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Application of multivariate statistical analysis methods to the dam hydrologic impact studies
Journal of Hydrology 371 (2009) 120–128
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Application of multivariate statistical analysis methods to the dam hydrologic impact studies Martin Matteau a, Ali A. Assani a,*, Mhamed Mesfioui b a
Laboratoire d’hydro-climatologie et de géomorphologie fluviale (Hydroclimatology and Fluvial Geomorphology Laboratory), Section de géographie (Geography Section), Pavillon Léon-Provencher, Université du Québec à Trois-Rivières, 3351 Boulevard des Forges, Trois-Rivières, Québec, Canada G9A 5H7 b Département de Mathématiques et d’Informatique (Department of Mathematics and Computer Science), Université du Québec à Trois-Rivières, 3351 Boulevard des Forges, Trois-Rivières, Québec, Canada G9A 5H7
a r t i c l e
i n f o
Article history: Received 4 August 2008 Received in revised form 18 December 2008 Accepted 25 March 2009
This manuscript was handled by K. Georgakakos, Editor-in-Chief, with the assistance of A.A. Tsonis, Associate Editor Keywords: Natural flow regime concept Seasonal streamflow characteristics Principal component analysis Canonical correlation analysis Dams Québec
s u m m a r y Introduced in the early 1990s in aquatic ecology as a new paradigm for restoration of rivers modified by anthropic activities, the ‘‘natural flow regime” concept has allowed the formulation of new problems in dam hydrologic impact studies. Within the context of this study, we posed two problems: (1) selection of the hydrologic variables most modified by dams and (2) identification of the factors that influence the extent of the hydrologic changes. Resolving these two problems necessitated the application of multivariate statistical analysis methods, in this instance, principal component analysis and canonical correlation analysis. These two methods thus are being applied for the first time to analysis of the hydrologic impacts of dams. The first method allowed selection of the hydrologic variables most modified downstream from dams in Québec. These are the variables best correlated to the first two principal components. As for the factors influencing the magnitude of these changes, canonical correlation analysis exposed the influence of the type of regulated regime (dam management mode), and to a lesser degree, the watershed size. Ó 2009 Elsevier B.V. All rights reserved.
Introduction The introduction of a new concept in a given scientific discipline makes it possible to pose new problems. Their solution requires the development and/or application of new data analysis methods. During the 1990s, the natural flow regime concept was developed in aquatic ecology as a new paradigm for restoration of the ecological integrity of rivers modified by anthropogenic activities (e.g. Karr, 1991; Poff et al., 1997; Ritcher et al., 1996). According to Lytle and Poff (2004), this concept has become a ‘‘fundamental part of the management and basic biological study of running water ecosystems”. The introduction of this concept in dam hydrologic impact studies has allowed the formulation of two fundamental problems of the dam hydrologic impact studies. – The first problem concerns the selection of the hydrologic variables most modified downstream from dams. This problem is very important in that it makes it possible to determine the abiotic and * Corresponding author. Tel.: +819 376 5011; fax: +819 376 5179. E-mail address: [email protected] (A.A. Assani). 0022-1694/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2009.03.022
biotic impacts induced by each of the hydrologic variables most modified downstream from dams, and to develop the standards that target only these variables to restore the ecological integrity of the regulated sections. This targeting makes the restoration standards more effective. But despite the importance of selection of the hydrologic variables most modified downstream from dams in the restoration of regulated rivers, no study dedicated to this subject exists to date in the scientific literature. Nevertheless, there have been a number of studies that have looked at the impacts of dams on a range of hydrologic variables, which could provide guidance on which variables tend to be most modified (e.g. Magilligan and Nislow, 2001; Poff et al., 2006, 2007; Pyron and Neuman, 2008; Richter et al., 1998; Singer, 2007; Yang et al., 2008). On the other hand, in the case of natural rivers, the natural flow regime concept has already been used to select the most relevant hydrologic variables for ecological characterization of rivers (e.g. Batalla et al., 2004; Black et al., 2005; Bragg et al., 2005; Claussen and Biggs, 2000; Monk et al., 2007; Olden and Poff, 2003; Pettit et al., 2001). – The second problem focuses on identification of the factors that influence the extent of the hydrologic changes experienced by the hydrologic variables downstream from dams. This
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identification also offers two major points of interest in the study of the hydrologic impacts of dams with a view to restoring the ecological integrity of regulated rivers. It allows determination of the factors that must be taken into account for the development of flood flow and low flow standards downstream from dams. It also allows selection of the relevant variables to estimate the flows downstream from dams when streamflow measurements are unavailable. Some studies have already been devoted to identification of the factors influencing the magnitude of the changes experienced by the hydrologic variables downstream from dams (Assani et al., 2005, 2006a, 2006b, 2007; Lajoie et al., 2007; Magilligan and Nislow, 2005). In methodological terms, solving these two problems necessitates the application of statistical methods never used to date in dam hydrologic impact studies. Regarding the first problem, the selection of the hydrologic variables most modified will be based on principal component analysis. This has never been used in dam hydrologic impact studies to solve this problem. Regarding the second problem, regression methods (simple and multiple) have already been used to identify the factors influencing hydrologic changes downstream from dams. However, these methods present several disadvantages that do not make the most of the natural flow regime concept in the analysis of hydrologic impacts of dams. Regression is unsuitable when multiple hydrologic variables (dependent variables) must be analyzed simultaneously, because it does not account for the effect of intragroup relationships on intergroup relationships. Moreover, due to the relatively high number of hydrologic variables to be analyzed, it becomes cumbersome to implement. The results are relatively unsynthetic and their interpretation then becomes difficult. Finally, in the case of simple regression, not all the explanatory factors are taken into account. To mitigate all these weaknesses, we propose using canonical correlation analysis for the first time to identify the factors that influ-
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ence the extent of the hydrologic changes experienced by the hydrologic variables downstream from dams. This method provides a general framework for many methods of multivariate analysis (discriminant analysis, multiple regression, canonical correspondence analysis, principal component analysis, etc.) (Ouarda et al., 2001). Consequently, it outperforms the regression methods used to date to identify the factors influencing the magnitude of the hydrologic changes downstream from dams. In light of these considerations, the objective of our study is to apply these two statistical analysis methods to (a) select the hydrologic variables most modified downstream from dams, through principal component analysis and (b) identify the factors allowing consideration of the extent of the hydrologic changes, through canonical correlation analysis. We will apply these two methods to the seasonal streamflows. These have never been analyzed in dam hydrologic impact studies. These streamflows are selected to show that the two methods can be applied on different scales. Methodology Selection of study stations and data sources This study pertains to 62 regulated flow stations of the St. Lawrence River (Fig. 1). Their watershed sizes range from 211 to 143,000 km2 and the maximum capacity of their reservoirs, from 74,000 to 25 billion m3. The selection of these stations was based on the following criteria: continuous streamflow measurement during a period of at least 10 years downstream from the dam or at the dam level, structure mainly intended for exploitation of hydroelectric power. We also analyzed 76 natural rivers so that we could compare the hydrologic variables measured on pristine rivers and regulated rivers (Fig. 1). The watershed sizes of the natural rivers range from 100 to 22,000 km2. The characteristics of the
Fig. 1. Location of stations on unregulated rivers (stars) and regulated rivers in Québec. Triangles = inversion regime; points = homogenization regime; rectangles = natural type flow regime.
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analyzed rivers have already been described elsewhere (Lajoie et al., 2007). The streamflow data analyzed come from Environment Canada’s Hydat CD-ROM (1996). The data on the dams were extracted from the Répertoire des barrages du Centre d’Expertise Hydrique du Québec (www.cehq.gouv.qc.ca/dams, consulted 03/ 08/2007). This dam directory contains various information on the identification, administrative category and type of use and on the technical characteristics of each dam (dam height, dam type, dam class, year of dam construction, etc.). These data allowed us to calculate the dam characteristics. Definition of hydrologic variables and explanatory factors The first stage was to define the hydrologic characteristics of the seasonal streamflow series by applying the ecological concept of ‘‘natural flow regime” (Ritcher et al., 1996; Poff et al., 1997). According to this concept, a river’s streamflows can be defined by the following five fundamental characteristics: magnitude, frequency, variability, duration and timing. Each of these five characteristics plays a fundamental role in the operation of aquatic ecosystems. Nonetheless, the number of characteristics to be defined depends on the hydrologic series analyzed (Assani et al., 2006a). On the seasonal and monthly scales, the following characteristics can be defined: magnitude, timing of maximum and minimum monthly average streamflows and seasonal streamflow variability. Assani and Tardif (2005) were able to show that these characteristics can be defined by 14 hydrologic variables (Table 1). – The variables relating to the magnitude of winter (W), spring (SP), summer (SU) and fall (F) seasonal streamflows and the variable relating to the magnitude of maximum (MAX) and minimum (MIN) monthly average streamflows. Instead of using the monthly average streamflows, they were grouped by season to reduce the size of the data matrix. This grouping also allows a better interpretation of the principal component analysis results. To be able to compare watersheds of different sizes, we calculated the seasonal streamflow coefficients, expressed as a percentage of total annual streamflow. This transformation also eliminates the effect of watershed size on the coefficients of correlation and the factor scores, in particular.
– The variables defining the timing of the maximum and minimum monthly average streamflows: TMAX and TMIM. For each river, we calculated the average month of occurrence of the maximum and minimum monthly average streamflows for the total number of streamflow measurement years. To avoid outlier averages, like those calculated between December and January, we decided to begin the hydrologic year in October. This was therefore considered as the first month of the year and September as the last (12th) month of the year. – The variables characterizing interseasonal and intermonthly streamflow variability: W/SP, SP/SU, SU/F, F/W, CV and CI. They define the annual variability (rate of change) of streamflows. The CI ratio is called the ‘‘monthly coefficient of immoderation” (Vivian, 1994). – The explanatory factors have been grouped in three categories (Table 2): – The factors that describe the physiographic characteristics of the watersheds: watershed size (DA) and the longitude (LONG) and latitude (LAT) of the gauging station located downstream from the dam. We should specify that latitude and longitude also include a site’s climatic conditions. We did not have precipitation and temperature data at each station. This is why these data were not analyzed in this study. – The factors relating to the dam characteristics: the maximum storage capacity of nearest upstream reservoir (CM) and the cumulative maximum storage capacity of all upstream reservoirs (CCM). This last factor is a measurement of the number of reservoirs built on the same watercourse. Apart from these two factors, we have also calculated the IR index, which is the ratio between the CM and the natural mean annual flow (converted in m3) entering the reservoir. This index measures the degree of water storage in a watershed. In case of the presence of numerous reservoirs, an equivalent index (IRC) was calculated, accounting for all the reservoirs located upstream. We should mention that the mean annual flow is little influenced by dams in Quebec (Assani et al., 2007). Its use is therefore justified to calculate the IRC values. In case of absence of data on natural mean annual flow entering a reservoir, these data were estimated by means of the equations established by Assani et al. (2007) for pristine rivers in Quebec. This
Table 1 The 14 hydrologic variables analyzed to classify and characterize regulated hydrologic regimes. Symbol
Meaning
Calculation method
W
Seasonal coefficient of winter streamflows
SP
Seasonal coefficient of spring streamflows
SU
Seasonal coefficient of summer streamflows
F
Seasonal coefficient of fall streamflows
W/SP
Ratio between winter streamflows and spring streamflows Ratio between spring streamflows and summer streamflows Ratio between summer streamflows and fall streamflows Ratio between fall streamflows and winter streamflows Monthly coefficient of the maximum monthly average streamflow Monthly coefficient of the minimum monthly average streamflow Monthly coefficient of immoderation Coefficients of variation Timing of maximum monthly average streamflows Timing of minimum monthly average streamflows
The ratio between the average of the sum of the average monthly streamflows from January to March and the total annual streamflow The ratio between the average of the sum of the average monthly streamflows from April to June and the total annual streamflow The ratio between the average of the sum of the average monthly streamflows from July to September and the total annual streamflow The ratio between the average of the sum of the average monthly streamflows from October to December and the total annual streamflow Quotient of W and SP
SP/SU SU/F F/W MAM MIM CI CV TMAX* TMIM* *
The first month of the year is October.
Quotient of SP and SU Quotient of SU and F Quotient of F and W The ratio between the maximum monthly average streamflow and the total annual streamflow (%) The ratio between the minimum monthly average streamflow and the total annual streamflow (%) The ratio between the maximum and minimum monthly streamflows The ratio between the standard deviation and the average monthly streamflow (%) Average month of occurrence of the maximum monthly average streamflows Average month of occurrence of the minimum monthly average streamflows
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M. Matteau et al. / Journal of Hydrology 371 (2009) 120–128 Table 2 Description of the independent variables. Category of variable
Type of variable a
Code
Calculation method
Unit of measure
Physiographic
Size Latitude Longitude
DA LAT LONG
– – –
Km2 (°) (°)
Dam characteristics
Maximum storage capacity of nearest upstream reservoir Cumulative maximum storage capacity of all upstream reservoirs Degree of storage Degree of cumulative storage
CM CCM IR IRC
– P CM upstream CM/MAF CCM/MAF
m3 m3 – –
Management modes or hydrologic regimes
Inversion Homogenization Natural
RRb RRb RRb
– – –
– – –
MAF = mean annual flows under pristine conditions. For some stations, MAF was estimated according to the regional equation established by Assani et al. (2007). a The values have been converted into natural logarithms. b Qualitative variables. These variables are rated from 1 (inversion regime) to 3 (natural flow regime).
estimate is based exclusively on watershed size, which explains more than 95% of the total variability of mean annual flow in Québec. – The factors describing the dam management modes (RR). In a series of studies, Assani et al. (2005, 2006a, 2007) identified three management modes. Each of these modes was associated with a specific hydrologic regime (Fig. 2). Three types of regulated hydrologic regimes were thus described. The first type of regime is the inversion flow regime. It is characterized by maximum streamflows in winter and minimum streamflows in spring. This is the opposite of the natural annual hydrologic cycle of streamflows in Quebec. This regime is generally associated with reservoirs often located upstream from the channels and designed to feed the hydroelectric generating stations located downstream. The second type of hydrologic regime, called the homogenization flow regime, is characterized by streamflows that remain almost constant all year around. Finally, the last type of regime, the natural flow regime, preserves the natural streamflow cycle. However, it is distinguished from the pristine flow regime by a slight increase in streamflows in winter and a slight decrease in streamflows in spring. For statistical analysis purposes, the three types of flow regimes, being qualitative variables, received the following ratings: 1 (the inversed flow regime), 2 (the homogenization flow regime) and 3 (natural-type flow regime). The inversion flow and natural flow regimes include nearly 80% of the stations, divided almost equally, while the homogenization flow regime includes less than 20% of the stations.
Statistical data analysis The first stage consisted of applying principal component analysis to the 14 hydrologic variables in order to select the hydrologic variables most modified by dams. This method was applied to the matrix composed of 62 lines (river stations analyzed) and 14 columns (mean hydrologic variables defined for each of these 62 regulated river stations). This selection was based exclusively on the loadings values of the hydrologic variables on the principal components according to ‘‘the maximum loading rule”. According to this rule, a hydrologic variable is associated with a principal component when its loading value is higher for this component than for the others (Vicente-Serrano, 2005). We applied the Kaiser criterion (1960) to determine the number of significant principal components. According to this criterion, a principal component is significant when its eigenvalue is P1, after varimax rotation. The theoretical presentation of the principal component analysis and
Fig. 2. The three types of regulated hydrologic regimes described in Québec. (a) Inversion regime; (b) homogenization regime; (c) natural flow regime.
its applications can be read in Compagnucci and Richman (2008), in particular. To determine the type and extent of the hydrologic changes downstream from dams, we compared the value of the hydrologic variables of regulated rivers associated with each of the significant principal components with the value of the hydrologic variables of pristine rivers. Finally, to determine the factors that influence the extent of the hydrologic change experienced by each hydrologic variable
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downstream from dams, we applied canonical correlation analysis. We correlated the 14 hydrologic variables to the 7 explanatory factors. This is the only method that allows simultaneous correlation of several dependent variables (hydrologic variables) with several independent variables (explanatory factors). The goal of the method is to be able to select the explanatory factors best correlated with the hydrologic variables in order to estimate the hydrologic variables subsequently. Canonical correlation analysis creates pairs of linear combinations between each group of variables (independent variables and dependent variables) called canonical variables, so that the correlation between the variables of the same pair is maximized and so that the correlation between the variables of two different pairs is nil. The analyses were performed with SAS version 8 software and the following description adapted from Vanderpoorten and Palm (1998). Let us consider p dependent variables xj (j = 1, . . ., p) and q dependent variables yk (k = 1, . . ., q), with x0j and y0k as their respective standardized variables. For each of these groups of standardized variables, the canonical variables are calculated as follows:
wl ¼ a1l x01 þ a2l x02þ . . . apl x0p ; Vl ¼
b1l y01
þ
b2l y02þ
SP) are relatively well correlated to this first principal component. The comparison of the values of these five variables between pristine rivers and regulated rivers reveals that downstream from dams, winter streamflows increase significantly (Fig. 3). Thus, the ratio between these streamflows and spring streamflows also increases (Fig. 3b). Conversely, the ratio between fall streamflows and winter streamflows decreases downstream from dams compared to natural rivers. This decrease is particularly significant for large watersheds. Spring streamflows, they decrease downstream from dams, but this decrease is greater for small watersheds than for large watersheds (Fig. 3c). Finally, the maximum monthly average streamflows occur early downstream from dams (Fig. 3d). The second principal component is strongly correlated to four hydrologic variables. It is positively correlated to CV, CI and MA but negatively to the magnitude of the minimum monthly average streamflows (MI). The first three variables decrease
ð1Þ
. . . bql y0q
ð2Þ
The maximum value of l corresponds to the number of variables of the smallest group. The canonical correlation coefficients ajl and bkl are calculated according to the two criteria 3 and 4:
Corrðwl þ 1; v l þ 1Þ < Corrðwl ; v l Þ
ð3Þ 0
Corr ðwl ; w0l Þ ¼ 0; corr ðv l ; v 0l Þ ¼ 0 and corr ðwl ; v 0l Þ ¼ 0 if l –l ð4Þ Results Selection by principal component analysis of the hydrologic variables most modified by dams The application of the Kayser criterion allowed us to extract five significant principal components with a total variance explained of over 90% (Table 3), more than half of which is explained by the first two components. The first principal component is strongly correlated negatively to winter streamflows (W) and to the ratio between these streamflows and spring streamflows (W/SP) but positively to the ratio between fall streamflows and winter streamflows (F/W). It will also be noted that two other hydrologic variables (TMAX and
Table 3 Matrix of loadings of hydrologic variables for the first five significant components after axes rotation by the varimax method. Variables
PC1
PCII
PCIII
PCIV
PCV
W SP SU F W/SP SP/SU SU/F F/W CV DMIN DMAX MI MA CI Eigenvalues VE (%)
0.904 0.694 0.152 0.252 0.904 0.066 0.313 0.844 0.297 0.168 0.794 0.168 0.436 0.241 4.040 28.9
0.011 0.054 0.160 0.003 0.011 0.366 0.002 0.289 0.881 0.086 0.189 0.899 0.777 0.814 3.139 22.4
0.144 0.265 0.948 0.025 0.144 0.899 0.806 0.351 0.254 0.097 0.100 0.026 0.300 0.097 2.777 19.8
0.374 0.657 0.179 0.957 0.374 0.119 0.463 0.099 0.138 0.006 0.070 0.017 0.216 0.186 2.003 14.3
0.046 0.009 0.064 0.003 0.046 0.053 0.061 0.036 0.072 0.968 0.201 0.128 0.028 0.065 1.021 7.3
VE = explained variance by principal components.
Fig. 3. Comparison of hydrologic variables correlated to the first principal component between natural rivers (open circles) and regulated rivers (triangles). (a) Winter discharge coefficients; (b) ratio between winter streamflows and spring streamflows; (c) spring discharge coefficients; (d) timing of maximum monthly average streamflows.
M. Matteau et al. / Journal of Hydrology 371 (2009) 120–128
significantly downstream from dams. This decrease is greater for large watersheds than for small watersheds (Fig. 4). Conversely, the values of the last variable increase downstream from dams. This increase is also greater for large watersheds than for small watersheds. The third component is correlated to three variables. It is positively correlated to SP/SU but negatively to SU and SU/F. The values of these last two variables decrease downstream from dams (Fig. 5) but increase for variable SP/SU. But these changes only affect large watersheds, contrary to the variables associated with the first two principal components. The fourth and fifth principal components are strongly correlated, respectively, to fall streamflows (F) and to the timing of the minimum monthly average streamflows (TMIN). This correlation is negative. For variable F, an upward trend is noted in the fall streamflows downstream from dams. But the difference be-
Fig. 4. Comparison of hydrologic variables correlated to the second principal component between natural rivers (open circles) and regulated rivers (triangles). (a) Minimum monthly average streamflows; (b) coefficients of variation of monthly streamflows; (c) coefficient of immoderation; (d) maximum monthly average streamflows.
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tween natural rivers and regulated rivers becomes less clear (Fig. 6). For variable TMIN, the minimum monthly average streamflows generally tend to occur late in the year downstream from dams. These results show that principal component analysis makes it possible to determine the hydrologic variables according to the extent of hydrologic changes experienced downstream from dams. The variables most modified downstream are associated with the first two principal components. Identification by canonical correlation analysis of the factors influencing the extent of hydrologic changes downstream from dams Table 4 reveals that only the first two canonical correlation coefficients are statistically significant. The value of the first coefficient exceeds 0.95. In fact, this value reflects a very strong link between the hydrologic variables and the explanatory factors. The analysis of coefficients of correlation between the canonical variables and the hydrologic variables and explanatory factors recorded in Table 5 shows that the first canonical variable V1 is strongly correlated to the type of regulated hydrologic regime (RR). It explains more than one third of the total variance. The second canonical variable V2 is correlated better to watershed size (DA). Its explained variance is about 17%. For the hydrologic variables, the first canonical variable W1 is significantly correlated to 8 variables (Table 6). We should remember that these variables
Fig. 5. Comparison of hydrologic variables correlated to the third principal component between natural rivers (open circles) and regulated rivers (triangles). (a) Summer discharge coefficients; (b) ratio between spring streamflows and summer streamflows; (c) ratio between summer streamflows and fall streamflows.
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Moreover, by associating the canonical variables extracted from the two groups of explanatory factors and hydrologic variables, this study shows that the eight hydrologic variables associated with W1 are influenced by the type of hydrologic regime (RR), while the MIM is influenced by watershed size. It follows that only these two factors influence the extent of the changes experienced by the hydrologic variables downstream from dams in Québec. The type of hydrologic regime undoubtedly is the principal factor, because the variance values associated with V1 and W1 are the highest. Fig. 7 gives the example of the influence of the type of regime on winter and spring seasonal streamflows. Regarding the influence of watershed size, the variance of the minimum monthly average streamflows between the natural rivers and the regulated rivers is greater for the large watersheds than for the small watersheds (Fig. 4a). This influence of watershed size has already been shown in other studies conducted on other temporal scales (Assani et al., 2005, 2006a, 2007; Lajoie et al., 2007). Discussion and conclusions The application of the ‘‘natural flow regime” concept to analysis of the hydrologic impacts of dams made it possible to pose new problems. These undeniably will contribute to the development of more effective streamflow standards to restore the regulated sections. The development of these standards must be based on the following two fundamental stages: - Select the hydrologic variables most modified by the dams and determined the abiotic and biotic impacts they induce. Only these variables must be targeted in the development of streamflow standards. - Identify the factors influencing the extent of the changes experienced by each of these hydrologic variables downstream from dams to integrate these factors into development of streamflow standards.
Fig. 6. Comparison of hydrologic variables correlated to the fourth (a) and fifth (b) principal components between natural rivers (open circles) and regulated rivers (triangles). (a) Fall discharge coefficients; (b) timing of minimum monthly average streamflows.
Table 4 Canonical correlation coefficients.
1 2 3 4 5 6 7
R
F
p>F
0.956 0.811 0.710 0.446 0.434 0.407 0.298
2.91 1.57 1.11 0.74 0.77 0.76 0.60
<0.0001 0.0103 0.3159 0.8490 0.7639 0.7124 0.7268
The statistically significant values appear in bold.
are correlated to the first two principal components. The second canonical variable W2 is significantly correlated to MI. This in turn is correlated to the second principal component. It follows that the canonical analysis confirms the result of the principal component analysis. Indeed, the hydrologic variables most modified by the dams are correlated to the first two canonical factors.
The resolution of these two complementary problems in the streamflow standards development process necessitated the application of statistical methods of multivariate analysis, in this instance, principal component analysis and canonical correlation analysis. We should remember that these two methods have never been used to date in studies dedicated to hydrologic impacts of dams. The first method was used to determine the hydrologic variables most modified downstream from dams. On a seasonal scale, it was shown that the hydrologic variables associated with the first two principal components are the most modified downstream from dams. Thus, the first principal component was correlated to the following variables: spring and winter streamflows, timing of maximum average monthly streamflows and seasonal streamflow variability. The second principal component was correlated to annual variability of monthly streamflows and minimum monthly average streamflow. The canonical correlation analysis exposed
Table 5 Coefficients of correlation between canonical variables (V) and explanatory factors.
RR DA CM CCM IR IRC LAT LONG VE (%)
V1
V2
V3
V4
V5
V6
V7
V8
0.979 0.165 0.563 0.431 0.486 0.435 0.335 0.380 31
0.085 0.691 0.258 0.050 0.508 0.072 0.513 0.307 16.8
0.000 0.657 0.004 0.301 0.255 0.280 0.573 0.133 14.5
0.181 0.145 0.381 0.727 0.293 0.730 0.440 0.518 25.8
0.027 0.192 0.481 0.243 0.452 0.249 0.267 0.174 9.9
0.026 0.012 0.054 0.243 0.026 0.243 0.150 0.662 8.3
0.004 0.082 0.487 0.275 0.272 0.272 0.100 0.091 6.9
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0
VE = explained variance by canonical roots.
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M. Matteau et al. / Journal of Hydrology 371 (2009) 120–128 Table 6 Coefficients of correlation between canonical variables (W) and explanatory factors.
W SP SU F W/SP SP/SU SU/F F/W CV TMIN TMAX MIM MAM CI VE (%)
W1
W2
W3
W4
W5
W6
W7
W8
0.869 0.906 0.031 0.742 0.869 0.163 0.498 0.606 0.628 0.189 0.663 0.103 0.793 0.039 31.6
0.082 0.214 0.236 0.180 0.082 0.172 0.199 0.327 0.559 0.226 0.036 0.636 0.382 0.381 9.9
0.127 0.183 0.431 0.336 0.127 0.378 0.110 0.497 0.171 0.352 0.156 0.240 0.119 0.072 7.3
0.277 0.154 0.224 0.110 0.277 0.133 0.320 0.183 0.077 0.166 0.007 0.310 0.082 0.147 3.9
0.074 0.091 0.146 0.078 0.074 0.137 0.209 0.176 0.114 0.510 0.215 0.221 0.087 0.358 4.6
0.007 0.014 0.088 0.175 0.007 0.089 0.247 0.076 0.091 0.214 0.353 0.0130 0.141 0.149 2.3
0.020 0.069 0.259 0.066 0.020 0.083 0.251 0.094 0.058 0.103 0.085 0.111 0.157 0.126 1.6
0.045 0.057 0.087 0.041 0.045 0.054 0.089 0.111 0.040 0.573 0.094 0.130 0.047 0.169 3.0
VE = explained variance by canonical roots.
Fig. 7. Comparison of winter (a) and spring (b) streamflows according to regulated and natural hydrologic regimes. Open circles = natural rivers; blue dot = inversion regime; green rectangle = homogenization regime; red triangle = natural flow regime.
the factors influencing the extent of the changes experienced by the hydrologic variables downstream from dams. These are the type of hydrologic regime and, to a lesser degree, watershed size. This result is very original in that no study dedicated to the impacts of dams accounts for the type of hydrologic regime, for the simple reason that a classification of hydrologic regimes of regulated rivers does not exist anywhere. We are the first to propose an initial classification of regulated rivers according to the hydrologic impacts induced by dams (Assani et al., 2005, 2006a) in Québec. This classification turns out to be very useful, due to the fact that it helps explain the extent of the hydrologic changes experienced by hydrologic variables downstream from dams.
In fact, a regulated hydrologic regime reflects the dam management mode. Consequently, all dams managed in the same way induce the same types of hydrologic impacts downstream. This typology of hydrologic impacts then becomes a key element in the development of streamflow standards. Indeed, each regulated hydrologic regime must correspond to specific standards for restoration of regulated sections because the hydrologic impacts vary from one regime (dam management mode) to another. In Québec, we thus identified three types of different regimes: the inversion, homogenization and natural flow regimes. The greatest hydrologic changes were observed downstream from dams that induce inversion of hydrologic regimes. This inversion triggers changes in all streamflow characteristics. This management mode is associated with the reservoirs intended to supply water to the hydroelectric generating stations built downstream. Thus, in spring during snow melt, water is stored in the reservoirs, causing low flows downstream from these reservoirs. In winter, the stored water is released to supply the generating stations for hydroelectric power production. Consequently, the flood flows occur in winter downstream from the reservoirs. It is the magnitude of the storage and release of water that differentiates this regime from homogenization. In the latter case, less water is stored and released than in an inversion regime. However, this magnitude also depends on watershed size. Storage and release are greater for small watersheds than for large watersheds. Finally, this study shows the significant contribution of the natural flow regime concept to dam hydrologic impact analysis. This concept allows definition of many hydrologic variables, analysis of which necessitates formulation of new problems and reliance on multivariate statistical methods. This contribution is important for the development of streamflow standards with a view to restoring the regulated sections. References Assani, A.A., Tardif, S., 2005. Classification, caractérisation et facteurs de variabilité spatiale des régimes hydrologiques naturels au Québec. Approche écogéographique. Revue des Sciences de l’Eau 18, 247–266. Assani, A.A., Gravel, E., Buffin-Bélanger, T., Roy, A.G., 2005. Impacts des barrages sur les caractéristiques des débits minimums annuels en fonction des régimes hydrologiques artificialisés au Québec (Canada). Revue des Sciences de l’Eau 18, 103–127. Assani, A.A., Stichelbout, E., Roy, A.G., Petit, F., 2006a. Comparison of impacts of dams on the annual maximum flow characteristics in three regulated hydrological regimes in Québec (Canada). Hydrological Processes 20, 3485– 3501. Assani, A.A., Tardif, S., Lajoie, F., 2006b. Statistical analysis of factors affecting the spatial variability of annual minimum flow characteristics in a cold temperate continental region (southern Québec, Canada). Journal of Hydrology 328, 753– 763.
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Assani, A.A., Lajoie, F., Laliberté, C., 2007. Impacts des barrages sur les caractéristiques des débits moyens annuels en fonction du mode de gestion et de la taille des bassins versants au Québec. Revue des Sciences de l’Eau 20, 127–146. Batalla, R.M., Gomez, C.M., Kondolf, G.M., 2004. Reservoir-induced hydrological changes in the Ebro River basin (NE Spain). Journal of Hydrology 290, 117– 136. Black, A.R., Rowan, J.S., Duck, R.W., Bragg, O.M., Clelland, B.E., 2005. DHRAM: A method for classifying river flow regime alterations for the EC Water Framework Directive. Aquatic Conservation Marine and Freshwater Ecosystems 15, 427–446. Bragg, O.M., Black, A.R., Duck, R.W., Rowan, J.S., 2005. Approaching the physicalbiological interface in rivers: a review of methods for ecological evaluation of flow regimes. Progress in Physical Geography 29, 506–531. Claussen, B., Biggs, B.J.F., 2000. Flow variable for ecological studies in temperature streams: grouping based on covariance. Journal of Hydrology 237, 184–197. Compagnucci, R.H., Richman, M.B., 2008. Can principal component analysis provide atmospheric circulation or teleconnexion patterns? International Journal of Climatology 28, 703–726. Environment Canada, 1996. HYDAT CDROM: Données sur les eaux de surface et sur les sediments. CDROM 2246, Ottawa. Kaiser, H.F., 1960. The application of electronic computers to factor analysis. Educational and Psychological Measurement 20, 141–151. Karr, J.R., 1991. Biological integrity: a long-neglected aspect of water resource management. Ecological Applications 1, 66–84. Lajoie, F., Assani, A.A., Roy, A.G., Mesfioui, M., 2007. Impacts of dams on monthly flow characteristics. The influence of watershed size and seasons. Journal of Hydrology 334, 423–439. Lytle, D.A., Poff, N.L., 2004. Adaptation to natural flow regimes. Trends in Ecology and Evolution 19, 94–100. Magilligan, F.J., Nislow, K.H., 2001. Long-term changes in regional hydrologic regime following impoundment in a humid-climate watershed. Journal of the American Water Resources Association 37, 1551–1569. Magilligan, F.J., Nislow, K.H., 2005. Changes in hydrologic regimes by dams. Geomorphology 71, 61–78. Monk, W.A., Wood, P.J., Hannah, D.M., Wilson, D.A., 2007. Selection of river flow indices for the assessment of hydroecological change. River Research and Applications 23, 113–122.
Olden, J.D., Poff, N.L., 2003. Redundancy and the choice of hydrologic indices for characterizing streamflow regimes. River Research and Applications 19, 101– 121. Ouarda, T.B.M.J., Girard, C., Cavadias, G.S., Bobée, B., 2001. Regional flood frequency estimation with canonical correlation analysis. Journal of Hydrology 254, 157– 173. Pettit, N.E., Froend, R.H., Davies, P.M., 2001. Identifying the natural flow regime and the relationship with riparian vegetation for two contrasting western Australian rivers. Regulated Rivers: Research & Management 17, 201–215. Poff, N.L., Allan, J.D., Bain, M.B., Karr, J.R., Prestegaard, K.L., Richter, B.D., Sparks, R.E., Stromberg, J.C., 1997. The natural flow regime. A paradigm for river conservation and restoration. BioScience 47, 769–784. Poff, N.L., Bledscoe, B.P., Cuhaciyan, C.O., 2006. Hydrologic variation with land use across the contiguous United States: geomorphic and ecological consequences for streams ecosystems. Geomorphology 79, 264–285. Poff, N.L., Olden, J.O., Merritt, D.M., Pepin, D.M., 2007. Homogenization of regional dynamics by dams and global biodiversity implications. Proceedings of the National Academy of Sciences of the United States 104, 5732–5737. Pyron, M., Neuman, K., 2008. Hydrologic alteration in the Wabash River watershed, USA. Rivers Research and Application 24, 1175–1184. Richter, B.D., Baumgartner, J.V., Braun, D.P., Powell, J., 1998. A spatial assessment of hydrologic alteration within a river network. Regulated Rivers: Research & Management 14, 329–340. Ritcher, B.D., Baumgartner, J.V., Powell, J., Braun, D.P., 1996. A method for assessing hydrologic alteration within ecosystem. Conservation Biology 10, 1163–1174. Singer, B.M., 2007. The influence of major dams on hydrology through the drainage network of the Sacramento River basin, California. River Research and Applications 23, 55–72. Vanderpoorten, A., Palm, R., 1998. Canonical variables of aquatic bryophyte combinations for predicting water trophic level. Hydrobiologia 386, 85–93. Vicente-Serrano, S.M., 2005. El Niño and La Niña influence on droughts at different timescales in the Iberian Peninsula. Water Resources Research 41, W12415. doi:10.1029/2004WR003908. Vivian, H., 1994. L’hydrologie artificialisée de l’Isère en amont de Grenoble. Essai de quantification des impacts des aménagements. Revue de Géographie Alpine 2, 97–112. Yang, T., Zhang, Q., Chen, Y.D., Tao, X., Xu, C-Y., Chen, X., 2008. A spatial assessment of hydrologic alteration caused by dam construction in the middle and lower Yellow River, China. Hydrological Processes 22, 3829–3843.
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Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol
Application of multivariate statistical analysis methods to the dam hydrologic impact studies Martin Matteau a, Ali A. Assani a,*, Mhamed Mesfioui b a
Laboratoire d’hydro-climatologie et de géomorphologie fluviale (Hydroclimatology and Fluvial Geomorphology Laboratory), Section de géographie (Geography Section), Pavillon Léon-Provencher, Université du Québec à Trois-Rivières, 3351 Boulevard des Forges, Trois-Rivières, Québec, Canada G9A 5H7 b Département de Mathématiques et d’Informatique (Department of Mathematics and Computer Science), Université du Québec à Trois-Rivières, 3351 Boulevard des Forges, Trois-Rivières, Québec, Canada G9A 5H7
a r t i c l e
i n f o
Article history: Received 4 August 2008 Received in revised form 18 December 2008 Accepted 25 March 2009
This manuscript was handled by K. Georgakakos, Editor-in-Chief, with the assistance of A.A. Tsonis, Associate Editor Keywords: Natural flow regime concept Seasonal streamflow characteristics Principal component analysis Canonical correlation analysis Dams Québec
s u m m a r y Introduced in the early 1990s in aquatic ecology as a new paradigm for restoration of rivers modified by anthropic activities, the ‘‘natural flow regime” concept has allowed the formulation of new problems in dam hydrologic impact studies. Within the context of this study, we posed two problems: (1) selection of the hydrologic variables most modified by dams and (2) identification of the factors that influence the extent of the hydrologic changes. Resolving these two problems necessitated the application of multivariate statistical analysis methods, in this instance, principal component analysis and canonical correlation analysis. These two methods thus are being applied for the first time to analysis of the hydrologic impacts of dams. The first method allowed selection of the hydrologic variables most modified downstream from dams in Québec. These are the variables best correlated to the first two principal components. As for the factors influencing the magnitude of these changes, canonical correlation analysis exposed the influence of the type of regulated regime (dam management mode), and to a lesser degree, the watershed size. Ó 2009 Elsevier B.V. All rights reserved.
Introduction The introduction of a new concept in a given scientific discipline makes it possible to pose new problems. Their solution requires the development and/or application of new data analysis methods. During the 1990s, the natural flow regime concept was developed in aquatic ecology as a new paradigm for restoration of the ecological integrity of rivers modified by anthropogenic activities (e.g. Karr, 1991; Poff et al., 1997; Ritcher et al., 1996). According to Lytle and Poff (2004), this concept has become a ‘‘fundamental part of the management and basic biological study of running water ecosystems”. The introduction of this concept in dam hydrologic impact studies has allowed the formulation of two fundamental problems of the dam hydrologic impact studies. – The first problem concerns the selection of the hydrologic variables most modified downstream from dams. This problem is very important in that it makes it possible to determine the abiotic and * Corresponding author. Tel.: +819 376 5011; fax: +819 376 5179. E-mail address: [email protected] (A.A. Assani). 0022-1694/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2009.03.022
biotic impacts induced by each of the hydrologic variables most modified downstream from dams, and to develop the standards that target only these variables to restore the ecological integrity of the regulated sections. This targeting makes the restoration standards more effective. But despite the importance of selection of the hydrologic variables most modified downstream from dams in the restoration of regulated rivers, no study dedicated to this subject exists to date in the scientific literature. Nevertheless, there have been a number of studies that have looked at the impacts of dams on a range of hydrologic variables, which could provide guidance on which variables tend to be most modified (e.g. Magilligan and Nislow, 2001; Poff et al., 2006, 2007; Pyron and Neuman, 2008; Richter et al., 1998; Singer, 2007; Yang et al., 2008). On the other hand, in the case of natural rivers, the natural flow regime concept has already been used to select the most relevant hydrologic variables for ecological characterization of rivers (e.g. Batalla et al., 2004; Black et al., 2005; Bragg et al., 2005; Claussen and Biggs, 2000; Monk et al., 2007; Olden and Poff, 2003; Pettit et al., 2001). – The second problem focuses on identification of the factors that influence the extent of the hydrologic changes experienced by the hydrologic variables downstream from dams. This
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identification also offers two major points of interest in the study of the hydrologic impacts of dams with a view to restoring the ecological integrity of regulated rivers. It allows determination of the factors that must be taken into account for the development of flood flow and low flow standards downstream from dams. It also allows selection of the relevant variables to estimate the flows downstream from dams when streamflow measurements are unavailable. Some studies have already been devoted to identification of the factors influencing the magnitude of the changes experienced by the hydrologic variables downstream from dams (Assani et al., 2005, 2006a, 2006b, 2007; Lajoie et al., 2007; Magilligan and Nislow, 2005). In methodological terms, solving these two problems necessitates the application of statistical methods never used to date in dam hydrologic impact studies. Regarding the first problem, the selection of the hydrologic variables most modified will be based on principal component analysis. This has never been used in dam hydrologic impact studies to solve this problem. Regarding the second problem, regression methods (simple and multiple) have already been used to identify the factors influencing hydrologic changes downstream from dams. However, these methods present several disadvantages that do not make the most of the natural flow regime concept in the analysis of hydrologic impacts of dams. Regression is unsuitable when multiple hydrologic variables (dependent variables) must be analyzed simultaneously, because it does not account for the effect of intragroup relationships on intergroup relationships. Moreover, due to the relatively high number of hydrologic variables to be analyzed, it becomes cumbersome to implement. The results are relatively unsynthetic and their interpretation then becomes difficult. Finally, in the case of simple regression, not all the explanatory factors are taken into account. To mitigate all these weaknesses, we propose using canonical correlation analysis for the first time to identify the factors that influ-
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ence the extent of the hydrologic changes experienced by the hydrologic variables downstream from dams. This method provides a general framework for many methods of multivariate analysis (discriminant analysis, multiple regression, canonical correspondence analysis, principal component analysis, etc.) (Ouarda et al., 2001). Consequently, it outperforms the regression methods used to date to identify the factors influencing the magnitude of the hydrologic changes downstream from dams. In light of these considerations, the objective of our study is to apply these two statistical analysis methods to (a) select the hydrologic variables most modified downstream from dams, through principal component analysis and (b) identify the factors allowing consideration of the extent of the hydrologic changes, through canonical correlation analysis. We will apply these two methods to the seasonal streamflows. These have never been analyzed in dam hydrologic impact studies. These streamflows are selected to show that the two methods can be applied on different scales. Methodology Selection of study stations and data sources This study pertains to 62 regulated flow stations of the St. Lawrence River (Fig. 1). Their watershed sizes range from 211 to 143,000 km2 and the maximum capacity of their reservoirs, from 74,000 to 25 billion m3. The selection of these stations was based on the following criteria: continuous streamflow measurement during a period of at least 10 years downstream from the dam or at the dam level, structure mainly intended for exploitation of hydroelectric power. We also analyzed 76 natural rivers so that we could compare the hydrologic variables measured on pristine rivers and regulated rivers (Fig. 1). The watershed sizes of the natural rivers range from 100 to 22,000 km2. The characteristics of the
Fig. 1. Location of stations on unregulated rivers (stars) and regulated rivers in Québec. Triangles = inversion regime; points = homogenization regime; rectangles = natural type flow regime.
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analyzed rivers have already been described elsewhere (Lajoie et al., 2007). The streamflow data analyzed come from Environment Canada’s Hydat CD-ROM (1996). The data on the dams were extracted from the Répertoire des barrages du Centre d’Expertise Hydrique du Québec (www.cehq.gouv.qc.ca/dams, consulted 03/ 08/2007). This dam directory contains various information on the identification, administrative category and type of use and on the technical characteristics of each dam (dam height, dam type, dam class, year of dam construction, etc.). These data allowed us to calculate the dam characteristics. Definition of hydrologic variables and explanatory factors The first stage was to define the hydrologic characteristics of the seasonal streamflow series by applying the ecological concept of ‘‘natural flow regime” (Ritcher et al., 1996; Poff et al., 1997). According to this concept, a river’s streamflows can be defined by the following five fundamental characteristics: magnitude, frequency, variability, duration and timing. Each of these five characteristics plays a fundamental role in the operation of aquatic ecosystems. Nonetheless, the number of characteristics to be defined depends on the hydrologic series analyzed (Assani et al., 2006a). On the seasonal and monthly scales, the following characteristics can be defined: magnitude, timing of maximum and minimum monthly average streamflows and seasonal streamflow variability. Assani and Tardif (2005) were able to show that these characteristics can be defined by 14 hydrologic variables (Table 1). – The variables relating to the magnitude of winter (W), spring (SP), summer (SU) and fall (F) seasonal streamflows and the variable relating to the magnitude of maximum (MAX) and minimum (MIN) monthly average streamflows. Instead of using the monthly average streamflows, they were grouped by season to reduce the size of the data matrix. This grouping also allows a better interpretation of the principal component analysis results. To be able to compare watersheds of different sizes, we calculated the seasonal streamflow coefficients, expressed as a percentage of total annual streamflow. This transformation also eliminates the effect of watershed size on the coefficients of correlation and the factor scores, in particular.
– The variables defining the timing of the maximum and minimum monthly average streamflows: TMAX and TMIM. For each river, we calculated the average month of occurrence of the maximum and minimum monthly average streamflows for the total number of streamflow measurement years. To avoid outlier averages, like those calculated between December and January, we decided to begin the hydrologic year in October. This was therefore considered as the first month of the year and September as the last (12th) month of the year. – The variables characterizing interseasonal and intermonthly streamflow variability: W/SP, SP/SU, SU/F, F/W, CV and CI. They define the annual variability (rate of change) of streamflows. The CI ratio is called the ‘‘monthly coefficient of immoderation” (Vivian, 1994). – The explanatory factors have been grouped in three categories (Table 2): – The factors that describe the physiographic characteristics of the watersheds: watershed size (DA) and the longitude (LONG) and latitude (LAT) of the gauging station located downstream from the dam. We should specify that latitude and longitude also include a site’s climatic conditions. We did not have precipitation and temperature data at each station. This is why these data were not analyzed in this study. – The factors relating to the dam characteristics: the maximum storage capacity of nearest upstream reservoir (CM) and the cumulative maximum storage capacity of all upstream reservoirs (CCM). This last factor is a measurement of the number of reservoirs built on the same watercourse. Apart from these two factors, we have also calculated the IR index, which is the ratio between the CM and the natural mean annual flow (converted in m3) entering the reservoir. This index measures the degree of water storage in a watershed. In case of the presence of numerous reservoirs, an equivalent index (IRC) was calculated, accounting for all the reservoirs located upstream. We should mention that the mean annual flow is little influenced by dams in Quebec (Assani et al., 2007). Its use is therefore justified to calculate the IRC values. In case of absence of data on natural mean annual flow entering a reservoir, these data were estimated by means of the equations established by Assani et al. (2007) for pristine rivers in Quebec. This
Table 1 The 14 hydrologic variables analyzed to classify and characterize regulated hydrologic regimes. Symbol
Meaning
Calculation method
W
Seasonal coefficient of winter streamflows
SP
Seasonal coefficient of spring streamflows
SU
Seasonal coefficient of summer streamflows
F
Seasonal coefficient of fall streamflows
W/SP
Ratio between winter streamflows and spring streamflows Ratio between spring streamflows and summer streamflows Ratio between summer streamflows and fall streamflows Ratio between fall streamflows and winter streamflows Monthly coefficient of the maximum monthly average streamflow Monthly coefficient of the minimum monthly average streamflow Monthly coefficient of immoderation Coefficients of variation Timing of maximum monthly average streamflows Timing of minimum monthly average streamflows
The ratio between the average of the sum of the average monthly streamflows from January to March and the total annual streamflow The ratio between the average of the sum of the average monthly streamflows from April to June and the total annual streamflow The ratio between the average of the sum of the average monthly streamflows from July to September and the total annual streamflow The ratio between the average of the sum of the average monthly streamflows from October to December and the total annual streamflow Quotient of W and SP
SP/SU SU/F F/W MAM MIM CI CV TMAX* TMIM* *
The first month of the year is October.
Quotient of SP and SU Quotient of SU and F Quotient of F and W The ratio between the maximum monthly average streamflow and the total annual streamflow (%) The ratio between the minimum monthly average streamflow and the total annual streamflow (%) The ratio between the maximum and minimum monthly streamflows The ratio between the standard deviation and the average monthly streamflow (%) Average month of occurrence of the maximum monthly average streamflows Average month of occurrence of the minimum monthly average streamflows
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M. Matteau et al. / Journal of Hydrology 371 (2009) 120–128 Table 2 Description of the independent variables. Category of variable
Type of variable a
Code
Calculation method
Unit of measure
Physiographic
Size Latitude Longitude
DA LAT LONG
– – –
Km2 (°) (°)
Dam characteristics
Maximum storage capacity of nearest upstream reservoir Cumulative maximum storage capacity of all upstream reservoirs Degree of storage Degree of cumulative storage
CM CCM IR IRC
– P CM upstream CM/MAF CCM/MAF
m3 m3 – –
Management modes or hydrologic regimes
Inversion Homogenization Natural
RRb RRb RRb
– – –
– – –
MAF = mean annual flows under pristine conditions. For some stations, MAF was estimated according to the regional equation established by Assani et al. (2007). a The values have been converted into natural logarithms. b Qualitative variables. These variables are rated from 1 (inversion regime) to 3 (natural flow regime).
estimate is based exclusively on watershed size, which explains more than 95% of the total variability of mean annual flow in Québec. – The factors describing the dam management modes (RR). In a series of studies, Assani et al. (2005, 2006a, 2007) identified three management modes. Each of these modes was associated with a specific hydrologic regime (Fig. 2). Three types of regulated hydrologic regimes were thus described. The first type of regime is the inversion flow regime. It is characterized by maximum streamflows in winter and minimum streamflows in spring. This is the opposite of the natural annual hydrologic cycle of streamflows in Quebec. This regime is generally associated with reservoirs often located upstream from the channels and designed to feed the hydroelectric generating stations located downstream. The second type of hydrologic regime, called the homogenization flow regime, is characterized by streamflows that remain almost constant all year around. Finally, the last type of regime, the natural flow regime, preserves the natural streamflow cycle. However, it is distinguished from the pristine flow regime by a slight increase in streamflows in winter and a slight decrease in streamflows in spring. For statistical analysis purposes, the three types of flow regimes, being qualitative variables, received the following ratings: 1 (the inversed flow regime), 2 (the homogenization flow regime) and 3 (natural-type flow regime). The inversion flow and natural flow regimes include nearly 80% of the stations, divided almost equally, while the homogenization flow regime includes less than 20% of the stations.
Statistical data analysis The first stage consisted of applying principal component analysis to the 14 hydrologic variables in order to select the hydrologic variables most modified by dams. This method was applied to the matrix composed of 62 lines (river stations analyzed) and 14 columns (mean hydrologic variables defined for each of these 62 regulated river stations). This selection was based exclusively on the loadings values of the hydrologic variables on the principal components according to ‘‘the maximum loading rule”. According to this rule, a hydrologic variable is associated with a principal component when its loading value is higher for this component than for the others (Vicente-Serrano, 2005). We applied the Kaiser criterion (1960) to determine the number of significant principal components. According to this criterion, a principal component is significant when its eigenvalue is P1, after varimax rotation. The theoretical presentation of the principal component analysis and
Fig. 2. The three types of regulated hydrologic regimes described in Québec. (a) Inversion regime; (b) homogenization regime; (c) natural flow regime.
its applications can be read in Compagnucci and Richman (2008), in particular. To determine the type and extent of the hydrologic changes downstream from dams, we compared the value of the hydrologic variables of regulated rivers associated with each of the significant principal components with the value of the hydrologic variables of pristine rivers. Finally, to determine the factors that influence the extent of the hydrologic change experienced by each hydrologic variable
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downstream from dams, we applied canonical correlation analysis. We correlated the 14 hydrologic variables to the 7 explanatory factors. This is the only method that allows simultaneous correlation of several dependent variables (hydrologic variables) with several independent variables (explanatory factors). The goal of the method is to be able to select the explanatory factors best correlated with the hydrologic variables in order to estimate the hydrologic variables subsequently. Canonical correlation analysis creates pairs of linear combinations between each group of variables (independent variables and dependent variables) called canonical variables, so that the correlation between the variables of the same pair is maximized and so that the correlation between the variables of two different pairs is nil. The analyses were performed with SAS version 8 software and the following description adapted from Vanderpoorten and Palm (1998). Let us consider p dependent variables xj (j = 1, . . ., p) and q dependent variables yk (k = 1, . . ., q), with x0j and y0k as their respective standardized variables. For each of these groups of standardized variables, the canonical variables are calculated as follows:
wl ¼ a1l x01 þ a2l x02þ . . . apl x0p ; Vl ¼
b1l y01
þ
b2l y02þ
SP) are relatively well correlated to this first principal component. The comparison of the values of these five variables between pristine rivers and regulated rivers reveals that downstream from dams, winter streamflows increase significantly (Fig. 3). Thus, the ratio between these streamflows and spring streamflows also increases (Fig. 3b). Conversely, the ratio between fall streamflows and winter streamflows decreases downstream from dams compared to natural rivers. This decrease is particularly significant for large watersheds. Spring streamflows, they decrease downstream from dams, but this decrease is greater for small watersheds than for large watersheds (Fig. 3c). Finally, the maximum monthly average streamflows occur early downstream from dams (Fig. 3d). The second principal component is strongly correlated to four hydrologic variables. It is positively correlated to CV, CI and MA but negatively to the magnitude of the minimum monthly average streamflows (MI). The first three variables decrease
ð1Þ
. . . bql y0q
ð2Þ
The maximum value of l corresponds to the number of variables of the smallest group. The canonical correlation coefficients ajl and bkl are calculated according to the two criteria 3 and 4:
Corrðwl þ 1; v l þ 1Þ < Corrðwl ; v l Þ
ð3Þ 0
Corr ðwl ; w0l Þ ¼ 0; corr ðv l ; v 0l Þ ¼ 0 and corr ðwl ; v 0l Þ ¼ 0 if l –l ð4Þ Results Selection by principal component analysis of the hydrologic variables most modified by dams The application of the Kayser criterion allowed us to extract five significant principal components with a total variance explained of over 90% (Table 3), more than half of which is explained by the first two components. The first principal component is strongly correlated negatively to winter streamflows (W) and to the ratio between these streamflows and spring streamflows (W/SP) but positively to the ratio between fall streamflows and winter streamflows (F/W). It will also be noted that two other hydrologic variables (TMAX and
Table 3 Matrix of loadings of hydrologic variables for the first five significant components after axes rotation by the varimax method. Variables
PC1
PCII
PCIII
PCIV
PCV
W SP SU F W/SP SP/SU SU/F F/W CV DMIN DMAX MI MA CI Eigenvalues VE (%)
0.904 0.694 0.152 0.252 0.904 0.066 0.313 0.844 0.297 0.168 0.794 0.168 0.436 0.241 4.040 28.9
0.011 0.054 0.160 0.003 0.011 0.366 0.002 0.289 0.881 0.086 0.189 0.899 0.777 0.814 3.139 22.4
0.144 0.265 0.948 0.025 0.144 0.899 0.806 0.351 0.254 0.097 0.100 0.026 0.300 0.097 2.777 19.8
0.374 0.657 0.179 0.957 0.374 0.119 0.463 0.099 0.138 0.006 0.070 0.017 0.216 0.186 2.003 14.3
0.046 0.009 0.064 0.003 0.046 0.053 0.061 0.036 0.072 0.968 0.201 0.128 0.028 0.065 1.021 7.3
VE = explained variance by principal components.
Fig. 3. Comparison of hydrologic variables correlated to the first principal component between natural rivers (open circles) and regulated rivers (triangles). (a) Winter discharge coefficients; (b) ratio between winter streamflows and spring streamflows; (c) spring discharge coefficients; (d) timing of maximum monthly average streamflows.
M. Matteau et al. / Journal of Hydrology 371 (2009) 120–128
significantly downstream from dams. This decrease is greater for large watersheds than for small watersheds (Fig. 4). Conversely, the values of the last variable increase downstream from dams. This increase is also greater for large watersheds than for small watersheds. The third component is correlated to three variables. It is positively correlated to SP/SU but negatively to SU and SU/F. The values of these last two variables decrease downstream from dams (Fig. 5) but increase for variable SP/SU. But these changes only affect large watersheds, contrary to the variables associated with the first two principal components. The fourth and fifth principal components are strongly correlated, respectively, to fall streamflows (F) and to the timing of the minimum monthly average streamflows (TMIN). This correlation is negative. For variable F, an upward trend is noted in the fall streamflows downstream from dams. But the difference be-
Fig. 4. Comparison of hydrologic variables correlated to the second principal component between natural rivers (open circles) and regulated rivers (triangles). (a) Minimum monthly average streamflows; (b) coefficients of variation of monthly streamflows; (c) coefficient of immoderation; (d) maximum monthly average streamflows.
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tween natural rivers and regulated rivers becomes less clear (Fig. 6). For variable TMIN, the minimum monthly average streamflows generally tend to occur late in the year downstream from dams. These results show that principal component analysis makes it possible to determine the hydrologic variables according to the extent of hydrologic changes experienced downstream from dams. The variables most modified downstream are associated with the first two principal components. Identification by canonical correlation analysis of the factors influencing the extent of hydrologic changes downstream from dams Table 4 reveals that only the first two canonical correlation coefficients are statistically significant. The value of the first coefficient exceeds 0.95. In fact, this value reflects a very strong link between the hydrologic variables and the explanatory factors. The analysis of coefficients of correlation between the canonical variables and the hydrologic variables and explanatory factors recorded in Table 5 shows that the first canonical variable V1 is strongly correlated to the type of regulated hydrologic regime (RR). It explains more than one third of the total variance. The second canonical variable V2 is correlated better to watershed size (DA). Its explained variance is about 17%. For the hydrologic variables, the first canonical variable W1 is significantly correlated to 8 variables (Table 6). We should remember that these variables
Fig. 5. Comparison of hydrologic variables correlated to the third principal component between natural rivers (open circles) and regulated rivers (triangles). (a) Summer discharge coefficients; (b) ratio between spring streamflows and summer streamflows; (c) ratio between summer streamflows and fall streamflows.
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Moreover, by associating the canonical variables extracted from the two groups of explanatory factors and hydrologic variables, this study shows that the eight hydrologic variables associated with W1 are influenced by the type of hydrologic regime (RR), while the MIM is influenced by watershed size. It follows that only these two factors influence the extent of the changes experienced by the hydrologic variables downstream from dams in Québec. The type of hydrologic regime undoubtedly is the principal factor, because the variance values associated with V1 and W1 are the highest. Fig. 7 gives the example of the influence of the type of regime on winter and spring seasonal streamflows. Regarding the influence of watershed size, the variance of the minimum monthly average streamflows between the natural rivers and the regulated rivers is greater for the large watersheds than for the small watersheds (Fig. 4a). This influence of watershed size has already been shown in other studies conducted on other temporal scales (Assani et al., 2005, 2006a, 2007; Lajoie et al., 2007). Discussion and conclusions The application of the ‘‘natural flow regime” concept to analysis of the hydrologic impacts of dams made it possible to pose new problems. These undeniably will contribute to the development of more effective streamflow standards to restore the regulated sections. The development of these standards must be based on the following two fundamental stages: - Select the hydrologic variables most modified by the dams and determined the abiotic and biotic impacts they induce. Only these variables must be targeted in the development of streamflow standards. - Identify the factors influencing the extent of the changes experienced by each of these hydrologic variables downstream from dams to integrate these factors into development of streamflow standards.
Fig. 6. Comparison of hydrologic variables correlated to the fourth (a) and fifth (b) principal components between natural rivers (open circles) and regulated rivers (triangles). (a) Fall discharge coefficients; (b) timing of minimum monthly average streamflows.
Table 4 Canonical correlation coefficients.
1 2 3 4 5 6 7
R
F
p>F
0.956 0.811 0.710 0.446 0.434 0.407 0.298
2.91 1.57 1.11 0.74 0.77 0.76 0.60
<0.0001 0.0103 0.3159 0.8490 0.7639 0.7124 0.7268
The statistically significant values appear in bold.
are correlated to the first two principal components. The second canonical variable W2 is significantly correlated to MI. This in turn is correlated to the second principal component. It follows that the canonical analysis confirms the result of the principal component analysis. Indeed, the hydrologic variables most modified by the dams are correlated to the first two canonical factors.
The resolution of these two complementary problems in the streamflow standards development process necessitated the application of statistical methods of multivariate analysis, in this instance, principal component analysis and canonical correlation analysis. We should remember that these two methods have never been used to date in studies dedicated to hydrologic impacts of dams. The first method was used to determine the hydrologic variables most modified downstream from dams. On a seasonal scale, it was shown that the hydrologic variables associated with the first two principal components are the most modified downstream from dams. Thus, the first principal component was correlated to the following variables: spring and winter streamflows, timing of maximum average monthly streamflows and seasonal streamflow variability. The second principal component was correlated to annual variability of monthly streamflows and minimum monthly average streamflow. The canonical correlation analysis exposed
Table 5 Coefficients of correlation between canonical variables (V) and explanatory factors.
RR DA CM CCM IR IRC LAT LONG VE (%)
V1
V2
V3
V4
V5
V6
V7
V8
0.979 0.165 0.563 0.431 0.486 0.435 0.335 0.380 31
0.085 0.691 0.258 0.050 0.508 0.072 0.513 0.307 16.8
0.000 0.657 0.004 0.301 0.255 0.280 0.573 0.133 14.5
0.181 0.145 0.381 0.727 0.293 0.730 0.440 0.518 25.8
0.027 0.192 0.481 0.243 0.452 0.249 0.267 0.174 9.9
0.026 0.012 0.054 0.243 0.026 0.243 0.150 0.662 8.3
0.004 0.082 0.487 0.275 0.272 0.272 0.100 0.091 6.9
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0
VE = explained variance by canonical roots.
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M. Matteau et al. / Journal of Hydrology 371 (2009) 120–128 Table 6 Coefficients of correlation between canonical variables (W) and explanatory factors.
W SP SU F W/SP SP/SU SU/F F/W CV TMIN TMAX MIM MAM CI VE (%)
W1
W2
W3
W4
W5
W6
W7
W8
0.869 0.906 0.031 0.742 0.869 0.163 0.498 0.606 0.628 0.189 0.663 0.103 0.793 0.039 31.6
0.082 0.214 0.236 0.180 0.082 0.172 0.199 0.327 0.559 0.226 0.036 0.636 0.382 0.381 9.9
0.127 0.183 0.431 0.336 0.127 0.378 0.110 0.497 0.171 0.352 0.156 0.240 0.119 0.072 7.3
0.277 0.154 0.224 0.110 0.277 0.133 0.320 0.183 0.077 0.166 0.007 0.310 0.082 0.147 3.9
0.074 0.091 0.146 0.078 0.074 0.137 0.209 0.176 0.114 0.510 0.215 0.221 0.087 0.358 4.6
0.007 0.014 0.088 0.175 0.007 0.089 0.247 0.076 0.091 0.214 0.353 0.0130 0.141 0.149 2.3
0.020 0.069 0.259 0.066 0.020 0.083 0.251 0.094 0.058 0.103 0.085 0.111 0.157 0.126 1.6
0.045 0.057 0.087 0.041 0.045 0.054 0.089 0.111 0.040 0.573 0.094 0.130 0.047 0.169 3.0
VE = explained variance by canonical roots.
Fig. 7. Comparison of winter (a) and spring (b) streamflows according to regulated and natural hydrologic regimes. Open circles = natural rivers; blue dot = inversion regime; green rectangle = homogenization regime; red triangle = natural flow regime.
the factors influencing the extent of the changes experienced by the hydrologic variables downstream from dams. These are the type of hydrologic regime and, to a lesser degree, watershed size. This result is very original in that no study dedicated to the impacts of dams accounts for the type of hydrologic regime, for the simple reason that a classification of hydrologic regimes of regulated rivers does not exist anywhere. We are the first to propose an initial classification of regulated rivers according to the hydrologic impacts induced by dams (Assani et al., 2005, 2006a) in Québec. This classification turns out to be very useful, due to the fact that it helps explain the extent of the hydrologic changes experienced by hydrologic variables downstream from dams.
In fact, a regulated hydrologic regime reflects the dam management mode. Consequently, all dams managed in the same way induce the same types of hydrologic impacts downstream. This typology of hydrologic impacts then becomes a key element in the development of streamflow standards. Indeed, each regulated hydrologic regime must correspond to specific standards for restoration of regulated sections because the hydrologic impacts vary from one regime (dam management mode) to another. In Québec, we thus identified three types of different regimes: the inversion, homogenization and natural flow regimes. The greatest hydrologic changes were observed downstream from dams that induce inversion of hydrologic regimes. This inversion triggers changes in all streamflow characteristics. This management mode is associated with the reservoirs intended to supply water to the hydroelectric generating stations built downstream. Thus, in spring during snow melt, water is stored in the reservoirs, causing low flows downstream from these reservoirs. In winter, the stored water is released to supply the generating stations for hydroelectric power production. Consequently, the flood flows occur in winter downstream from the reservoirs. It is the magnitude of the storage and release of water that differentiates this regime from homogenization. In the latter case, less water is stored and released than in an inversion regime. However, this magnitude also depends on watershed size. Storage and release are greater for small watersheds than for large watersheds. Finally, this study shows the significant contribution of the natural flow regime concept to dam hydrologic impact analysis. This concept allows definition of many hydrologic variables, analysis of which necessitates formulation of new problems and reliance on multivariate statistical methods. This contribution is important for the development of streamflow standards with a view to restoring the regulated sections. References Assani, A.A., Tardif, S., 2005. Classification, caractérisation et facteurs de variabilité spatiale des régimes hydrologiques naturels au Québec. Approche écogéographique. Revue des Sciences de l’Eau 18, 247–266. Assani, A.A., Gravel, E., Buffin-Bélanger, T., Roy, A.G., 2005. Impacts des barrages sur les caractéristiques des débits minimums annuels en fonction des régimes hydrologiques artificialisés au Québec (Canada). Revue des Sciences de l’Eau 18, 103–127. Assani, A.A., Stichelbout, E., Roy, A.G., Petit, F., 2006a. Comparison of impacts of dams on the annual maximum flow characteristics in three regulated hydrological regimes in Québec (Canada). Hydrological Processes 20, 3485– 3501. Assani, A.A., Tardif, S., Lajoie, F., 2006b. Statistical analysis of factors affecting the spatial variability of annual minimum flow characteristics in a cold temperate continental region (southern Québec, Canada). Journal of Hydrology 328, 753– 763.
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