Application of Entropy Concept for Input Selection of Wavelet-ANN based Rainfall-Runoff Modeling

Abstract

This paper presents a Wavelet-based Artificial Neural Network (WANN) approach to model rainfall-runoff process of the Delaney Creek and Payne Creek watersheds with distinct hydro-geomorphological characteristics, located in Florida. Wavelet is utilized to handle the multi-frequency characteristics of the process in daily and monthly time scales. Thus, rainfall and runoff time series were decomposed into several sub-series by various mother wavelets. Due to multiple components obtained through wavelet decomposition, input sets to the Feed Forward Neural Network (FFNN) were enhanced. The application of two information content based criteria (i.e., entropy, H, and mutual information, MI) to select more reliable input sets (among all potential input sets) and to have better insight into the physics of process is considered as the basic innovation of the study which led to a more accurate and compact model. The increase in the number of input of the FFNN might lead to a complex structure and low performance. The results demonstrated that MI as a supervised feature extraction criterion could lead to more reliable outcomes due to its non-linear nature. Furthermore, results indicated the superiority of proposed entropy-based WANN model (EWANN) in comparison to simple FFNN. Moreover, multi-step-ahead FFNN, conventional WANN and classic Auto Regressive Integrated Moving Average with eXogenous inputs (ARIMAX) models could not reveal appropriate forecasting results with regard to EWANN model. The superiority of the EW-ANN over the WANN and FFNN models is not only in terms of efficiency criteria, but also due to its appropriate ability to provide information about the physics of the process. The consequences of EWANN for rainfall-runoff modeling of two watersheds revealed that the proposed EWANN could simulate the process of a small and flat sub-basin slightly reliable than a sloppy and wild watershed. The poor outcome of monthly modeling in regard to daily modeling might be due to involvement of more uncertainty in the monthly data.

Discrete principal‐monotonicity inference for hydro‐system analysis under irregular nonlinearities, data uncertainties, and multivariate dependencies. Part II: Application to streamflow simulation in the Xingshan Watershed, China

“…Because of the existence of temporal heterogeneity in hydrological systems, the calibration efficiency may not be very high. Data uncertainties as well as other types of uncertainties may lead to instability of the DPMI modelling efficiencies (Ahmadi et al ., ; Nourani et al ., ; Rahmani and Zarghami, ; Shen et al ., ; Wang et al ., ). Simplifications in the process of DPMI , such as quantification of the correspondence between predictors and streamflow as the principal monotonicity, may also decrease the capability of DPMI at reflecting real‐world hydrological systems.…”

Discrete principal‐monotonicity inference for hydro‐system analysis under irregular nonlinearities, data uncertainties, and multivariate dependencies. Part I: methodology development

“…In DPMI, the responsive relationship from influencing factors (named as predictors) to the hydrological variable of interest (named as the predictand) will be discretized as interrelated end nodes, i.e. groups of paired samples of predictors and the predictand, under irregular nonlinearities, data uncertainties, and multivariate dependencies (Ahmadi et al ., ; Nourani et al ., ; Rahmani and Zarghami, ; Shen et al ., ; Wang et al ., ). In detail, a discrete distribution transformation approach will be developed to enable transformation of non‐normally distributed predictand samples as a normal distribution and invertible restoration of the simulated predictand values as the original non‐normal distribution.…”

Short-Term Peak Flow Rate Prediction and Flood Risk Assessment Using Fuzzy Linear Regression

“…In addition, a simpler model structure means that the propagation of uncertainty from different sources is easier to assess. The use of data-driven models, such as neural networks, statistical methods or regression-based techniques (e.g., Li et al, 2015b, Li et al, 2015cYang et al, 2015), has been widespread in hydrology, particularly for short term daily flow rate forecasts, using a variety of input variables (Garen, 1992;Zealand et al, 1999;Campolo et al, 1999;Schilling and Walter, 2005;Adamowski and Sun, 2010;Duncan et al, 2011;Li et al, 2015a;Nourani et al, 2015). A recent regression based study predicted flow in the Bow River in Calgary, using a base difference regression model (Veiga et al, 2014).…”