Implementing novel hybrid models to improve indirect measurement of the daily soil temperature: Elman neural network coupled with gravitational search algorithm and ant colony optimization

•The daily ST time series of two stations in Iran were estimated at different depths.•The ENN was coupled with the GSA and ACO.•Generally, the hybrid ENN-GSA and ENN-ACO performed better than the classical ENN.•The ENN-GSA is the best-performing model. Soil temperature (ST) as a vital variable of soil plays a key role in agriculture products, surface energy transactions, soil moisture balance, etc. In developing countries like Iran, access to the ST data may be limited. Hence, estimating this parameter by an appropriate alternative approach is of great importance. Two novel hybrid models are developed in this study based on Elman neural network (ENN) coupled with gravitational search algorithm (GSA) and ant colony optimization (ACO) for improving the daily ST estimation at various soil depths (i.e., ENN-GSA and ENN-ACO). In fact, both the optimization algorithms including the GSA and ACO were applied to train the parameters of ENN. To achieve this, the daily data from two stations, namely the Isfahan and Rasht located in Iran were employed during 1998–2017. The classical ENN and hybrid ENN-GSA and ENN-ACO models are developed using the other meteorological parameters under eleven different scenarios. The results illustrated that the proposed hybrid models outperformed the classical ENN for estimating the daily ST of the studied locations at different depths; however, the hybrid ENN-GSA was the best-performing model at the studied stations and whole the soil depths. In addition, all the standalone and hybrid models illustrated the highest accuracy under full-input pattern.