Study Of Distribution Of Flood Forecasting Error Based On Maximum Entropy

As the main non-engineering measure of flood control and disaster mitigation,catchment flood forecasting plays an important role in practical flood control work.However,due to the impact of various factors,such as the uncertainty of forecast model,the inaccuracy of parameter estimation and the low precision of data,there always exists error between the flood forecasting value and the measured value.The existence of these error will not only affect the application of forecasting model in flood control and disaster mitigation work,bring adverse effects to the flood control work,sometimes even can cause great loss.In order to ensure that the decision-makers can correctly estimate the influence of the forecasting error on flood control,it is very important to study the distribution characteristics of the forecasting error.The paper takes Chongyang river catchment as an example,the distribution characteristics of forecasting error of the multiple linear regression model and the BP neural network model are studied by maximum entropy principle,and the corresponding error probability density functions are obtained.Then,analyzing and comparing the fitting effect between the maximum entropy probability density function of flood forecast error and the normal probability density function,and the optimal third-order maximum entropy probability density function is selected.The main researches are as follow:(1)Combining with the actual circumstance of Chongyang river catchment and the trial results to comprehensively analysis,the flood propagation time from Wuyishan hydrological station in the tributary upstream Chongyang river to Jianyang hydrological station in the lower Chongyang river(?1,)and the flood travel time from Masha hydrological station in the tributary upstream Mayang river to Jianyang hydrological station in the lower Chongyang river(r2)are determined.Giving an appropriate variable ?3 according to ?1 and ?2(?3??1 or ?3??2,generally),selecting the flood discharge of Wuyishan hydrological station in the tributary upstream Chongyang riverQi(t-?1),the flood discharge of Masha hydrological station in the tributary upstream Mayang riverQ2(t-?2)and the flood discharge of Jianyang hydrological station in the lower Chongyang riverQ(t-?3)as input factors,the flood discharge of Jianyang hydrological station in the lower Chongyang riverQ(t)as output,to establish multiple linear regression flood forecasting model,BP neural network flood forecasting model,then using these two models for flood forecasting.Where Q1(t-?1)represents the flood discharge variable of Wuyishan hydrological station at ?1 hours before,Q2(t-?2)represents the flood discharge variable of Masha hydrological station at ?2 hours before,Q(t-?3)represents the flood discharge variable of Jianyang hydrological station at ?3 hours before and Q(t)represents the corresponding flood discharge variable of Jianyang hydrological station.(2)Based on the data of 8 flood flows from 2002 to 2013,the flood forecasting is carried out by using multiple linear regression model and BP neural network model,and two sets of forecasting error data are obtained.(3)The maximum entropy principle is applied to study the forecasting error probability density functions of the multiple linear regression model and the BP neural network model,using the error data of forecasting models to give the corresponding constraint conditions.The two-order,three-order and four-order maximum entropy probability density functions of the multiple linear regression model and the BP neural network model forecasting error are obtained by nonlinar programming method,error function method and Newton's method respectively.For the sake of comparison,the normal probability density function of flood forecasting error is obtained.The results show that the fitting effect of two-order maximum entropy probability density function is similar to that of normal probability density function,three-order maximum entropy probability density function can better fit the distribution of error data,but when the maximum entropy orders are greater than three orders,the fitting effect of maximum entropy distribution can not significantly improve with the increase of order.(4)Three-order maximum entropy probability density function is used for flood forecasting error risk assessment of the multiple linear regression model and the BP neural network model,and the probabilities of different forecasting errors of the two forecast models are calculated respectively.The results of risk assessment can provide reference for flood control dispatching decision.