| Hydrology, water resources and water environmental system is a huge variable nonlinear dynamic system, in which the change of runoff dominates the whole system change and it has major influence on regional economy and environmental resources. Due to the comprehensive influence of climate, geographical environment, social development and human existence needs, the complex variation of runoff exhibits random, mutation and nonlinear features etc. However, traditional methods of the original analysis and prediction are faced with challenges and dilemma, which leads to that the analysis and prediction of the runoff change features has always been the hotspot and difficulty at home and abroad research for a long time.The main work of this paper shows as follows:(1) On the basis of analyzing iterated function system and fractal interpolation, the traditional fractal interpolation extrapolation algorithm is improved based on extrapolation thought and the concrete steps of improved interpolation extrapolation algorithm is given.(2) The several methods for calculating the vertical scale factor are analyzed and compared. Then the method of consideration to the local details and global feature of the object to be interpolated is adopted to calculate the vertical scale factor.(3) Introducing the metabolism thought of the grey theory into the runoff prediction, the metabolic fractal interpolation forecasting model is established through screening the different dimensions and can be used to predict the runoff. Compared with ARMA model, the prediction accuracy of the metabolic fractal interpolation forecasting model is relatively higher.(4) In order to depict the variation of runoff easily, the runoff series is divided into two kinds:high flow and low flow, then the high flow years and low flow years are predicted, respectively. The combined use of above method and the metabolic fractal interpolation forecasting model provides new idea and new method for improving the runoff prediction precision.
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