effectiveness of multisite weather generator for hydrological

EFFECTIVENESS OF MULTI-SITE WEATHER GENERATORFOR HYDROLOGICAL MODELING1

Malika Khalili, Francois Brissette, and Robert Leconte2

ABSTRACT: A multi-site weather generator has been developed using the concept of spatial autocorrelation.The multi-site generation approach reproduces the spatial autocorrelations observed between a set of weatherstations as well as the correlations between each pair of stations. Its performance has been assessed in twoprevious studies using both precipitation and temperature data. The main objective of this paper is to assess theefficiency of this multi-site weather generator compared to a uni-site generator with respect to hydrological mod-eling. A hydrological model, known as Hydrotel, was applied over the Chute du Diable watershed, located in theCanadian province of Quebec. The distributed nature of Hydrotel accounts for the spatial variations throughoutthe watershed, and thus allows a more in-depth assessment of the effect of spatially dependent meteorologicalinput on runoff generation. Simulated streamflows using both the multi-site and uni-site generated weatherdata were statistically compared to flows modeled using observed data. Overall, the hydrological modeling usingthe multi-site weather generator significantly outperformed that using the uni-site generator. This lattercombined to Hydrotel resulted in a significant underestimation of extreme streamflows in all seasons.

(KEY TERMS: weather generator; hydrological modeling; meteorology; precipitation; temperature; stochasticmodels; streamflow; watersheds.)

Khalili, Malika, Francois Brissette, and Robert Leconte, 2011. Effectiveness of Multi-site Weather Generator forHydrological Modeling. Journal of the American Water Resources Association (JAWRA) 47(2):303-314. DOI:10.1111/j.1752-1688.2010.00514.x

INTRODUCTION

The evaluation of the effects of climate change onriver hydrological regimes using hydrological modelscoupled to climate projections is one of the issues cov-ered by climate change studies. Engineering design,water resource management, water supply, and waterquality studies also require hydrological watershedmodeling. Meteorological data are used as the pri-mary input for hydrological models, and various

applications, including extreme event analyses,require long time series of meteorological data, whichunfortunately, are not always readily available.

Stochastic weather generators were used to producemeteorological data time series for practically any timeperiod (Richardson, 1981; Semenov and Barrow, 1997).The statistical properties of the simulated time seriesare similar to those of the observed ones. Weathergenerators are particularly useful for climate changestudies. Using climate change projections derived fromGlobal Circulation Models, the weather generator

1Paper No. JAWRA-10-0040-P of the Journal of the American Water Resources Association (JAWRA). Received April 1, 2010; acceptedNovember 9, 2010. ª 2011 American Water Resources Association. Discussions are open until six months from print publication.

2Respectively, Postdoctoral Fellow (Khalili), Department of Civil Engineering and Applied Mechanics, Macdonald Engineering Building,McGill University, 817 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6 [Ph.D. Student at Ecole de Technologie Superieure atthe time this paper was prepared]; Professor (Brissette), Department of Construction Engineering, Ecole de Technologie Superieure,Montreal, Quebec, Canada; and Professor (Leconte), Department of Civil Engineering, University of Sherbrooke, Sherbrooke, Quebec, Canada[Professor at Ecole de Technologie Superieure at the time this paper was prepared] (E-Mail ⁄ Khalili: [email protected]).

JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 303 JAWRA

JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION

Vol. 47, No. 2 AMERICAN WATER RESOURCES ASSOCIATION April 2011

parameters can be ‘‘perturbed’’ to simulate future timeseries (Kilsby et al., 2007; Mareuil et al., 2007).

The WGEN weather generator (Richardson, 1981;Richardson and Wright, 1984) and the Long-AshtonResearch Station Weather Generator (LARS-WG)(Semenov and Barrow, 1997) are well-known uni-siteparametric weather generators. WGEN uses the first-order two-state Markov chain model to generate pre-cipitation occurrences and a selected distributionfunction to model precipitation amounts on rainydays, whereas the LARS-WG uses semiempiricaldistributions to model precipitation occurrences andamounts. The weather generator developed byBrandsma and Buishand (1997) is a nonparametricuni-site generator, which uses the resampling of aweather variable vector on a day of interest fromthe historical data by conditioning on the simulatedvalues of previous days.

Multi-site weather generators have been developedto take into account the correlations existing betweenweather stations, a feature which cannot be addressedby uni-site generators. The literature contains models,which use the atmospheric circulation patterns, suchas the space-time models (Bardossy and Plate,1992;Bogardi et al., 1993), and the nonhomogeneous hiddenMarkov models (Hughes and Guttorp, 1994a,b;Hughes et al., 1999; Bellone et al., 2000). However,these models are complex, and do not reproduce anadequate spatial dependence between the weatherstations. Buishand and Brandsma (2001) regionalizedthe uni-site weather generator cited above (Brandsmaand Buishand, 1997), but because of the nearest-neighbor resampling from historical data it requires,this weather generator is not appropriate for climatechange studies. Wilks (1998) regionalized WGENusing serially independent, but spatially correlated,random numbers. This multi-site weather generatorproduces adequate results, but it also has a cumber-some structure involving a lot of parameters, such asthe collection of k (k ) 1) ⁄ 2 empirical relationships fora network of k stations, relating the correlations ofthe random numbers and the correlations of theprecipitation occurrences and amounts. These curvesmust be developed for all possible pairs of stations andfor each month.

The multi-site weather generators presented abovefocus mainly on precipitation processes, which areprecipitation occurrences and amounts. Very fewmulti-site models include other meteorological vari-ables. Wilks (1999) presented an extension of theweakly stationary generating process used in WGENfor the multi-site generation of maximum tempera-ture, minimum temperature, and solar radiationdata. However, this method, which extends the modeldimension from 3 to 3k, significantly increases thesize of correlation matrices, and thus precludes the

model solution. The multi-site weather generator ofBuishand and Brandsma (2001) uses the resamplingfrom the historic record for both precipitation andtemperature data, but the method does not permitthe generation of time series with climate change.

A multi-site generation approach for daily precipi-tation and temperature data has been developed byKhalili et al. (2007, 2009) using the spatial autocorre-lation concept. The interest for this concept lies in itsability to describe the spatial dependence betweenneighboring sites over the entire watershed with asingle number. The multi-site generation approachproved successful when applied for simulating dailyweather data. Using a proper weight matrix tocompute the spatial autocorrelation allowed thereproduction of the daily spatial autocorrelationsbetween the set of weather stations as well as themonthly correlations between each pair of stations.

According to Wilks and Wilby (1999), Srikanthanand McMahon (2001), Harmel et al. (2002), andMehrotra et al. (2005), ignoring the spatial correla-tion between weather stations using uni-site weathergenerators in hydrological modeling studies mayintroduce significant errors to model results. How-ever, this assertion has not been established inpractice as major studies usually tend to evaluatehydrological modeling using uni-site weather genera-tors (Harmel et al., 2000; Siriwardena et al., 2002;Dubrovsky et al., 2004).

Very few studies have actually investigated the per-formance and usefulness of multi-site weather genera-tors for hydrological modeling. Watson et al. (2005)evaluated the response of the semidistributed hydro-logical model Soil and Water Assessment Tool to uni-site and multi-site weather generators (Wilks, 1998)over the Woady Yaloak River catchment (306 km2) inAustralia. The authors report little distinctionbetween the two weather generators based on themeans and standard deviations of annual, monthly,and daily runoff, and recommend more studies toassess further the usefulness of multi-site weathergenerators in hydrological modeling. As Woady Yal-oak is a small and flat watershed (306 km2), it wassomewhat expected that a uni-site weather generatorwould give results comparable to those of a multi-sitegenerator.

Khalili et al. (2006) carried out a comparisonbetween WGEN and multi-site weather generator(Khalili et al., 2007, 2009) using a lumped conceptualhydrological model (Bisson and Roberge, 1983). Themulti-site and uni-site simulated precipitation timeseries were spatially averaged over the watershedand used as input to the lumped model. One interest-ing observation was that although the precipitationdata were averaged over the basin, some spatialdependence was retained in the averaging process,

KHALILI, BRISSETTE, AND LECONTE

JAWRA 304 JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION

which resulted in an improved summer-autumn flowmodeling for the multi-site approach.

This article thus aims to compare the performanceof a multi-site weather generator (Khalili et al., 2007,2009) against the uni-site WGEN weather generatorin modeling the hydrological regime of the Chutedu Diable watershed in the Canadian province ofQuebec. This study uses a distributed hydrologicalmodel called Hydrotel (Fortin et al., 2001a,b). Using adistributed modeling approach provides greaterinsights into the performance of each multi-site anduni-site weather generator. The uni-site and multi-site weather generators (Khalili et al., 2007, 2009)are described in the Appendix. The following sectionspresent the hydrological modeling and the results ofthe comparison.

HYDROLOGICAL MODELING

Study Area

The multi-site generation approach for daily pre-cipitation and temperature data as described in theAppendix has been applied to the Peribonca River basin(26, 000 km2). The watershed is located north of theLac-Saint-Jean, in the Canadian province of Quebec,and has four subbasins: Passes-Dangereuses(11,000 km2), Lac Manouane (5,000 km2), Chute duDiable (9,700 km2), and Chute a la Savane (1,300 km2).Seven weather stations were used: Bonnard, Chutedes Passes, Chute du Diable, Hemon, Peribonca,Normandin�cda, and St-Leon-De-Labrecque. Thesestations are located either within or around the Chutedu Diable subbasin. This latter was therefore used forthe hydrological modeling experiment (Figure 1).

The Chute du Diable watershed is a mountainousarea, with elevation ranging from 169 to 640 m,which results in heterogeneous climate and confirmsthe importance of using the multi-site weather gener-ator. The Chute du Diable watershed climate is coldand snowy, with monthly average precipitationamounts ranging from 38 to 142 mm. Its soil is typi-cally composed of till and sand (Table 1). The Chutedu Diable land use is dominated by the evergreenclass, followed by the mixed class (Table 2).

Hydrotel Model Application

The main reason for selecting the Hydrotel model(Fortin et al., 2001a,b) for this study was its ability totake into account the spatial variability of meteoro-logical and hydrological processes. The distributed

structure of this model allowed a more thoroughinvestigation of the performance of the multi-siteweather generator. Another advantage of this modelwas its ability to be adapted to available data and tooffer a variety of physical, conceptual, and empiricalhydrological processes.

Applying the Hydrotel model previously requiredthe application of Physitel software, to prepare theChute du Diable watershed physiographic database.

FIGURE 1. Chute du Diable Watershed With Locationsof Weather and Hydroelectric Central Stations.

TABLE 1. Soil Type on Chute du Diable Watershed.

Soil Type Area (%)

Till_sand 94.5Till and organic deposit 4.5Organic deposit 0.3Till_sand_gravel 0.6

EFFECTIVENESS OF MULTI-SITE WEATHER GENERATOR FOR HYDROLOGICAL MODELING


This software program uses a digital elevation modelto compute the slope of all the constituted cells andthen to determine the flow directions through them.Physitel used these flow directions and the location ofthe watershed outlet to determine the complete struc-ture of the Chute du Diable watershed. A total of 310Relatively Homogenous Hydrological Units (RHHU)were then constituted in this watershed. These verysmall subwatersheds permitted an adequate simula-tion and mapping of the aerial distribution of hydro-logical processes (Fortin et al., 2001a). The observedstreamflows of this watershed were proposed byALCAN, which owns and operates the meteorologicaland streamflow stations. Figure 2 illustrates thetopography of the Chute du Diable watershed and itsriver reaches, as obtained from Physitel.

In addition to the watershed database provided byPhysitel, Hydrotel required hydrometeorological data.Precipitation and temperature data from the selectedstations were used as well as the streamflows inthe Chute du Diable watershed. In fact, the modelcalibration was realized using the observed hydrome-teorological data.

Calibration and Validation

Hydrotel submodels were selected according to theirability to simulate the hydrological processes and alsoto available data. First, interpolation of meteorologicaldata to each RHHU was required to ensure the spatialdistribution of meteorological data on the watershed,and to that end, weighted means from the nearestthree stations were used. Hydrotel then separatedprecipitation data at each time step into rainfall andsnowfall according to the maximum and minimumtemperature data at that time. Snow accumulation andmelt were computed over each RHHU using a mixeddegree-day-energy-budget approach (Fortin et al.,2001a). Depending on data availability, Hydrotel offersvarious options to simulate the potential evapotranspi-ration for each RHHU. The Thornthwaite equation wasused for this study. A three-layer vertical water budgetsubmodel (BV3C) (Fortin et al., 2001a) simulated themoisture in the soil column at each RHHU. The BV3Csubmodel computed the water amounts available forinfiltration, runoff, interflow, and base flow. Surfaceand subsurface flows were propagated from one RHHUto the next and toward the hydrographic network usingthe kinematic wave equation. The flow in the hydro-graphic network was routed to the watershed outletusing the diffusive wave equation.

Hydrotel model was calibrated for the Chute duDiable watershed using observed meteorological andstreamflow data from 1963 to 1976. This particularperiod was selected because it was also used for themulti-site weather generation process. More specifi-cally, the spatial autocorrelations of the meteorologi-cal data were computed using a shared recordedperiod between the selected weather stations, whichran from 1963 to 1976. The Nash-Sutcliffe coefficient,calculated using daily data, was equal to or higherthan 0.8 for the full calibration period, and for eachyear separately. Validation was performed using the1980-1998 hydrological years, with an overall Nash-Sutcliffe coefficient of 0.77.

Although the weather generator can produce timeseries of infinite length, these generated series arenot the prediction of the future climate, but have sim-ilar statistics to those of the observed period to whichthe weather generator has been fitted. 50-year timeseries of weather data were generated, from whichstreamflows were simulated using Hydrotel. Theseflows were statistically compared to 30-year time ser-ies of flows simulated using the observed weatherdata, referred to as the ‘‘reconstituted’’ streamflows,and spanning from 1960 to 1989, to allow a more‘‘objective’’ evaluation of the weather generator per-formances.

Flood frequency analysis, which may be the bet-ter indicator of extreme values, was carried out to

FIGURE 2. River Reaches and Altitudes (m) of the Chutedu Diable Watershed Obtained From Physitel.

TABLE 2. Land-Use Occupation on Chute du Diable Watershed.

Land-Use Class Area (%)

Crop_Grass 0.1Crop_Wood 2.4Shrubland 0.8Deciduous 2.2Evergreen 65.0Mixed 26.1Water 3.4



compare the likelihood of extreme streamflow events.The Pearson III frequency distribution was found tofit better with the summer and spring data, whereasthe Gumbel frequency distribution was retained forautumn. The method of moments was used for parame-ter estimation, and Weibull or Hazen equations wereused for the plotting position, according to the resultconsistency. Distributions were fitted on the normalprobability paper.

RESULTS AND DISCUSSION

Once calibrated, Hydrotel was then driven withweather data produced by the multi-site and uni-siteweather generators. The resulting streamflows werethen compared to the reconstituted streamflows, toverify the performance of each of the weather genera-tion approaches in hydrological modeling. The twosimulation results using multi-site and uni-site gen-erated weather data revealed the impacts consecutiveto using the uni-site weather generator. Usingweather data produced by WGEN led to a significantunderestimation of the summer-autumn peak flows(see Figure 3). On the other hand, using weatherdata produced by the multi-site weather generatorresulted in simulated summer-autumn flows, whichbetter resembled the reconstituted flows. Note thatthese curves are randomly selected from multiplerealizations, and it is expected that they shouldnot exactly match because of the stochastic processdriving the weather generators. The reconstitutedstreamflows in Figure 3 are those obtained for theyear 1971.

The behavior of the hydrograph simulated usinguni-site generated weather data can be explained bythe very nature of the uni-site weather generator,which does not take into account the spatial depen-dence existing between the weather stations, particu-larly for the precipitation processes, which exhibit ahigh spatial variability and are the main driving fac-tor in the hydrological modeling. The weather dataare generated at a single site independently of theothers, whereas weather events typically exhibit aspatially organized pattern over a region. The sur-rounding weather stations should be interdependentbecause they experience the same or very nearly thesame weather events (Odland, 1988).

Monitoring precipitations over the watershed ateach step of the simulation run was used to look forcloser simulation details. For instance, the highesttotal amounts of precipitations over the entirewatershed recorded in September as rainfall wasretrieved from the observed and the simulated data.The heavy total rainfall amounts in September overthe entire watershed was much more significant forobserved (290 mm) and multi-site simulated patterns(229 mm) than for uni-site simulated ones (94 mm).Figures 4a, 4b, and 4c display the spatial distributionof these heavy total rainfall amounts for observed,multi-site and uni-site simulated cases over theChute du Diable watershed. The observed precipita-tions exhibit a significant spatial dependence and themulti-site weather generator succeeded in simulatingthe precipitation processes with a realistic spatial dis-tribution, while the uni-site weather generatorresulted in a local rain, mainly in the southeast ofthe watershed. Therefore, ignoring the spatial depen-dence over the Chute du Diable watershed will affectthe magnitude of the simulated flow.

FIGURE 3. Reconstituted and Simulated StreamflowsUsing Multi-site and Uni-site Weather Generators.

The curves are randomly selected.

FIGURE 4. Spatial Distribution of Heavy Total RainfallAmounts Occurring in September Over the Chute du

Diable Watershed From (a) Observed Data, (b) Multi-siteGenerated Data, and (c) Uni-site Generated Data.



Tables 3 and 4 show that the extreme stream-flows simulated by Hydrotel using the uni-site weathergenerator were considerably lower than those simu-lated with the observed weather data for both thesummer (Figure 5) and autumn (Figure 6) seasons andfor all the return periods. The underestimation is lesssignificant using the multi-site weather generator.

The underestimation of the extreme streamflowsobtained mainly in autumn, using the multi-siteweather generator, was expected because of its limitedability to simulate the more extreme daily precipita-tion amounts using the exponential precipitation func-tion. This underestimation is much more pronouncedwith the uni-site generated input because of the inde-pendence of the weather stations, which can result in alarge rainfall at a given station, but none at all atanother station nearby, on a same day. However, themarked difference in autumn is caused by the largereconstituted streamflow depths (998 and 981 m3 ⁄ s)generated on November 5, 1966, and on October 20,1967, respectively. These two outliers (Figure 6a),

which are very distant from the remaining data, canmore probably be due to a misrepresentation of theweather stations. When these outliers were omitted,similar frequency results were obtained with bothreconstituted and simulated streamflows using themulti-site weather generator (Table 4).

Regarding the spring season, Table 3 shows aslight overestimation of the simulated streamflowsusing the multi-site weather generator especiallyfrom two-year return period, and a slight underesti-mation from lower to upper return periods resultedfrom the uni-site generated weather data combinedwith Hydrotel (see Table 3; Figure 7).

Hydrotel responses to observed and simulatedweather data was also evaluated using streamflowaverages. Figure 8 illustrates the monthly averagesof daily streamflows obtained using observed as wellas multi-site and uni-site generated data. The threekinds of streamflows are generally in good agree-ment. The monthly averages of simulated stream-flows obtained using the multi-site weather generator

TABLE 3. Summer and Winter-Spring Flood Frequency Using Observed Data, Multi-site, and Uni-site Generated Datain Hydrotel Model, and Uni-site Generated Watershed Averaged Weather Time Series With the Lumped Approach.

Summer

ReturnPeriod (years)

ObservedData_Hydrotel

Multi-siteGenerator_Hydrotel

Uni-siteGenerator_Hydrotel

Uni-siteGenerator_Lumped Approach

1 308.46 279.28 252.25 235.782 585.97 422.59 412.82 499.535 738.13 553.03 503.05 682.18

10 820.49 640.19 552.46 792.0520 889.97 723.04 594.46 890.6950 969.80 828.88 643.03 1,010.63Winter-spring1 896.13 835.39 873.82 836.422 1,146.45 1,183.90 1,132.26 1,197.225 1,308.70 1,372.24 1,275.93 1,414.98

10 1,403.59 1,473.45 1,354.22 1,538.3220 1,487.41 1,558.47 1,420.54 1,645.2750 1,587.87 1,655.74 1,497.02 1,771.28

TABLE 4. Autumn Flood Frequency Using Observed Data With Outliers (30 pieces of data) and WithoutOutliers (28 pieces of data), Multi-site, and Uni-site Generated Data in Hydrotel Model, andUni-site Generated Watershed Averaged Weather Time Series With the Lumped Approach.

Autumn

ReturnPeriod (years)

30 ObservedData_Hydrotel

28 ObservedData_Hydrotel

Multi-siteGenerator_Hydrotel

Uni-siteGenerator_Hydrotel

Uni-site Generator_LumpedApproach

1 283.08 328.37 268.22 236.66 268.212 474.31 449.56 401.17 336.58 410.125 622.38 543.39 504.12 413.95 520.02

10 720.42 605.52 572.28 465.17 592.7820 814.46 665.12 637.66 514.31 662.5750 936.19 742.26 722.29 577.91 752.91



FIGURE 5. Summer Streamflow Frequency DistributionsUsing (a) Observed Data, (b) Multi-site Generated Data,

and (c) Uni-site Generated Data.

FIGURE 6. Autumn Streamflow Frequency DistributionsUsing (a) Observed Data, (b) Multi-site Generated Data,




are the closest to those reconstituted. However, anoverestimation of the streamflow average is obtainedfor May, and is more pronounced for the simulatedstreamflows obtained with the uni-site weathergenerator. This overestimation does not mean thatmulti-site and uni-site weather generators inflate thevolume in the Chute du Diable watershed, but rather,it is related to the limited variability of the generatedair temperature data. In fact, the winter and springstreamflows are principally linked to the accumula-tion and melt of snow cover. This melt was modeledby Hydrotel using air temperature as the driv-ing meteorological variable. Further investigationsrevealed that the simulated air temperature data didnot display as much variability as the observedrecords, particularly with the uni-site weather gener-ator. This limitation also affected the streamflow var-iability, as shown by Figure 9, which is mostlyunderestimated using the uni-site weather generator.

Figure 10 shows the standard deviations ofobserved and simulated daily air temperatures. Thesedata are derived from Hydrotel as the air tempera-tures over the entire watershed. It therefore appearsthat observed and multi-site generated air tempera-tures show considerable variability, and are generallyin good accordance, except for December, January,February, and March, which constituted thewinter season for this watershed. Uni-site generatedair temperatures show lower variability. The misre-production of the variability obtained with theuni-site weather generator and slightly in winter,with the multi-site generator, affects the melt of thesnow cover, and consequently, the timing of thespring peak flow. In fact, using the weather gener-ated data, the spring peak flow for each simulatedyear occurs almost always in May, but from April toJune, using observed data because of the mid-winterthaw. Therefore, using the weather generators, the

FIGURE 7. Spring Streamflow Frequency DistributionsUsing (a) Observed Data, (b) Multi-site Generated Data,


FIGURE 8. Monthly Streamflow Averages.



occurrence of the spring peak flows in May annuallycauses the highest streamflow average in this month,as shown in Figure 8. However, from observed data,the much longer snowmelt flood occurrence periodcauses the highest streamflows to be spread outbetween April, May, and June in the observed years,causing a moderate streamflow average peak.

Figure 10 presents another advantage of the multi-site weather generator. It appears that taking intoaccount the spatial dependence between the synthetictemperature data satisfactorily reproduces the airtemperature variability. The latter may be improvedto be adequately reproduced in winter to allow a rea-sonable timing of spring peak flows and more accu-rate streamflow standard deviations.

Finally, a comparison has been made between themulti-site weather generator coupled to Hydrotel,and the uni-site weather generator, used to producethe watershed averaged weather time series, coupledto the lumped approach. Tables 3 and 4 show that

the latter procedure overestimated the 2 to 50-yearreturn period streamflows during spring season,while the first tended to underestimate the stream-flows for autumn and summer seasons. The overesti-mation observed using the uni-site generated datacan be explained by the lumped approach, whichassigned the watershed averaged weather time seriesto the total watershed area. However, the underesti-mation using the multi-site weather generator mainlyresulted from the exponential distribution, whichunderestimated the more extreme daily precipitationamounts occurring in summer and autumn, asexplained above. Using the uni-site generatedwatershed weather time series average, the underes-timation due to the exponential distribution was,however, compensated by the overestimation due tothe lumped approach to give approximately goodresults for the high streamflows in summer, as shownby Table 3, and the autumn streamflows when com-pared to the reconstituted results without outliers(Table 4).

These results confirm the importance of using thedistributed hydrological approach, which is more rep-resentative of the climate spatial variability. Mostimportantly, they confirm the necessity of couplingthe distributed hydrological model with the multi-siteweather generator, which allows taking into accountthe spatial dependence of the weather stations andincreasing the credibility of the hydrological modelingresults. Also, the multi-site weather generatoraccounts for the precipitation spatial heterogeneity,which allows to simulate better the flows at any pointinside the watershed hydrographical network, ascompared to using a watershed averaged weathertime series that the uni-site generator can onlyproduce. Indeed, using the average approach may, inall likelihood, overestimate the flow rates in certainsubwatersheds, where the averaged precipitation canbe larger than the corresponding multi-site estima-tion, while the opposite can occur in the subwater-sheds, in which the uni-site model underpredicts theprecipitation as compared to the multi-site approach.

CONCLUSION

The results of this study indicate an underestima-tion of summer-autumn peak flows using the uni-siteweather generator. However, realistic summer-autumn simulated peak flows were obtained with themulti-site synthetic weather data since the spatialautocorrelations over the watershed and the correla-tions between each pair of stations were adequatelyreproduced by the multi-site weather generator.

FIGURE 9. Monthly Streamflow Standard Deviations.

FIGURE 10. Monthly Air Temperature Standard Deviations.



Frequency analyses indicated a strong under-estimation of extreme streamflows in summer andautumn using the uni-site weather generator.A slight underestimation was obtained for summerand autumn seasons using the multi-site weathergenerator, mainly due to the exponential functionused to model the precipitation amounts. The magni-tude of the spring floods was slightly overestimatedusing the multi-site weather generator, while a slightunderestimation resulted from the use of the uni-sitegenerator.

Monthly streamflow averages were computed forthe reconstituted streamflows as well as for the simu-lated ones using the uni-site and multi-site weathergenerators. Generally, there was good agreementbetween the observed and the simulated streamflowaverages. An overestimation of the simulated stream-flow averages was obtained in May, and was morepronounced using the uni-site weather generator.This overestimation was explained by a limited vari-ability of the simulated air temperature data, particu-larly with the uni-site weather generator, whichdirectly affected the timing of the spring freshet.

A comparison has been also made between themulti-site weather generator, coupled to the distrib-uted hydrological model, and the uni-site generator,used to compute the watershed averaged weathertime series, coupled to the lumped approach. Theresults showed that the multi-site weather generator,coupled to the distributed hydrological model, isrequired to account for weather spatial variation anddependence, which improve the simulated stream-flow, especially in a watershed whose size and topo-graphy result in weather spatial variability.

APPENDIX

Uni-site Weather Generator

The uni-site weather generator used for this studyis WGEN (Richardson, 1981; Richardson and Wright,1984). It uses a first-order two-state Markov chain tosimulate the daily precipitation occurrence xt (i) atsite i on day t. The operation consists of computingtwo transitional probabilities p01 and p11 (1 and 0 forwet and dry status respectively) and selecting oneaccording to the occurrence status of the previousday. The selected transitional probability, called thecritical probability pc, will be compared against auniform random number ut (i) generated from a uni-form [0, 1] distribution. The day of interest will bewet xt (i) = 1 if this random number is smaller thanthe critical probability, and dry xt (i) = 0 otherwise:

xt ið Þ ¼ 1; if ut ið Þ � pc ið Þ0; otherwise

:

�ðA1Þ

The precipitation amount in a given wet day isderived by inverting a precipitation probability distri-bution function. In the case of an exponential func-tion, the amount is:

rt ið Þ ¼ � ln 1� vt ið Þð Þ=ktðiÞ; ðA2Þ

where rt (i) is the synthetic precipitation amount atsite i on day t; vt (i) is a uniform [0, 1] random num-ber, independent from ut (i), and kt (i) is the rateparameter of the exponential distribution function atsite i on day t.

WGEN generates maximum temperature, mini-mum temperature, and solar radiation using theweakly stationary generating process proposed byMatalas (1967):

vp;iðjÞ ¼ A vp;i�1ð jÞ þ B ep;ið jÞ; ðA3Þ

where vp,i(j) and vp,i)1(j) are (3 · 1) matrices of maxi-mum temperature (j = 1), minimum temperature(j = 2), and solar radiation (j = 3) residuals for days iand i ) 1 of year p. The residuals are obtained fromthe standardization of the meteorological variables.ep;i jð Þ is the (3 · 1) matrix of independent standardnormal random numbers N[0,1] for day i of year p.A and B are (3 · 3) matrices whose elements aredefined from lag 0 and lag 1 serial and cross-correla-tion coefficient matrices of observed residuals.

Multi-site Weather Generator

Khalili et al. (2007, 2009) generalized the WGENpresented above using the spatial autocorrelation con-cept. This statistic has the advantage of describing thespatial dependence observed over an entire watershedwith a single number, commonly the Moran’s I (Moran,1950; Odland, 1988; Griffith, 2003), defined as:

I ¼

Pni¼1

ðxi � xÞPnj¼1

wijðxj � xÞ=Pni¼1

Pnj¼1

wij

!

Pni¼1

ðxi � xÞ2=n; ðA4Þ

where xi denotes the observed value of a single vari-able X at location i, x is the average of the xi over nlocations, and wij is the spatial weight between twolocations i and j, described by the weather variablecorrelations between this pair of stations.

More specifically, the multi-site generation appro-ach of daily precipitation occurrence and amount data(Khalili et al., 2007) uses spatially autocorrelatedrandom numbers, in Equations (A1) and (A2), whose



spatial autocorrelations permit the reproduction ofobserved daily spatial autocorrelations in the simu-lated precipitation time series. The monthly inter-station correlations are automatically reproduced.A moving average process (Cliff and Ord, 1981;Cressie, 1993) is used with suitable coefficients (Khaliliet al., 2007) to generate spatially autocorrelated ran-dom numbers, such that:

V ¼ c�W � uþ u; ðA5Þ

where V(n, 1) is a vector of n spatially autocorrelatedrandom numbers to be used for n stations; W(n, n) is aweight matrix whose elements are wij; u(n, 1) is a vectorof n independent and uniformly [0,1] distributed ran-dom numbers, and c is the moving average coefficient.

As the usual exponential function does not allowthe spatial intermittence property of the precipitationamounts to be fulfilled, spatial exponential functionsare developed. The rate parameters of these functionsare generated according to the spatial dependencecomputed for the occurrence values at the set of sta-tions on a given day (Khalili et al., 2009). Thisapproach was proposed because of the strong depen-dence existing between the mean of the precipitationamounts and the occurrence states at the set of sta-tions. The spatial autocorrelation concept is againused to specify this spatial dependence of the occur-rence processes over the watershed.

The multi-site generation approach of daily tem-perature and solar radiation data (Khalili et al.,2009) considers the weakly stationary generating pro-cess (Equation A3) as used in WGEN, but with spa-tially autocorrelated random numbers (Equation A5)in ep;i jð Þ. Three spatial moving average processes arethus used to model the maximum temperature, mini-mum temperature, and solar radiation, such that:

VT max ¼ cT max �W � uT max þ uT max; ðA6Þ

VT min ¼ cT min �W � uT min þ uT min; ðA7Þ

VSr ¼ cSr �W � uSr þ uSr: ðA8Þ

The regionalization is carried out using Equation(A3) along with ep;i jð Þ containing three random num-bers, from VT max n; 1ð Þ, VT min n; 1ð Þ, and VSr n; 1ð Þ,respectively.

ACKNOWLEDGMENTS

This research was supported by the Natural Science andEngineering Research Council of Canada, Hydro-Quebec, and theOuranos Consortium on climate change, through developmentgrant. Their support is gratefully acknowledged. The authors alsoacknowledge Mrs. Marie Minville for the preparation of the Chutedu Diable watershed physiographic database.

LITERATURE CITED

Bardossy, A. and E.J. Plate, 1992. Space-Time Model for DailyRainfall Using Atmospheric Circulation Patterns. WaterResources Research 28:1247-1259.

Bellone, E., J.P. Hughes, and P. Guttorp, 2000. A Hidden MarkovModel for Downscaling Synoptic Atmospheric Patterns to Precipi-tation Amounts. Climate Research 15:1-12.

Bisson, J.L. and F. Roberge, 1983. Prevision des Apports Naturels:Experience D’Hydro-Quebec. Proceedings of the Workshop onthe Streamflow Forecast, Toronto, Canada, November 1983.

Bogardi, I., I. Matyasovszky, A. Bardossy, and L. Duckstein, 1993.Application of a Space-Time Stochastic Model for Daily Precipi-tation Using Atmospheric Circulation Patterns. Journal ofGeophysical Research 98:16653-16667.

Brandsma, T. and T.A. Buishand, 1997. Rainfall Generator for theRhine Basin: Single-Site Generation of Weather Variables byNearest-Neighbour Resampling. KNMI-publicatie 186-1, KNMI,De Bilt, the Netherlands, 47 pp.

Buishand, T.A. and T. Brandsma, 2001. Multisite Simulation ofDaily Precipitation and Temperature in the Rhine Basin byNearest-Neighbour Resampling. Water Resources Research37(11):2761-2776.

Cliff, A.D. and J.K. Ord, 1981. Spatial Processes: Models andApplications. Pion, London.

Cressie, N.A.C., 1993. Statistics for Spatial Data. Wiley Series inProbability and Mathematical Statistics. John Wiley & Sons,New York, 900 pp.

Dubrovsky, M., J. Buchtele, and Z. Zalud, 2004. High-Frequencyand Low-Frequency Variability in Stochastic Daily WeatherGenerator and Its Effect on Agricultural and HydrologicModelling. Climatic Change 63:145-179.

Fortin, J.P., R. Turcotte, S. Massicotte, R. Moussa, J. Fitzback, andJ.P. Villeneuve, 2001a. Distributed Watershed Model Compati-ble With Remote Sensing and GIS Data. I: Description of Model.Journal of Hydrologic Engineering 6(2):91-99.

Fortin, J.P., R. Turcotte, S. Massicotte, R. Moussa, J. Fitzback, andJ.P. Villeneuve, 2001b. Distributed Watershed Model CompatibleWith Remote Sensing and GIS Data. II: Application to ChaudiereWatershed. Journal of Hydrologic Engineering 6(2):100-108.

Griffith, D.A., 2003. Spatial Autocorrelation and Spatial Filtering:Gaining Understanding Through Theory and Scientific Visuali-zation. Advances in Spatial Science, Springer, Berlin, 247 pp.

Harmel, R.D., G. Johnson, and C.W. Richardson, 2002. The GEMExperience: Weather Generator Technology Development inthe USDA. Bulletin of the American Meteorological Society 83:954-957.

Harmel, R.D., C.W. Richardson, and K.W. King, 2000. HydrologicResponse of a Small Watershed Model to Generated Precipita-tion. Transactions of the ASAE 43:1483-1488.

Hughes, J.P. and P. Guttorp, 1994a. A Class of Stochastic Modelsfor Relating Synoptic Atmospheric Patterns to Regional HydrologicPhenomena. Water Resources Research 30:1535-1546.

Hughes, J.P. and P. Guttorp, 1994b. Incorporating SpatialDependence and Atmospheric Data in a Model of Precipitation.Journal of Applied Meteorology 33:1503-1515.

Hughes, J.P., P. Guttorp, and S. Charles, 1999. A NonhomogeneousHidden Markov Model for Precipitation Occurrence. AppliedStatistics 48:15-30.

Khalili, M., F. Brissette, and R. Leconte, 2009. StochasticMulti-Site Generation of Daily Weather Data. StochasticEnvironmental Research and Risk Assessment 23(6):837-849.

Khalili, M., R. Leconte, and F. Brissette, 2006. Efficient WatershedModeling Using a Multi-Site Weather Generator for Meteoro-logical Data. Geo-Environment and Landscape Evolution II.Transaction of Wessex Institute of Technology, United Kingdom.pp. 273-281, DOI: 10.2495/GEO060281.



Khalili, M., R. Leconte, and F. Brissette, 2007. StochasticMulti-Site Generation of Daily Precipitation Data Using SpatialAutocorrelation. Journal of Hydrometeorology 8(3):396-412.

Kilsby, C.G., P.D. Jones, A. Burton, A.C. Ford, H.J. Fowler,C. Harpham, P. James, A. Smith, and R.L. Wilby, 2007. A DailyWeather Generator for Use in Climate Change Studies. Envi-ronmental Modelling and Software 22:1705-1719.

Mareuil, A., R. Leconte, F. Brissette, and M. Minville, 2007.Impacts of Climate Change on the Frequency and Severityof Floods in the Chateauguay River Basin, Canada. RevueCanadienne de Genie Civil 34(9):1048-1060.

Matalas, N.C., 1967. Mathematical Assessment of SyntheticHydrology. Water Resources Research 3(4):937-945.

Mehrotra, R., R. Srikanthan, and A. Sharma 2005. Comparisonof Three Approaches for Stochastic Simulation of Multi-SitePrecipitation Occurrence. 20th Hydrology and Water ResourcesSymposium: Water Capital, February 20-23, 2005, RydgesLakeside, Canberra.

Moran, P.A.P., 1950. Notes on Continuous Stochastic Phenomena.Biometrika 37:17-23.

Odland, J., 1988. Spatial Autocorrelation. Sage Publications,Newbury Park, 87 pp.

Richardson, C.W., 1981. Stochastic Simulation of Daily Precipita-tion, Temperature, and Solar Radiation. Water ResourcesResearch 17(1):182-190.

Richardson, C.W. and D.A. Wright, 1984. WGEN: A Model forGenerating Daily Weather Variables. US Department ofAgriculture, Washington, D.C., Agricultural Research Service,ARS-8, 83 pp.

Semenov, M.A. and E.M. Barrow, 1997. Use of a StochasticWeather Generator in the Development of Climate ChangeScenarios. Climatic Change 22:67-84.

Siriwardena, L., R. Srikanthan, and T.A. McMahon, 2002.Evaluation of Two Daily Rainfall Data Generation Models.Technical Report 02 ⁄ 14, CRC for Catchment Hydrology, MonashUniversity, Australia.

Srikanthan, R. and T.A. McMahon, 2001. Stochastic Generation ofAnnual, Monthly and Daily Climate Data: A Review. Hydrologyand Earth System Sciences 5:653-670.

Watson, B.M., R. Srikanthan, S. Selvalingam, and M. Ghafouri,2005. Hydrologic Response of SWAT to Single Site andMulti-Site Daily Rainfall Generation Models. Proceedings ofMODSIM05 International Congress on Modelling and Simulation,Melbourne, Australia, pp. 2981-2987.

Wilks, D.S., 1998. Multisite Generalization of a Daily StochasticPrecipitation Generation Model. Journal of Hydrology 210:178-191.

Wilks, D.S., 1999. Simultaneous Stochastic Simulation of DailyPrecipitation, Temperature and Solar Radiation at MultipleSites in Complex Terrain. Agricultural and Forest Meteorology96:85-101.

Wilks, D.S. and R.L. Wilby, 1999. The Weather Generation Game:A Review of Stochastic Weather Models. Progress in PhysicalGeography 23:329-357.



effectiveness of multisite weather generator for hydrological

Documents