A quantitative pattern similarity prediction model based on chaos theory
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Abstract:
Hydrologic system is a high complexity and nonlinearity system,which exhibits great temporal and spatial variations.Deterministic and stochastic are the two broad methods that have been applied to modeling hydrological processes.The former approach considered the cyclic and periodic nature of hydrological processes,whereas the latter approach considered the complexity and irregularity.Both the deterministic and stochastic components are present in the hydrological system and intertwine to affect the variation of hydrological processes.Chaos theory can provide a bridge between deterministic and stochastic methods to investigate the inherent stochasticity of deterministic systems.It is recognized that simple deterministic systems are capable of generating a complex randomlike phenomenon due to the nonlinear action within the system.Recently,many applications of chaos theory to hydrology have been reported and yielded fruitful outcomes.However,there is enough research on chaotic characteristic identification,while the studies on chaotic prediction need to be further improved and expanded.Longterm hydrological prediction has always been a crucial issue in hydrology with several challenges and impediments.Due to the nonlinear and chaotic characteristics of the hydrologic process,it is difficult to make accurate forecasting,especially for prediction with longer lead time at monthly or yearly scale. The similarity model of phase space is a classical prediction approach based on chaos theory.The prediction approach was improred by proposing a quantitative type coupled similarity identification technique.The degree of spatial proximity between two phase points is defined as the "quantity" similarity by the Euclidean distance criterion,while the similarity degree of internal structure between two phase points is defined as the "type" similarity by the accumulated unit-step function.Moreover,a two-objective optimization model based on the quantity-type similarity was established for hydrological prediction within the chaos theory framework and then solved by the tolerant algorithm of stratified sequence.An example was illustrated for the future 12-month rainfall predictions. Both the original model and improved model were applied to the Danjiangkou reservoir basin for monthly rainfall prediction.The monthly rainfall in 2016 was predicted based on the monthly rainfall data set from 1981 to 2015.The chaotic characteristics were identified and the related parameters (time delay and embedded dimension) were determined by the autoregressive function and G-P algorithm.The similar phase points were selected by the euclidean distance (quantity similarity) in the original model by the coupled "quantity" and "type" similarity in the improved model.For the original model,6 months showed the absolute of the relative errors less than 25%.For the improved model,8 months yielded the absolute of the relative errors less than 25%.Compared to the original model,the annual average of absolute values of relative error in monthly rainfall prediction was reduced from 44% to 23%.In contrary to the original model,the correlation coefficient R was lifted from 0.74 to 0.93.Overall,the improved model had better performance for predicting monthly rainfall in most months. In conclusion,the"quantitative"-"type" similarity predictive model based on chaos theory is effective and feasible,providing a new way for monthly rainfall prediction.The coupled "quantity-pattern" similarity model was proposed for long-term prediction,and the concept of the model is applicable to hydrological time series forecasting with different lead time scales.
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