### A Multi-variables Multi -sites Model for Forecasting Hydrological Data Series

*Journal of Engineering*

2014, Volume 20, Issue 7, Pages 85-102

2014, Volume 20, Issue 7, Pages 85-102

#### Abstract

A multivariate multisite hydrological data forecasting model was derived and checked using a case study. The philosophy is to use simultaneously the cross-variable correlations, cross-site correlations and the time lag correlations. The case study is of two variables, three sites, the variables are the monthly rainfall and evaporation; the sites are Sulaimania, Dokan, and Darbandikhan.. The model form is similar to the first order auto regressive model, but in matrices form. A matrix for the different relative correlations mentioned above and another for their relative residuals were derived and used as the model parameters. A mathematical filter was used for both matrices to obtain the elements. The application of this model indicates it's capability of preserving the statistical characteristics of the observed series. The preservation was checked by using (t-test) and (F-test) for the monthly means and variances which gives 98.6% success for means and 81% success for variances. Moreover for the same data two well-known models were used for the sake of comparison with the developed model. The single-site single-variable auto regressive first order and the multi-variable single-site models. The results of the three models were compared using (Akike test) which indicates that the developed model is more successful ,since it gave minimum (AIC) value for Sulaimania rainfall, Darbandikhan rainfall, and Darbandikhan evaporation, while Matalas model gave minimum (AIC) value for Sulaimania evaporation and Dokan rainfall, and Markov AR (1) model gave minimum (AIC) value for only Dokan evaporation).However, for these last cases the (AIC) given by the developed model is slightly greater than the minimum corresponding value.

#### Keywords

forecasting, multi-sites, multi-variables, cross sites correlation, serial correlation, cross variables correlations, hydrology.#### Metrics