investigation of relationship between hydrologic processes of precipitation, evaporation and stream flow using linear time series models (case study: western basins of lake urmia)

introduction: studying the hydrological cycle, especially in large scales such as water catchments, is difficult and complicated despite the fact that the numbers of hydrological components are limited. this complexity rises from complex interactions between hydrological components and environment. recognition, determination and modeling of all interactive processes are needed to address this issue, but it's not feasible for dealing with practical engineering problems. so, it is more convenient to consider hydrological components as stochastic phenomenon, and use stochastic models for modeling them. stochastic simulation of time series models related to water resources, particularly hydrologic time series, have been widely used in recent decades in order to solve issues pertaining planning and management of water resource systems. in this study time series models fitted to the precipitation, evaporation and stream flow series separately and the relationships between stream flow and precipitation processes are investigated. in fact, the three mentioned processes should be modeled in parallel to each other in order to acquire a comprehensive vision of hydrological conditions in the region. moreover, the relationship between the hydrologic processes has been mostly studied with respect to their trends. it is desirable to investigate the relationship between trends of hydrological processes and climate change, while the relationship of the models has not been taken into consideration. the main objective of this study is to investigate the relationship between hydrological processes and their effects on each other and the selected models. material and method: in the current study, the four sub-basins of lake urmia basin namely zolachay (a), nazloochay (b), shahrchay (c) and barandoozchay (d) were considered. precipitation, evaporation and stream flow time series were modeled by linear time series. fundamental assumptions of time series analysis namely normalization and stationarity were considered. skewness test applied to evaluate normalization of evaporation, precipitation and stream flow time series and logarithmic transformation function executed for in order to improve normalization. stationarity of studied time series were evaluated by well-known powerful adf and kpss stationarity tests. time series model's order was determined using modified aicc test and the portmanteau goodness of fit test was used to evaluate the adequacy of developed linear time series models. man-kendall trend analysis was also conducted for the precipitation amount, the number of rainy days, the maximum precipitation with 24 hours duration, the evaporation and stream flow in monthly and annual time scales. results and discussion: inferring to the physical base of arma models provided by salas et al (1998), the precipitation has been considered independently and stochastically. if this assumption is not true in a given basin, it is expected that the ma component of stream flow discharge model be eliminated or washed out. this case occurred in basins a, b and c. in these basins, the behavior of precipitation and evaporation was autoregressive. it was observed that the stream flow discharge behavior also follows autoregressive models that had greater lags than precipitation and evaporation lags. this result proved that the precipitation, evaporation, and stream flow processes in the basin were regular processes. in basin d, the behavior of precipitation was stochastic and followed the ma model, which was related to the stochastic processes. in this basin, the stochastic behavior of precipitation affected the stream flow behavior, and it was observed that the stochastic term of ma also appeared in the stream flow. thus, this leads to decrease the memory of stream flow discharge. the fact that the ma component in the stream flow discharge was greater than the ma component in precipitation indicated that during the process of producing stream flow discharge from precipitation, the stochastic factors performed an important role. conclusion: a comprehensive investigation on hydrological time series models of precipitation, evaporation and stream flow were investigated in this study. the framework of the study consists of trend analysis using mann-kendall test and time series. trend analysis results indicate the significant changes of water resources in the studied area. it means that sustainable development in studied area is greatly threatened. the results of parallel modeling of precipitation, evaporation and stream flow time series showed that the behavior of stream flow models are greatly affected by precipitation models. in other words, this study evaluate the physical concept of arma models in real-world monthly time scale for three main hydrologic cycle components and suggest that considering parallel hydrological time series modeling could increase the accuracy to select a model for simulation and prediction of stream flow time series. in addition, it suggested that there is a relation between climate pattern and hydrological time series models.