Flood Frequency Analyses for New Brunswick Rivers

Flood Frequency Analyses for New Brunswick Rivers
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
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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
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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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