| Summary: | Forecasting soil temperature at multiple depths is considered to be a core decision-making task for examining future changes in surface and sub-surface meteorological processes, land–atmosphere energy exchange, resilient agricultural systems for improved crop health and eco-environmental risk assessment. The aim of this paper is to estimate monthly soil temperature (ST) at multiple depth: 5, 10, 20, 50 and 100 cm with a hybrid multi-layer perceptron algorithm integrated with the firefly optimizer algorithm (MLP-FFA). To develop the hybrid MLP-FFA model, the monthly ST and relevant meteorological variables for the city of Adana (Turkey) are collated for the period of 2000–2007. Construction of hybrid MLP-FFA model is drawn upon a limited set of predictors, denoted as soil depth, periodicity (or the respective month), air temperature, pressure and solar radiation, while the objective variable for MLP-FFA model is the forecasted ST at multiple depths. To the evaluate MLP-FFA, statistical metrics applied to test the model’s performance are: the root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and mean bias error (MBE) where the sign of the difference is also considered. In conjunction with statistical metrics, a Taylor diagram is utilized to visualize the degree of similarity between the observed and forecasted soil moisture. In terms of the forecasted results, the hybrid MLP-FFA model is seen to outperform the standalone MLP model. The optimal MLP-FFA is attained for soil temperature forecasting at a depth of 20 cm (RMSE, MAPE of 0.546 °C, 2.40%) whereas the optimal MLP is attained for soil temperature forecasting at a depth of 50 cm (RMSE of 0.544 °C, 2.21%). Conclusively, the study advocates through statistical metrics attained the better utility of the hybrid MLP-FFA hybrid model. Given its superior performance, it is ascertained that the hybrid MLP model integrated with Firefly optimizer is a qualified ancillary tool that can be applied to generate precise soil temperature forecasts at multiple soil depths. Keywords: Artificial neural network, Hybrid firefly algorithm, Soil temperature, Turkish State Meteorological Service
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