# Estimation of Thermal Diffusivity for Greenhouse Soil Temperature Simulation
## 4 Discussion  
As reported, the thermal diffusivity (\(k\)) for sand varies across depths and weather conditions within a range of \(10^{-5}\)-\(10^{-7}\) m\({}^{2}\) s\({}^{-1}\)[12]; \(k\) for quartz sand is \(12.5\times 10^{-7}\) m\({}^{2}\) s\({}^{-1}\)[15], and the \(k\) for loamy sand is approximately 2.5-8.4 \(\times\) 10\({}^{-7}\) m\({}^{2}\) s\({}^{-1}\)[21]. Table 1 shows the estimated the \(k\) values under different weather conditions and for different seasons. The phase-shift method yielded different results on clear-sky days when the greenhouse was cooled and or not cooled. The phase-shift, arctangent and logarithmic methods were greatly influenced by the weather conditions since the results on cloudy days  
Figure 7: Simulation results of heating season soil temperature at 0.1 m, 0.2 m and 0.3 m soil depths from the soil su4 fface temperature at different heating set points (21 \({}^{\circ}\)C, 14.4 \({}^{\circ}\)C and 4.4 \({}^{\circ}\)C).  
differed largely from those on clear-sky days. The results obtained from the amplitude and min-max methods are more consistent with those obtained from the other methods under the conditions tested. Both of these methods calculated the amplitude of the temperature with similar results.  
The soil temperature oscillates as a sinusoidal function of time around an average value that is constant for all depths [18], and the temperature deep into the soil after a certain depth becomes constant and is considered equal to the average soil temperature [22]. In fact, the soil temperature is affected by the solar radiation, soil moisture content, soil cover, and LAI [23; 21; 24; 25]. The estimation method used heat to determine the average soil temperature agrees with the results obtained by [PERSON] [26] (i.e., daily soil temperature decreased exponentially with increasing soil depth) and [PERSON] [27] (i.e., the amplitude of the annual temperature wave attenuates exponentially with increasing soil depth).  
Table 2 shows the performance of the soil temperature prediction model under different environmental conditions for both the cooling and heating seasons. Outdoor sky condition effects (clear sky or rainy), indoor environmental control effects (active cooling or no active cooling) and various heating set points were taken into account. On a clear day, during the cooling season, especially without a cooling system, the greenhouse air temperature is higher than that outside the greenhouse (Figure 1). Thus, the soil surface temperature is higher than the greenhouse air temperature. Using the energy balance for the greenhouse floor between the indoor air and soil surface [28], the simulation results are higher than the observed values at depths of 0.2 m and 0.3 m (Figures 6b and 6c, respectively). The RMSE for any soil depth is higher than the RMSE for the soil surface, indicating that the simulation model is sensitive to the surface temperature during the cooling season. During the heating season, using the energy balance for the two distinct soil sublayers of the soil surface [29], the fraction of solar radiation received by the greenhouse floor equals the sum of the rate of energy loss from the soil surface to the indoor air and the rate of energy loss from the soil surface to the sub soil [30; 31]. Therefore, when the set point of the heating system is low (4.4 \({}^{\circ}\)C), the greenhouse is similar to the outside, and the estimation of the temperature is more consistent with the observed values (Figure 7). Table 2 also shows that the RMSE for the cooling season is generally larger than those for the heating season, partly because the soil temperature in the greenhouse is affected by both the air temperature and the amount of solar radiation. Overall, these results suggest that Equations (8) and (18) performed well in predicting the greenhouse soil temperature.