Development of a linear–nonlinear hybrid special model to predict monthly runoff in a catchment area and evaluate its performance with novel machine learning methods

Abstract

Accurate forecasting of runoff as an important hydrological variable is a key task for water resources planning and management. Given the importance of this variable, in the current study, a multivariate linear stochastic model (MLSM) is combined with a multilayer nonlinear machine learning model (MNMLM) to generate a hybrid model for the spatial and temporal simulation of runoff in the Quebec basin, Canada. Monthly hydrological data from 2001 to 2013, including precipitation and runoff data from nine stations and Normalized Difference Vegetation Index (NDVI) extraction of MODIS data, are applied as input to the proposed hybrid model. At the first step of the hybrid modeling, data normality and stationary were examined by performing various tests. In the second step, MLSM was developed by defining four different scenarios and as a result 15 sub-scenarios. The first and second scenarios were developed based on one exogenous variable (precipitation or NDVI). In contrast, the second and third scenarios were developed based on two additional variables. In the first and third scenarios, the data are modeled without preprocessing. In the second and fourth scenarios, a preprocessing step is performed on the data. Then, in the third step, various combinations based on different time delays from runoff data were applied for developing nonlinear model. The comparisons are made between observed and simulated time series at various stations and based on the root mean squared error (RMSE), mean absolute error (MAE), correlation coefficient (R) and Akaike information criterion (AIC). The efficiency of the proposed hybrid model is compared with a novel machine learning model that was introduced in 2021 by Sultani et al., and it was also compared with the results obtained from the linear and nonlinear models. In most stations, delays (t-1) and (t-24) are identified as the most effective delays in hybrid and nonlinear modeling of runoff. Also, in most stations, the use of climatic parameters and physiographic factors as exogenous variables along with runoff data improves the results compared to the use of one variable. Results showed that at all stations, proposed hybrid model generally leads to more accurate estimates of runoff compared with various linear and nonlinear models. More accurate estimates of peak runoff values at all stations were another excellence of proposed hybrid model than other models.