Daily soil temperature modeling using ‘panel-data’ concept

<p>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 <i>Khorasan-Razavi</i> 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 (<math><mrow><msub><mi>T</mi><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></math> and <math><mrow><msub><mi>R</mi><mrow><mi>t</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></math>, respectively) and the average air temperature of the past 7 days (<i>T</i>_w) 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 (<i>R</i>² <i>=</i> 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 <i>t</i>-test, which showed the superiority of the panel-data models.</p