An extreme learning machine model for the simulation of monthly mean streamflow water level in eastern Queensland

Abstract

A predictive model for streamflow has practical implications for understanding the drought hydrology, environmental monitoring and agriculture, ecosystems and resource management. In this study, the state-or-art extreme learning machine (ELM) model was utilized to simulate the mean streamflow water level (Q(WL)) for three hydrological sites in eastern Queensland (Gowrie Creek, Albert, and Mary River). The performance of the ELM model was benchmarked with the artificial neural network (ANN) model. The ELM model was a fast computational method using single-layer feedforward neural networks and randomly determined hidden neurons that learns the historical patterns embedded in the input variables. A set of nine predictors with the month (to consider the seasonality of Q(WL)); rainfall; Southern Oscillation Index; Pacific Decadal Oscillation Index; ENSO Modoki Index; Indian Ocean Dipole Index; and Nino 3.0, Nino 3.4, and Nino 4.0 sea surface temperatures (SSTs) were utilized. A selection of variables was performed using cross correlation with Q(WL), yielding the best inputs defined by (month; P; Nino 3.0 SST; Nino 4.0 SST; Southern Oscillation Index (SOI); ENSO Modoki Index (EMI)) for Gowrie Creek, (month; P; SOI; Pacific Decadal Oscillation (PDO); Indian Ocean Dipole (IOD); EMI) for Albert River, and by (month; P; Nino 3.4 SST; Nino 4.0 SST; SOI; EMI) for Mary River site. A three-layer neuronal structure trialed with activation equations defined by sigmoid, logarithmic, tangent sigmoid, sine, hardlim, triangular, and radial basis was utilized, resulting in optimum ELM model with hard-limit function and architecture 6-106-1 (Gowrie Creek), 6-74-1 (Albert River), and 6-146-1 (Mary River). The alternative ELM and ANN models with two inputs (month and rainfall) and the ELM model with all nine inputs were also developed. The performance was evaluated using the mean absolute error (MAE), coefficient of determination (r(2)), Willmott's Index (d), peak deviation (P-dv), and Nash-Sutcliffe coefficient (E-NS). The results verified that the ELM model as more accurate than the ANN model. Inputting the best input variables improved the performance of both models where optimum ELM yielded R-2 approximate to(0.964, 0.957, and 0.997), d approximate to(0.968, 0.982, and 0.986), and MAE approximate to(0.053, 0.023, and 0.079) for Gowrie Creek, Albert River, and Mary River, respectively, and optimum ANN model yielded smaller R-2 and d and larger simulation errors. When all inputs were utilized, simulations were consistently worse with R-2 (0.732, 0.859, and 0.932 (Gowrie Creek), d (0.802, 0.876, and 0.903 (Albert River), and MAE (0.144, 0.049, and 0.222 (Mary River) although they were relatively better than using the month and rainfall as inputs. Also, with the best input combinations, the frequency of simulation errors fell in the smallest error bracket. Therefore, it can be ascertained that the ELM model offered an efficient approach for the streamflow simulation and, therefore, can be explored for its practicality in hydrological modeling.