Streamflow prediction with large climate indices using several hybrid multilayer perceptrons and copula Bayesian model averaging

Streamflow prediction help the modelers to manage water resources in watersheds. It gives essential information for flood control and reservoir operation. This study uses the copula-based -Bayesian model averaging (CBMA) as an improved version of the BMA model for predicting streamflow in the Golok River, the Kelantan River, the Lanas River, and the Nenggiri River of Malaysia. The CBMA corrected the assumption of the utilization of Gaussian distortion in the BMA. While the BMA used normal distribution for the variables, the CBMA uses different distribution and copula functions for the variables. This study works on the Archimedes optimization algorithm (AOA) to train the mutlilayer perceptron (MLP) model. The ability of the MLP-AOA model was benchmarked against the MLP-bat algorithm (BA), MLP-particle swarm optimization (MLP-PSO), and the MLP-firefly algorithm (MLP-FFA). The models used significant climate signals, namely, the southern oscillation index (SOI), El NiNo-Southern Oscillation (ENSO), North Atlantic oscillation (NAO), and the pacific decadal oscillation (PDO) as the inputs to the models. The Gamma test (GT) was coupled with the AOA to provide the hybrid GT for choosing the best inputs. The gamma test was used to determine the suitable lag times of the Nino 3.4, PDO, NAO, and SOI as the inputs. The novelty of the current paper includes introducing new hybrid MLP models, new gamma test for choosing the best input combination, the comprehensive uncertainty analysis of outputs, and the use of an advanced ensemble CBMA model for predicting streamflow. First, the outputs of the MLP-AOA, MLP-BA, MLP-FFA, MLP-PSO, and MLP were obtained, following which, the CBMA as an ensemble framework based on outputs of the hybrid and standalone MLP models was used to predict monthly streamflow. The CBMA at the training level, decreased the root mean square error (RMSE) of BMA, MLP-AOA, MLP-BA, MLP-FFA, MLP-PSO, and MLP models by 28%, 32%, 52%, 53 53%, and 55%, respectively. The CBMA at the training level of another station decreased the mean absolute error (MAE) of BMA, MLP-AOA, MLP-BA, MLP-FFA, MLP-PSO, and MLP models by 6.04, 29%,42%, 49%, 52%, and 52%, respectively. The Nash Sutcliff efficiency (NSE) of the CBMA at the training level was 0.94 while it was 0.92, 0.90, 0.85, 0.84, 0.82, and 0.80 for the BMA, MLP-AOA, MLP-BA, MLP-FFA, MLP-PSO, and MLP models. The RMSE of the MLP-AOA was reported 4.3%, 12%, 14%, and 17% lower than those of the MLP-BA, MLP-FFA, MLP-PSO, and MLP models, respectively. The current research showed the CBMA and the BMA models had high abilities for predicting monthly streamflow. The results of this current study indicated that the CBMA and BMA provided lower uncertainty the standalone MLP models. The general results indicated that the streamflows in the hotter months decreased and flood control is of higher priority during the other months.