Theor Appl Climatol DOI 10.1007/s00704-015-1691-8
ORIGINAL PAPER
Links between the spatial structure of weather generator and hydrological modeling Zhi Li 1 & Zhemin Lü 1 & Jingjing Li 1 & Xiaoping Shi 1
Received: 3 May 2015 / Accepted: 28 November 2015 # Springer-Verlag Wien 2015
Abstract Impacts of the spatial structure of weather generators on hydrological modeling have been largely qualitatively discussed; however, their links have been rarely quantified. The precipitation occurrence and amount were respectively generated with Markov chain and the mixed exponential distribution for single sites, and then the procedures were extended to multi-site simulation according to Wilks (1998). In the multi-site model, precipitation amounts were respectively generated with untapered or tapered mixed exponential scale parameters. The generated precipitation series were used as inputs of Soil and Water Assessment Tool (SWAT) to interpret the links between the spatial structure of weather generators and hydrological modeling. The single-site and multi-site model using untapered scale parameters gave similar averages for monthly and annual streamflow; however, the untapered multi-site model was superior to simulating hydrological variability. The single-site model underestimated the maxima and variances while overestimated the minima of streamflow; therefore, the use of single-site models for hydrological variability simulation should be cautious. The multi-site model using tapered scale parameters greatly overestimated the averages, extremes, and variances of streamflow. The Wilks model for multi-site precipitation simulation using tapered scale parameters is not appropriate for hydrological modeling, and the untapered version is thus recommended. Overall, the spatial structure of weather generators has significant impacts
* Zhi Li
[email protected] 1
State Key Laboratory of Soil Erosion and Dryland Farming on Loess Plateau, College of Natural Resources and Environment, Northwest A & F University, Yangling, Shaanxi 712100, China
on hydrological modeling, especially for hydrological variability simulation; therefore, the links between them should be paid great attentions.
1 Introduction Precipitation is one of the most important meteorological variables for hydrological modeling. In cases long series of observed precipitation are not available, they can be stochastically generated by weather generators. Though weather generators are very convenient for precipitation simulation, those operated on single site (SSWG) cannot preserve the inter-site correlations of occurrences or amounts. SSWG can be used by the lumped hydrological models to satisfactorily simulate the hydrological variability since only single-site climate inputs are needed; however, it is not suitable for the distributed hydrological models since multi-site climate inputs are needed. Underestimation of the spatial structure of climate makes the high flow in one subbasin be offset by low flow in the neighboring subbasin, and further results in underestimation of hydrological extremes (Clark et al., 2004; Khalili et al., 2011; Thyer and Kuczera, 2003; Wilks, 1998). To incorporate the spatial structure of climate, several kinds of multi-site weather generator (MSWG) have been developed, such as hidden Markov chain model (Boorman and Sefton, 1997; Rex, 1993; Thyer and Kuczera, 2003), resampling method (Beersma and Buishand, 2003; Caraway et al., 2014; Jim et al., 2005; Jules and Buishand, 2003; Reilly and Schimmelpfennig, 2000; Wilby et al., 2003), chain-dependent models (Brissette et al., 2007; Mehrotra and Sharma, 2007; Qian et al., 2002; Wilks, 1998), and semi-parametric methods (Angulo et al., 1998; Cannon, 2008; Fowler et al., 2005; Jeong et al., 2013; Li, 2014; Mehrotra and Sharma, 2007; Palutikof et al., 2002). Though each method has its own advantages and
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limitations, these methods can satisfactorily reproduce the statistical parameters and spatiotemporal structure of climate. Among MSWG, the chain-dependent model developed by Wilks (1998) is a parametric method and has been discussed by many studies, such as algorithm improvement (Brissette et al., 2007; Mehrotra and Sharma, 2007; Qian et al., 2002), multi-site precipitation downscaling (Wilks, 1999), and impact study (Watson et al., 2005). Linking the precipitation amount or occurrence correlations to the random number correlations by developing empirical curves for each station pair and for each month, this model satisfactorily simulates the inter-site correlations of precipitation and is more efficient after algorithm improvement by Brissette et al. (2007). This method has also been proved to be superior in simulating precipitation occurrence than the other methods (Mehrotra et al., 2006). Though the generated climates from SSWG and MSWG are both used for hydrological modeling, their impacts have been rarely quantified. Though a few studies have discussed this issue through combing a certain distributed hydrological model with different precipitation generators, the results are quite different. Watson et al. (2005) concluded that no distinct differences existed in the simulated streamflow through combining Soil and Water Assessment Tools (SWAT) with the Wilks method in a watershed with an area of 306 km2 and three weather stations. However, Khalili et al. (2011) found that MSWG generated better flood than SSWG using HydroTEL and MSWG of spatial autocorrelation method in a watershed with an area of 26, 000 km2 and seven weather stations. Our previous study got similar results as Khalili et al. (2011) through combining a two-stage weather generator (TSWG) with SWAT in a watershed with an area of 45,421 km2 and 15 weather stations (Li, 2014). Therefore, quantitative assessment is still necessary to further determine the impacts of SSWG and MSWG on hydrological modeling. This study will thus assess the impacts of single- and multisite chain-dependent precipitation models following Wilks (1998) on hydrological modeling and interpret the mechanism causing the differences. The statistics of precipitation from SSWG and MSWG were directly compared to give information for their possible effects on hydrological modeling, and then the hydrological responses of SWAT to SSWG and MSWG were compared to give suggestions for weather generator choice.
2 Data and methodology 2.1 Data and example catchment Daily precipitation data from 15 meteorological stations across the Jing River catchment and monthly streamflow data
from the catchment outlet during 1961–2001 were used. The Jing River is a second-order tributary of the Yellow River (Fig. 1). With an area of 45,421 km2, the catchment has a climate of subhumid to semi-arid from the southeast to northwest. The average annual precipitation in the catchment is 542.1 mm, and the average annual temperature is 9.0 °C. With 50–60 % of the annual precipitation falling between June and September in forms of heavy storms, the extreme precipitation events greatly contributed to flood generation; at the same time, the spatiotemporal variations in precipitation due to the large area of the catchment have great impacts on flood generation. Therefore, the example catchment would be good enough for interpreting the impacts of spatial structure of weather generators on hydrological modeling. 2.2 Single-site precipitation generation A chain-dependent process was employed for the singlesite precipitation generation. As the algorithms have been described in details by many studies (Li et al., 2013; Richardson and Nicks, 1990; Wilks and Wilby, 1999), the procedure was briefly described as follows. The first-order two-state Markov chain was used to generate precipitation occurrence (wet and dry events). After the observed conditional probability was calculated for each station and for each month, their values were compared with the outputs from a uniform [0, 1] random number generator to stochastically simulate the precipitation occurrence. A wet day was simulated if the random number was smaller than the critical probability. The mixed exponential distribution was used to assign the nonzero precipitation amounts. As a distribution with three parameters, it is a mixture of two one-parameter exponential distributions. p −x 1−p −x f ð xÞ ¼ þ ; 0 ≤ p ≤ 1; β 1 exp exp β1 β1 β2 β2 > 0; β2 > 0
ð1Þ
where p denotes the mixing probability, and β1 and β2 are the scale parameters of the two exponential distributions. The nonzero precipitation amounts were simulated using the following equation: rt ¼ −βt lnðvt Þ
ð2Þ
where vt is a uniform random number, and βt is either β1 or β2 and is dependent on the mixing probability, α. After estimating the parameters for precipitation occurrence and amounts, 100 years of daily precipitation were generated for each station.
Links between the spatial structure of weather generator and hydrological Fig. 1 Location of the Jing River catchment (left) and the seasonal pattern of precipitation (right)
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2.3 Multi-site precipitation generation MSWG was constructed by driving SSWG with a series of spatially correlated random numbers according to Wilks (1998). For precipitation amount generation, two models dealing with selection of the mixed exponential scale parameters were used in the Wilks (1998) method. The first model, denoted as MSWG with untapered scale parameters (hereafter represented by MSWGuntaper), directly assigned the smaller/ greater of the two mixed exponential scale parameters to nonzero amounts with smaller/greater expected values (Eq. 3), which was based on the relationship between the uniform variate for precipitation occurrence ut(k) and the mixed parameter of the mixed exponential distribution α(k). . 8 < β1 ðk Þ; ut ðk Þ pc ðk Þ≤ αðk Þ . ð3Þ β t ðk Þ ¼ : β ðk Þ; ut ðk Þ p ðk Þ > αðk Þ 2 c where k represents station number; pc(k) is the critical probability; βt, β1, and β2 is the chosen, greater, and smaller of the mixed exponential scale parameters. However, the continuity ratios of this model were not good enough. As precipitation occurrence and amount were generated independently in weather generator, the observed links between them were possibly destroyed. Continuity ratio was thus used by Wilks (1998) to interpret the links between precipitation amounts and occurrences. continuity ratio ¼
E ðY t ðk ÞjY t ðk Þ > 0; Y t ðℓ Þ ¼ 0Þ E ðY t ðk ÞjY t ðk Þ > 0; Y t ðℓ Þ > 0Þ
ð4Þ
E(Yt(k)|Yt(k)>0,Yt(ℓ)=0) is the mean of the nonzero precipitation amounts at station k given zero precipitation at station ℓ; E(Yt(k)|Yt(k)>0,Yt(ℓ)>0) is the mean of the nonzero precipitation amounts at station k given nonzero precipitation at station ℓ.
To give better continuity ratios, the large precipitation amount simulation was improved by continuously varying the larger of the two scale parameters (Eq. 5), which was denoted as MSWG with tapered scale parameters (hereafter represented by MSWGtaper). MSWGtaper gave better continuity ratios than MSWGuntaper; however, the form of tapering for the scale parameter β1(k) made the variances from Eq. 5 as 4/3 times of those from Eq. (3) (Wilks, 1998).
β t ðk Þ ¼
8 > < β2 ðk Þ þ 2½β 1 ðk Þ−β2 ðk Þ 1− > : β ðk Þ; 2
. ut ðk Þ ; ut ðk Þ pc ðk Þ ≤αðk Þ αðk Þpc ðk Þ .
ut ðk Þ pc ðk Þ > αðk Þ
ð5Þ To assess the impacts of different precipitation amount model on hydrological modeling, they were both used in this study to generate different series of precipitation based on the same occurrence matrix.
Table 1 Number of station-month combinations for daily or monthly precipitation, and number of stations for annual precipitation that pass the rank sum test and squared rank test (stations or combinations passing the test/total stations or combinations) Precipitation distributions Rank sum test Daily precipitation Monthly precipitation Annual precipitation Squared rank test Daily precipitation Monthly precipitation Annual precipitation
SSWG
MSWGuntaper
MSWGtaper
180/180 180/180 15/15
167/180 180/180 15/15
174/180 180/180 15/15
174/180 146/180 14/15
174/180 144/180 15/15
172/180 160/180 10/15
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Simulated monthly precipitation STD, mm
80
To calibrate SWAT, only monthly streamflow during the 1960s was used since they have been influenced greatly thereafter due to a large number of soil conservation measures (Li et al., 2009). Five-year data were used for calibration and validation, respectively. The Nash-Sutcliffe model efficiency coefficient was 0.80 for calibration and 0.79 for validation, implying SWAT can satisfactorily model the streamflow in the Jing River catchment. As the focus of this paper was on the effects of MSWG, the detailed calibration steps and results were not presented. The streamflow for the period of 1971–2001 was then simulated by SWAT with the calibrated parameters. As the soil conservation measures have substantially decreased the average and floods of streamflow and they cannot be incorporated into SWAT, exclusion of their impacts is very important for the simulation of natural rainfall-runoff relationships (Li, 2014). Therefore, the observed discharge used hereafter was represented by the modeled data instead of the observed data. When using the synthetic precipitation as inputs of SWAT, the first 5-year data were used as warm up period, and the following 95-year data were used to compare the effects of weather generators on hydrological modeling.
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Fig. 2 Standard deviations (STD) of the observed and simulated monthly precipitation
2.4 Hydrological modeling Soil and Water Assessment Tools (SWAT) (Arnold et al., 1998) was used to assess the impacts of precipitation generation on hydrological modeling. To minimize the impacts of the other meteorological variables, only precipitation data were used as inputs, while temperature, wind speed, and relative humidity were generated for only one station by the embedded weather generator of SWAT. As the meteorological variables generated by SWAT were conditioned on the dry/wet status of precipitation, the inter-variable relationships were preserved (Neitsch et al., 2005). This step was to highlight the rainfallrunoff relationship while minimize the impacts of the other meteorological variables. 10% 0.4
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The statistics of different precipitation series, such as mean, variance, and inter-site correlations, were firstly compared with those observed to give basic information for the hydrological modeling. Wilcoxon rank sum and squared rank tests (p = 0.05) were employed for mean and variance equality test since precipitation are often skewed. As nonparametric
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2.5 Assessment procedure
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Fig. 3 10th, 30th, 50th, 70th, 90th, and 99th percentiles (not the values below this point but at this point) of the observed and simulated daily precipitation
Links between the spatial structure of weather generator and hydrological
methods, they can be used for any distributions and have great efficiency on non-normal distributions (Conover, 1971). The generated inter-site correlations and continuity ratios were compared with those observed. To further investigate the distribution of the generated precipitation, the 10th, 30th, 50th, 70th, 90th, and 99th percentiles were compared with the corresponding observation. The second part assessed the impacts of the generated precipitation on streamflow modeling. The streamflow series were first simulated by SWAT using three series of precipitation (SSWG, MSWGuntaper, and MSWGtaper) as inputs, and then the effects of weather generators were evaluated by comparing parameters such as mean and standard deviation. In addition, cumulative frequency analysis was used to determine whether the generated and historical streamflow had the same distribution or variability.
percentiles well while overestimated the higher percentiles, especially for the 99th percentiles; however, MSWGtaper greatly overestimated the lower percentiles (30th, 50th, and 70th) while well reproduced the higher percentiles (90th and 99th percentiles). The good performances of MSWGtaper for reproducing higher percentiles were due to the adjustments of the mixed scale parameters as mentioned above. The inter-site correlations of daily precipitation occurrences (the same occurrences for two amount models) and amounts were satisfactorily preserved (Fig. 4), though the results were no better than those in Wilks (1998). Most of the observed spatial correlations of occurrences or amounts were underestimated. The inter-site correlations of synthetic precipitation amounts from MSWGtaper were slightly greater than 1.0
(a) Occurrence
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The mean daily, monthly, and annual precipitation amounts were satisfactorily reproduced by the precipitation models though those from SSWG were a little better than those from MSWGuntaper and MSWGtaper according to the results of rank sum test (Table 1). For variance equality of daily precipitation, three models gave similar results; however, for monthly precipitation, MSWGtaper performed better than SSWG and MSWGuntaper since the station-month combinations passing the squared rank test were 160, 146, and 144, respectively. As shown in the results of SSWG and MSWGuntaper (Fig. 2), weather generators without considering the low-frequency variability usually underestimate the variances (Chen et al., 2010; Khazaei et al., 2013; Mehrotra and Sharma, 2007); however, MSWGtaper presented better variance simulation since it overestimated the variances (Wilks, 1998). The variance overestimation from MSWGtaper increased the variability of monthly precipitation and further influenced those of annual precipitation, which is the reason why stations passing the squared rank test for annual precipitation from MSWGtaper were less than those from SSWG and MSWGuntaper (Table 1). The percentiles of the observed and simulated daily precipitation were shown in Fig. 3, and their differences can be used to quantify the ability of different models to reproduce the observed distribution. Overall, the observed distribution across all percentiles cannot be exactly reproduced by any model. The 10th percentiles from each model were not simulated well because of the threshold definition of wet events (0.1 mm). SSWG appeared to simulate all percentiles well except for an underestimation of the 99th values, which is similar as the assessment carried out across the Loess Plateau (Li et al., 2014). MSWGuntaper simulated the lower
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those from MSWGuntaper; however, they appeared to be very similar. As for the continuity ratios, three precipitation models presented quite different results (Fig. 5). Without considering spatial correlations, SSWG cannot represent the observed continuity ratios since most synthetic values were close to one (Fig. 5a). MSWGuntaper overestimated the observed continuity ratios (Fig. 5b) while MSWGtaper greatly improved the ability of precipitation model to reproduce the continuity ratios (Fig. 5c). However, MSWGtaper significantly overestimated the greater values of monthly total precipitation (Fig. 5f) while SSWG and MSWGuntaper gave similar values as the observed (Fig. 5d, e). This problem was also due to the variance overestimation from MSWGtaper and obviously increased the monthly precipitation of flood season.
were presented in Table 2. Obviously, the mean annual and monthly streamflow were overestimated by 3, 9, and 26 % by SSWG, MSWGuntaper and MSWGtaper, respectively. MSWGuntaper performed well in simulating the maxima and standard deviations of annual or monthly streamflow while SSWG/MSWGtaper greatly underestimated/overestimated the corresponding values. To further investigate the impacts of precipitation simulation on hydrological modeling, the statistics of monthly streamflow and cumulative frequency of annual streamflow were compared in Fig. 6. For the averages of monthly streamflow, SSWG and MSWGuntaper performed satisfactorily for all months, while MSWGtaper greatly overestimated those between July and September. The variances of monthly streamflow were underestimated by SSWG while overestimated by MSWGtaper between May and November. The maxima of monthly streamflow were overestimated for most months by MSWGtaper, and those between July and September were two to four times of the observed. For the minima of monthly streamflow, SSWG overestimated those of most months while the other two precipitation models performed similar. Overall, the greatest overestimation/
3.2 Impacts of precipitation generation on hydrological modeling Driving SWAT by the synthetic precipitation, three series of streamflow were generated and their statistical parameters
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Fig. 5 Continuity ratios and monthly total amounts between the observed and simulated precipitation
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Links between the spatial structure of weather generator and hydrological Table 2
Statistical parameters of the observed and simulated annual and monthly streamflow
Statistics
Annual streamflow
Monthly streamflow
Average, mm
OBS 38.5
SSWG 39.7
MSWGutaper 42.0
MSWGtaper 48.7
OBS 3.2
SSWG 3.3
MSWGutaper 3.5
MSWGtaper 4.1
STDEV Max, mm
13.5 73.7
6.9 53.4
14.6 83.1
22.0 121.8
4.0 28.3
3.0 15.9
4.0 29.2
5.8 70.2
Min, mm
19.7
24.5
12.7
17.4
0.03
0.05
0.04
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OBS observation, SSWG single-site weather generator, MSWGuntaper multi-site weather generator untapered version, MSWGtaper multi-site weather generator tapered version
4 Summary and discussion
underestimation of monthly streamflow occurred between July and September. Besides standard deviation (or variance), the cumulative frequency of annual streamflow was used to quantify the impacts of precipitation simulation on hydrological variability simulation (Fig. 6c). MSWGuntaper gave the best simulation while SSWG/MSWG t a p e r greatly underestimated/ overestimated the corresponding values and the differences increased with return periods, which implies that MSWGuntaper can satisfactorily simulate the hydrological variability.
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According to Wilks (1998) method, a single-site chain-dependent precipitation model was extended to a multi-site version, among which the precipitation occurrence and amount were respectively simulated by the first-order two-state Markov chain and the mixed exponential distribution. In multi-site model, precipitation amounts were generated with untapered or tapered scale parameters. After comparing the statistics of precipitation models, the synthetic precipitation series were fed to the distributed hydrological model SWAT to investigate
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Fig. 6 Statistics of monthly streamflow and cumulative frequency of annual streamflow
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the links between the spatial structure of weather generators and hydrological modeling. For precipitation simulation, the single- and multi-site precipitation models gave similar averages; however, the multisite model can satisfactorily simulate the inter-site correlations of precipitation occurrences and amounts. The multi-site model with tapered mixed exponential scale parameters, compared with that with untapered scale parameters, performed better for simulating monthly precipitation variances, interstation correlations, and continuity ratios; however, it overestimated the averages and variances of monthly precipitation during the flood season. As for the impacts of precipitation generation on hydrological modeling, the single-site and untapered multi-site model gave similar results for monthly and annual mean values; however, the untapered multi-site model was superior to simulating the extremes and variances of streamflow. The singlesite model underestimated the maxima and variance while overestimated the minima; therefore, the use of single-site precipitation model for hydrological extremes should be cautious. In spite of the good performances in precipitation generation, the tapered multi-site model greatly overestimated the mean, variances, and extremes of streamflow. Therefore, though the tapered multi-site model was superior to keeping some characteristics of the observed precipitation, it gave greater errors for hydrological modeling, especially for maxima and variances of streamflow. The untapered multi-site precipitation model is thus recommended for impact study, especially for hydrological extremes simulation. The present study assessed the impacts of precipitation generation on hydrological modeling using monthly streamflow and found that the Wilks method with untapered scale parameter was the best model. However, the precipitation of higher percentiles (90th and 99th) was overestimated by the untapered model while preserved well by the tapered model (Fig. 3), which indicates that the tapered model might give better daily flood simulation. Therefore, for long-term variability of streamflow, the untapered multi-site model is good enough; however, for daily extreme event simulation, the tapered multi-site model might be better, though further evaluation should be carried out. Some qualitative studies deduced that the hydrological variability, simulated with climate not considering its spatial structure, would be underestimated (Clark et al., 2004; Thyer and Kuczera, 2003; Wilks, 1998). However, contradicting results were given by three quantitative studies. The effects of spatial structure of climate on hydrological modeling were not detected in the watershed with an area of 306 km2 and three weather stations (Watson et al., 2005). while significant in two watersheds with greater areas and more weather stations, i.e., 26,000 km2 and seven weather stations (Khalili et al., 2011) as well as 45,421 km2 and 15 weather stations (Li 2014). The differences are possibly due to the catchment
scales and its resultant spatiotemporal variations in climate. For example, the cross correlations of daily precipitation occurrence and amount from Watson et al. (2005) mainly concentrated within a small range (mostly 0.6–0.7 for occurrence and 0.7–0.8 for amount), while those for the latter two watersheds were scattered in a larger range (for both occurrence and amount, 0.3–0.7 for Khalili et al. (2011) while 0.5–0.8 for Li (2014)). Therefore, the stochastically generated climate should incorporate the spatial structure of climate when they are used for hydrological variability simulation, which is especially important for a large-scale watershed. Acknowledgments We appreciate the Data Sharing Infrastructure of Loess Plateau for providing the streamflow and climate data. This study is jointly funded by the National Natural Science Foundation of China (41101022), Fok Ying Tung Foundation (141016), and Chinese Universities Scientific Fund (2014YQ003 and 2452015105). The constructive comments from the reviewers are greatly appreciated.
References Angulo JM, González-Manteiga W, Febrero-Bande M, Alonso FJ (1998) Semi-parametric statistical approaches for space-time process prediction. Environ Ecol Stat 5(4):297–316 Arnold JG, Srinivasan R, Muttiah RS, Williams JR (1998) Large area hydrologic modeling and assessment. Part 1. Model development. J Am Water Resour Assoc 34(1):1–17 Beersma J, Buishand T (2003) Multi-site simulation of daily precipitation and temperature conditional on the atmospheric circulation. Clim Res 25:212–133 Boorman DB, Sefton CEM (1997) Recognising the uncertainty in the quantification of the effects of climate change on hydrological response. Clim Chang 35(4):415–434 Brissette FP, Khalili M, Leconte R (2007) Efficient stochastic generation of multi-site synthetic precipitation data. J Hydrol 345(3–4):121– 133 Cannon AJ (2008) Probabilistic multisite precipitation downscaling by an expanded bernoulli–gamma density network. J Hydrometeorol 9(6): 1284–1300. doi:10.1175/2008JHM960.1 Caraway NM, McCreight JL, Rajagopalan B (2014) Multisite stochastic weather generation using cluster analysis and k-nearest neighbor time series resampling. J Hydrol 508:197–213 Chen J, Brissette FP, Leconte R (2010) A daily stochastic weather generator for preserving low-frequency of climate variability. J Hydrol 388(3–4):480–490. doi:10.1016/j.jhydrol.2010.05.032 Clark MP, Gangopadhyay S, Hay L, Rajagopalan B, Wilby RJ (2004) The schaake shuffle: a method for reconstructing space-time variability in forecasted precipitation and temperature fields. J Hydrometeorol 5:243–262 Conover WJ (1971) Practical nonparametric statistics. John Wiley & Sons, New York, p. 462 pp Fowler HJ, Kilsby CG, O’Connell PE, Burton A (2005) A weather-type conditioned multi-site stochastic rainfall model for the generation of scenarios of climatic variability and change. J Hydrol 308(1–4):50– 66 Jeong DI, St-Hilaire A, Ouarda TBMJ, Gachon P (2013) A multi-site statistical downscaling model for daily precipitation using global scale GCM precipitation outputs. Int J Climatol 33(10):2431– 2447. doi:10.1002/joc.3598
Links between the spatial structure of weather generator and hydrological Jim H, Craig T, Alison K (2005) Influence diagrams for representing uncertainty in climate-related propositions. Clim Chang 69(2): 343–365 Jules JB, Buishand TA (2003) Multi-site simulation of daily precipitation and temperature conditional on the atmospheric circulation. Clim Res 25(2):121–133. doi:10.3354/cr025121 Khalili M, Brissette F, Leconte R (2011) Effectiveness of multi-site weather generator for hydrological modeling. JAWRA Journal of the American Water Resources Association 47(2):303–314. doi:10. 1111/j.1752-1688.2010.00514.x Khazaei M, Ahmadi S, Saghafian B, Zahabiyoun B (2013) A new daily weather generator to preserve extremes and low-frequency variability. Clim Chang 119(3–4):631–645. doi:10.1007/s10584-013-07405 Li Z (2014) A new framework for multi-site weather generator: a twostage model combining a parametric method with a distribution-free shuffle procedure. Climate Dynamics. 43(3–4):657–669. doi:10. 1007/s00382-013-1979-2 Li Z, Brissette F, Chen J (2013) Finding the most appropriate precipitation probability distribution for stochastic weather generation and hydrological modelling in Nordic watersheds. Hydrol Process 27(25): 3718–3729. doi:10.1002/hyp.9499 Li Z, Brissette F, Chen J (2014) Assessing the applicability of six precipitation probability distribution models on the Loess Plateau of China. Int J Climatol 34(2):462–471. doi:10.1002/ joc.3699 Li Z, Liu WZ, Zhang XC, Zheng FL (2009) Impacts of land use change and climate variability on hydrology in an agricultural catchment on the Loess Plateau of China. J Hydrol 377(1–2):35–42. doi:10.1016/ j.jhydrol.2009.08.007 Mehrotra R, Sharma A (2007) A semi-parametric model for stochastic generation of multi-site daily rainfall exhibiting low-frequency variability. J Hydrol 335(1–2):180–193
Mehrotra R, Srikanthan R, Sharma A (2006) A comparison of three stochastic multi-site precipitation occurrence generators. J Hydrol 331(1–2):280–292 Neitsch SL, Arnold JG, Kiniry JR, Williams JR 2005 Soil and water assessment tool theoretical documentation-version. 2005 pp 524 Palutikof JP, Goodess CM, Watkins SJ, Holt T (2002) Generating rainfall and temperature scenarios at multiple sites: examples from the Mediterranean. J Clim 15(24):3529–3548 Qian B, Corte-Real J, Xu H (2002) Multisite stochastic weather models for impact studies. Int J Climatol 22:1377–1397 Reilly J, Schimmelpfennig D (2000) Irreversibility, uncertainty, and learning: portraits of adaptation to long-term climate change. Clim Chang 45(1):253–278 Rex JF (1993) The dynamics of uncertainty: application to parameterization constants in climate models. Clim Dyn 8(3):135–150 Richardson CW, Nicks AD 1990 Weather generator description. EPICErosion/Productivity Impact Calculator: 1. Model Documentation, 1768. Technical BuUetin, USDA ARS, 235 pp Thyer M, Kuczera G (2003) A hidden Markov model for modelling longterm persistence in multi-site rainfall time series. 2. Real data analysis. J Hydrol 275(1–2):27–48 Watson BM, Srikanthan R, Selvalingam S, Ghafouri M 2005 Hydrologic response of SWAT to single site and multi-site daily rainfall generation models. Proceedings of MODSIM05 International Congress on Modelling and Simulation, Melbourne, Australia, pp 2981–2987 Wilby RL, Tomlinson OJ, Dawson CW (2003) Multi-site simulation of precipitation by conditional resampling. Clim Res 23:183–199 Wilks DS (1998) Multisite generalization of a daily stochastic precipitation generation model. J Hydrol 210:178–191 Wilks DS (1999) Multisite downscaling of daily precipitation with a stochastic weather generator. Clim Res 11:125–136 Wilks DS, Wilby RL (1999) The weather generation game: a review of stochastic weather models. Prog Phys Geogr 23(3):329–357
