Efficiency of Statistical Downscaling Models of SDSM and LARS-WG in the Simulation of Meteorological Parameters in Lake Urmia Basin

Introduction
Linking resolution global climate models to local scale as a micro climatic process is a significant issue. Recently, attempts have been made by the climatology scientists to develop dynamics and statistical downscaling methods to express climate change at a local and regional scale. Two general techniques are been used for downscaling of the output of general circulation models (GCM). The further is by statistical methods in which the output of a statistical model (MOS) and a planned approach to weather short-term numerical prediction is presented. The later is regional climate model (RCM), same as limited GCM model in a subnet of network global model by dynamic method that uses climatic conditions temporal changes according to GCM model. Both methods play an important role to determine the potential effects of the climate change caused by increased greenhouse gas emissions. Much work is done to use this method for downscaling of the global model output in different areas in which the performance of the model is assessed. Uncertainty analysis has been done on these methods or compared by other statistical methods.
 
Materials and Methods
In this study for more accurate validation of the two methods, uncertainty analysis is done on input data of daily temperature and precipitation. In uncertainty analysis of daily temperature data because of similarity of the statistical distribution to normal distribution, the monthly mean of downscaled data are statistically compared with observed data. In this case, parametric or non-parametric tests can be used to compare means. However, in uncertainty analysis of daily rainfall data because of lack of normality, comparison of the averages of downscaled data and observed data are not sufficient and should be compared with the dry and wet periods. In this method, the statistical distribution of downscaled dry and wet period durations is compared with the observed ones.
Before the uncertainty analysis, first, an exploratory analysis is performed on the data in the data statistical condition and the approach to data analysis to be ascertained. This analysis is based on the study of statistical assumptions of the model. If these assumptions are not established, the statistical analysis parametric methods and respective tests lose their credibility and nonparametric methods must be used. These assumptions are:
1. Data come from normal or near to normal distribution.
2. Data standard average is close to zero or there is no outlier.
3. Data have little temporary correlation.
Daily rainfall varies because of the skewness of the right (frequency of daily precipitation amounts toward zero), the normal assumption is questionable. Therefore, power transformations are used for normality of rainfall data in statistical analysis and modeling. On the other hand, the daily temperature data are normal in nature and there is not outlier. But, because of temporary correlation of daily temperature, the third assumption did not establish for them. Therefore, parametric methods are used for statistical analysis and comparative tests.
 
Results and Discussion
According to the three basic assumptions of the model, daily rainfall data are far from a normal distribution and the data have a lot of outlier points. But, there is not significant correlation period. Unlike the daily maximum and minimum temperature data of relatively normal distribution, they have not had many outlier points. But, there is a significant correlation of the data with time. Therefore, it can be concluded that none of the data of temperature and precipitation have conditions of the three basic assumptions. Therefore, non-parametric methods must be used for statistical analysis and modeling. Or alternative parameters are used such as the number of days wet or dry.
For the uncertainty analysis and comparison of the two models SDSM and LARS-WG we have used graphical and statistical methods. In this study, the absolute values of the differences between downscaled values and observed values in the 1961-1990 statistical periods are used as an indicator in the graphical analysis. Results of graphical analysis show that values of the absolute differences in different months of the SDSM model parameters are the minimum and maximum daily temperature LARS-WG is better than the model. The daily rainfall amounts during the months of absolute difference of the two models are relatively close to each other. Of course, the results of stations in Tabriz and Urmia are slightly different but are not significant.
To evaluate the significance difference between observation and downscaled values in two models, we have used Mann-Whitney test. The results show that for the minimum temperature, in both models SDSM and LARS-WG almost in half of the months, the model error is significant, although the SDSM model is better. However, the tendency to work and choose the most appropriate model for large-scale predictor variables from the NCEP-NCAR data were obtained from the appropriate geographic region and it is possible to achieve better performance. Parameter maximum daily temperature for the SDSM model has better performance than the LARS-WG, which confirmed the results of the chart. The downscaled maximum daily temperature has less error than the minimum daily temperature. Especially in SDSM model in Tabriz station only January has a significant error in the model. It has good performance for daily precipitation models. Especially in Tabriz station the values of the model error is not significant in any of the months. In accordance with the similar results, the performance of the two models is similar for the daily rainfall.
 
Conclusion
The results of this study indicates that in accordance with the results of the statistical downscaling SDSM and LARS-WG on stations of Tabriz and Urmia for daily minimum and maximum parameters, SDSM model has better performance than the LARS-WG. For daily precipitation performance, the two models are similar in the two stations. However, as the statistical distribution of daily rainfall data is not normal, the results of the models cannot be trusted. It is suggested that instead of precipitation, in the analysis we used the number of dry and wet days.