Daily soil temperature modeling using ‘panel-data’ concept

The purpose of this research was to predict soil temperature profile using ‘panel-data’ models. Panel-data analysis endows regression analysis with both spatial and temporal dimensions. The spatial dimension pertains to a set of cross-sectional units of observation. The temporal dimension pertains to periodic observations of a set of variables characterizing these cross-sectional units over a particular time-span. This study was conducted in Khorasan-Razavi Province, Iran. Daily mean soil temperatures for 9 years (2001–2009), in 6 different depths (5, 10, 20, 30, 50 and 100 cm) under bare soil surface at 10 meteorological stations were used. The data were divided into two sub-sets for training (parameter training) over the period of 2001–2008, and validation over the period of the year 2009. The panel-data models were developed using the average air temperature and rainfall of the day before ( $ {T_{d - 1}} $ Td−1 and $ {R_{t - 1}} $ Rt−1, respectively) and the average air temperature of the past 7 days (Tw) as inputs in order to predict the average soil temperature of the next day. The results showed that the two-way fixed effects models were superior. The performance indicators (R2 = 0.94 to 0.99, RMSE = 0.46 to 1.29 and MBE = −0.83 and 0.74) revealed the effectiveness of this model. In addition, these results were compared with the results of classic linear regression models using t-test, which showed the superiority of the panel-data models.