Upper and Lower Bound Interval Forecasting Methodology Based on Ideal Boundary and Multiple Linear Regression Models

The uncertainty research of hydrological forecast attracts the attention of a host of hydrological experts. Prediction Interval (PI) is a convinced method that can ensure the forecasting accuracy meanwhile take uncertainty range into consideration. While the existed Prediction Interval methods need algorithm optimization and are susceptible to local optima, so it is particularly urgent to provide an efficient Prediction Interval (PI) model with excellent performance. This paper proposes a novel upper and lower bound interval estimation model to rapidly define the PI and reduce the amount of calculation to implement convenient and high precise hydrological forecast. Above all, the ideal upper and lower bounds are defined according to the relative width or absolute width. Then, the proposed model is utilized to forecast interval runoff via least square method and multiple linear regression methods. The estimated interval inclusion ratio, interval width, symmetry, and root-mean-square error which are popular used to judge the precision serve as accuracy evaluation indexes. The measured discharge data from five hydrological stations which located upstream of the Yangtze River is applied for interval forecasting. Compared with the results of neural network-based upper and lower bound interval estimation model, the proposed method yields higher forecasting accuracy, meanwhile, the ideal upper and lower bounds successfully minimize the number of processes which require a mass of parameter searching and optimization.