Modelling daily soil temperature by hydro-meteorological data at different depths using a novel data-intelligence model: deep echo state network model

Soil temperature (T_s) is an essential regulator of a plant’s root growth, evapotranspiration rates, and hence soil water content. Over the last few years, in response to the climatic change, significant amount of research has been conducted worldwide to understand the quantitative link between soil temperature and the climatic factors, and it was highlighted that the hydrothermal conditions in the soil are continuously changing in response to the change of the hydro-meteorological factors. A large amount of the models have been developed and used in the past for the analysis and modelling of soil temperature, however, none of them has investigated the robustness and feasibilities of the deep echo state network (Deep ESN) model. A more accurate model for forecasting T_s presents many worldwide opportunities in improving irrigation efficiency in arid climates and help attain sustainable water resources management. This research compares the application of the novel Deep ESN model versus three conventional machine learning models for soil temperature forecasting at 10 and 20 cm depths. We combined several critical daily hydro-meteorological data into six different input combinations for constructing the Deep ESN model. The accuracy of the developed soil temperature models is evaluated using three deterministic indices. The results of the evaluation indicate that the Deep ESN model outperformed conventional machine learning methods and can reduce the root mean square error (RMSE) accuracy of the traditional models between 30 and 60% in both stations. In the test phase, the most accurate estimation was obtained by Deep ESN at depths of 10 cm by RMSE = 2.41 °C and 20 cm by RMSE = 1.28 °C in Champaign station and RMSE = 2.17 °C (10 cm) and RMSE = 1.52 °C (20 cm) in Springfield station. The superior performance of the Deep ESN model confirmed that this model can be successfully applied for modelling T_s based on meteorological paarameters.