Study on the Structure of Hydrological Nonlinear Statistical Model

Natural river basin is a typical complex open system. As water exists in this system, its movement is bound to be affected by the interaction of its various influencing factors. Since this effect does not conform to the principle of linear superposition, the trajectory of water, that is, hydrological phenomenon, shows extremely complex nonlinear characteristics. The nonlinear statistical models for describing hydrological phenomena can be divided into two types according to their structural characteristics. (1)The superposition of nonlinear function of each influence factor (SM); (2) The product of nonlinear function of each influence factor (PM). This paper explores which model structure is more consistent with hydrological phenomena through dimensional analysis, residual analysis and variance analysis for several examples. The results show that, the dimensions of SM cannot be harmonious, while PM can be harmonious. The residual of SM is significantly larger than that of PM. By deriving the variance of different model structures, it is found that the SM can only describe the the variation of the mathematical expectation of hydrological phenomena, but can not reflect the variation of variance, that is, the model implies the assumption that the variance is stable. The PM can describe the trending changes in mathematical expectations and variances in hydrological phenomena. Therefore, the PM can more accurately describe the hydrological system with nonlinear characteristics. This conclusion is of great significance for the accurate understanding of hydrological phenomena, especially under the background of continuous variation of hydrological variables caused by global climate change and intensified impact of human activities, the advantage of PM is more significant.