively; and QT denotes the T-year flood (in m³/s). At this point, it should be noted that no difference will be made between regression parameters, their estimators and their estimated values, such that the lower-cases a, b1, and b2 shall be used ex-changeably to refer to any of those quantities. It should also be noted here that two regression models are presented in equation (11): the first one only considers DA as predictor, while the second uses both DA and MAP. Later in this report, estimated regional regression equations will be given for both cases. 11 Parameters for both regression models shown in equation (11) were calculated using the statistical freeware R (2009). However, in order to fit the regression, QT , DA, and MAP must first be transformed to the natural logarithmic scale. Once the variables were log transformed, the model was fitted to yield the following parameter estimates: a*, b1, and b2. Note that a* needs to be exponentiated to obtain a; that is a = exp{a*} in equation (11). Often a major concern when fitting a regression model is the possibility that there may by “outliers” that exert undue influences on the final fit. For example, it could be suspected that some larger basins might greatly influence the regression fit if included in the model (this might result in a final model that does not well describe the smaller basins). In this study, simple regression diagnostics based on the “leverage effect” (see, Kutner et al., 2005) were employed for the purpose of detecting such unwanted effects. 2.4 Index Flood Method The index-flood method was originally proposed by Dalrymple (1960) and has since then been extensively used in flood hydrology. The main reason for its success lies in its great simplicity of implementation, as well as in its flexibility to be modified or extended. In fact, the index-flood method has undergone many reformulations through the years. In this study, two versions of the method are briefly described. 2.4.1 Averaging Approach The first version of the index-flood method presented here corresponds to that originally proposed by Dalrymple (1960), and is referred to here as the averaging approach. The main idea behind this approach is to express the estimated floods (from distinct sites) using what is called the index of floods (or simply index). The latter 12 permits the estimation of higher return floods using data from lower return floods (e.g., estimation of 100-year flood from data on the 2-year flood) and can be described as follows: 1. Single station analyses are carried out using appropriate frequency distributions and the recurrence intervals of interest are estimated for each site. 2. Dimensionless flood indices are calculated for each site by dividing the estimated flows of different recurrence intervals by a scaling factor. For example, common choices of scaling factors are the mean annual flood (MAFL), estimated from the sample; and the 2-year flood (QD2), estimated from the fitted distribution. 3. For a recurrence interval T, the average of indices is estimated for all sites and this value corresponds to the regional index for that specific recurrence interval. This version of the index-flood method has the property of giving equal weights to all stations considered regardless of the number of observations available at each site. Depending on the situation, this property could be regarded as either an advantage or a drawback. For instance, longer record lengths are generally available for large basins, although, for most design projects, interest lies in mid-size basins with record lengths often substantially shorter. In some instances, it may be important not to give too much weight on large basins in comparison to mid-size basins (with less data) when calculating the regional index. In the application of the index-flood method, it is assumed that all stations are somewhat similar; that is, they are part of a homogeneous region. In the present study, the plausibility of the assumption of a homogeneous region 13 was assessed based on spatial inspection of the indices, as will be discussed further in the “Results and Discussion” section. 2.4.2 Pooling Approach A second index-flood method presented here is based on the pooling of observations from all sites when calculating the index (Hosking and Wallis, 1997; Salvadori et al., 2007). This approach makes the following assumptions (Hosking and Wallis, 1997): 1. Observations at any given site are identically distributed. 2. Observations at any given site are serially independent. 3. Observations at different sites are independent. 4. Frequency distributions at different sites are identical apart from a scale factor. 5. The “true” frequency distribution function is correctly identified. Assumptions 1 to 2 were already stated in the present study and are generally reasonably made in most situations. Assumption 3 rarely holds in practice, but early studies (e.g., Matalas and Benson, 1961; Stedinger, 1983) have shown that, when ignoring between-site dependence, the variability associated with the estimates is underestimated; however, the estimates themselves remain unbiased. Thus, if only point estimates are of interest, then this assumption can be relaxed. Assumption 4 is somewhat equivalent to saying that all sites considered come from a same 14 homogeneous region. With the pooling approach index-method, it is actually possible to test the validity of assumption 4 using classical statistical hypotheses tests (such tests results will be presented in the “Results and Discussion” section). Finally, assumption 5 simply means that the fitted frequency distribution is regarded as the “true distribution” from which the observations are assumed to have been generated (in this case, the GEV distribution). The pooling approach version of the index-flood method can therefore be described as follows: 1. A flood index is estimated for each station. Usually, the index is estimated from the sample (e.g. sample mean or median), although more sophisticated indices can be used (e.g. QD2 obtained from prior analysis). 2. All observations are normalized by dividing them with the estimated index. 3. The normalized data from all stations are then pooled together to form a new sample (i.e., a regional sample). 4. A frequency distribution is fitted to the regional sample and the resulting parameter estimates correspond to the regional parameters. These parameters can then be used to obtain regional recurrence interval estimates for gauged and ungauged stations. The above method is more formally expressed using mathematical notation. That said, let ψ i denote the index for station i , for i = 1, 2,..., k and where k is the total 15 number of sites. Let also X ij denote the j th random variable that comes from site i , for j = 1, 2,..., ni , and where ni is the number of available observations at site i . Finally, let I ij = X ij / ψ i denote a random variable distributed according to a regional GEV iid distribution; I ij ~ GEV (ξψ , σψ ', μψ ') for all ij ’s, where iid stands for “independent and identically distributed”, and where ξψ , σψ ' , and μψ ' are the regional parameters (note: here GEV could be replaced by any other distribution). Thus, for an index ψ , a regional estimate of the recurrence interval QˆT is given by QˆT = FˆGEV −1 (1 − 1/ T ) *ψ , where FˆGEV −1 is the inverse CDF of GEV (ξˆψ , σˆψ ', μˆψ ') , the estimated regional GEV distribution. If ψ is taken to be one of the ψ i ’s, then QˆT corresponds to an T-year flood at-site ( i ) estimate and may be re-written as Qˆ i ,T . The main difference between the pooling approach and the averaging approach lies in the relative importance of each station in determining the regional estimates. While the averaging approach gives equal weights to all stations, the pooling approach gives more importance to stations with more data. If assumption 4 can be shown to be reasonable for a given application, then pooling of all observations could be expected to provide better results. 2.5 Daily to Instantaneous Flows All analyses so far pertained to the mean daily discharge (or annual maximum daily discharge). However, for many practical applications, there is an interest in the design of structures using instantaneous peak flows (or annual maximum instantaneous daily discharge). The flood frequency analyses could easily have been carried out using instantaneous flows rather than daily flows; however, past studies have relied on ratios between instantaneous flows to daily flow. The present study will also calculate 16 instantaneous flows based on daily flows. Previous studies have dealt with this problem by constructing envelope curves, which are based on observed (maximum) ratios of the instantaneous peak flow to mean flow in relationship with the basins’ drainage size. 3.0 Results and Discussion 3.1 Single Station Flood Frequency Analyses For LN3 and GEV, respectively, results of the 56 single station high flow frequency analyses are provided in Table 3 and Table 4, for recurrence intervals of 2, 10, 20, 50 and 100 years. For the Saint John River (Mactaquac), which has a drainage area of 39900 km2, the 2-year flood was estimated to be 5809 m3/s using LN3. This corresponds to the highest estimated 2-year flood in New Brunswick. Conversely, the lowest estimated 2-year flood (LN3) was 1.09 m3/s, and was observed at Narrows Mountain Brook, which has a drainage area of 3.89 km2. Using the GEV distribution, the 2-year flood was estimated at 5840 m3/s and 1.08 m3/s; being quite similar to those obtained using LN3. Notably greater differences among distributions were noted at higher recurrence intervals. For all 56 stations, the maximum likelihood parameter estimates, as well as their corresponding NLL values and AD statistics, are presented in Table 5 (LN3) and Table 6 (GEV). The NLL criterion favored the LN3 approximately 52% of the time; however, from a practical point of view, NLL values were almost identical for both distributions. Similar NLL values for the two distributions suggest that they are almost equally likely under the observed data. From the single station Q-Q plots (Appendix A) it is clear that, for the majority of the single analysis, both the LN3 and GEV fitted the data almost 17 exactly the same (especially in the central portion of the plot). In fact, when discrepancies existed, they were mostly located in the tails, level at which the AD statistic is more sensitive than the NNL. As an example, the Q-Q plot for the station 01AL004 located along Narrows Mountain Brook is presented (Figure 2; see also Figure A.10b, Appendix A). For the upper right portion of this plot (at high recurrence intervals), it is evident that GEV adjusts better to the observational data than LN3. Results of the AD statistics favor GEV over LN3 approximately 64% of the time. The relation between the AD for both the GEV and LN3 is illustrated in Figure 3. Many of the data points are below the line (representing equal values) which suggests a better regional fit for GEV. Moreover, of the 64% identified above, 44% corresponds to cases where a difference greater than 10% was observed. Although these results have no statistical bases, they are an indication of a potential overall superiority of GEV over LN3. In the case of the Narrows Mountain Brook (for station 01AL004, Figure 2), the AD values for the GEV and LN3 (Table 6 and Table 5) were 0.170 and 0.215, respectively. These results show the impact of a single data point (highest observed flood) on the overall AD values, as GEV and LN3 were almost identical for all other data points. Thus, based on the AD and the Q-Q plots, it was observed that both LN3 and GEV yielded reasonable estimates for most stations; with GEV performing slight better in some cases. As such, discharges as a function of the different recurrence intervals are available for both the GEV and the LN3 distributions (Table 3 and 4). Based on these results, the regional high flow frequency analysis (presented in the next sub-section) was carried out and corresponding regression equations were calculated using the GEV. 18 3.2 Regional Flood Frequency Analyses 3.2.1 Regression Method In order to estimate high flows for ungauged basins, regional regression equations for the relation between estimated high flows and basin sizes and precipitation were developed using five recurrence intervals estimated for the GEV distribution (QD2, QD10, QD20, QD50, and QD100). For these five regional regression equations (see equation 11), the estimated coefficients are presented in Table 7, along with their corresponding coefficients of determination (R²). For the regression models with only the drainage area as a predictor, R² varied between 0.964 and 0.985. In fact, the coefficient of determination can be observed to increase for decreasing recurrence intervals. It should be noted that the R2 values are those obtained from the regression of transformed (natural logarithmic) variables. It should also be noted that these regression equations were developed for a specific range of basin sizes and should not be applied outside those ranges (ranges are provided in Table 7). Results from Table 7 also suggest that including the precipitation as a predictor only slightly improves the R2. The relationship between the 100-year floods (estimated from GEV distribution) and the drainage areas is illustrated in Figure 4 (note: the latter corresponds to the regression model with only the drainage area as a predictor). Although this figure presents the regression equation for the GEV only, data points for both the GEV and LN3 were presented. This figure also shows the fitted regression line from the previous flood report (Environment Canada and New Brunswick Department of Municipal Affairs and Environment, 1987) and it can be observed that both regression lines are almost identical. The fits for the other recurrence intervals are presented in Appendix B. Finally, estimated coefficients for a regional regression model with the mean annual flood (MAFL) as the dependent variable is also presented in Table 7. The MAFL values will be use in the index-flood method. 19 As described previously (“Material and Methods” section), it was deemed necessary to assess whether or not there existed extreme data points that could exert undue influences on the regression equations. Regression diagnostics based on the “leverage effect” showed that no such points existed, and, therefore, the regression equations are expected to correspond to good approximations of floods for the province of New Brunswick. Moreover, it was possible by visual inspection of Figure 4, to conclude that no particular data point was pulling the regression line unduly. 3.2.2 Index Flood Method Regional flood indices calculated for both index-flood approaches (described in section 2.4.1 and 2.4.2) and for the recurrence periods 2, 10, 20, 50, and 100 years. A concern when using the index-flood method is whether the stations are part of the same homogeneous region. For the averaging approach, homogeneity was assessed based on at-site index in relation to their positions within the province. No spatial patterns could be identified, and it was thus concluded that the index could be applied on a province-wide basis. However, it is well known that at-site index value can be a function of drainage size: larger indices tend to be observed for smaller basins and viceversa. A homogeneity assessment was carried out for the pooling approach. The method explicitly assumes that observations come from a same theoretical distribution. This can be tested statistically using classical hypotheses testing. Therefore, a classical test derived from an extension of the Shapiro-Wilk statistic (e.g. Ashkar et al., 1997) was used to assess the plausibility of this assumption (in this case the GEV). A significance level was fixed at α = 0.10 and 56 independent tests were carried out (this is only possible under the assumption of between-site independence). Stations that yielded a p-value smaller than α = 0.10 were rejected (i.e., fitted GEV distribution regarded as inconsistent with the actual data). In this study, 9 of 56 tests were rejected. 20 These 9 “critical” stations corresponded to: 01AD002 (14700 km2), 01AF002 (21900 km2), 01AJ001 (34200 km2), 01AL004 (3.89 km2), 01AM001 (557 km2), 01AQ001 (239 km2), 01BP001 (1340 km2), 01BR001 (177 km2), and 01DL001 (63.2 km2). From the 9 “critical” stations, it was noted that three stations were among the four largest basins. This suggests that these large basins might not be directly comparable with other stations and these large rivers had an index of flood less than 2.0. As such, the index method might provide poor estimates for large basins and large basins might unduly pull down the regional estimates. For this reason, the statistical test was conducted a second time, leaving out the four largest basins. That time, 5 stations of 52 were rejected, but the probability of rejecting 5 (or more) out of 52 tests solely at random was determined to be of approximately 0.55. Nonetheless, it seems worthwhile to point out the five stations that were rejected for this second test: 01AL004 (3.89 km2), 01AQ001 (239 km2), 01BP001 (1340 km2), 01BR001 (177 km2), and 01DL001 (63.2 km2). These stations, with the exception of 01BR001, showed an index of flood (QD100/QD2) greater than 4.0 and many stations corresponded to somewhat small basins. Although without statistical bases, this might be regarded as an indication that the results obtained from the index flood method should be used cautiously, especially for both large and small basins. The results of the index flood methods are presented in Table 8. The two versions of the method were carried out using both the MAFL (sample mean) and the estimated at-site QD2 (theoretical median). For both the averaging and pooling approaches, the indices obtained using MAFL as normalizing factor were systematically lower (8% to 10%) than those calculated using QD2. For consistency, although the test results are only strictly valid for the indices from the pooling approach, all indices were calculated leaving out large rivers (i.e., stations 01AK004, 01AJ001, 01AF002, and 01AD002). Indices ranged between 1.64 (QD10) to 2.70 (QD100) for the averaging approach and 1.65 (QD10) to 2.62 (QD100) for the pooling 21 approach. Indices using the MAFL as the normalizing factor showed consistent but slightly lower value. Similarly, Table 8 presents the results of the flood index for only the four largest basins. As expected, the indices for that analysis are systematically lower than those of other stations in New Brunswick. As mentioned previously, results of the index of floods show that caution should be exercised when using the regional indices for very large basins or very small basin because their flood behaviour could be slightly different. This is true for both the averaging and the polling approaches. Results presented in Table 8 can be used to calculate flows for different recurrence intervals at ungauged basins provided that low return floods are known (e.g. QD2 or MAFL), both of which can be obtained by regression (Table 7). 3.4 Instantaneous Flows and Envelope Curves The 56 single station frequency analyses, as well as the regional analyses were carried out using the daily flows (annual maximum daily discharge). However, as mentioned previously, for design and risk management purposes, some knowledge about the instantaneous peak flows (annual maximum instantaneous discharge) is often required. In this study, envelope curves were thus constructed to this end; that is, as a means of converting the information acquired for daily mean flow so they can be used in terms of instantaneous peak flow. Here, the (maximum) ratio of the instantaneous peak flow to mean flow (QP/QD) was considered, and its relationship with the drainage area was studied. For each station and each year, the ratio QP/QD was computed, and both the mean and maximum QP/QD ratio was retained (Table 9). In total, ratios were available for 54 of the 56 stations. Mean QP/QD ratios varied between 1.01 and 1.90 and higher ratios generally showed a higher variability (e.g., QP/QD = 1.90 and Cv = 32.4%). Maximum 22 recorded QP/QD ratios were also reported in Table 9, with values ranging from 1.05 (St. Francis R.) to 3.35 (Hayden Brook). Figure 5 shows a scatter plot of these values plotted against their corresponding drainage area (km2), from which the following main observations can be made: • for stations with drainage areas less than 200 km2, the ratio QP/QD does not exceed 3.5; • for stations with drainage areas ranging from 200 to 800 km2, the ratio QP/QD does not exceed 2.5; • and for stations with drainage areas greater than 800 km2, the ratio QP/QD does not exceed 2 (however, note that Aroostook River (6060 km2) has a maximum QP/QD value of 2.0; Figure 5). Based on these results, envelope curves of instantaneous flow can be developed for the different recurrence intervals. Of particular interest is the envelope curve for the estimated 100-year flood. The latter is shown in Figure 6. The envelope curve in the present study (represented by the dashed lines) was obtained by multiplying QD100 by the appropriate QP/QD factors presented in Figure 5. Also shown in this figure is the highest instantaneous daily discharge recorded for each station. As can be observed, most of the stations fall below the envelope curve with the exception of a few. For instance, three stations were identified with flows close to or higher than the envelope curve. Those stations correspond to the Point Wolfe River (130 km2 and Qmax = 258 m3/s in 1999), the Northwest Oromocto River at Tracy (557 km2 and Qmax = 776 m3/s in 1970) and the Renous River at McGraw Brook (611 km2 and Qmax = 697 m3/s in 1970). From those three stations, only the Northwest Oromocto River would have exceeded the present study envelope curve. In addition, the envelope curves from two previous 23 studies (Environment Canada and New Brunswick Department of Municipal Affairs and Environment, 1987; Montreal Engineering Co. Ltd, 1969) are also presented; study of 1969 (blue) and study of 1987 (red). For comparison purposes, the regional equations of previous reports were (Montreal Engineering Co. Ltd, 1969): Q = 250 A 3 Q = 3.47 A Q = 500 A 3 Q = 6.94 A 4 3 (12a) 4 (SI units) 4 3 (12b) (13a) 4 (SI units) (13b) where Q is in cubic feet per second (cfs) and A is in square miles (mile2) in equation 12a and 13a. The same equations are given in SI units (12b and 13b) where Q is in m3/s and A in km2. The equation from Environment Canada and New Brunswick Department of Municipal Affairs and Environment (1987) was: Q = 6.18 A0.73 where Q is in m3/s and A in km2. (14) 24 The envelope curve suggested by (Montreal Engineering Co. Ltd, 1969; equation 12) was exceeded for many stations, which casts some doubts upon the current use of such equation. However, the second envelope curve provided (equation 13) was very similar to the results suggested in the present study. On the other hand, the envelope curve suggested in the 1987 study was only exceeded for three stations. Finally, the envelope curve in the present study, which was build from longer data series, can be seen to be slightly more conservative than that from the 1987 study, being exceeded only once, and closely approached on two instances. Although this new envelope curve is expected to provide users with reliable flood estimates for most basins, it is essential to carry out flood estimates based on best available information at the time of the study as well as exercising good judgement of the level of risk associated with flood damage. For points that lie somewhat close to the curve, particular attention is needed and more conservative multiplicative factors can be used. In fact, it is for the user to decide which multiplicative factor should be used for any given situation. Moreover, the physical characteristics of the basin of interest should always be taken into consideration when carrying out flood frequency estimates as well as other potential flood estimation techniques (e.g., probable maximum flood, etc.). 4.0 Summary and Conclusions Flood frequency estimation remains an important topic for design purposes in New Brunswick. Flood data constitute the main source of information for this analysis. As such, the present study aimed at revisiting regional flood frequency estimates, as more data are now available, and at comparing them with those of previous studies. To carry out the analysis, 56 stations were analyzed. Maximum daily discharges (m3/s) for 25 each year were analyzed using both the generalized extreme value (GEV) and the 3parameter lognormal (LN3) distribution functions. Goodness-of-fit assessments (e.g., Anderson-Darling statistic, AD) suggested the GEV model to be the overall most appropriate distribution function. These findings were also strengthened by extreme value theory, which suggests that the annual maxima (such as flood data) be modeled as realizations of random variables distributed according to a member of the generalized extreme value (GEV) family of distributions. Based on such considerations, the GEV was therefore subsequently used in developing regional regression equations. Regional regression equations allowed the estimation of at-site floods as a function of drainage area (or drainage area and precipitation) for various recurrence intervals (i.e., 2, 10, 20, 50 and 100). In all cases, the fitted regression models were consistent with the calculated T-year flood events, such that they could be applied to predict floods for ungauged basins (within their range of application). In addition to regional regression equations, the regionalization of floods was carried out based on two versions of the index flood method. Classical hypotheses testing and the index of flood results suggested that large and small basins should be treated with caution, as there indices could be statistically different. As such, the index of floods was divided in two homogenous groups of stations (i.e. one group with only the four largest stations, and the rest of the stations). For design purposes, interest often lies in estimating the instantaneous daily peak discharge rather than the daily mean flow. Therefore, as both the single station and regional regression equations were derived for daily flows, envelope curves of instantaneous flows were developed based on 54 hydrometric sites. The relation between the ratio QP/QD-max and drainage area suggested the use of three factors of QP/QD-max (2, 2.5 and 3.5) that varied in accordance with the drainage area. 26 5.0 Acknowledgements This study was funded by New Brunswick Environmental Trust Fund and their support is greatly appreciated. We thank Darryl Pupek for comments and suggestions during the course of this project. We also thank Brent Newton and Brian Burrell for reviewing the manuscript. 6.0 References Acres Consulting Services Ltd. 1977. Regional flood frequency analysis, Canada – New Brunswick Flood Damage Reduction Program. Tech. rept. D'Agostino, R.B., and M.A. Stephens. 1986. Goodness-of-fit Techniques. New York: Marcel Dekker, Inc. 576p. Anderson, T.W., and D.A. Darling. 1952. Asymptotic theory of certain “goodness of fit” criteria based on stochastic process. Annals of mathematical statistics 23(2): 193-212. Ashkar, F., Arsenault, M. and Zoglat, A.,1997. On the discrimination between statistical distributions for hydrological frequency analysis. Proceedings of the CSCE Annual Conference: "Major Public Works: Key Technologies for the 21st Century", Sherbrooke, Quebec, Canada, Vol. 3, 169-178. 27 Caissie, D. and S. Robichaud. 2009. Towards a better understanding of the natural flow regimes and streamflow characteristics of rivers of the Maritime Provinces. Can. Tech. Rep. Fish. Aquat. Sci. 2843: viii + 53p. Chow, V.T., D.R. Maidment and L.W. Mays. 1988. Applied hydrology. McGraw-Hill Book Company, New York, 572p. Coles, S. 2001. An introduction to statistical modeling of extreme value. Springer: London. 224p. Dalrymple, T. 1960. Flood Frequency Methods. U.S. Geol. Surv. Water Supply Pap., 1543-A:11-51. Environment Canada. 2007. HYDAT 2005 CD-ROM. Windows Version 2.04 released June 2007. Water Survey of Canada, Meteorological Service of Canada, Ottawa, Ontario. Environment Canada and New Brunswick Department of Municipal Affairs and Environment. 1987. Flood frequency analyses, New Brunswick, A guide to the estimation of flood flows for New Brunswick rivers and streams. April 1987, 49p. Hosking, F.R.M., J.R. Wallis. 1997. Regional Frequency Analysis: An Approach Based on L-Moments. Cambridge University Press. 242p. Kutner, M.H., C.J. Nachtsheim, J. Neter, and W. Li. 2005. Applied Linear Statistical Models. McGraw Hill. 1396p. 28 Matalas, N.C., M.A. and Benson. 1961. Effects of interstation correlation on regression analysis. J. Geophys. Res. – Atmospheres 66(10): 3285-3293. Montreal Engineering Company Ltd. 1969. Maritime Provinces Water Resources Study – Stage 1, Appendix XI, Surface Water Resources, prepared for the Atlantic Development Board. R Development Core Team. 2009. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, ISBN 3-900051-07-0, Vienna, Austria. Salvadori, G., De Michele, C., Kottedoda, N.T. and Rosso, R. 2007. Extremes in Nature: An Approach using Copulas. Springer: The Netherlands. 292p. Stedinger, J.R. 1983. Estimating a regional frequency distribution. Water Resour. Res., 19(2): 503-510. 29 Table 1. Analysed hydrometric stations for the flood frequency analysis Station Drainage number Station Name Area (km²) 01AD002 Saint John River at Fort Kent 14700 01AD003 Saint Francis River at outlet of Glasier Lake 1350 01AF002 Saint John River at Grand Falls (Reg) 21900 01AF003 Green River near Rivière-Verte (Reg) 1150 01AG002 Limestone River at Four Falls 199 01AG003 Aroostook River near Tinker (Reg) 6060 01AH005 Mamozekel River near Campbell River 230 01AJ001 Saint John River near East Florenceville (Reg) 34200 01AJ003 Meduxnekeag River near Belleville 1210 01AJ004 Big Presque Isle Stream at Tracey Mills 484 01AJ010 Becaguimec Stream at Coldstream 350 01AJ011 Cold Stream at Coldstream 156 01AK001 Shogomoc Stream near Trans Canada Highway 234 01AK004 Saint John River below Mactaquac (Reg) 39900 01AK005 Middle Branch Nashwaaksis Stream near Royal Road 26.9 01AK007 Nackawic River near Temperance Vale 240 01AK008 Eel River near Scott Siding 531 01AL002 Nashwaak River at Durham Bridge 1450 01AL003 Hayden Brook near Narrows Mountain 6.48 01AL004 Narrows Mountain Brook near Narrows Mountain 3.89 01AM001 North Branch Oromocto River at Tracy 557 01AN001 Castaway Brook near Castaway 34.4 01AN002 Salmon River at Castaway 1050 01AP002 Canaan River at East Canaan 668 01AP004 Kennebecasis River at Apohaqui 1100 01AP006 Nerepis River near Fowlers Corner 293 01AQ001 Lepreau River at Lepreau 239 01AQ002 Magaguadavic River at Elmcroft (Reg) 1420 01AR006 Dennis Stream near St. Stephen 115 01AR008 Bocabec River above Tide 43 01BC001 Restigouche River below Kedgwick River 3160 01BE001 Upsalquitch River at Upsalquitch 2270 01BJ001 Tetagouche River near West Bathurst 363 01BJ003 Jacquet River near Durham Centre 510 01BJ004 Eel River near Eel River Crossing 88.6 01BJ007 Restgouche River above Rafting Ground Brook 7740 01BK004 Nepisiquit River near Pabineau Falls (Reg) 2090 01BL001 Bass River at Bass River 175 01BL002 Rivière Caraquet at Burnsville 173 01BL003 Big Tracadie River at Murphy Bridge Crossing 383 01BO001 Southwest Miramichi River at Blackville 5050 01BO002 Renous River at McGraw Brook 611 01BO003 Barnaby River below Semiwagan River 484 01BP001 Little Southwest Miramichi River at Lyttleton 1340 01BQ001 Northwest Miramichi River at Trout Brook 948 01BR001 Kouchibouguac River near Vautour 177 01BS001 Coal Branch River at Beersville 166 01BU002 Petitcodiac River near Petitcodiac 391 01BU003 Turtle Creek at Turtle Creek 129 01BU004 Palmer's Creek near Dorchester 34.2 01BV005 Ratcliffe Brook below Otter Lake 29.3 01BV006 Point Wolfe River at Fundy National Park 130 01BV007 Upper Salmon River at Alma 181 01BD002 Matapedia Amont de la Rivière Assemetquagan, QC 2770 01DL001 Kelley River (Mill Creek) at Eight Mile Ford, NS 63.2 01BF001 Rivière Nouvelle au Pont, QC 1140 Acutal Period of Record used 1927-2007 1952-2008 1931-2007 1963-79,1981-1993 1968-1993 1975-2007 1973-1990 1952-1994 1968-2007 1968-2007 1974-2007 1974-1993 1919-40,1944-2007 1967-1994 1966-1993 1968-2007 1974-1993 1962-2007 1971-1993 1972-2003 1963-2007 1972-81,1983-1993 1974-2007 1926-40,1963-2008 1962-2008 1976-1993 1917-2008 1917-32,1943-2007 1967-2008 1967-1979 1963-2007 1919-32,1944-2007 1923-33,1952-1994 1965-2007 1968-1983 1969-2007 1958-1974 1966-1990 1970-2007 1971-2007 1919-32,1962-2007 1966-1994 1973-1994 1952-2007 1962-2007 1931-32,1970-1994 1964-2008 1962-2008 1963-2008 1967-1985 1961-1971 1964-2008 1968-1978 1970-92,1995,1997 1970-96,1999-2007 1965-1997 Number of years 79 57 77 30 26 33 18 43 40 40 34 20 86 28 28 40 20 46 23 32 45 21 34 61 47 18 92 81 42 13 45 78 54 43 16 39 17 25 38 37 60 29 22 56 46 27 45 47 46 19 11 45 11 25 36 33 30 Table 2. Summary of physiographic and climatic characteristics for selected hydrometric stations (data from report by Environment Canada and New Brunswick Department of Municipal Affairs and Environment, 1987) Percentage of Mean annual Average water Station lakes+swamps precipitation content of snow (%) (mm) cover on March 31 (mm) Saint John River (Fort Kent) 5.71 997 231 St Francis River 2.81 1060 224 Saint John River (Grand Falls) 4.90 1010 231 Green River 1.21 1070 252 Limestone River 9.78 975 159 Aroostook River 5.83 934 190 Mamozekel River 0.04 1030 198 Saint John River (East Florenceville) 4.97 1010 217 Meduxnekeag River 5.61 958 157 Big Presque Isle Stream 3.70 925 140 Becaguimec Stream 0.77 1130 126 Cold Stream 0.08 1100 129 Shogomoc Stream 11.9 1120 147 Saint John River (Mactaquac) 5.33 1010 205 Middle Branch Nashwaaksis Stream 2.16 1220 145 Nackawic River 5.11 1060 129 Eel River (Scott Siding) 13.3 1070 142 Nashwaak River 1.39 1210 167 Hayden Brook 0.56 1230 190 Narrows Mountain Brook 0.61 1230 190 North Branch Oromocto River 15.1 1150 117 Castaway Brook 6.60 1180 130 Salmon River 6.41 1130 146 Canaan River 3.57 1040 137 Kennebecasis River 0.72 1190 108 Nerepis River 1.28 1140 110 Lepreau River 10.2 1240 101 Magaguadavic River 7.39 1175 126 Dennis Stream 8.37 1160 110 Bocabec River 6.44 1180 85 Restigouche River (Kedgwick) 0.73 1140 240 Upsalquitch River 0.63 1080 232 Tetagouche River 2.24 988 235 Jacquet River 2.00 1050 235 Eel River ( Eel River Crossing) 0.68 1100 216 Restigouche River (Rafting Ground) 0.77 1120 224 Nepisiquit River 2.35 1010 241 Bass River 8.11 1010 209 Rivière Caraquet 10.4 1130 194 Big Tracadie River 2.34 1090 204 Southwest Miramichi River 3.52 1090 177 Renous River 6.22 1180 199 Barnaby River 10.7 1080 170 Little Southwest Miramichi River 5.06 1180 222 Northwest Miramichi River 3.96 1130 213 Kouchibouguac River 11.7 1050 161 Coal Branch River 5.23 1070 150 Petitcodiac River 0.76 1030 124 Turtle Creek 0.31 1310 125 Palmer's Creek 0.15 1210 98 Ratcliffe Brook 3.14 1410 108 Point Wolfe River 1.05 1390 140 Upper Salmon River 0.54 1380 144 Rivère Matapedia, QC 2.54 1040 265 Kelley River, NS 4.29 1250 100 Rivière Nouvelle, QC 0.17 1060 228 31 Table 3. Results of single station flood frequency analyses using the 3 Parameter Lognormal (LN3) distribution Daily discharge Station QD2 QD10 QD20 QD50 QD100 (m³/s) (m³/s) (m³/s) (m³/s) (m³/s) Saint John River (Fort Kent) 2303 3265 3582 3965 4237 St Francis River 197 315 359 416 458 Saint John River (Grand Falls) 3194 4663 5136 5701 6099 Green River 219 348 392 447 486 Limestone River 33.6 49.1 55.4 63.7 70.1 Aroostook River 936 1342 1481 1653 1777 Mamozekel River 39.9 65.7 76.0 89.8 100 Saint John River (East Florenceville) 4761 7239 7989 8861 9459 Meduxnekeag River 236 380 435 506 559 Big Presque Isle Stream 92.1 158 187 228 262 Becaguimec Stream 79.4 136 160 191 216 Cold Stream 34.1 63.0 75.7 93.3 107 Shogomoc Stream 36.5 57.5 65.4 75.6 83.3 Saint John River (Mactaquac) 5809 8877 10126 11802 13106 Middle Branch Nashwaaksis Stream 6.12 10.9 13.2 16.4 19.1 Nackawic River 51.4 84.1 97.6 116 130 Eel River (Scott Siding) 70.3 99.1 108 119 127 Nashwaak River 320 555 650 778 877 Hayden Brook 1.93 3.93 4.81 6.02 6.99 Narrows Mountain Brook 1.09 1.99 2.47 3.23 3.89 North Branch Oromocto River 120 216 262 330 387 Castaway Brook 8.44 12.9 14.5 16.6 18.1 Salmon River 197 258 277 298 313 Canaan River 144 207 228 253 271 Kennebecasis River 228 400 475 579 662 Nerepis River 83.3 124 139 159 174 Lepreau River 61.6 124 156 207 251 Magaguadavic River 220 352 405 476 531 Dennis Stream 24.1 38.9 44.8 52.6 58.7 Bocabec River 11.3 21.6 26.0 31.9 36.6 Restigouche River (Kedgwick) 573 871 976 1109 1206 Upsalquitch River 341 534 604 693 759 Tetagouche River 72.9 116 132 154 170 Jacquet River 111 162 180 203 219 Eel River ( Eel River Crossing) 25.7 42.2 50.5 63.2 74.0 Restigouche River (Rafting Ground) 1331 2113 2434 2866 3203 Nepisiquit River 344 625 744 908 1039 Bass River 39.1 66.9 79.8 98.3 114 Rivière Caraquet 31.7 56.0 65.7 78.7 88.8 Big Tracadie River 61.9 96.8 110 128 141 Southwest Miramichi River 841 1315 1493 1724 1897 Renous River 131 228 273 336 388 Barnaby River 94.8 155 181 216 244 Little Southwest Miramichi River 222 424 526 678 808 Northwest Miramichi River 180 312 367 442 500 Kouchibouguac River 34.3 55.5 65.8 81.1 94.0 Coal Branch River 44.9 67.0 74.5 83.7 90.3 Petitcodiac River 87.0 137 156 179 197 Turtle Creek 37.1 64.4 75.7 90.8 103 Palmer's Creek 12.4 21.6 25.2 29.9 33.6 Ratcliffe Brook 12.3 25.1 30.7 38.7 45.2 Point Wolfe River 59.7 102 120 144 163 Upper Salmon River 82.3 138 161 193 219 Rivère Matapedia, QC 438 631 699 783 845 Kelley River, NS 17.3 30.7 37.8 48.8 58.3 258 384 428 483 523 Rivière Nouvelle, QC 32 Table 4. Results of single station flood frequency analyses using the Generalized Extreme Value (GEV) distribution Daily discharge Station QD2 QD10 QD20 QD50 QD100 (m³/s) (m³/s) (m³/s) (m³/s) (m³/s) Saint John River (Fort Kent) 2313 3254 3542 3867 4080 St Francis River 196 315 361 422 467 Saint John River (Grand Falls) 3196 4666 5115 5623 5954 Green River 219 349 394 448 486 Limestone River 33.5 48.9 55.4 64.4 71.6 Aroostook River 945 1328 1447 1582 1671 Mamozekel River 40.0 65.2 75.4 89.3 100 Saint John River (East Florenceville) 4745 7269 7982 8747 9223 Meduxnekeag River 236 378 433 505 559 Big Presque Isle Stream 92.1 156 187 232 272 Becaguimec Stream 79.6 135 158 190 216 Cold Stream 34.1 62.3 75.5 95 111 Shogomoc Stream 36.4 57.7 66.2 77.4 86.1 Saint John River (Mactaquac) 5840 8775 9964 11562 12804 Middle Branch Nashwaaksis Stream 6.09 10.8 13.3 17.2 20.8 Nackawic River 51.0 83.7 98.5 120 138 Eel River (Scott Siding) 70.5 98.9 107 116 122 Nashwaak River 320 551 650 787 897 Hayden Brook 1.94 3.88 4.78 6.09 7.20 Narrows Mountain Brook 1.08 1.96 2.53 3.56 4.64 North Branch Oromocto River 120 213 262 342 417 Castaway Brook 8.44 12.9 14.6 16.6 18.1 Salmon River 198 258 275 292 302 Canaan River 144 208 228 252 267 Kennebecasis River 229 396 472 583 675 Nerepis River 83.3 124 139 160 176 Lepreau River 61.1 121 159 225 293 Magaguadavic River 219 351 409 491 558 Dennis Stream 24.0 38.8 45.0 53.7 60.7 Bocabec River 11.3 21.4 26.0 32.8 38.4 Restigouche River (Kedgwick) 572 874 985 1123 1223 Upsalquitch River 340 532 601 688 750 Tetagouche River 72.8 116 132 155 172 Jacquet River 111 163 181 204 221 Eel River ( Eel River Crossing) 26.0 41.5 49.8 63.1 75.5 Restigouche River (Rafting Ground) 1331 2098 2428 2888 3260 Nepisiquit River 349 611 719 866 981 Bass River 39.2 66.0 79.4 100 119 Rivière Caraquet 31.6 55.8 66.2 80.8 92.6 Big Tracadie River 61.7 96.8 111 130 145 Southwest Miramichi River 838 1318 1509 1762 1956 Renous River 132 225 271 339 399 Barnaby River 95.1 153 179 215 244 Little Southwest Miramichi River 221 418 531 724 913 Northwest Miramichi River 179 310 369 454 524 Kouchibouguac River 34.8 54.2 63.7 78.0 90.5 Coal Branch River 45.0 66.8 74.0 82.3 88.0 Petitcodiac River 86.7 138 158 184 204 Turtle Creek 37.0 64.0 75.9 92.8 107 Palmer's Creek 12.4 21.4 25.0 29.9 33.7 Ratcliffe Brook 12.3 24.6 30.3 38.6 45.5 Point Wolfe River 60.3 100 117 141 159 Upper Salmon River 82.4 136 160 194 222 Rivère Matapedia, QC 437 638 711 802 869 Kelley River, NS 17.2 30.4 38.6 53.4 68.6 Rivière Nouvelle, QC 259 383 425 474 507 33 Table 5. Parameters for the 3 parameter lognormal distribution (single station analysis), the Anderson-Darling (AD) statistic and the negative log-likelyhood (NNL) value Station Shape Scale Threshold AD NLL Saint John River (Fort Kent) 8.19 0.184 -1305 0.338 625.6 St Francis River 5.39 0.337 -22.90 0.189 326.2 Saint John River (Grand Falls) 8.80 0.156 -3446 0.232 643.8 Green River 5.85 0.244 -129.1 0.318 175.9 Limestone River 3.03 0.437 12.88 0.161 94.16 Aroostook River 7.04 0.237 -207 0.223 231.7 Mamozekel River 3.54 0.436 5.410 0.372 74.32 Saint John River (East Florenceville) 10.02 0.0815 -17749 0.190 384.4 Meduxnekeag River 5.49 0.364 -6.088 0.426 235.9 Big Presque Isle Stream 4.11 0.573 31.40 0.366 198.7 Becaguimec Stream 4.21 0.477 12.18 0.319 166.2 Cold Stream 3.35 0.548 5.661 0.200 83.30 Shogomoc Stream 3.58 0.358 0.6118 0.296 341.7 Saint John River (Mactaquac) 8.26 0.455 1937 0.162 249.0 Middle Branch Nashwaaksis Stream 1.34 0.635 2.294 0.333 64.57 Nackawic River 3.65 0.481 13.09 0.638 173.3 Eel River (Scott Siding) 4.99 0.139 -77.12 0.305 88.84 Nashwaak River 5.70 0.452 20.88 0.237 291.0 Hayden Brook 0.68 0.545 -0.05081 0.445 34.40 Narrows Mountain Brook -0.76 0.835 0.6218 0.215 15.36 North Branch Oromocto River 4.22 0.684 52.33 0.336 236.8 Castaway Brook 2.25 0.301 -1.080 0.233 51.88 Salmon River 6.43 0.0736 -426.2 0.304 178.3 Canaan River 5.53 0.175 -107.9 0.272 317.5 Kennebecasis River 5.14 0.543 57.46 0.219 279.7 Nerepis River 4.23 0.360 14.38 0.307 83.33 Lepreau River 3.54 0.803 27.10 0.410 436.1 Magaguadavic River 5.16 0.439 45.34 0.517 466.5 Dennis Stream 3.00 0.431 4.072 0.163 150.2 Bocabec River 2.41 0.509 0.1653 0.233 41.04 Restigouche River (Kedgwick) 6.54 0.280 -117.7 0.322 300.7 Upsalquitch River 6.01 0.302 -68.63 0.280 486.5 Tetagouche River 4.24 0.376 3.532 0.190 252.7 Jacquet River 4.77 0.280 -6.382 0.154 211.3 Eel River ( Eel River Crossing) 2.31 0.754 15.59 0.370 55.19 Restigouche River (Rafting Ground) 6.86 0.466 375.2 0.243 293.2 Nepisiquit River 5.70 0.515 43.76 0.273 109.8 Bass River 3.11 0.629 16.67 0.177 101.6 Rivière Caraquet 3.47 0.439 -0.3835 0.301 154.5 Big Tracadie River 4.01 0.382 6.634 0.212 165.3 Southwest Miramichi River 6.71 0.356 20.15 0.578 425.7 Renous River 4.41 0.609 49.31 0.348 154.6 Barnaby River 4.16 0.516 30.50 0.266 108.2 Little Southwest Miramichi River 4.86 0.738 93.82 0.380 334.3 Northwest Miramichi River 5.05 0.481 24.16 0.350 263.8 Kouchibouguac River 2.68 0.699 19.64 0.519 101.1 Coal Branch River 4.22 0.220 -22.98 0.469 185.5 Petitcodiac River 4.60 0.319 -12.60 0.533 229.3 Turtle Creek 3.50 0.470 4.082 0.147 191.4 Palmer's Creek 2.57 0.415 -0.5980 0.212 59.01 Ratcliffe Brook 2.48 0.569 0.3231 0.197 36.68 Point Wolfe River 3.85 0.502 12.94 0.415 205.9 Upper Salmon River 4.12 0.503 21.07 0.265 53.32 Rivère Matapedia, QC 6.18 0.263 -42.79 0.582 156.5 Kelley River, NS 1.99 0.811 10.03 0.300 115.2 Rivière Nouvelle, QC 5.80 0.254 -70.98 0.399 192.9 34 Table 6. Parameters for the Generalized Extreme Value distribution function (single station analysis), the Anderson Darling (AD) statistic and the negative log-likelyhood (NLL) value Station Loc Scale Shape AD Saint John River (Fort Kent) 2092 620 -0.168 0.311 St Francis River 173 62.7 0.008 0.171 Saint John River (Grand Falls) 2853 967 -0.167 0.230 Green River 192 76.3 -0.079 0.323 Limestone River 30.8 7.37 0.079 0.143 Aroostook River 856 250 -0.159 0.235 Mamozekel River 35.4 12.5 0.051 0.370 Saint John River (East Florenceville) 4115 1791 -0.228 0.203 Meduxnekeag River 209 74.6 0.008 0.416 Big Presque Isle Stream 81.9 26.9 0.175 0.315 Becaguimec Stream 69.9 26.2 0.082 0.355 Cold Stream 29.5 12.2 0.156 0.192 Shogomoc Stream 32.4 10.8 0.031 0.304 Saint John River (Mactaquac) 5298 1468 0.045 0.176 Middle Branch Nashwaaksis Stream 5.39 1.82 0.244 0.335 Nackawic River 45.6 14.5 0.133 0.619 Eel River (Scott Siding) 63.7 19.5 -0.202 0.318 Nashwaak River 279 110 0.085 0.213 Hayden Brook 1.62 0.85 0.148 0.397 Narrows Mountain Brook 0.98 0.264 0.416 0.170 North Branch Oromocto River 107 34.1 0.269 0.282 Castaway Brook 7.53 2.5 -0.037 0.235 Salmon River 182 44.7 -0.259 0.318 Canaan River 129 40.8 -0.142 0.260 Kennebecasis River 201 73.5 0.139 0.216 Nerepis River 75.6 21.0 0.016 0.301 Lepreau River 53.6 18.9 0.385 0.255 Magaguadavic River 196 61.2 0.105 0.405 Dennis Stream 21.4 7.00 0.084 0.126 Bocabec River 9.62 4.45 0.141 0.199 Restigouche River (Kedgwick) 510 169 -0.038 0.319 Upsalquitch River 301 108 -0.043 0.298 Tetagouche River 64.8 21.9 0.027 0.181 Jacquet River 101 29.0 -0.047 0.154 Eel River ( Eel River Crossing) 23.7 5.77 0.264 0.408 Restigouche River (Rafting Ground) 1196 361 0.092 0.218 Nepisiquit River 302 128 0.061 0.316 Bass River 35.1 10.7 0.212 0.159 Rivière Caraquet 27.3 11.3 0.094 0.242 Big Tracadie River 55.2 17.6 0.045 0.212 Southwest Miramichi River 748 245 0.030 0.532 Renous River 117 38.5 0.189 0.337 Barnaby River 85.1 26.7 0.108 0.291 Little Southwest Miramichi River 195 67.1 0.327 0.313 Northwest Miramichi River 157 59.1 0.125 0.290 Kouchibouguac River 31.7 8.04 0.188 0.611 Coal Branch River 40.1 13.6 -0.121 0.478 Petitcodiac River 76.8 27.2 0.007 0.513 Turtle Creek 32.3 12.4 0.110 0.138 Palmer's Creek 10.8 4.48 0.045 0.220 Ratcliffe Brook 10.3 5.38 0.145 0.212 Point Wolfe River 53.2 19.3 0.075 0.389 Upper Salmon River 73.1 24.7 0.112 0.266 Rivère Matapedia, QC 397 112 -0.037 0.594 Kelley River, NS 15.6 4.08 0.393 0.266 Rivière Nouvelle, QC 232 76 -0.105 0.379 NLL 625.4 326.1 643.6 175.9 94.13 231.6 74.40 384.3 235.9 198.8 166.4 83.40 341.6 249.2 64.88 173.4 88.75 291.1 34.33 15.51 236.7 51.90 178.1 317.4 280.0 83.32 435.9 465.5 150.0 40.95 300.6 486.5 252.7 211.3 55.70 293.3 110.0 101.8 154.2 165.3 425.4 154.8 108.5 334.4 263.6 101.9 185.4 229.0 191.5 59.07 36.83 206.3 53.40 156.4 115.5 192.9 35 Table 7. Regional regression coefficient estimates and R² (GEV distribution) a b1 b2 R²* MAFL** 0.463476 0.884 * 0.984 4.2645E-06 0.926 1.617 0.990 QD2 (m 3/s) 0.394690 0.897 * 0.985 1.1131E-05 0.935 1.460 0.990 QD10 (m 3/s) 0.753188 0.871 * 0.981 1.3152E-06 0.919 1.848 0.988 3 QD20 (m /s) 0.950031 0.857 * 0.977 5.5022E-07 0.910 2.002 0.987 3 QD50 (m /s) 1.273837 0.839 * 0.971 1.7180E-07 0.896 2.205 0.983 1.580312 0.824 * 0.964 QD100 (m 3/s) 7.0216E-08 0.886 2.360 0.978 * The R² was obtained from the log-transformed regression equations. ** Represents the Mean Annual Flood (MAFL), to be used in conjuction with the index-flood method. Range of application of regression equations: Drainage area = 3.89 km² to 39900 km² Mean Annual Precipitation = 925 mm to 1410 mm 36 Table 8. Regional flood indices using the index of flow method in New Brunswick (values in parentheses represents the coefficient of variations (Cv,%) Averaging Approach (excluding 4 largest basins) MAFL QD2 QD2 QD10 QD20 QD50 QD100 0.92 (4.2%) 1.50 (5.6%) 1.76 (9.3%) 2.13 (15.3%) 2.45 (20.7%) 1.00 (n/a) 1.64 (9.3%) 1.93 (13.5%) 2.35 (19.8%) 2.70 (25.4%) Averaging Approach (4 largest basins only) MAFL QD2 0.97 (2.0%) 1.43 (3.8%) 1.58 (4.1%) 1.75 (5.6%) 1.87 (7.6%) 1.00 (n/a) 1.47 (3.7%) 1.62 (4.9%) 1.80 (7.2%) 1.93 (9.4%) Pooling Approach (excluding 4 largest basins) MAFL 0.92 1.51 1.76 2.10 2.36 QD2 1.00 1.65 1.93 2.31 2.62 Pooling Approach (4 largest basins only) MAFL 0.98 1.43 1.56 1.71 1.81 QD2 1.00 1.46 1.60 1.75 1.85 37 Table 9. Results of mean and maximum QP/QD ratio and associated variability (Cv, %) for analysed hydrometric stations QP/QD Maximum Station Mean QP/QD Recorded QP/QD Ratio Ratio Cv (%) Saint John River (Fort Kent) 1.04 7.11 1.48 St Francis River 1.01 0.90 1.05 Saint John River (Grand Falls) 1.07 11.9 1.78 Green River 1.07 5.00 1.20 Limestone River 1.21 16.9 2.08 Aroostook River 1.14 20.2 2.01 Mamozekel River 1.18 9.80 1.45 Saint John River (East Florenceville) 1.07 7.03 1.25 Meduxnekeag River 1.13 8.97 1.52 Big Presque Isle Stream 1.14 8.43 1.37 Becaguimec Stream 1.18 9.00 1.41 Cold Stream 1.33 17.8 2.05 Shogomoc Stream 1.03 2.06 1.09 Saint John River (Mactaquac) 1.07 4.16 1.19 Middle Branch Nashwaaksis Stream 1.45 27.8 2.61 Nackawic River 1.14 7.21 1.31 Eel River (Scott Siding) 1.02 1.92 1.07 Nashwaak River 1.19 11.0 1.51 Hayden Brook 1.90 32.4 3.35 Narrows Mountain Brook 1.63 26.0 2.70 North Branch Oromocto River 1.23 12.0 1.70 Castaway Brook 1.29 11.9 1.71 Salmon River 1.14 6.70 1.35 Canaan River 1.19 12.6 1.83 Kennebecasis River 1.19 10.2 1.54 Nerepis River 1.48 19.3 2.10 Lepreau River 1.20 10.0 1.65 Magaguadavic River 1.08 7.71 1.41 Dennis Stream 1.25 16.7 1.82 Bocabec River 1.30 12.8 1.56 Restigouche River (Kedgwick) 1.05 4.04 1.18 Upsalquitch River 1.06 3.55 1.16 Tetagouche River 1.14 8.98 1.47 Jacquet River 1.17 8.62 1.43 Eel River ( Eel River Crossing) 1.14 6.51 1.29 Restigouche River (Rafting Ground) 1.05 4.57 1.24 Nepisiquit River 1.08 6.43 1.25 Bass River 1.17 9.14 1.42 Rivière Caraquet 1.17 9.33 1.54 Big Tracadie River 1.07 4.66 1.28 Southwest Miramichi River 1.14 13.9 1.68 Renous River 1.22 20.6 2.18 Barnaby River 1.11 7.30 1.32 Little Southwest Miramichi River 1.11 6.78 1.35 Northwest Miramichi River 1.14 10.0 1.61 Kouchibouguac River 1.19 8.99 1.52 Coal Branch River 1.34 16.8 2.02 Petitcodiac River 1.28 18.9 2.12 Turtle Creek 1.42 18.7 2.11 Palmer's Creek 1.78 21.4 2.53 Ratcliffe Brook 1.33 7.76 1.49 Point Wolfe River 1.84 26.0 2.99 Upper Salmon River 1.86 22.7 2.42 Rivère Matapedia, QC N/A N/A N/A Kelley River, NS 1.48 22.4 2.17 Rivière Nouvelle, QC N/A N/A N/A Note: QP/QD represents the ratio between the instantaneous and daily flow 38 1BF1 1BD2 1BJ7 1BJ4 1BJ3 1BE1 1BC1 1BL1 1BJ1 1BK4 1AH5 1AD3 1BQ1 1AF2 1BP1 N 1AG2 1AG3 1AJ1 1AJ4 1BS1 1AJ11 1AL3 1AL4 1AK7 1AK8 1BR1 1BO1 1AJ10 1AJ3 1BO3 1BO2 E S 1BL3 1AF3 1AD2 W 1BL2 1AN2 1AN1 1AL2 1AK5 1AK1 1AP2 1BU2 1AK4 1BU3 1BU4 1AP4 1AM1 1BV7 1BV6 1AP6 1DL1 1BV5 1AQ2 1AR6 1AR8 1AQ1 Figure 1. Location of selected hydrometric stations (56 stations). 1DL1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -2 -1 0 2 Reduced variable (Y) 1 3 3p Lognormal 4 Generalize Extreme Value Observations Station: 01AL004 Figure 2. Flood frequency analysis for Narrows Mountain Brook (NB), station 01AL004 Maximum Annual Discharge (m³/s) 5 5 39 AD statistics for the GEV 0.1 0.2 0.3 AD statistics for the LN3 0.4 Line of equal value 0.5 0.6 0.7 Figure 3. Relation between the Anderson-Darling (AD) statistics obtained from the 3-parameter Lognormal (LN3) and Generalized Extreme Value (GEV) distributions 0.1 0.2 0.3 0.4 0.5 0.6 0.7 40 Daily discharge (100-year flood, QD100, m3/s) 1 10 1000 Drainage area (km2) 100 10000 Regression (GEV, 2010) Regression (EC & NB 1987) Generalized Extreme Value 3p Lognormal 100000 Figure 4. Estimated 100-year flood (daily discharge) as a function of drainage area (km2) for all 56 hydrometric stations (GEV and LN3). Regional regression line for both the present study (QD100 = 1.58 A0.842) and the EC & NB study (1987; QD100= 1.33 A0.855) are presented. 1 10 100 1000 10000 100000 41 1 10 Maximum QP/QD by station 1000 Drainage area (km2) 100 10000 100000 Figure 5. Ratio of instantaneous peak flow to daily flow (QP/QD) for the 54 analysed hydrometric stations (see Table 9 for more details). 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 42 Ratio of instantaneous peak flow to daily flow (QP/QD) Maximum instantaneous peak discharge (m3/s) 1 10 Envelope curve (EC & NB 1987) Equation 14 of this report; Q = 6.18 A0.73 1000 Drainage area (km2) 100 10000 100000 Regression equation (QD100, this report Table 7); Q = 1.58 A0.82 Envelope curve (Montreal Engineering Co. Ltd, 1969) Equation 12 of this report; Q = 3.47 A0.75 Envelope curve (present study) Envelope curve (Montreal Engineering Co. Ltd, 1969) Equation 13 of this report; Q = 6.94 A0.75 Figure 6. Envelope curve of the present study for instantaneous flows (m3/s) in relation to those of previous studies. Data points represent the maximum instantaneous discharge (highest recorded flow) for each station in NB. 1 10 100 1000 10000 100000 43 44 Appendix A Single Station Flood Frequency Analyses 45 4500 a) Maximum Annual Discharge (m³/s) 4000 3500 3000 2500 2000 1500 Station: 01AD002 1000 Observations Generalized Extreme Value 500 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 600 Maximum Annual Discharge (m³/s) b) 500 400 300 200 Station: 01AD003 Observations 100 Generalize Extreme Value 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.1 Flood frequency analysis for a) Saint John River at Fort Kent and b) St Francis River 5 46 7000 a) Maximum Annual Discharge (m³/s) 6000 5000 4000 3000 Station: 01AF002 2000 Observations Generalized Extreme Value 1000 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 500 b) Maximum Annual Discharge (m³/s) 450 400 350 300 250 200 Station: 01AF003 150 Observations 100 Generalized Extreme Value 50 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.2 Flood frequency analysis for a) Saint John River at Grand Falls and b) Green River 5 47 80 a) Maximum Annual Discharge (m³/s) 70 60 50 40 30 Station: 01AG002 20 Observations Generalize Extreme Value 10 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 2000 b) Maximum Annual Discharge (m³/s) 1800 1600 1400 1200 1000 800 Station: 01AG003 600 Observations 400 Generalized Extreme Value 200 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.3 Flood frequency analysis for a) Limestone River and b) Aroostook River 5 48 a) Maximum Annual Discharge (m³/s) 100 80 60 40 Station: 01AH005 Observations 20 Generalized Extreme Value 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 10000 b) Maximum Annual Discharge (m³/s) 9000 8000 7000 6000 5000 4000 Station: 01AJ001 3000 Observations 2000 Generalize Extreme Value 1000 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.4 Flood frequency analysis for a) Mamozekel River and b) Saint John River near East Florenceville 5 49 600 Maximum Annual Discharge (m³/s) a) 500 400 300 200 Station: 01AJ003 Observations Generalized Extreme Value 100 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 300 Maximum Annual Discharge (m³/s) b) 250 200 150 100 Station: 01AJ004 Observations 50 Generalized Extreme Value 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.5 Flood frequency analysis for a) Meduxnekeag River and b) Big Presque Isle Stream 5 50 250 Maximum Annual Discharge (m³/s) a) 200 150 100 Station: 01AJ010 Observations 50 Generalized Extreme Value 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 120 Maximum Annual Discharge (m³/s) b) 100 80 60 40 Station: 01AJ011 Observations 20 Generalized Extreme Value 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.6 Flood frequency analysis for a) Becaguimec Stream and b) Cold Stream 5 51 140 Maximum Annual Discharge (m³/s) a) 120 100 80 60 Station: 01AK001 40 Observations Generalized Extreme Value 20 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) Maximum Annual Discharge (m³/s) b) 12250 10250 8250 6250 Station: 01AK004 Observations 4250 Generalized Extreme Value 3p Lognormal 2250 -2 -1 0 1 2 3 4 5 Reduced variable (Y) Figure A.7 Flood frequency analysis for a) Shogomoc Stream and b) Saint John River below Mactaquac 52 a) Maximum Annual Discharge (m³/s) 20 15 10 Station: 01AK005 Observations 5 Generalize Extreme Value 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 160 b) Maximum Annual Discharge (m³/s) 140 120 100 80 60 Station: 01AK007 40 Observations Generalized Extreme Value 20 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.8 Flood frequency analysis for a) Middle Branch Nashwaaksis Stream and b) Nackawic River 5 53 Maximum Annual Discharge (m³/s) 140 a) 120 100 80 60 Station: 01AK008 40 Observations Generalize Extreme Value 20 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 1000 b) Maximum Annual Discharge (m³/s) 900 800 700 600 500 400 Station: 01AL002 300 Observations 200 Generalize Extreme Value 100 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.9 Flood frequency analysis for a) Eel River and b) Nashwaak River 5 54 9 a) Maximum Annual Discharge (m³/s) 8 7 6 5 4 3 Station: 01AL003 Observations 2 Generalized Extreme Value 1 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 5 b) Maximum Annual Discharge (m³/s) 4.5 4 3.5 3 2.5 2 Station: 01AL004 1.5 Observations 1 Generalized Extreme Value 0.5 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.10 Flood frequency analysis for a) Hayden Brook and b) Narrows Mountain Brook 5 55 500 a) Maximum Annual Discharge (m³/s) 450 400 350 300 250 200 150 Station: 01AM001 Observations 100 Generalized Extreme Value 50 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 20 b) Maximum Annual Discharge (m³/s) 18 16 14 12 10 8 Station: 01AN001 6 Observations 4 Generalized Extreme Value 2 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.11 Flood frequency analysis for a) North Branch Oromocto River and b) Castaway Brook 5 56 Maximum Annual Discharge (m³/s) 350 a) 300 250 200 150 Station: 01AN002 100 Observations Generalized Extreme Value 50 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 350 Maximum Annual Discharge (m³/s) b) 300 250 200 150 Station: 01AP002 100 Observations Generalize Extreme Value 50 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.12 Flood frequency analysis for a) Salmon River and b) Canaan River 5 57 800 a) Maximum Annual Discharge (m³/s) 700 600 500 400 300 Station: 01AP004 200 Observations Generalize Extreme Value 100 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) Maximum Annual Discharge (m³/s) 200 b) 180 160 140 120 100 80 60 Station: 01AP006 Observations 40 Generalized Extreme Value 20 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.13 Flood frequency analysis for a) Kennebecasis River and b) Nerepis River 5 58 400 a) Maximum Annual Discharge (m³/s) 350 300 250 200 150 Station: 01AQ001 100 Observations Generalized Extreme Value 50 3p Lognoraml 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) b) Maximum Annual Discharge (m³/s) 700 600 500 400 300 Station: 01AQ002 200 Observations Generalized Extreme Value 100 3p Lognormal 0 -2 -1 0 1 2 3 Reduced variable (Y) Figure A.14 Flood frequency analysis for a) Lepreau River and b) Magaguadavic River 4 5 59 Maximum Annual Discharge (m³/s) 100 a) 90 80 70 60 50 40 30 Station: 01AR006 Observations 20 Generalized Extreme Value 10 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 40 b) Maximum Annual Discharge (m³/s) 35 30 25 20 15 Station: 01AR008 10 Observations Generalized Extreme Value 5 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.15 Flood frequency analysis for a) Dennis Stream and b) Bocabec River 5 60 Maximum Annual Discharge (m³/s) 1400 a) 1200 1000 800 600 Station: 01BC001 400 Observations Generalized Extreme Value 200 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 800 b) Maximum Annual Discharge (m³/s) 700 600 500 400 300 Station: 01BE001 200 Observations Generalize Extreme Value 100 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.16 Flood frequency analysis for a) Restigouche River and b) Upsalquitch River 5 61 a) Maximum Annual Discharge (m³/s) 160 140 120 100 80 60 Station: 01BJ001 Observations 40 Generalize Extreme Value 20 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 250 Maximum Annual Discharge (m³/s) b) 200 150 100 Station: 01BJ003 Observations 50 Generalized Extreme Value 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.17 Flood frequency analysis for a) Tetagouche River and b) Jacquet River 5 62 80 a) Maximum Annual Discharge (m³/s) 70 60 50 40 30 Station: 01BJ004 20 Observations Generalize Extreme Value 10 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 3500 Maximum Annual Discharge (m³/s) b) 3000 2500 2000 1500 Station: 01BJ007 1000 Observations Generalized Extreme Value 500 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.18 Flood frequency analysis for a) Eel River and b) Restigouche River 5 63 a) Maximum Annual Discharge (m³/s) 1000 800 600 400 Station: 01BK004 Observations 200 Generalize Extreme Value 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) Maximum Annual Discharge (m³/s) 120 b) 100 80 60 40 Station: 01BL001 Observations Generalized Extreme Value 20 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.19 Flood frequency analysis for a) Nepisiquit River and b) Bass River 5 64 100 a) Maximum Annual Discharge (m³/s) 90 80 70 60 50 40 Station: 01BL002 30 Observations 20 Generalized Extreme Value 10 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 180 b) Maximum Annual Discharge (m³/s) 160 140 120 100 80 Station: 01BL003 60 Observations 40 Generalized Extreme Value 3p Lognormal 20 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.20 Flood frequency analysis for a) Rivière Caraquet and b) Big Tracadie River 5 65 a) Maximum Annual Discharge (m³/s) 2000 1500 1000 Station: 01BO001 Observations 500 Generalized Extreme Value 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) Maximum Annual Discharge (m³/s) 400 b) 350 300 250 200 150 Station: 01BO002 100 Observations Generalize Extreme Value 50 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.21 Flood frequency analysis for a) Southwest Miramichi River and b) Renous River 5 66 250 Maximum Annual Discharge (m³/s) a) 200 150 100 Station: 01BO003 Observations 50 Generalize Extreme Value 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 1000 b) Maximum Annual Discharge (m³/s) 900 800 700 600 500 400 Station: 01BP001 300 Observations 200 Generalized Extreme Value 100 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.22 Flood frequency analysis for a) Barnaby River and b) Little Southwest Miramichi River 5 67 600 Maximum Annual Discharge (m³/s) a) 500 400 300 200 Station: 01BQ001 Observations Generalized Extreme Value 100 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 100 Maximum Annual Discharge (m³/s) 90 b) 80 70 60 50 40 Station: 01BR001 30 Observations 20 Generalize Extreme Value 10 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.23 Flood frequency analysis for a) Northwest Miramichi River and b) Kouchibouguac River 5 68 100 a) Maximum Annual Discharge (m³/s) 90 80 70 60 50 40 Station: 01BS001 30 Observations 20 Generalized Extreme Value 3p Lognormal 10 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 250 Maximum Annual Discharge (m³/s) b) 200 150 100 Station: 01BU002 Observations 50 Generalized Extreme Value 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.24 Flood frequency analysis for a) Coal Branch River and b) Petitcodiac River 5 69 Maximum Annual Discharge (m³/s) 120 a) 100 80 60 40 Station: 01BU003 Observations Generalized Extreme Value 20 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 40 b) Maximum Annual Discharge (m³/s) 35 30 25 20 15 Station: 01BU004 10 Observations Generalized Extreme Value 5 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.25 Flood frequency analysis for a) Turtle Creek and b) Palmer’s Creek 5 70 50 a) Maximum Annual Discharge (m³/s) 45 40 35 30 25 20 Station: 01BV005 15 Observations 10 Generalized Extreme Value 5 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 180 b) Maximum Annual Discharge (m³/s) 160 140 120 100 80 60 Station: 01BV006 Observations 40 Generalized Extreme Value 20 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.26 Flood frequency analysis for a) Ratcliffe Brook and b) Point Wolfe River 5 71 Maximum Annual Discharge (m³/s) a) 200 150 100 Station: 01BV007 Observations 50 Generalize Extreme Value 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) 900 b) Maximum Annual Discharge (m³/s) 800 700 600 500 400 300 Station: 01BD002 Observations 200 Generalize Extreme Value 100 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.27 Flood frequency analysis for a) Upper Salmon River and b) Rivière Matapedia, QC 5 72 Maximum Annual Discharge (m³/s) 70 a) 60 50 40 30 Station: 01DL001 20 Observations Generalize Extreme Value 10 3p Lognormal 0 -2 -1 0 1 2 3 4 5 Reduced variable (Y) b) Maximum Annual Discharge (m³/s) 500 400 300 200 Station: 01BF001 Observations 100 Generalize Extreme Value 3p Lognormal 0 -2 -1 0 1 2 3 4 Reduced variable (Y) Figure A.28 Flood frequency analysis for a) Kelley River, NS and b) Rivière Nouvelle au Pont, QC 5 73 Appendix B Regional Flood Frequency Analyses 1 10 100 1000 1 10 Drainage area (km2) 100 1000 10000 Regression (EC & NB 1987) Regression (GEV, 2010) Generalized Extreme Value 3p Lognormal 100000 Figure B.1 Estimated 2‐year flood (daily discharge) as a function of drainage area (km2) for all 56 hydrometric stations (GEV and LN3). Regional regression line for both the present study and the EC & NB study (1987) are presented. D Daily discha rge (2‐year flood, QD2,m3/s) 10000 74 D Daily discha rge (10‐year flood, QD10,m3/s) 1 10 Drainage area (km2) 100 1000 10000 Regression (EC & NB 1987) Regression (GEV, 2010) Generalized Extreme Value 3p Lognormal 100000 Figure B.2 Estimated 10‐year flood (daily discharge) as a function of drainage area (km2) for all 56 hydrometric stations (GEV and LN3). Regional regression line for both the present study and the EC & NB study (1987) are presented. 1 10 100 1000 10000 75 D Daily discha rge (20‐year flood, QD20,m3/s) 1 10 1000 Drainage area (km2) 100 10000 Regression (EC & NB 1987) Regression (GEV, 2010) Generalized Extreme Value 3p Lognormal 100000 Figure B.3 Estimated 20‐year flood (daily discharge) as a function of drainage area (km2) for all 56 hydrometric stations (GEV and LN3). Regional regression line for both the present study and the EC & NB study (1987) are presented. 1 10 100 1000 10000 100000 76 D Daily discha rge (50‐year flood, QD50,m3/s) 1 10 1000 Drainage area (km2) 100 10000 Regression (EC & NB 1987) Regression (GEV, 2010) Generalized Extreme Value 3p Lognormal 100000 Figure B.4 Estimated 50‐year flood (daily discharge) as a function of drainage area (km2) for all 56 hydrometric stations (GEV and LN3). Regional regression line for both the present study and the EC & NB study (1987) are presented. 1 10 100 1000 10000 100000 77

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