Contents lists available at ScienceDirect Soil & Tillage Research journal homepage: www.elsevier.com/locate/still Developing novel hybrid models for estimation of daily soil temperature at various depths Saeid Mehdizadeh a, *, Farshad Fathian b , Mir Jafar Sadegh Safari c , Ali Khosravi d a Department of Water Engineering, Urmia University, Urmia, Iran b Department of Water Science & Engineering, Faculty of Agriculture, Vali-e-Asr University of Rafsanjan, P.O.Box 77188-97111, Rafsanjan, Iran c Department of Civil Engineering, Yaşar University, Izmir, Turkey d Department of Mechanical Engineering, School of Engineering, Aalto University, Helsinki, Finland ARTICLE INFO Keywords: Estimation Daily soil temperature Fractionally autoregressive integrated moving average Feed-forward back propagation neural networks Gene expression programming ABSTRACT Estimation of soil temperature (ST) as one of the vital parameters of soil, which has an impact on many chemical and physical characteristics of soil, is of great importance in soil science. This study applies a time series-based model, namely fractionally autoregressive integrated moving average (FARIMA), as well as two machine learning-based models consisting of feed-forward back propagation neural networks (FFBPNN) and gene ex- pression programming (GEP) for daily ST estimation. In doing so, the daily ST data of three stations at four depths (5, 10, 50, and 100 cm) in Iran were used for the time period from 1998 to 2017. Studied stations were selected from different climates including arid (Isfahan station), semi-arid (Urmia station), and very humid (Rasht station) to evaluate the performance of models and generalize the outcomes in different climate classes. The performances of the developed models are evaluated via three statistical metrics including the root mean square error (RMSE), mean absolute error (MAE), and relative RMSE (RRMSE). Results obtained demonstrated that the machine learning-based FFBPNN and GEP models performed better than the time series-based FARIMA approach at all depths. As a result, negligible differences were observed between the accuracies of FFBPNN and GEP. In addition, this study developed novel hybrid models through combining the FFBPNN and GEP techniques with the FARIMA to enhance the accuracy of traditional FARIMA, FFBPNN, and GEP. The developed hybrid models named GEP-FARIMA and FFBPNN-FARIMA were found to achieve better estimates of daily ST data at different depths in comparison with the classical models. The daily ST estimates with the highest accuracy were observed at a depth of 50 cm via the GEP-FARIMA at Isfahan station (RMSE = 0.05 °C, MAE = 0.03 °C, RRMSE = 0.25% for the testing phase), the GEP-FARIMA at Urmia station (RMSE = 0.04 °C, MAE = 0.03 °C, RRMSE = 0.26% for the testing phase), and the FFBPNN-FARIMA at Rasht station (RMSE = 0.07 °C, MAE = 0.05 °C, RRMSE = 0.35% for the testing phase). 1. Introduction Soil temperature (ST) is one of the crucial parameters of soil that controls the equilibrium of the heat energy amongst atmosphere and ground surface (Sanikhani et al., 2018), underground physical pro- cesses and carbon budget (Samadianfard et al., 2018a). Soil thermal regime determines the directions and rates of physical processes in soil such as moisture gradient and thermal fluxes (Araghi et al., 2017). It can also affect mass transfer in soil, soil structure and nutrient uptake (Børresen et al., 2007; Li et al., 2008; Wu et al., 2010; Xing et al., 2018), plant growth (Brar et al., 1992; Liu and Huang, 2005), seed germination (Nabi and Muillins, 2008), accumulation of organic matter in soil, soil respiration, organic matter destruction (Seyfried et al., 2001; Schimel et al., 2004; Rube, 2005; Xing et al., 2018), root development, ap- pearance and growth of seedling (Hillel, 1998). Despite the importance and critical need for the knowledge of ST values in various fields of engineering, particularly in agriculture, ac- cessibility to the ST data is very limited in many areas (i.e., developing countries). ST values should be measured by thermometers installed at different soil depths, which is a time-consuming and costly task (Hu et al., 2016; Feng et al., 2019). The measurement error for the ST thermometers is 0.1 °C. Thus, alternative approaches have recently at- tracted much attention. In this regard, some traditional approaches including the soil heat flow, energy balance, empirical correlations with https://doi.org/10.1016/j.still.2019.104513 Received 8 June 2019; Received in revised form 10 October 2019; Accepted 16 November 2019 ⁎ Corresponding author. E-mail addresses: saied.mehdizadeh@gmail.com (S. Mehdizadeh), f.fathian@vru.ac.ir (F. Fathian), jafar.safari@yasar.edu.tr (M.J.S. Safari), ali.khosravi@aalto.fi (A. Khosravi). Soil & Tillage Research 197 (2020) 104513 0167-1987/ © 2019 Elsevier B.V. All rights reserved. T