An Improved Stochastic Weather Generator for Hydrological Impact ...

An Improved Stochastic Weather Generator for Hydrological Impact Studies Annie Caron, Robert Leconte and François Brissette

Abstract: A stochastic weather generator based on the WGEN model has been tested on 13 meteorological stations in Quebec, Canada. The generator, called WeaGETS, accounts for longer persistence of wet and dry spells by including second and third order Markov chain models. It also includes regional correction factors to adjust the precipitation percentile values as simulated by the WGEN model with respect to observed precipitation. This is a first step toward the development of a model to construct basin scale projections of future changes in climate intended for hydrological impact studies. A direct validation of the generator using selected extreme indices of precipitation has shown that the modified generator generally performed better than WGEN at simulating daily precipitation distribution, quantity and occurrence. Some discrepancies still remained or were amplified which appear to be season-related, suggesting recourse to seasonal correction factors. However, because the generator is aimed at developing climate change projections, no additional parameters were introduced in the model to keep it as parsimonious as possible. WeaGETS was indirectly validated by conducting a series of hydrological modelling experiments on the Châteauguay River Basin located in southern Quebec. Results of the simulations show that WeaGETS was able to adequately represent the duration of summer low flow events as well as the annual direct runoff. However an overestimation of the peak flows was observed for the more extreme flood events with return periods exceeding 50 years. Whether or not such an overestimation is solely caused by the generator overestimating extreme precipitation events and/or consistent combinations of precipitation and temperature needs to be further addressed through additional modelling experiments on various watersheds and with more observed climatic data before drawing definitive conclusions. Résumé : Un générateur météorologique stochastique basé sur le modèle WGEN a été testé sur 13 stations météorologiques dans la province du Québec au Canada. Le générateur, appelé WeaGETS, tient compte d’une plus grande persistance d’épisodes de sécheresse et d’événements pluvieux par l’inclusion de chaines de Markov du second et troisième ordre dans le processus de génération des occurrences de jours secs et pluvieux. Il inclut également un facteur de correction pour les valeurs des percentiles de précipitation simulées par le modèle WGEN. Il s’agit d’une première étape pour construire des projections climatiques à l’échelle du bassin, applicables aux études d’impact en hydrologie. Une validation directe du générateur par Annie Caron1,2, Robert Leconte1 and François Brissette1 1 2

Département de génie de la construction, École de technologie supérieure, Montréal, QC H3C 1K3 Currently at SNC-Lavalin inc., Montréal, QC H2Z 1Z3

Submitted April 2007; accepted April 2008. Written comments on this paper will be accepted until March 2009. Canadian Water Resources Journal Revue canadienne des ressources hydriques

Vol. 33(3): 233–256 (2008)

© 2008 Canadian Water Resources Association

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Canadian Water Resources Journal/Revue canadienne des ressources hydriques

l’emploi d’indices d’extrêmes de précipitation a démontré que le générateur modifié offre généralement une performance supérieure à WGEN pour simuler la distribution, la quantité et l’occurrence des précipitations journalières. Toutefois, certains écarts demeurent ou sont amplifiés par rapport aux observations. Ces écarts pourraient dépendre de la saison, suggérant le recours à des facteurs de correction saisonniers. Toutefois, puisque le générateur est destiné à produire des projections climatiques, l’ajout de nouveaux facteurs de correction n’a pas été retenu de manière à conserver le caractère parcimonieux du modèle. WeaGETS a également été validé de manière indirecte par le biais d’expériences de modélisation hydrologique effectuées sur le bassin versant de la rivière Châteauguay, dans le sud du Québec. Les résultats des simulations montrent que WeaGETS permet de simuler la durée d’étiages estivaux de même que le volume annuel de ruissellement direct. Toutefois, une surestimation des débits de pointe a été observée pour les événements les plus extrêmes dont les périodes de retour dépassent 50 années. L’hypothèse que cette surestimation soit causée par le générateur doit être scrutée en de plus amples détails par le biais d’autres expériences de modélisation sur différents bassins versants et avec davantage d’observations météorologiques, avant d’en tirer des conclusions définitives.

Introduction There is growing evidence that the climate of the earth will change as a consequence of anthropogenic greenhouse gas (GHG) emissions, with repercussions on our daily lives and the environment that are yet to be assessed. According to global climate models (GCMs), the increase in anthropogenic greenhouse gas emissions, such as CO2, is modifying the chemical composition of the atmosphere such that the global annual air temperature will increase in a likely range of 1.1 to 6.4oC over the course of the century with respect to current climate conditions (IPCC, 2007). Precipitation regimes will also be affected, with changes in magnitude and direction more uncertain

than for temperature. Adaptation strategies will need to be implemented to cope with climate change. As an example, it is likely that reservoir operating rules will need to be modified, as streamflow will be affected by changes in precipitation and temperature regimes. Because GCMs offer coarse spatial resolution (in the order of 350 × 350 km), impact analyses require downscaling the climate projections produced by these models at the local scale (i.e., commensurable with the impact assessment at hand). Regional climate projections can be generated either through statistical or dynamical downscaling methods. In statistical downscaling, the basic assumption is that regional climate is conditioned by the large scale climatic state as well as local/regional physiographic features (Wilby et al., 2004). This allows the derivation of statistical relationships between largescale climate variables, the predictors, and local/regional variables, the predictands. Dynamical downscaling involves solving physically based equations describing atmospheric flow and the exchange of heat, humidity and momentum with the earth surface at the regional scale. This Limited Area Model, of Regional Climate Model (RCM) runs at higher resolution than GCM (spatial resolution typically the order of 50 × 50 km) over a limited area of the globe, and uses boundary conditions from GCM results. Statistical downscaling methods offer a number of advantages over regional climate models. First, they can directly incorporate the observational record of the region and thus can be used to provide site-specific information. Secondly, they are less expensive than computationally intensive dynamical downscaling approaches. However, they assume that the statistical relationships between the large scale predictors and the predictand remain unaltered in a changing climate, as the physical links are always there, but the statistical combination of these processes and their relative importance in the evolvement of the predictand are assumed to be stationary. A limitation of statistical downscaling methods is that they can only provide information at locations where observations are available. One approach to downscale GCM climate information at the local scale is through the use of stochastic weather generators. According to Wilks and Wilby (1999), weather generators can be considered as sophisticated random generators that replicate the statistical attributes of a local weather variable (e.g., © 2008 Canadian Water Resources Association

Caron, Leconte and Brissette

mean, variance) but not observed weather sequences. Weather generators can be adapted for statistical downscaling by conditioning their parameters on large-scale weather predictors (Wilby et al., 2004) such as those simulated by GCMs, offering the possibility of producing projections of future changes in climate at the local scale. This paper will assess the performance of WeaGETS (which stands for Weather Generator of the École de Technologie Supérieure) (Caron, 2006), a stochastic weather generator inspired by the WGEN approach developed by Richardson (1981), to simulate daily precipitation occurrence and quantity at various weather stations representative of the climatic regimes in Quebec, Canada. This will be done using a direct approach (i.e., by comparing selected precipitation indices computed from observed and simulated precipitation time series); and also by an indirect approach through a comparison of observed versus simulated hydrological regimes in a watershed located in southern Quebec.

Why a WGEN-Based Approach? Semenov (2007) identified a number of criteria for climate projections to be useful in the assessment of impact of climate change based on process-based models. Among others, the projections should include the full set of climate variables required by the impact model with at least daily resolution. For hydrological impact studies, desired variables include precipitation and temperature as most lumped models make use of these data as input. A majority of existing weather generators,including WGEN and LARS-WG,simulate these basic climate variables. Other variables such as solar radiation, wind speed and relative humidity are also required in the more physically-based and often spatially distributed hydrological models. Examples of weather generators simulating more comprehensive climate data sets include WXGEN (Williams, 1995) and CLIGEN (Zhang and Garbrecht, 2003). An attractive feature of WGEN-type models is their parsimony. This is another desired characteristic of stochastic weather models when used to develop projections of future changes in climate, as only a reduced number of parameters need to be modified using downscaling approaches to generate the projections.

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Note that there are drawbacks inherent to using a WGEN approach, which typically simulates wet and dry series indirectly using a first-order two-state (wet and dry) Markov chain, in climate change studies. First, models based on this approach have a limited memory of rare events and, as an example, could fail to simulate accurately long dry series at certain locations (Racsko et al., 1991). Other approaches that better reproduce the full characteristics of observed wet/dry spells lengths could have been considered. LARS-WG, for example, performs better than WGEN as every single series from the observed precipitation data is represented in the semi-empirical distributions used to generate the series (Qian et al., 2004; Semenov et al., 1998). However, being a reshuffling approach, LARSWG cannot generate wet/dry series (precipitation intensities, wet/dry spells) outside from the range for which it is calibrated. This can be problematic if the observations used in the calibration process do not contain rare events, as such extreme events will not be generated even if long time series (e.g., 100-200 years) are simulated. This is a shortcoming in the context of risk analysis—a criterion identified by Semenov (2007) for constructing high resolution climate change scenarios. The above limitation is not found with WGEN-type models as the transition probabilities used in these models can result in the generation of extreme events falling outside of the calibration range. Also, if an extreme event is included in a rather small series of observations, say ten to 15 years, such an event may be given an unreasonably strong weight in the generating process using LARS-WG. Finally, there is no robust procedure for downscaling the parameters describing climate variability in LARS-WG (Semenov and Barrow, 1997) as model parsimony is an issue (e.g., 21 parameters to describe the distribution of wet/dry spell length, see Caron, 2006). As a consequence, climate change impact studies conducted so far with LARS-WG assumed no changes in variability (Weiss et al., 2003; Khan et al., 2006). An exception is the study by Semenov (2007), who introduced changes in duration of monthly mean dry and wet series by using daily precipitation from a RCM. However, RCM simulations of current climate have not been extensively tested and there is a strong need for a rigorous assessment of current RCM output to evaluate the confidence in RCM simulations (Hay et al., 2002). Furthermore, RCM output typically has a significantly higher number of precipitation days than measured at © 2008 Canadian Water Resources Association

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individual stations, which occurs in part because RCM precipitation represents an area, not a point (Hay et al., 2002). The direct use of daily precipitation occurrence retrieved from RCM runs to estimate changes in variability is therefore prone to errors. Techniques to adjust WGEN parameters for climate change studies have been proposed that further advocate using a WGEN-type approach over other weather generation techniques for climate change studies. For example, Wilks (1992) presented an adjustment procedure based on exploiting the link between daily statistics of observations and the means and variances of monthlyaveraged data provided by GCMs. Secondly, as suggested by Wilby et al. (2004), changes to parameters governing wet/dry spell lengths in WGEN-type models can affect simulated temperature even before modifications are applied to the parameters governing these variables. This is because WGEN-type models condition temperature (and other variables such as radiation) generation on whether or not there is precipitation in a given day—a characteristic also found in other generators such as LARS-WG. Although one can argue that the accurate and joint modification of parameters for both precipitation and temperature is, in theory at least, a relevant argument for selecting an appropriate weather generating scheme, such criteria cannot in fact be used to choose one type over another as this is a problem inherent to all weather generators. This problem was also recognized by Wilks (1992) who notes that these additional changes are generally small unless very extreme changes in precipitation climatology are expected.

Methodology The WGEN Approach to Simulate Daily Precipitation

WGEN (Richardson, 1981; Richardson and Wright, 1984) simulates both the daily precipitation occurrence and quantity. A first-order two-states Markov chain approach is used to simulate precipitation occurrence Xi(k) at site k on day i, which also allows for some persistence of wet and dry events. A random number ut(k) between 0 and 1 is drawn from a uniform distribution, and compared with a critical transitional

probability that depends on the state, wet (1) or dry (0), of the previous day i-1 (1) in which p01 is the probability of a wet day following a dry day, and p11 is the probability of a wet day following a wet day. A wet day is simulated when the random number is less than this critical probability, and a dry day is simulated otherwise (2) The transitional probabilities p01 and p11 are calculated from series of daily observations of precipitation. The seasonal variability of the transitional probabilities is captured by partitioning the year in short time periods, say t = 14 or 28 days, and by calculating the probabilities for each time period. Richardson (1981) adjusts a finite Fourier series over the computed t-day transitional probabilities, from which daily values can be extracted. Richardson and Wright (1984) assume that the transitional probabilities are constant for a given month but vary from month to month. Daily precipitation amounts at site ri(k) are obtained by pooling a second random number vi(k) from a uniform distribution, which is be used to invert a probability density function that best describes rainfall quantities. Among the most frequently used distributions for daily rainfall amounts are the oneparameter exponential (Todorovic and Woolhiser, 1974) and the two-parameter gamma (Buishand, 1978) distributions. The gamma distribution is included in WGEN (Richardson and Wright, 1984) (3) where α and β are the shape and scale parameters, respectively, describing the gamma distribution, calculated using maximum likelihood estimators (Haan, 1977). The seasonal variability of these parameters can be accounted for by a procedure similar to the one presented for parameters p01 and p11 above.



The Weather Generator WeaGETS

WGEN reflects some persistence of wet and dry day events. However, wet and dry spells extending over many days can only be imperfectly modelled, because of the short-term memory (one day) due to the use of a first-order Markov chain, which cannot produce accurate persistence of wet/dry events (Semenov et al., 1998; Katz and Parlange, 1998). Also, previous studies (e.g., Katz et al., 2002) have consistently demonstrated that the two-parameter Gamma distribution underestimates daily precipitation quantities for the more extreme events. Modifications were proposed to WGEN to better account for the underestimation of the more extreme precipitation events and to correct for the misrepresentation of the precipitation occurrence. The resulting generator, called WeaGETS, is now introduced. Modelling the daily precipitation amounts. There is evidence that the distribution of hydrologic and climatic variables, including daily maximum precipitation amount, are heavy tailed (Katz et al., 2002; Buishand, 1991). An example of a heavy tailed distribution is the three-parameter generalized extreme value distribution with the shape parameter less than zero, also called the Fréchet distribution (Bury, 1999). Although heavy-tailed distributions, such as the Fréchet, have been proposed to simulate extremes of precipitation (Kharin and Zwiers, 2000), an approach based on a correction factor was retained here to adjust for the underestimation of daily precipitation inherent in using gamma distributions. The main reason for choosing this approach is that heavy tailed distributions, while enhancing estimation of precipitation extremes, may also deteriorate results for the more moderate to low precipitation events. A correction factor would only need to be applied to the portions of the distribution function that produce the underestimation, thereby ensuring an improved fit over the full range of precipitation events, not just over the extreme values. While it is true in theory that applying a correction factor would introduce an unwanted discontinuity in the precipitation distribution function, in practice its effect will be small as will be seen in the upcoming results.

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The correction factor proposed in this study is a multiplicative factor that adjusts the simulated precipitation percentile values to the observed ones as (4) where prec_perobserved and prec_persmulated are the precipitation percentile values associated with daily observed and simulated precipitation, respectively. Modelling the precipitation occurrence. When time series of precipitation displays extended wet or dry spells, a first-order two-state (dry or wet) Markov model may fail to adequately represent the precipitation occurrence, and a model with longer memory is needed. Second and third-order models were introduced in WeaGETS to add more memory to the precipitation generating process in an attempt to cover a wider range of climate characteristics. In a second-order two-state Markov chain model, the state of a given day will depend on the states of the two previous days. A total of eight transitional probabilities thus need to be provided, depicting all possible combinations of given wet/dry states for the two days preceding the day to be established. However, because the two states that are modelled are mutually exclusive, only four transitional probabilities need to be calculated from the observed precipitation time series, and the other four can be retrieved from them. The equation describing the transitional probabilities of the second-order Markov model is

(5)

A total of eight transitional probabilities are to be computed from observations in a third-order two-states Markov model (p0001, p1111, etc.). Further increasing the order of the Markov model is discouraged, as more parameters will have to be adjusted to adequately simulate a changed climate. Various approaches have been proposed to adjust the transitional probabilities of first-order models to a changed climate (Wilks, 1992; Wilby and Wigley, 2000). These and other approaches have yet to be investigated with higher order Markov models. © 2008 Canadian Water Resources Association

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Modelling daily temperature. WeaGETS can also generate times series of daily maximum and minimum air temperature. The original WGEN algorithm (Richardson, 1981) has been incorporated in WeaGETS, which is a first-order linear regressive multivariate generation model suggested by Matalas (1967) for generating residual time series of air temperature. Means and variances of temperature are approximated by Fourier series through the year, which provided better results than the use of cosine functions reported in the subsequent WGEN version of Richardson and Wright (1984) (Semenov et al., 1998).

Evaluation Criteria Direct and indirect performance criteria were used to evaluate and compare WeaGETS against WGEN. The parameters of both WGEN and WeaGETS were first estimated using observed daily precipitation, minimum and maximum air temperature data from Environment Canada’s National Climate Data and Information Archive. A total of 13 weather stations located in Quebec (Caron, 2006) were selected to account for a range of temperature and precipitation regimes, as the regional variability, forced by numerous factors including land mass, orography and the proximity of oceanic basins, is strongly non-homogeneous across the province. The weather stations are listed in Table 1, along with selected 1971-2000 temperature and precipitation normals extracted from Environment Canada’s database. Observed time series lengths are 30 or 31 years. This compares well with Richardson (1981), who used 20 years of data to estimate the parameters of the precipitation model in WGEN. Missing values accounted for less than 1.5% of the observations. No attempts were made to fill in the missing gaps as the values where dispersed in the database and only marginally affected the determination of the weather generators’ parameters. The parameter estimation phase, which can be viewed as a calibration step, was followed by a validation phase through a comparison of the generated weather time series against station observations using selected indices, and also indirectly through a sequence of hydrological modelling experiments. These so-called ‘direct’ and ‘indirect’ vadidation phases are now introduced. Note that the split-sample approach by which a model is calibrated

on a given time period, say during wet and cool years, and validated using another time window, for example during dry and warm years, is not relevant here as both WGEN and WeaGETS by definition generate a stationary climate. Direct performance criteria. Selected indices describing precipitation occurrence, quantity and distribution were computed from station observations and compared against those retrieved from WGEN and WeaGETS precipitation time series generated at the same stations. The selected indices originate from the STARDEX (Statistical and Regional dynamical Downscaling of Extremes for European Regions) research project (STARDEX, 2007), whose main objective was to provide a rigorous and systematic intercomparison and evaluation of various downscaling methods for the construction of projections of climatic extremes encompassing a range of climate regimes across Europe. Note that STARDEX indices were used to evaluate statistical downscaling models in regions other than Europe, for example Asia (Wetterhall et al., 2006). More specifically, the indices retained in this study include five of the six precipitation core indices recommended by STARDEX for the analysis of observed change in extremes, evaluating the performance of the downscaling models and quantifying expected changes in extremes in the future. The indices were directly issued from the STARDEX Diagnostic Extreme Indices Software, Version 3.1.1, available online (STARDEX, 2007). Differences greater than 5% (arbitrarily set up) were identified to assess the performance of WeaGETS as compared to WGEN in statistically simulating the observed daily precipitation occurrence and intensity. Simulated precipitation distributions were also compared against observed distributions. Kolmogorov-Smirnov tests were carried out to establish whether or not the simulated precipitation distributions were statistically similar to the observed distributions at a 5% level of significance. Results for selected Quebec stations are presented in this paper. No temperature indices were computed in this work as WeaGETS and WGEN share the same temperature generating algorithms. Indirect performance criteria. Synthetic time series of daily precipitation and temperature values were used as input to a hydrological model. Resulting simulated hydrological variables were compared against values © 2008 Canadian Water Resources Association

71°03’ 78°05’ 77°49’ 68°13’ 74°03’ 71°23’ 66°49’ 66°15’ 71°41’ 73°41 73°51

45°28’

48°47’

58°28’

49°46’

48°36’

45°07’

46°48’

54°48’

50°13’

45°26’

45°10’

45°13’

Dorval

Gaspé

Inukjuak

Matagami

Mont-Joli

Ormstown

Quebec City

Schefferville

Sept-Îles

Sherbrooke

Ste-Clothilde

Ste-Martine

64°29’

71°00’

48°20’

Bagotville

Long.

Lat.

Station

74

56

241

53

522

74

46

52

281

26

33

76

1971-2001

1971-2000

1973-2003

1973-2003

1973-2003

1973-2003

1971-2000

1973-2003

1974-2003

1974-2003

1973-2003

1971-2000

1973-2003

Period

(m)

159

Calibration

Alt.

661 764 752 265 618 606 775 924 408 757 874 826 813

951 979 1117 460 906 929 949 1230 823 1156 1144 1028 984

Rain (mm)

(mm)

Precip

11.3

11.2

10.2

5.4

-0.5

9.0

11.3

7.5

5.5

-3.4

8.6

11.1

7.9

(oC)

Tmax

1.4

1.3

-2.0

-3.8

-10.0

-1.0

1.5

-1.3

-6.9

-10.6

-2.7

1.4

-3.2

(oC)

Tmin

114

111

101

30.2

21.1

93.6

115.3

67

69.6

4.8

71.8

112.7

83.4

18.4

18.3

36

48

104.1

31.0

17.6

22.1

82.9

112.3

30.0

16.9

50.9

(days)

(days)

Tmin 20oC

Tmax

129

153

192

173

216

182

155

177

195

164

162

163

200

(days)

>0.2mm

Precip

34

34

38

38

22

41

31

28

25

9

35

32

27

(days)

>10mm

Precip

Table 1. Weather stations used in the direct performance assessment. Stations are also shown in Figure 5. Precipitation and temperature data are from Environment Canada’s climate data base.

Caron, Leconte and Brissette 239


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simulated by the model using daily meteorological observations. The HSAMI hydrological model (Bisson and Roberge, 1983; Fortin, 2000) was utilized in this study to simulate flows of the Châteauguay River Basin, a watershed located south of Montreal (QC) that discharges into the St-Lawrence River. The HSAMI model is a lumped, conceptual model developed by Hydro-Québec to produce flow simulations and forecasts for managing its water resources systems. The model uses daily precipitation, minimum and maximum temperature and simulates, in continuous mode, the complete hydrological cycle of northern watersheds. Precipitation is partitioned into rainfall or snow according to a threshold temperature index method. Snowmelt is simulated using a degreeday approach. A production function, consisting of three interconnected linear reservoirs, simulates the vertical motion of water in a soil column, including infiltration and percolation in the deep saturated zone layer. Evapotranspiration contributes to deplete the unsaturated soil zone. The water produced is routed through the watershed outlet according to the unit hydrograph concept. The model can also account for

the presence of reservoirs in the routing the flow to the outlet. Figure 1 schematises the HSAMI model. The drainage area of the Châteauguay River Basin (CRB) is 2543 km2. It is located on the south shore of the St-Lawrence River, with approximately 60% in Canada and 40% in the United States. The mean annual precipitation is about 1000 mm. The probability of observing a daily precipitation of more than 0.2 mm is approximately 50% (Fortin et al., 2006). Topography is very gentle in the northern agricultural and urbanised portion of the basin, while the southern portion, which reaches the Appalachian range, is mostly forested and hilly. The flow regime is dominated by snowmelt runoff with flows that can exceed 800 m3/s. In contrast, summer flows can be as low as 2 m3/s. However, some summer floods can reach 300 m3/s, as a result of strong convective systems responsible for heavy storm events. The mean annual flow rate is approximately 35 m3/s (Awadallah et al., 1999). Roy (2000) established the 20-year and 100-year summer-fall floods at 381 and 513 m3/s, respectively. The 20-year and 100-year rainfall of 24-h duration have been estimated at 96 and 124 mm, respectively, using the data published

Figure 1. The HSAMI hydrological model.



241

•

•

Direct annual runoff. This is the portion of the total precipitation that does not infiltrate. It corresponds to approximately 40% of the total amount of precipitation in the CRB, based on estimates of annual precipitation and average flow rate; Magnitude of spring and summer-fall peak flows.

Results and Discussion Direct Performance Assessment

Figure 2. The Châteauguay River Basin (CRB), Canada.

by Hogg and Carr (1985). Location of the CRB is presented in Figure 2. Because weather generators can only reproduce time series of meteorological variables that are statistically similar to observations, it is not possible to perform a direct comparison between simulated and observed streamflows. Rather, the value of a hydrological variable (e.g., spring peak flow) simulated by HSAMI using meteorological observations was compared against the range of values of the same variable, this time simulated using WeaGETS realisations of the current climate. The hydrological indices selected for performance assessment are: •

Duration of consecutive low flow values. A threshold flow value of 12 m3/s, corresponding to the lowest mean monthly flow recorded in the CRB, was used to establish periods of low flow regimes;

Thirty 300-year synthetic time series of daily precipitation, maximum and minimum temperature were produced for every station listed in Table 1 with WGEN and WeaGETS to assess the performance of each generator in statistically reproducing the observed time series. The number and length of the simulated series were selected to obtain convergence of results and to generate more extreme events. Results pertaining to WeaGETS third-order Markov chain model using a gamma distribution function with annual correction factors are presented in this paper. A more exhaustive evaluation can be found in Caron (2006). Table 2 presents seasonal values of STARDEX statistical indices of precipitation occurrence, quantities and distribution for Dorval, Quebec City and MontJoli (see Figure 5 for location of the stations). Seasons are denoted as follow: DJF for winter, MAM for spring, JJA for summer and SON for fall. These stations display a range of annual precipitation quantities (9291230 mm/year, see Table 1) and temperatures (Tmax = 7.5-11.1oC; Tmin = -1.3–1.4oC). WGEN model. Generally, it was found for both distribution functions that simulated precipitation by WGEN is underestimated at the higher percentile values (i.e., above 80%) while an overestimation is noted at the lower percentile values (between 20 and 60%) for most of the 13 stations analyzed (Caron, 2006). For example, the 99% percentile of the precipitation amounts at the Dorval Station, located in southern Quebec, was underestimated by 14% for the fall season using a 2-parameter Gamma distribution (Caron, 2006), with an equivalent underestimation of the maximum three-day rainfall total for the same season. A Q-Q plot of the daily precipitation for the © 2008 Canadian Water Resources Association

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Table 2. Comparison between STARDEX precipitation distribution, quantities and occurrence indices computed using observed (Obs), WGEN (WG) and WeaGETS (WGTS) time series for selected weather stations in Quebec: a) Dorval; b) Québec City; c) Mont-Joli. Definitions of the indices are presented in the Appendix. Seasons are as follows: June, July and August (JJA); September, October and November (SON); December, January and February (DJF); March, April and May (MAM). The bold numbers indicate simulated values which are different by more than 5% from the corresponding observed values. A day is considered as wet when precipitation is ≥ 0.25 mm. See Table 1 for the calibration period of each station. a) Dorval Station Dorval Station

JJA Obs

WG

SON WGTS

Obs

WG

DJF WGTS

Obs

WG

MAM WGTS

Obs

WG

WGTS

Precip. distribution - prec_per60 - prec_per80 - prec_per99

6.20 7.06 13.22 13.42 37.65 37.42

6.28 12.98 38.23

5.43 6.20 10.68 11.93 40.29 34.61

5.23 11.19 38.52

3.85 4.75 8.77 9.00 26.80 26.48

3.75 7.90 27.49

4.96 5.69 10.37 10.55 28.61 29.19

4.88 9.94 30.36

Precip. quantity - rain_per_rainday - max_rain_3d - prec>10mm

7.75 8.17 51.58 50.00 9.20 8.98

7.73 50.90 9.03

6.90 7.28 53.77 46.26 8.30 8.22

6.73 47.18 8.18

5.19 5.54 37.87 36.04 7.33 6.32

4.93 36.74 6.29

6.13 6.46 40.17 40.49 7.70 7.24

6.03 41.66 7.31

Precip. occurrence - consec_dry_day - wet_day_pers - dry_day_pers - p10

8.43 10.02 0.44 0.41 0.66 0.69 0.53 0.58

8.86 0.45 0.67 0.54

6.69 0.52 0.56 0.47

9.70 10.28 0.53 0.48 0.68 0.69 0.46 0.51

9.65 0.53 0.67 0.46

8.77 0.49 0.64 0.49

9.43 0.44 0.67 0.55

8.70 0.48 0.64 0.51

7.80 0.52 0.57 0.47

7.77 0.46 0.61 0.54

b) Quebec City Station Quebec City Station

JJA Obs

WG

SON WGTS

Obs

WG

DJF WGTS

Obs

WG

MAM WGTS

Obs

WG

WGTS


7.51 8.00 14.03 15.09 43.54 42.88

7.39 14.85 43.41

6.34 6.87 12.04 12.88 41.77 37.54

6.16 12.50 38.22

4.09 4.93 8.88 9.17 30.09 27.07

4.02 8.31 28.50

6.00 6.21 12.05 11.52 33.12 32.41

5.45 11.00 33.31


8.77 9.19 58.61 58.95 11.43 11.71

8.84 60.06 11.73

7.59 7.90 56.06 51.81 10.77 10.32

7.52 52.81 10.24

5.43 5.65 42.36 38.26 8.06 7.28

5.15 39.62 7.42

6.90 5.65 46.08 45.38 9.43 8.52

5.15 46.36 8.59

6.73 0.61 0.55 0.39

9.47 10.14 0.56 0.52 0.67 0.69 0.43 0.47

10.04 0.56 0.67 0.43


8.33 0.49 0.63 0.50

8.94 0.47 0.65 0.52

8.48 0.50 0.63 0.49

8.00 0.55 0.61 0.45

8.35 0.49 0.63 0.50

7.98 0.52 0.61 0.47

7.70 0.60 0.55 0.39

7.29 0.54 0.59 0.46



243

c) Mont-Joli Station Mont-Joli Station

JJA Obs

WG

SON WGTS

Obs

WG

DJF WGTS

Obs

WG

MAM WGTS

Obs

WG

WGTS


6.07 6.49 11.42 12.00 33.34 32.89

5.84 11.88 37.51

4.75 5.37 9.18 9.94 33.17 28.09

4.63 9.43 31.00

3.43 4.09 7.02 7.48 25.79 21.97

3.45 6.85 23.65

4.83 5.01 8.77 9.13 26.65 24.60

4.37 8.66 26.80


6.97 7.36 48.26 44.59 8.50 8.22

8.84 60.06 11.73

5.84 6.11 45.71 38.57 7.00 6.93

5.79 41.00 7.10

4.37 4.64 37.72 31.42 6.00 5.34

4.29 33.11 5.65

5.52 5.61 40.47 34.74 2.28 2.14

4.29 33.11 5.65

6.23 0.63 0.54 0.36

10.57 10.21 0.56 0.49 0.67 0.69 0.43 0.50

9.99 0.54 0.67 0.45


9.20 0.44 0.65 0.55

9.67 0.42 0.68 0.57

9.05 0.45 0.66 0.54

7.50 0.51 0.61 0.49

8.62 0.45 0.64 0.54

fall season at Dorval is presented in Figure 3 (20, 40, 50, 60, 80, 90, 95 and 99 percentiles shown), which shows the underestimation of precipitation of WGEN at higher percentile values. The average amount of rain per wet day was overestimated by WGEN by 6-7% in all four seasons at that station. Precipitation occurrence was also incorrectly simulated (e.g., summer and fall seasons at all stations, see Table 2). Similar results for other stations in Quebec suggest that the gamma distribution is not appropriate for modelling extreme events, at least in that province. The gamma distribution is recognized to have limitations for extreme simulations (Wilks, 1995). Given that extremes are more likely to occur under a changed climate (Katz and Brown, 1994), WGEN needs to be modified to be used for climate change impact studies. Synthetic temperature time series generated using the original WGEN algorithm of Richardson (1981), generally displayed similar monthly means and variability of daily values as compared to station observations for all stations analysed. Typical results are shown in Figure 4 for the maximum daily temperatures at the Dorval station. Note that the standard deviation of maximum temperature was underestimated for some winter-spring months (November, January, April) while overestimated in July. A possible explanation

8.19 0.49 0.62 0.49

5.97 0.64 0.53 0.35

6.91 0.56 0.57 0.43

for this discrepancy may be related to the smoothing effect introduced by the Fourier series applied to interpolate the means and variances for temperature. Semenov et al. (1998) reported that WGEN behaves poorly for temperature when mean values were close to zero. However, such conclusion does not apply here as the original WGEN procedure for temperatures was used, instead of the Richardson and Wright (1984) formulation employed by Semenov et al. This latter approach interpolates coefficients of variation for temperature instead of variances, whose large magnitudes prevented adequate fitting. WeaGETS model. A comparative performance assessment of WeaGETS and WGEN against observations is presented in Table 2. Differences between observed and simulated precipitation indices greater than 5% are highlighted in the table to facilitate a visual appreciation of the performance of each weather generator. Table 2 reveals that WeaGETS generally performed better than WGEN for indices characterizing the precipitation distribution. Note that a few corrected values notably overshot the observed target (e.g., the 99th summer percentile for MontJoli), suggesting that the correction factors may have to be seasonally adapted to better reflect various © 2008 Canadian Water Resources Association

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Table 3 shows the results of the Kolmogorov-Smirnov tests carried out at the monthly time scale to the simulated versus observed precipitation distributions. Shown in the table is the number of times the null hypothesis that the simulated distribution is similar to the observed distribution was rejected in a given month at a 5% level of significance. Again, WeaGETS performed overall better than WGEN, for all stations analysed and months considered. Note that both generators failed to correctly simulate the precipitation distribution for the month of January. Whether or not this poor performance is climate related (although winter precipitation regime is usually Figure 3. Q-Q plot of the daily precipitation for the fall season at driven by strong large scale forcings that the Dorval station. are less complex than summer mesoscale and convective systems), is caused by snow gauge undercatchment, or is simply the result of a very large recorded snow fall that was incorrectly simulated, needs to be fully investigated. The introduction of the regional correction factors Cf enhanced the overall performance of WeaGETS as compared to WGEN for generating precipitation quantities (see Table 2). This is particularly true for the mean seasonal precipitation and for the precipitation averaged over wet days. Although a notable improvement is also observed for the maximum rainfall over three days (and also five and ten days, see Caron, 2006) an underestimation still Figure 4. Comparison of monthly means and standard deviations remains, particularly during the winter of maximum daily temperatures for observed data and synthetic season. As snow accumulates during winter, the underestimation should bear minimal data generated by WGEN, Dorval station. consequences on the volume of spring weather systems affecting the precipitation regimes. runoff for the current climate, as it is generally more For instance, in fall, the meteorological systems merge influenced by total precipitation amounts, and less by meso-scale and synoptic events that are responsible individual storm events. An exception would be during for a large range of heavy precipitation. However, the the spring melt period, where an intense precipitation introduction of seasonal factors would reduce model event can exacerbate the snowmelt input. Under a parsimony, an undesirable feature for climate change changed climate, where precipitation as rainfall and impacts studies, as more parameters would need to be mid-season thaw events are more likely to occur, such adjusted to take into account the evolution of climate. an underestimation may have non negligible effects, and For that reason, time invariant correction factors were more research is required to enhance the performance kept in WeaGETS, although these have their limits as of WeaGETS for those particular hydrometeorological results of Mont-Joli have revealed. conditions. © 2008 Canadian Water Resources Association


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Table 3. Fisher and Student–t tests for selected STARDEX indices computed from WGEN (WG) and WeaGETS (WGTS) precipitation time series. The numbers below indicate the number of times a given simulated index was shown to be statistically different at a 5% level of significance from the corresponding observed index. Thirty time series of 300 years were generated at each station with both generators. See Table 1 for the calibration period of each station. Dorval STARDEX indices

Fisher

Quebec City Student-t

WG

WGTS

WG

WGTS

0 0 15 0

0 0 3 0

29 0 29 0

0 0 0 0

Fisher WG

Mont-Joli

Student-t

WGTS

Fisher

Student-t

WG

WGTS

WG

WGTS

WG

WGTS

0 0 0 0

0 1 3 0

0 0 0 0

1 0 0 0

0 0 0 3

0 0 8 1

0 0 0 0

0 0 1 0

0 30 1 1

0 0 0 0

0 0 0 0

0 0 0 0

27 30 28 0

0 1 0 0

30 0 5 30

0 30 24 0

14 0 0 3

0 0 0 0

0 0 0 0

18 30 28 9

0 0 0 0

8 1 0 0

0 28 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 30 0 0

0 0 0 0

Summer

consec_dry_day wet_day_pers dry_day_pers rain_per_rainday

0 0 0 0 Fall


6 0 2 0

3 0 7 0

0 30 26 0

0 0 0 0

0 7 0 1


28 0 28 0

30 0 18 6

0 30 30 0

28 0 0 2

30 14 26 30


0 0 0 0

0 0 0 0

0 30 0 0

0 0 0 0

Winter

Spring

2 0 0 0

Adding more memory to the precipitation occurrence process also enhanced the performance of WeaGETS to reproduce longer series of wet and dry events (see Table 2). Index values for wet and dry day persistence, seasonal dry and wet spell mean and P00 and P10 are close to those retrieved from the observations. A few dissimilarities remain, for instance with the standard deviations of the wet and dry spell durations, suggesting that WeaGETS is still experiencing difficulties in adequately generating the variability of wet and dry series. Two-way Student-t and Fisher statistical tests were conducted to compare the inter-annual mean and variance of simulated STARDEX indices against

those retrieved from the observations. Results further confirmed the superiority of WeaGETS over WGEN for all but a handful of tests. In particular, adding a third order Markov chain model clearly enhanced the performance of WeaGETS over that of WGEN for simulating the persistence of dry and wet day events (Caron, 2006). Note however that the performance of WeaGETS for the DJF (winter) season was below that of WGEN for the Dorval and Quebec City stations. Although the exact reason for this behaviour is yet to be fully assessed, an initial investigation points to a possible incorrect simulation of the daily transitional probabilities, which may have translated into errors © 2008 Canadian Water Resources Association

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in the simulated precipitation occurrence. More specifically, differences as large as 25% were noted between observed and fitted transitional probabilities (e.g., P0000, the probability of a dry day given that the previous three days are dry) during the winter season, which were caused by an excessive smoothing of the transitional probability function obtained by applying a Fourier finite series to the observations. Correction factors for precipitation. The weather stations used in the analysis (see Table 1) were grouped according to similarities in the values of the shape parameter of the gamma distribution function used to model the precipitation quantities. This resulted in a subdivision of the province into five areas: Gaspésie and Côte Nord (Region 1), the St-Lawrence River corridor (Region 2), Southern Quebec (Region 3), North-West Quebec (Region 4), and Northern Quebec (Region 5). Figure 5 shows the resulting regions for which representative shape distribution parameters were

derived, along with the location of the weather stations used in the analysis. For each region, annual correction factors Cf (see Equation (4)), which correspond to the mean over 30 simulations, were obtained for each station for the 20-60% and for the >80% percentile values by matching as closely as possible the generated percentile values to the observed ones and average Cf values were computed. The average Cf for the higher percentile values (>80%) are shown in Figure 5. Numbers above one indicate that the higher percentile daily precipitation quantities were underestimated using the gamma distribution function. With the exception of Region 2, a North-South downward gradient of the Cf values can be observed. Note that total annual precipitation in Quebec generally tends to increase from North to South (Environment Canada, 1986). Whether or not a relationship truly exists between Cf and climate variables is an open question that can only be answered through in-depth analyses using more weather stations. If such an assumption is proven to

Figure 5. WeaGETS precipitation correction factors for percentile values > 80%. © 2008 Canadian Water Resources Association


be true, this may point to possible linkages between the correction factor and climate related parameters, such as synoptic and mesoscale processes that exert various forcings on precipitation occurrence and intensity, and therefore to the possibility of downscaling the factor using climate projections generated from global and regional scale climate models. Indirect Performance Assessment

Seven meteorological stations located within, or in proximity to, the CRB were selected to construct a basin wide climatology following the Thiessen polygon approach (Linsley et al., 1982). Daily precipitation and air temperature covering years 1959-95 (37 years) were extracted from Environment Canada’s National Climate Data and Information Archive. The resulting virtual meteorological station is a necessary step to the modelling procedure since HSAMI is a lumped model and WeaGETS is a single-site weather generator. Multi-site generator approaches that take into account the spatial correlations at the daily scale between meteorological stations include Wilks (1998); Khalili

247

et al. (2007); and Brissette et al. (2007), but were not used in this analysis. A split sampling technique was used to calibrate and validate HSAMI. Periods 1959-1976 and 1977-1995 were selected for model calibration and validation, respectively (Mareuil et al., 2007). WeaGETS and WGEN parameters were computed using meteorological data from the virtual weather station spanning the same time period, followed by the generation of an ensemble of 30 possible realisations of the 1959-1995 climate, thereby capturing, at least partially, the natural climate variability of the CRB area. Hydrological indices were next retrieved from flows simulated by HSAMI using the synthetic 19591995 climate, referred to as ‘simulated flows’, and compared to those simulated using the 1959-1995 meteorological observations, referred to as ‘observed flows’. This procedure allowed minimizing any hydrological model-related biases in the performance analysis of the weather generators. The simulated versus observed maximum annual low flow durations spanning years 1959-1995 are presented in Figure 6. Each of the 37 points on the figure corresponds to the observed maximum annual

Figure 6. Simulated versus observed maximal annual low flow durations of the CRB. © 2008 Canadian Water Resources Association

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low flow duration against its corresponding simulated value averaged over the 30 climate realisations. Retrieved durations were previously ranked from lowest to highest prior to matching an observation with its corresponding simulated value. The standard deviation of the simulated values is also displayed in this figure. Figure 6 shows that WeaGETS was capable of satisfactorily reproducing the low flow periods for up to 20-day durations. An underestimation still persists for the longer durations (i.e., greater than 30 days). Whether this underestimation is significant and should be corrected would depend on the type of impact studies. For example, it may be of interest to correctly simulate extended droughts in those basins where sustainable agriculture depends heavily on irrigation practices and where reliable sources of water are limited. Note however that the underestimation lies within the retrieved standard deviation. A comparison of the average annual direct runoff obtained for both observed and simulated actual climate conditions is presented in Figure 7. Simulated runoff was obtained by averaging runoff over the 30 realisations

of the actual climate for both WeaGETS and WGEN generators. All the points describing the runoff for the observed/WeaGETS simulated climate lie close to the 1:1 line, implying that WeaGETS derived climatology was able to successfully model the overall hydrological regime of the CRB. The monthly distribution of runoff was also well reproduced as shown in Figure 8. However, WGEN derived annual runoff was significantly overestimated.This positive bias is at first sight surprising, given that WGEN tends to underestimate precipitation extremes (e.g., the larger events responsible for the more important summer flows). However, their occurrence is infrequent and may only marginally affect the annual runoff. Because WGEN overestimates, albeit slightly, the much more frequent small to moderate precipitation events, which appears as an overestimation of the the amount of precipitation per wet day (see Table 2), spring runoff will be considerably raised as a result of a deeper snowpack and limited infiltration in the frozen ground. The performance of WeaGETS to simulate the annual peak flow is presented in Figure 9. No distinction is made in the figure between the spring and the summer-fall peak flows, although the annual peak flow

Figure 7. Simulated versus observed direct annual runoff for the CRB. © 2008 Canadian Water Resources Association


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Figure 8. Average runoff hydrographs of the Châteauguay River Basin (CRB) simulated from station observations (1959-1995) and WeaGETS 37-year climatology.

in the CRB is usually the result of the spring freshet. WeaGETS was able to produce simulated peak flows that were closer to the observations than WGEN. However, note that the peak flow values above 500 m3/sec were significantly overestimated with both WeaGETS and WGEN. Given that the 20- and 100-year summer floods have been previously estimated at 381 and 513 m3/s, respectively (Roy, 2000), it appears that the more extreme spring peak flows events, which are snowmelt induced, are overestimated with WeaGETS. A number of factors may be responsible for this overestimation. First, the magnitude of the peak runoff is strongly affected by the temperature regime during the melt season and can be exacerbated by significant precipitation events. A close examination of the simulated climate conditions revealed the largest peak flows were frequently the result of sustained high temperatures along with a major rainfall event. Table 4 presents typical weather events observed and simulated by WeaGETS that led to significant peak flow values. As can be seen in Table 4, major simulated peak flows were the result of either a large precipitation event (24-26 mm) with high temperatures (11-13oC), see events #5 and 13; or of an extreme rainfall (55-74 mm) with lesser, but still high temperatures, see events #8 and 22. Compared to the observed meteorology in Table 4, the combination of air temperature and precipitation as simulated by WeaGETS represented more extreme

conditions. As WeaGETS simulates precipitation amounts and temperature independently, a question arises whether it is able to reproduce consistent combinations of these meteorological variables, which becomes especially crucial for accurately modelling the spring freshet. A more thorough investigation of the performance of WeaGETS (and other weather generators) is required to elucidate that issue. Secondly, recall that the results presented in Figure 9 were derived from 30 series of 37 years each. Since all climate realisations are statistically independent, the chances that WeaGETS will produce at least one flood event with a return period of 30 × 37 = 1110 years is 63%, as compared to a 3% chance of producing a flood with the same return period, but for one climate realisation only. In other words, there is a strong possibility that a few very large precipitation events have been produced by WeaGETS, resulting in significant snow accumulations and/or spring rainfall that would affect the magnitude of the resulting spring peak flows. The overestimation of the peak flows observed above 500 m3/s may be at least partly attributed to pooling from a large sample (1110 years), and not necessarily from an overestimation, per se, of the larger precipitation amounts produced by WeaGETS. Separate flood frequency analyses for spring and summer-fall seasons were also conducted. Results are summarised in Table 5. The flow data were adjusted © 2008 Canadian Water Resources Association

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Figure 9. Simulated versus observed peak flow for the CRB.

Table 4. Temperature and precipitation conditions that led to significant spring peak flows for the CRB. Numbered events refer to climate scenarios (37 events total) simulated by WeaGETS. Observed events are identified by their year of occurrence. Q is peak flow. T and P are daily air temperature and total precipitation at peak flow date. T4 and P4 are average air temperature and total precipitation during the four days preceding peak flow. Event

#5 #8 #13 #22 1967 1973

Peak Flow

Q

T

T4

P

P4

Date

(m /s)

( C)

( C)

(mm)

(mm)

1133 1009 984 1135 740 626

13 9.5 10.9 6.3 9.5 6.8

8.5 5.9 14.9 4.2 6.2 7.1

26 55 24 74 29 37

10 0 9 7 0 0

April 11 April 8 April 11 March 23 April 2 April 1

3

o

using a log-Pearson type III distribution, which is the default distribution for flood frequency analysis in the United States (IACWD, 1982) and has also been used in Canada (Watt et al., 1989). Results confirm that the more extreme snowmelt flood events (i.e., for return periods of 50 years and above) are larger than those observed. An even more significant overestimation of

o

the summer-fall floods is noticed, which is foreseeable given that the sensitivity of runoff to single storm events is more important for summer floods as compared to spring floods, which are sensitive to accumulated precipitation over the winter season as well as individual storms during the melt event. Moreover, it is the larger storm events that proportionally produce © 2008 Canadian Water Resources Association


251

Table 5. Spring and summer-fall peak flow values for return periods of five to 100 years. Return Period (Years)

100 50 20 10 5 2

Spring Obs

706 687 648 601 526 347

WeaGETS

Summer-Fall % diff

Obs

13 9 3 -1 -3 0

438 393 328 274 215 125

798 749 670 597 507 347

the most runoff because soils quickly reach saturation and therefore limit infiltration. Note that the maximum recorded daily precipitation in the CRB over the 1959-1995 period was 100 mm, as compared to daily precipitation amounts exceeding 135 mm as generated by WeaGETS. As mentioned above, it is very likely that WeaGETS will generate daily precipitation quantities greater than 100 mm over a period spanning 30 × 37 years, which explains, at least partially, the higher peak flow values obtained using WeaGETS, as opposed to using the observed climatology. This does not necessarily translate into an overestimation of the high return period flows as both the observed and the simulated 50- and 100-year return flows result from extrapolation processes. The observed high T-return flows are directly extrapolated from 37 years of flow rates simulated using observed climatology. The simulated high T-return flows are retrieved from a much longer time series (30 × 37 years) with two extrapolation schemes involved in the flow generation mechanism: 1) large precipitation events extrapolated using WeaGETS; and 2) simulated flows falling outside the range for which the hydrological model was calibrated. Resorting to a more physicallybased hydrological model would help shed some light on this unresolved issue.

Conclusions A stochastic weather generator based on the WGEN model (Richardson, 1981) has been tested on 13 weather stations in Quebec. This is a first step toward the development of a downscaling model to construct basin scale projections of future changes

WeaGETS

530 449 348 277 208 118

% diff

21 14 6 1 -3 -6

in climate intended for hydrological impact studies. As the original WGEN was shown to result in nonnegligible errors for both precipitation magnitude and occurrence, in particular for the more extreme events, regional correction factors were introduced in the model to readjust the precipitation quantities, while the memory of the original WGEN model was increased by resorting to second and third order representations of the Markov chain process describing precipitation occurrence. A direct validation using selected precipitation indices has shown that the modified generator, WeaGETS, tested with the third order Markov chain model, generally performed better than WGEN. However, some discrepancies remained or were amplified that appear to be season-related, suggesting recourse to seasonal correction factors. Because the generator is aimed at developing climate change projections, it was decided not to introduce additional parameters in the model to keep the model parsimonious. More development is needed to improve WeaGETS to better account for seasonal forcing factors linked to precipitation events. WeaGETS was also indirectly validated by conducting a series of hydrological modelling experiments on a watershed located in southern Quebec. Results of the simulations show that WeaGETS was able to adequately represent the duration of low flow events as well as the annual and seasonal direct runoff. However, an overestimation of the peak flows was observed for the more extreme events with return periods exceeding 50 years. Whether such an overestimation during the melt season is related to the capacity of the generator to coherently reproduce the combination of precipitations and air temperatures © 2008 Canadian Water Resources Association

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defining the current climate needs to be fully assessed; more work is required to analyze these results. Weather generators such as WeaGETS are capable of generating long time series of precipitation, which occasionally result in extremes much larger than those recorded at weather stations. Such capacity is useful for risk analysis. It does not come as a surprise that summer peak flows are higher than observed. However, the generator needs to be more fully tested on various watersheds with more weather stations before drawing definitive conclusions, as other issues such as those related to the modelled variability and persistence of precipitation events may also affect the simulated flow magnitude. Finally,WeaGETS is a single site weather generator. Its use in hydrological studies is more appropriate for watersheds where daily precipitation does not vary spatially. For basins where precipitation varies spatially in a significant manner, it may be preferable to use multi-site weather generators, coupled to distributed hydrological models, for conducting climate change impact studies on water resources. The development of multi-site weather generators is currently under way (Khalili et al., 2007; Brissette et al., 2007).

Acknowledgements This work has been funded by the Natural Sciences and Engineering Research Council (NSERC), Hydro-Québec and the Ouranos Consortium on regional climatology and adaptation to climate change. Scientific support from Hydro-Québec and Ouranos is also gratefully acknowledged.

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Appendix Definition of Selected STARDEX Precipitation Indices consec_dry_day: maximum number of consecutive dry days (days) dry_day_pers: mean dry day persistence = total number of consecutive dry days for a period divided by the total number of dry days for the same period max_rain_3d: greatest 3-day total precipitation (mm) p10: probability of a dry day following a wet day. A wet day is defined here as a day when total precipitation exceeds 0.25 mm. prec_per60: 60th percentile of wet day amounts (mm/day). Percentile ranks were calculated using the Cunnane (1978) plotting positions. prec_per80: 80th percentile of wet day amounts (mm/day) prec_per99: 99th percentile of wet day amounts (mm/day) prec>10mm : number of days with precipitation above 10 mm (days) rain_per_rainday: average daily precipitation amount for wet day (mm/day) wet_day_pers: mean wet day persistence = total number of consecutive wet days for a period divided by the total number of wetdays for the same period
