Introduction: The pattern of annual precipitation in developing areas and the related industries is known as one the most important infrastructure in such studies. This investigation is based on statistical analysis of the frequency of the total annual amount of precipitation using Empirical Orthogonal Function (EOF). The long time statistical studies support the effectiveness of the implemented statistical EOF in the area. Fuzzy logic is a new fold of logical reasoning that is estimated rather than a fixed and exact form. It has been developed to implement the concept of partial truth, where the truth value may vary between completely true and false. In this study, two concepts for fuzzification are implemented, the first one is based on Standardized Precipitation Index (SPI) and the other is founded on long term annual precipitation. These two concepts have been compared for analyzing the stability of extracted patterns of EOF on the area of interest.
Materials and Methods: Investigation of the spatiotemporal pattern of annual rainfall in the Ghazvin province, as one of the most important developing area, is an important issue. This pattern may highly affect the future program for this region in the North West of Iran. This investigation is based on about thirty years of annual precipitation fifty rain gauge stations over the area of interest. The precipitation data from the Islamic Republic of Iran Ministry of Energy have been used. The first regionalization was implemented by means of the EOF method. The first extracted component described more than 80% of the total information on the annual precipitation over the area, and its spatio-temporal pattern was classified as one the most stable structures as well. In this paper based on Empirical Orthogonal Function (EOF) and its fuzzy form (FEOF), spatial and temporal behavior and stability of regional precipitation are investigated. Normal EOF is categorized as the linear decomposition method, but these new fuzzy weighted methods are classified as a class of nonlinear structures as well. EOF, FEOF and SPI was performed using "MATLAB" software. Finally, based on the linear and nonlinear spatio-temporal pattern recognition, the original space-time precipitation structure of the studied area has been evaluated.
Results and Discussion: After extracting the most important space-time pattern of precipitation based on EOF and FEOF, the stability of the linear form was evaluated. These three approaches, EOF, FEOF based on SPI weight and mean annual precipitation, represent the whole information via their first component and their projected first spatial patterns depict is high compatibility as is possible because of the structure of long term rainfall over the studied area. These spatial compatibilities are presented in Fig. 5, Fig. 6, Fig. 9 and Fig. 11. The temporal variabilities of the first component are also showed in Fig. 12 to Fig. 14.
Conclusion: These resulted patterns are investigated for considering the anomalous structure of rainfall. These resulted anomaly models are very similar and take a unique variation form and, this similarity may be explained as stable precipitation structure over the area of interest. The most important point in the space-time projections is the well-matched structure of the area DEM and first spatial component. This shows the impact of elevation on the configuration of space-time precipitation in this mountainous area. On the other hand, two spatial fronts of highlighted and intensive precipitation recognized in the projected first components may be taken as signs of two important rain cloud paths over internal of Iran as well. On the projected second spatial terms, both of linear and nonlinear methods, some local areas with high or low intensive precipitation can be concluded. But their spatial compatibilities are less than the first spatial components. Based on this comparison, the linearity of the space-time structure of precipitation over the Ghazvin province could be inferred.