Development of representative indicators of hydrologic alteration
Development of representative indicators of hydrologic alteration
Yongxuan Gao a ,Richard M.Vogel a,*,Charles N.Kroll b ,N.LeRoy Poff c ,Julian D.Olden d
a
Department of Civil and Environmental Engineering,Tufts University,Medford,MA 02155,United States
b
Department of Environmental Resources and Forest Engineering,SUNY College of Environmental Science and Forestry,Syracuse,NY 13210,United States c
Department of Biology and Graduate Degree Program in Ecology,Colorado State University,Fort Collins,CO 80523,United States d
School of Aquatic and Fishery Sciences,University of Washington,P.O.Box 355020,Seattle,WA 98195,United States
a r t i c l e i n f o Article history:
Received 31October 2008
Received in revised form 9May 2009Accepted 1June 2009
This manuscript was handled by
K.Georgakakos,Editor-in-Chief,with the assistance of Taha Ouarda,Associate Editor Keywords:Hydroecology Ecohydrology Instream ?ow Ecode?cit
Principal component analysis Flow duration curve
s u m m a r y
In an ideal world,a few overall indicators of hydrologic alteration would adequately describe the degree of hydrologic alteration caused by various forms of river regulation.Currently over 170hydrologic indi-cators have been developed to describe different components of ?ow regimes,including the widely used Indicators of Hydrologic Alteration (IHA)that characterize the impact of river regulation on ?ow regimes in environmental ?ow studies.Many of these IHA indicators are intercorrelated,resulting in considerable information redundancy,which could lead to ineffective environmental ?ow management decisions.The objective of this research is to develop a small set of independent and representative hydrologic indica-tors that can best characterize hydrologic alteration caused by reservoirs and other forms of river regu-lation.Two sets of pre-and post-dam stream?ow records are used:(1)based on arti?cial simulations of a wide range of reservoir release rules and (2)stream?ow records for 189gaging stations throughout the United States.Principal component analysis was used to address the intercorrelation among the IHA parameters.Results revealed that the recently introduced metrics termed ecode?cit and ecosurplus can provide a good overall representation of the degree of alteration of a stream?ow time series.Across both datasets,32individual IHA statistics and several potential generalized indices,three indices based on the ecode?cit and ecosurplus explained the most variability associated with the ensemble of 32IHA statistics.
ó2009Elsevier B.V.All rights reserved.
Introduction
Rivers provide numerous goods and services for humankind,including a source of water for domestic,industrial and agricul-tural purposes,a means of power generation and waste disposal,routes for navigation,and sites for recreation and spiritual activi-ties (Ripl,2003).At the same time,?ow variability is well recog-nized by ecologists as being the primary driver of riverine ecosystem function and structure (Poff et al.,1997).Ironically,the great utility of rivers has also resulted in their demise through their extensive exploitation throughout the world,a process greatly facilitated by the construction of thousands of dams glob-ally (Nilsson et al.,2005;Poff et al.,2007).Although human manip-ulation of river ?ows provides many societal bene?ts,it also degrades and eliminates valuable ecosystem services and threat-ens freshwater biodiversity by altering natural ?ow regimes (Bunn and Arthington,2002;Magilligan and Nislow,2005).There is now widespread understanding that the environment is a legitimate
user of the river and that environmental ?ows,or the provision of water within rivers to conserve freshwater biodiversity while meeting the water demand of human society,are needed for most riverine systems (Brown and King,2003).However,there is little consensus as to which hydrologic indicators should be used to summarize instream ?ow properties analogous to the use of the widely accepted metrics in the ?eld of water supply engineering,such as mean annual water supply yield and reliability of a reservoir.
To evaluate the ecological effect of reservoir operations and other forms of river regulation,and to design optimal reservoir re-lease rules,indicators are needed to evaluate the overall ecological health of the river and the degree of hydrologic alteration caused by a particular operating policy.To date,over 170hydrologic met-rics have been published to summarize various aspects of the ?ow regime,although there has been little consideration of the correlation among indicators or the statistical redundancy involved (see Olden and Poff,2003).Consequently,researchers are now confronted with the task of having to choose among a large number of competing hydrologic indicators.One commonly used suite of metrics for characterizing the impact of regulation on ?ow regimes are the Indicators of Hydrologic Alteration (IHA)developed by Richter et al.(1996)of The Nature Conservancy.
0022-1694/$-see front matter ó2009Elsevier B.V.All rights reserved.doi:10.1016/j.jhydrol.2009.06.009
*Corresponding author.Tel.:+16176274260;fax:+16176273994.
E-mail addresses:xuan.gao@https://www.wendangku.net/doc/458759603.html, (Y.Gao),richard.vogel@https://www.wendangku.net/doc/458759603.html, (R.M.Vogel),cnkroll@https://www.wendangku.net/doc/458759603.html, (C.N.Kroll),poff@https://www.wendangku.net/doc/458759603.html, (N.LeRoy Poff),olden@https://www.wendangku.net/doc/458759603.html, (J.D.Olden).
Journal of Hydrology 374(2009)
136–147
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Journal of Hydrology
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The IHA contains33hydrologic parameters that characterize the intra-and inter-annual variation in?ows,according to the follow-ing?ve characteristics of?ow regimes:magnitude of monthly stream?ows,magnitude and duration of annual extreme?ows, timing of annual extreme?ows,frequency and duration of high and low pulses,rate and frequency of?ow changes(Mathews and Richter,2007).Similar to most other proposed indicators, many IHA parameters are intercorrelated(Olden and Poff,2003), promoting a level of numerical redundancy and potentially com-plicating environmental?ow assessments(Arthington et al.2006).
Developing a small number of statistics that capture key compo-nents of ecologically relevant?ow variation will:(1)contribute to a general approach for characterizing?ow alteration,(2)minimize statistical redundancy and computational effort in future analyses, and(3)facilitate our ability to obtain Pareto-optimal solutions for environmental?ow schemes(see Shiau and Wu,2006,2007;Suen and Eheart,2006).Pareto-optimal solutions for environmental?ow schemes involve a determination of the tradeoffs between human water supply and ecological?ow objectives.While there are a wide range of possible water supply objectives,ranging from such con-cepts as vulnerability,resilience and reliability,to water quality, security and cost,many studies simply focus on a single objective such as reliability.By comparison,there is no accepted single or even small set of environmental or instream?ow objectives.Thus one of the biggest current challenges associated with balancing hu-man and ecological?ow needs involves a determination of a small set of representative indicators which re?ect alteration to ecologi-cal?ow regimes.This is the subject of our paper.
Previous studies have sought to explore redundancy among hydrologic metrics.For example,Olden and Poff(2003)used prin-cipal component analysis(PCA)to evaluate patterns of statistical variation among171published hydrologic indicators and con-cluded that the33IHAs capture the majority of the variation, and thus can be used to represent the major aspects of the?ow re-gime.Similarly,Yang et al.(2008)identi?ed a small subset of hydrologic indicators that were the most representative of ecolog-ical?ow regimes.They evaluated three approaches(genetic pro-gramming,principal component analysis and autecology matrix) resulting the selection of six IHA parameters(Date of minimum, Rise Rate,Number of reversals,3-day maximum,7-day minimum and May?ow)as the most ecologically relevant hydrologic indica-tors(ERHIs).
The primary goal of our study is to determine,among a large suite of indicators of hydrologic alteration,the combination of sta-tistics that best provide an overall measure of hydrologic alter-ation.For this purpose,we consider the suite of IHA statistics,as well as a few generalized indicators of the ecological?ow regimes termed the Dundee Hydrological Regime Alteration Method (DHRAM)(Black et al.,2005)and the recently introduced indices termed ecosurplus and ecode?cit(Vogel et al.,2007). Methodology
Data
The IHA is a suite of statistics developed by The US Nature Con-servancy(https://www.wendangku.net/doc/458759603.html,/)to assess the degree of hydro-logic alteration caused by human activities.It consists of67 parameters,which are subdivided into two groups-33IHA param-eters and34EFC(Environmental Flow Component)parameters. These hydrologic parameters were developed based on their eco-logical relevance and their ability to re?ect human-induced changes in?ow regimes across a broad range of in?uences includ-ing dam operations,water diversions,ground-water pumping,and landscape modi?cation(Mathews and Richter,2007).The IHA parameters,listed in Table1,are the subject of this study(see IHA User’s Manual(The Nature Conservancy,2006)for de?nition of the parameters).A common approach to assessing hydrologic alteration involves a comparison of?ow regimes between pres-ent-day(impacted)and past(unimpacted)time periods.Following Richter et al.(1996),we considered the percentage change in the median values of the IHA parameters between unregulated(pre-dam)and regulated(post-dam)?ow regimes for two sets of stream?ow data,a simulated set and an empirical set.The param-eter‘‘number of zero-?ow days”was excluded from the analysis, because there was no zero-?ow day for most of the gages during the unregulated periods in our study;thus the percentage of change could not be computed because the denominator was zero.
The simulated data series was the same series introduced by Vogel et al.(2007)for the purpose of evaluating a wide range of reservoir release policies corresponding to a wide range of hypo-thetical reservoir systems all simulated for a single river.The unregulated stream?ow data in the simulated data set come from the USGS gage01333000(Green River at Williamstown,MA;drain-age area=110km2),and the regulated stream?ow,for the simu-lated data set,are generated from the water management software,Water Evaluation And Planning System(WEAP),devel-oped by the Stockholm Environment Institute(Yates et al.,2005). Stream?ow regulation in this case refers to12release rules operat-ing on eight imaginary reservoirs with storage ratios(ratio of stor-age capacity S to mean annual in?ow l)in the range of0.01–3(see Vogel et al.,2007for further details).Hence,the number of obser-vations of the simulated stream?ow series is12?8=96.Since this dataset is only based on a single river gage,we felt it was impor-tant to expand our experiment by using another dataset,described below,which employs actual stream?ow data subject to a variety of?ow alteration schemes from many rivers and dams.
A second data set,termed the empirical data set,is a set of stream?ow data from189USGS stream?ow gages in third-through seventh-order rivers distributed across the continental US.Flow gages were located0.1–74km downstream of dams (mean=17km).The following criteria were used to ensure that the record of each gage re?ected the in?uence of a single dam: (1)no pre-existing upstream mainstem dam,(2)at least15years of daily stream?ow data both before and after the dam completion date,(3)no more than two tributary inputs between the upstream dam and the gage,and(4)no dams on tributaries with an esti-mated drainage area larger than the mainstem river of the candi-date dam(see Poff et al.,2007for more details).Fig.1shows the locations of the189dams.No information is available regarding the type of reservoir release rules employed by these dams.
Multicollinearity of IHA statistics
Figs.2and3illustrate boxplots of the correlation coef?cients between each IHA statistic and the remaining31IHA statistics
Table1
Thirty-three indicators of hydrologic alteration.
October?ow September?ow Number of zero-?ow days a November?ow1-day minimum Base?ow index December?ow3-day minimum Date of minimum
January?ow7-day minimum Date of maximum February?ow30-day minimum Low pulse count
March?ow90-day minimum Low pulse duration
April?ow1-day maximum High pulse count
May?ow3-day maximum High pulse duration
June?ow7-day maximum Rise rate
July?ow30-day maximum Fall rate
August?ow90-day maximum Number of reversals
a This parameter is excluded from the study.
Y.Gao et al./Journal of Hydrology374(2009)136–147137
138Y.Gao et al./Journal of Hydrology374(2009)136–147
for the simulated and empirical data sets,respectively.As shown in the?gures,some of the IHA statistics are highly correlated.The absolute values of the correlation coef?cients among the IHA sta-tistics in the simulated data set range from0.002to1.00,with a mean of0.45with many larger than0.95.The absolute values of the correlation coef?cients in the empirical data set range from 0.0to0.993,with a mean of0.194.The correlations among statis-tics are not as strong in the empirical data set,but still there are several correlation coef?cients that are higher than0.95.
Figs.2and3document that the IHA statistics are highly inter-correlated.Hence a principal component analysis(PCA)was con-ducted in Section3to reduce the dimensionality of the IHA data set while retaining as much of the variation inherent in the original data set as possible.This analysis enabled us to examine patterns of intercorrelation among the IHA statistics,thus providing an ap-proach to select a subset of statistically non-redundant IHA parameters.
Generalized indices:eco-?ow statistics and DHRAM
Several researchers have developed generalized indices to eval-uate the overall impact of stream?ow regulation on?ow regimes. Vogel et al.(2007)introduced the nondimensional metrics of eco-de?cit and ecosurplus,which are based on a?ow duration curve (FDC).Importantly the ecode?cit and ecosurplus can be computed over any time period of interest(month,season,or year)and re-?ect the overall loss or gain,respectively,in stream?ow due to?ow regulation during that period(Vogel et al.,2007).The ecosurplus and ecode?cit can be computed using either a period of record FDC or a median annual FDC which is used here(see Vogel and Fennessey,1994,for further details).A median annual FDC re?ects the variability of daily stream?ow during a typical or median year. The bold curve in Fig.4is the median annual FDC for a stream that is not subject to regulation and the dotted curve represents the median annual FDC for the same stream subject to regulation. The area below the unregulated FDC and above the regulated FDC represents the amount of water now unavailable to river due to?ow alteration caused by the withdrawal.Ecode?cit is then de?ned as the ratio of this area over the total area under the unreg-ulated median annual FDC.This ratio represents the fraction of stream?ow no longer available to the river during that period. Conversely,ecosurplus is the area above the unregulated FDC and below the regulated FDC divided by the total area under the unregulated median FDC.Thus,ecode?cit and ecosurplus are dimensionless measures which represent the de?cit or surplus of stream?ow resulting from?ow alteration,as a fraction of the mean stream?ow in a typical or median year.It is also important to men-tion that the ecode?cit and ecosurplus can be computed using di-rect ecological measures such as habitat suitability measures.See Vogel and Fennessey(1995)for a discussion of how habitat suit-ability indices can be used in combination with FDC’s.
In this study,we divide the year into three seasons:spring (March–June),winter(November–February)and summer(July–October),and computed both the annual and seasonal ecode?cits and ecosurpluses.We also introduce a new overall index of hydro-logic alteration termed total seasonal ecochange,which is the sum of all the seasonal ecode?cits and ecosurpluses within a year.The pre?x‘‘eco”is added to the word de?cit and surplus,because that any change in the natural?ow regime can impair ecological integ-rity,depending on the magnitude,timing,duration,and frequency of those deviations(Poff et al.,1997).Hence,we hypothesize that both ecosurplus and ecode?cits are important metrics of ecosys-tem health.Even though FDCs do not account for the timing of stream?ows,the use of seasonal ecode?cit and ecosurplus can cap-ture some timing impacts(Vogel et al.,2007).We term this new class of nine metrics the eco-?ow statistics.
Another generalized index of hydrologic alteration is the Dun-dee Hydrological Regime Alteration Method(DHRAM)developed by Black et al.(2005)to assess the severity and extent of human alteration to hydrologic regimes.DHRAM yields a score(from0 to30)based on the overall percentage of change in the33IHA parameters before and after stream?ow regulation.The higher the score,the greater the impact the system has on the?ow regime and higher the risk of damage to the ecosystem.The score enables one to determine the DHRAM class between Class1(Un-impacted condition)and Class5(severely impacted condition)(Black et al., 2005).The raw DHRAM scores,not the?nal class designation,were used in the present study.
IHA subset selection using PCA
The power of PCA lies in?nding a subset of the matrix of origi-nal variables X to represent as much as possible of the overall inter-nal variation of X.When p,the number of variables observed,is
Y.Gao et al./Journal of Hydrology374(2009)136–147139
large as is the case here for the IHA statistics,it is often the case that a subset of m variables,with m<
Next,a single variable(i.e.one IHA statistic)was selected to represent each of the retained PCs.The variable that has the high-est loading(in absolute value)on a PC is selected to represent that PC(Dunteman,1989).Table2summarizes the loadings of the four PCs retained for the simulated data set and Table3summarizes the loadings of the eight PCs retained for the empirical data set.The resulting representative IHA parameters for the simulated data are May?ow,30-day minimum,Date of maximum and Rise rate. They represent particular facets of the?ow regime that are rela-tively independent of one another,because they are derived from different PCs(Olden and Poff,2003).The resulting eight represen-tative parameters for the empirical data are November?ow,Febru-ary?ow,March?ow,June?ow,30-day minimum,7-day maximum,High pulse duration and Rise rate.
A close examination of Tables2and3reveals that the IHA sta-tistics that have similar values of loadings form clusters,which are highlighted using gray shading in the tables.Such a clustering ef-fect is more prominent in PCs that explain a greater degree of var-iation.The clusters indicate which group of IHA statistics dominate,or relate to,a particular PC and,therefore,can be used to interpret the PC axis.For example,in the simulated data set, PC1was related to both monthly?ow statistics and high?ow mag-nitude statistics,PC2was related to base?ow magnitude and monthly?ow,and PC3was related to high?ow magnitude and rate of change of the?ow.PC4showed mixed loadings with no particular dominance or clustering of IHA statistics observed.
In the empirical data set,PC1can be interpreted as being dom-inated by base?ow magnitude and monthly?ow;PC2can be interpreted as being dominated by high?ow magnitude;PC3can be interpreted as monthly?ow,rate of change and frequency; PC4can be interpreted as monthly?ow and rate of change;PC5 can be interpreted by monthly?ow and frequency;and PC6can be interpreted by timing of extreme events.Both PC7and PC8 show mixed loadings and no dominance or clustering by any group of IHA statistics.
In the above analyses,the selection of dominant IHA statistics using k s and loadings is arbitrary.For example,if we had decided to retain only60%of the variation of the original data,we would have retained fewer PCs.To avoid the arbitrary nature of the above analysis and its associated uncertainty,another approach was to develop a comprehensive or overall index that can represent all of the32IHA parameters.Additional analyses were performed to evaluate if any of the generalized indices such as the eco-?ow sta-tistics or DHRAM was an effective overall index and to con?rm if the above selected subsets of IHA statistics were truly representa-tive indicators of hydrologic alteration.
Analysis1–multiple linear regression:generalized index vs. the32IHA statistics
This analysis evaluated whether the generalized indices,eco-de?cit,ecosurplus or DHRAM,were correlated to the32IHA statis-tics and if they could be considered as an effective overall measure to represent the entire set of IHA statistics.A separate multiple lin-ear regression(MLR)was performed for each of the10generalized indices using the32IHA parameters as the predictor(explanatory) variables for each data set.The names of the10generalized indices and the results from this analysis are given in Table4.
For the simulated data set,almost all of the generalized indices (except winter and spring ecosurplus)had adjusted coef?cient of determination(R2-adj)values in excess of0.99.In contrast,for the empirical data set,only three generalized indices had R2-adj values that exceeded0.8:total seasonal ecochange(0.807),sum-mer ecosurplus(0.929)and winter ecosurplus(0.919).Across both datasets,the three generalized indices,total seasonal ecochange, summer ecosurplus and winter ecosurplus,explained the most variability in the32IHA statistics.Furthermore,those three eco-?ow statistics explained much more of the variability in IHA statis-tics than the DHRAM index for the empirical data set.
140Y.Gao et al./Journal of Hydrology374(2009)136–147
Analysis2–Pearson’s r and Kendal’s Tau between a generalized index and an individual PC
The goal of analysis2was to evaluate whether the various gen-eralized indices could be used to represent the variability in the32 IHA statistics explained by each PC.Each generalized index was plotted against the scores of each PC.Fig.6is an example of such plots.In Fig.6,we observe a relationship between the annual eco-de?cit and the?rst two PCs for both data sets.In general,the rela-tionships among the generalized indices and the PCs are nonlinear, hence we investigated their correlation using the nonparametric correlation coef?cient,Kendall’s Tau,as well as the traditional lin-ear measure of correlation,Pearson’s r.Fig.7a–d shows the abso-lute value of the two correlation coef?cients.Values of the two correlation coef?cients and their p values are reported in Appendix A.
In the simulated data set,the highest Pearson’s r and highest Kendall’s Tau values always corresponded to either PC1or PC2 and were always in excess of0.5.The absolute value of the highest Pearson’s r ranged from0.545(spring ecosurplus vs.PC1)to0.987 (annual ecode?cit vs.PC1).The absolute values of the highest Ken-dall’s Tau ranged from0.563(DHRAM score vs.PC1and summer ecode?cit vs.PC2)to0.938(annual ecode?cit vs.PC1).
In the empirical data set,the highest Pearson’s r values and highest Kendall’s Tau values always occurred with the?rst3PCs, except Pearson’s r for summer ecode?cit,which was with PC6. The absolute values of the highest Pearson’s r ranged from0.241 (summer ecode?cit vs.PC6)to0.751(winter ecosurplus vs.PC3). The absolute values of the highest Kendall’s Tau ranged from 0.273(summer ecode?cit vs.PC1)to0.631(annual ecode?cit vs. PC2).Analysis3–PCA on different subsets of the empirical data set Since the reservoirs associated with both data sets have a wide range of different storage ratios,we investigated if the magnitude of the storage ratio,s=S/l,would have an impact on our analy-ses.To investigate the effect of s on the results,the189dams were divided into three subsets:(1)s<0.1(n=139),(2)s<0.01 (n=102),(3)s>0.01(n=87).Here the storage ratio can be inter-preted as the average number of years of watershed runoff that the reservoir can hold so that values of s=0.01and0.1represent 3.6and36days of storage,respectively.We grouped the dams into categories according to their storage ratio because Vogel et al.(1999)show that S/l plays a key role in the behavior of water supply reservoirs and Vogel et al.(2007)document that reservoirs with larger storage ratios tend to have a greater impact on the overall ecological?ow regime.Results of the PCA and the MLR between each of the generalized index and the32IHA statis-tics for the subsets are shown in Fig.8and Tables5and6.The results of these analyses on subsets of the databases were not dif-ferent from the results obtained earlier using the entire empirical data set.
Discussion
PCA subset selection
The PCA resulted in the selection of four IHA statistics from the simulated data set,eight from the empirical data set,and eight from each subset of the empirical data set.Results of the analyses on different subsets of the empirical data set were not signi?cantly different from the original empirical data set.
Table2
Loadings for the?rst four PCs of the simulated data set.
Note:The value in bold italics for each PC is the highest loading corresponding to that PC.
Y.Gao et al./Journal of Hydrology374(2009)136–147141
Hence,we conclude that storage ratio does not play a signi?cant role in determining which IHA statistics are most representative of ecological?ow regimes.
The six ERHIs selected by Yang et al.(2008)are date of mini-mum,rise rate,number of reversals,3-day maximum,7-day min-imum and May?ow.Table5lists those IHA statistics that were selected in our analyses for both data sets.The four groups of IHA statistics selected are not exactly the same,but a closer exam-ination reveals that most of them contain three common ele-ments:at least one monthly?ow statistic,two extreme event statistics representing both high and low extremes,and one sta-tistic associated with frequency of the low pulse and high pulse. These three elements can also be seen in Yang et al.’s(2008) selection of the six ERHIs,although our subset selection is not the same as theirs.Similar patterns can also be found by examin-ing the loadings of the PCs in Tables2and3.There appears to be clusters of IHA statistics that dominate each PC and each of those clusters match with one of the three elements identi?ed above. Each of these elements corresponds to a certain type of ecological in?uence,and one of the?ve?ow regime characteristics identi-?ed by Richter et al.(1996).
Interpretation of the principal components and selection of the most representative subset of indicators requires statistically sound criteria,and should be combined with physical and biological knowledge of the stream?ow regimes of interest(Olden and Poff, 2003).In order to justify the selection of a particular subset of IHA statistics from PCA,the ecological relevance of those parameters needs to be demonstrated.
Effectiveness of the eco-?ow statistics as overall metrics of hydrologic alteration
In analysis1,multivariate linear regression was performed to investigate relationships between each of the10generalized indi-ces and the32IHA statistics.Our results in Table4indicated a strong relationship between all10generalized indices and the32 IHA statistics in the simulated data set.The values of R2-adj derived from the empirical data set(see Tables4and6)are not as high as those derived from simulated data set though a few eco-?ow statistics in the empirical data set had R2-adj values that were higher than0.8(winter ecosurplus,summer ecosurplus and total seasonal ecochange).Across both datasets,the three generalized indices,total seasonal ecochange,summer ecosurplus and winter
Table3
Loadings for the?rst8PCs of the empirical data set.
Note:The value in bold italics for each PC is the highest loading corresponding to that PC.
Table4
Adjusted coef?cient of determination(R2-adj)of the multivariate linear regression between a generalized index and the32IHA parameters for both data sets.
Generalized index Simulated data set
(n=96)Empirical data set (n=189)
Annual ecode?cit0.9980.603
Annual ecosurplus0.9890.663
Winter ecode?cit0.9900.453
Winter ecosurplus0.8980.919
Spring ecode?cit0.9950.699
Spring ecosurplus0.7830.559
Summer ecode?cit0.9980.296
Summer ecosurplus0.9930.929
Total seasonal ecochange0.9950.807
DHRAM score0.9880.540
142Y.Gao et al./Journal of Hydrology374(2009)136–147
ecosurplus,explained the most variability in the32IHA statistics. Furthermore,those three eco-?ow statistics explained much more of the variability in IHA statistics,than the DHRAM index for the empirical data set.
In analysis2,correlation coef?cients(Pearson’s r and Kendal’s Tau)were computed between each generalized index and the indi-vidual PCs.The results indicate a strong correlation between each generalized index and one of the?rst two PCs in the simulated data set,and between a generalized index and one of the?rst three PCs in the empirical data set.
In terms of correlations with the IHA statistics,DHRAM per-forms similarly to the eco-?ow statistics for the simulated data set(Tables4and6,and Fig.7a and b),because it has similar values of R2-adj,Kendall’s Tau and Pearson’s r values to the eco-?ow sta-tistics.However,in the empirical data set,DHRAM has generally lower values of R2-adj,Kendall’s Tau and Pearson’s r(Tables4 and6,and Fig.7c and d)than the eco-?ow statistics.Therefore, the eco-?ow statistics appear to be a better generalized index than DHRAM.
Conclusions
There is an increasing need to account for natural differences in ?ow variability among rivers and to understand the importance of such differences for the protection of freshwater biodiversity and maintenance of goods and services that rivers provide(Arthington et al.,2006).One should not ignore natural system complexity in favor of simple and static environmental?ow‘‘rules”to manage our water resources.On the other hand,there is a need to develop a reduced suite of indices to replace the commonly used33IHA parameters and to provide an accurate overall determination of the impact of hydrologic alteration.The use of a single or just a few indices of hydrologic alteration can minimize statistical redun-dancy and lead to signi?cant reductions in the complexity associ-ated with the formulation and development of optimal reservoir operation policies and other river regulation schemes.There should be a balance between statistical simplicity and natural sys-tem complexity to enable the design of logical and environmen-tally sustainable reservoir release rules and river regulation guidelines.
This study has sought to evaluate the ability of a set of general-ized indices of hydrologic alteration to describe the variations in stream discharge resulting from reservoir operating release rules. In general,we found that the eco-?ow statistics termed the ecodef-icit and the ecosurplus can provide good overall measures of hydrologic alteration.The annual ecode?cit appears to be the best generalized index among all the indices in the simulated data set. On the other hand,winter ecosurplus and summer ecosurplus ap-pear to perform best in the empirical data set.In addition,total seasonal ecochange appears to a good generalized index in both data sets since it accounts for all the seasonal de?cits and surpluses and because it accounts for seasonal changes,thus taking timing of the?ow into consideration.The total seasonal ecochange resulted in high values of R2-adj values with the32IHA parameters in both data sets and all subsets of the empirical data set;and resulted in a high correlation with PC1even when the Pearson’s r and Kendall’s Tau values of the seasonal ecode?cit and ecosurplus were low,as indicated(Fig.7a–d).
We expected the results for the simulated data set and the empirical data set to differ,because the simulated data set only considers a wide range of reservoir release rules for a wide range of hypothetical reservoir systems on a single river,whereas the empirical data set considers a wide range of reservoir release rules for a wide range of actual reservoir systems on189rivers that occur across a wide spectrum hydroclimatic regions.The empirical data set may also contain variations in stream?ow that are not caused by the reservoirs release rules.Nevertheless,the ecode?cit and ecosurplus indices as well as the total seasonal ecochange statistic still appear to be good generalized indices of hydrologic alteration.Furthermore,the eco-?ow statistics are computed in a manner that is independent of other IHA statistics, hence they are statistical aggregates of other indicators and their application may eliminate some of the statistical redundancy and
Y.Gao et al./Journal of Hydrology374(2009)136–147143
intercorrelation issues that plague other more commonly used statistics.Although nine eco-?ow statistics are introduced here,it is our intention to advance only a few such statistics to avoid intercorrelation.
Our results are speci?c to the two data sets employed.Future work should be conducted to extend our analyses using other data sets where reservoir operating rules are better understood and controlled,other types of river regulation schemes,as well as other methods for selecting ERHI’s including the bootstrap approach introduced by Yu et al.(1998)and the genetic programming and autecology matrix approaches introduced by Yang et al.(2008).In addition,future research should evaluate other recently
(a) Simulated Data Set
0.20.40.60.8
1Annual Ecodeficit Annual Ecosurplus Winter Ecodeficit Winter Ecosurplus Spring Ecodeficit Spring Ecosuplus Summer Ecodeficit Summer Ecosurplus Total Seasonal Ecochange
DHRAM Score
P e a r s o n 's r
PC1PC2PC3PC4
(b) Simulated Data Set
0.20.40.60.8
1Annual Ecodeficit Annual Ecosurplus Winter Ecodeficit Winter Ecosurplus Spring Ecodeficit Spring Ecosuplus Summer Ecodeficit Summer Ecosurplus Total Seasonal Ecochange
DHRAM Score
K e n d a l l 's T a u
PC1
PC2
PC3PC4
(c) Empirical Data Set
0.20.40.60.8Annual Ecodeficit Annual Ecosurplus Winter Ecodeficit Winter Ecosurplus Spring Ecodeficit Spring Ecosuplus Summer Ecodeficit Summer Ecosurplus Total Seasonal Ecochange
DHRAM Score
P e a r s o n 's r
PC1
PC2
PC3PC4
(d) Empirical Data Set
0.20.40.60.8Annual Ecodeficit Annual Ecosurplus Winter Ecodeficit Winter Ecosurplus Spring Ecodeficit Spring Ecosuplus Summer Ecodeficit Summer Ecosurplus Total Seasonal Ecochange
DHRAM Score
K e n d a l l 's T a u
PC1PC2PC3PC4
Fig.7.Absolute values of Pearson’s r and Kendall’s Tau between the generalized index and the ?rst 4PCs of the simulated data set (a and b)and the empirical data set (c and d).
144Y.Gao et al./Journal of Hydrology 374(2009)136–147
introduced generalized indices of hydrologic alteration,such the index D o introduced in Eq.(4)of Shiau and Wu(2007)and Eqs.
(1)and(2)of Shiau and Wu(2006)and the indices recommended by Monk et al.(2007).Importantly,future research should also address systematic approaches for integrating indicators of hydrologic alteration into studies which seek to integrate the tradeoffs among various hydrologic and ecologic factors into planning studies(Loucks2006).
Generally,small values of the ecode?cit/ecosurplus correspond to low values of hydrologic alteration.However,unlike DHRAM scores,which enable water resources managers to determine the level of risks that a particular reservoir regulation scheme has on a river,the ecode?cit/ecosurplus does not yet include the level of risks.Future research should:(1)investigate the hydrologic and ecological signi?cance of the values of ecode?cit/ecosurplus needed to fully address the ecologically-based environmental?ow requirement;and(2)establish a system to classify what level of ecode?cit/ecosurplus is acceptable and unacceptable for a particu-lar reservoir operation in a river.
Acknowledgements
The?rst author received an EGU Young Scientist Outstanding Poster Presentation award for her poster presentation of this re-search at the European Geosciences Union General Assembly 2008in Vienna,Austria–Hydrological Sciences Division.This re-search was supported in part by a grant from the US Environ-mental Protection Agency’s(EPA)Science to Achieve Results (STAR)program.Although the research described in this manu-script has been partially funded by the US EPA(NCER Grant
Table5
Summary of PCA subset selection for the simulated data set and different subsets of the empirical data sets.
Simulated data set(n=96)Real data real
All dams(n=189)s<0.1(n=139)s<0.01(n=102)s>0.01(n=87)
PC1May?ow30-day minimum30-day minimum30-day minimum7-day minimum PC230-day minimum7-day maximum30-day maximum30-day maximum7-day maximum PC3Rise rate February?ow December?ow Fall rate February?ow
PC4Date of maximum November?ow Fall rate May?ow November?ow PC5June?ow March?ow February?ow June?ow
PC6March?ow Date of maximum High pulse duration Date of minimum PC7Rise rate Date of minimum December?ow October?ow
PC8High pulse duration Rise rate April?ow Date of maximum
Table6
Adjusted coef?cient of determination(R2-adj)of the multivariate linear regression for different subsets of the empirical data sets.
Generalized Index All Dams(n=189)s<0.1(n=139)s<0.01(n=102)s>0.01(n=87)
Annual ecode?cit0.6030.5780.6540.626
Annual ecosurplus0.6630.7380.8250.554
Winter ecode?cit0.4530.3750.5220.460
Winter ecosurplus0.9190.9400.8830.938
Spring ecode?cit0.6990.6520.5520.716
Spring ecosurplus0.5590.7560.8210.487
Summer ecode?cit0.2960.4450.3850.304
Summer ecosurplus0.9290.8570.9120.928
Total seasonal ecochange0.8070.7700.7970.818
DHRAM score0.5400.3310.5210.633
Y.Gao et al./Journal of Hydrology374(2009)136–147145
X3832386),it has not been subjected to any EPA review and therefore does not necessarily re?ect the views of the Agency, and no of?cial endorsement should be inferred.The authors are also grateful to Colin Apse and Mark Smith of the Nature Conservancy,and Jack Sieber and Brian Joyce of the Stockholm Environment Institute for their input on an early version of this manuscript;Stacey Arch?eld of the US Geological Survey for her assistance with the simulated data set;and Antarpreet Singh Jut-la and Jim Limbrunner of Tufts University their assistance in cod-ing Matlab and VBA.
Appendix A.Values of Pearson’s r and Kendall’s Tau in experiment2
(a)Pearson’s r and the corresponding p value between the generalized indices and the?rst4PCs of the simulated data set. Generalized index PC1PC2PC3PC4
r p r p r p r p Annual ecode?cit0.9870.000à0.0130.900à0.1100.2880.0510.621 Annual ecosurplusà0.1210.2410.8630.0000.2280.0260.1240.227 Winter ecode?cit0.9490.000à0.0230.8220.1080.2970.2120.038 Winter ecosurplusà0.3560.0000.5650.0000.0370.721à0.1170.255 Spring ecode?cit0.9580.0000.1330.197à0.2190.0320.0130.900 Spring ecosurplusà0.5450.0000.2190.032à0.0490.637à0.2900.004 Summer ecode?cit0.7450.000à0.5460.0000.3530.0000.0900.386 Summer ecosurplusà0.0830.4220.8830.0000.2000.0510.1250.226 Total seasonal ecochange0.9880.000à0.0510.6210.0630.5410.0710.489 DHRAM score0.7590.0000.4970.0000.2920.004à0.1880.067
(b)Kendall’s Tau and the corresponding p value between the generalized indices and the?rst4PCs of the simulated data set.
Generalized index PC1PC2PC3PC4
N P s p s p s p Annual ecode?cit0.9380.000à0.1200.086à0.2020.0040.0700.314 Annual ecosurplusà0.0860.2880.5960.0000.1960.0150.0710.383 Winter ecode?cit0.8120.000à0.0610.385à0.0420.5470.1900.007 Winter ecosurplusà0.1820.0220.6280.0000.0950.231à0.0130.874 Spring ecode?cit0.8920.000à0.0370.599à0.2300.0010.0870.212 Spring ecosurplusà0.5910.0000.2030.0120.0020.982à0.4030.000 Summer ecode?cit0.5250.000à0.5630.0000.0220.7610.1540.029 Summer ecosurplusà0.0630.4340.7270.0000.1340.0960.0990.221 Total seasonal ecochange0.9290.000à0.1280.066à0.1150.0980.0750.282 DHRAM score0.5630.0000.0920.2010.1930.0070.1530.033
(c)Pearson’s r and the corresponding p value between the generalized indices and the?rst8PCs of the empirical data set.
Generalized index PC1PC2PC3PC4PC5PC6PC7PC8
r p r P r p r p p r r p r p r p
Annual
ecode?cit
0.0680.353à0.6790.000à0.1720.0180.0010.986à0.0780.2830.0720.327à0.0750.3020.0090.900
Annual
ecosurplus
à0.2540.0000.5480.0000.2260.002à0.0280.698à0.1940.007à0.0720.3220.1670.021à0.2710.000 Winter
ecode?cit
à0.0060.935à0.3500.000à0.4480.000à0.0580.4280.0200.786à0.0250.7340.0790.283à0.2150.003
Winter
ecosurplus
à0.1090.136à0.0320.6630.7510.0000.4910.0000.0390.5920.1110.129à0.0290.688à0.1110.127 Spring
ecode?cit
0.0560.442à0.7060.0000.1030.1590.2730.0000.0930.202à0.0190.793à0.0180.805à0.0870.236 Spring
ecosurplus
à0.1630.0250.4320.0000.0270.711à0.1430.049à0.3810.0000.0730.3180.0430.553à0.3270.000
Summer
ecode?cit
0.1420.051à0.2020.0050.0370.6130.0860.238à0.1130.1210.2410.001à0.1810.0130.0540.462 Summer
ecosurplus
à0.5860.000à0.1430.050à0.1610.0270.1090.1350.1060.147à0.2950.0000.2240.002à0.1990.006 Total seasonal
ecochange
à0.4370.000à0.2030.0050.3600.0000.4060.0000.0240.744à0.0750.3060.1150.114à0.2950.000 DHRAM scoreà0.4380.000à0.3580.0000.0760.2990.1240.0890.0110.880à0.1520.0360.1730.017à0.1810.013 146Y.Gao et al./Journal of Hydrology374(2009)136–147
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(d)Kendall’s Tau and the corresponding p value between the generalized indices and the?rst8PCs of the empirical data set.
Generalized index PC1PC2PC3PC4PC5PC6PC7PC8
s p s p s p s p s p s p s p s p
Annual
ecode?cit
0.1110.023à0.6310.000à0.2240.000à0.0020.973à0.0800.1020.1060.031à0.1900.0000.0120.810
Annual
ecosurplus
à0.4650.0000.3360.0000.3440.0000.0040.939à0.1880.000à0.1300.0080.2050.000à0.0620.203 Winter
ecode?cit
0.1500.003à0.2900.000à0.4150.000à0.1350.0080.0460.363à0.0980.051à0.0990.051à0.0580.253
Winter
ecosurplus
à0.4110.0000.1560.0010.5720.0000.1820.000à0.1650.001à0.0080.8740.1070.0290.0260.605 Spring
ecode?cit
0.1160.018à0.6160.000à0.1520.0020.1160.0180.0620.2060.0090.854à0.1190.015à0.0370.450
Spring
ecosurplus
à0.2740.0000.5080.0000.2440.000à0.1680.001à0.2520.0000.0210.6760.0720.1430.0310.530 Summer
ecode?cit
0.2730.000à0.1410.006à0.0740.148à0.0600.2430.0040.9420.2700.000à0.2320.000à0.0700.171 Summer
ecosurplus
à0.5080.0000.0140.7750.0870.0770.0510.296à0.1320.007à0.3400.0000.2180.0000.0160.740 Total seasonal
ecochange
à0.4730.000à0.1000.0410.1710.0000.1450.003à0.1700.001à0.1910.0000.0970.0490.0050.915 DHRAM Scoreà0.3430.000à0.2220.0000.0880.0850.1120.028à0.0500.321à0.1760.0010.0880.0820.0260.602
Y.Gao et al./Journal of Hydrology374(2009)136–147147