شبیه سازی تصادفی بارش روزانه با استفاده از مدل‌های خطی تعمیم یافته در اقلیم نیمه خشک

Introduction
Long sequences of rainfall data are required as inputs to many water resource and flood management applications. However, observed rainfall data are rarely sufficient to characterize the full range of rainfall variability at the temporal and spatial scales of interest particularly when the purpose is to make long-term predictions such as those needed for climate change assessment as well as in spatially distributed modelling. To overcome this, stochastic models are commonly used to generate synthetic sequences of rainfall that are statistically consistent with the observed record at one or more gauged sites. Stochastic models also have the potential to quantify uncertainty due to missing values in the observed record and to downscale the outputs of global climate models. a particular challenge for these models is the application to arid and semi-arid regions because of the generally high variability in rainfall, sparse networks of rain gauges and potential data quality problems.
Methodology
In this article, generalized linear model is applied to develop time-series data records of daily rainfall from11 synoptic stations in a 22066.67 km2 relatively sparse sub-basin of Shoor River basin for period of 1991–2010,to be used in hydrological models. To set temporal and spatial rainfall structures ,we used GLMs model .A GLM for daily rainfall is specified in two parts. The pattern of wet and dry days (rainfall occurrence) at a site is typically modelled using logistic regression. Second, a distribution function is fitted to the amount of rainfall on each wet day. For both precipitation occurrence and amounts models, model parameters are determined using the maximum-likelihood estimation (MLE) method. Also model performance can be assessed using simple but informative tests, such as the Pearson residuals. By defining suitable dependence structures between sites, it is possible to build a multivariate GLM. For the occurrence model, we have used a beta-binomial distribution for the number of wet sites on any day. For the amounts model, we have used the inter-site correlation structure of the Anscombe residuals.
Results and discussion Following the procedure explained earlier, precipitation occurrence and amounts were modelled sequentially. In the occurrence model, most predictors are temporal predictors and interactions thereof (12 predictors out of 19). while in the amounts model it is the spatial predictors and their interactions which are more significantIn the final model the absolute magnitude of the ratio of the parameter’s value to its standard error can be regarded as an indicator of the covariate’s strength in the model. Aside from these indicators, we need to check that the Pearson residuals are within the 95% confidence interval. Among the external covariates, Humidity, temperature from reanalysis data were significant external predictors in the occurrence model. In addition, mean Pearson residuals are used to check the systematic model components. almost all the mean Pearson residuals by month, year and site are within the 95% confidence intervals for both occurrence and amounts models. However In the annual plots, it can be seen that some years have residuals placed outside the confidence interval indicating that these years may not be well represented by the models (but, results in Figure 4 show that observed annual and seasonal rainfall in these years are within the simulated bounds implying that the combined occurrence and amounts models produce reasonable annual totals even within these extreme years). This can be considered as evidence of good model performance, and shows that the structure of the precipitation characteristics by month, year and site are all well captured by the models. To indicate the spatial structure of errors, bubble maps for mean residuals by sites for both occurrence and amount models are plotted. Random distribution of residuals in space and lack of systematic structure in either of these plots can be interpreted that spatial variation of both rainfall occurrence and amount are well captured by the fitted models. To further check whether the GLM developed for this basin has captured the temporal structure of the observed data, we used the GLM to simulate rainfall at sites G5, G12 and G14 for the period 1981–1990, which is outside the fitting period. These particular sites were chosen on the basis of data availability prior to the period used for fitting. For spatial validation, rainfall data were simulated for the period 1991–2010 at stations G3, G11 and G13, which were not used at all for fitting. Again, from this plot, it can be seen that in general the GLM seems to adequately simulate the observed data.
Summary and conclusions The aim of this work was to investigate the potential applicability of a GLM for stochastic simulation of multisite daily rainfall in semi-arid areas and to develop a model that can be used to infill and extend historical rainfall data. In our application, logistic regression was used to simulate rainfall occurrence and two-parameter gamma distributions were used to simulate amounts on wet days. Inter-site dependence models were included for both occurrence and amounts. The main predictors of rainfall in the Shoor case study were found to be location effects, seasonality and temporal dependence. Humidity, temperature and from re-analysis data were significant external predictors. Analysis of model residuals showed that in general the model captured the seasonal, annual and spatial structure of rainfall in the basin. The simulation results indicated that in general the model results were consistent with the observed rainfall properties especially when we used from external predictors. Spatial and temporal validation tests showed that the GLM adequately simulated rainfall for the periods and gauges not used during model fitting. It can be concluded that the GLM provides a useful tool for simulating multi-site rainfall in the semi-arid Shoor basin for water resources purposes and may potentially be applicable to climate change analysis and to other semi-arid regions.