# Estimation of Thermal Diffusivity for Greenhouse Soil Temperature Simulation
## 1 Introduction  
Collecting excess daytime solar energy to heat a greenhouse at night is an economic approach to conserve greenhouse energy consumption. Solar radiation is captured by the soil during the daytime and released at nighttime to warm the greenhouse air. To better understand the heat transfer mechanisms between the soil and the greenhouse air, studying the thermal transfer capacity of the greenhouse soil is desirable [1, 2]. In this study, the two most important soil thermal properties are the heat transfer coefficients between the floor and the greenhouse air, as well as between the floor surface and the greater ground depths [3, 4, 5, 6].  
The response to temperature changes in the soil is often not instantaneous due to the large soil heat capacity. To study the time delay, researchers have often used soil temperature data to estimate the thermal diffusivity. [PERSON] and [PERSON] (1983) estimated soil thermal diffusivities based on measured soil temperature data using six different methods (the amplitude, phase-shift, arctangent, logarithmic, numerical, and harmonic methods). The calculated apparent thermal diffusivities were then used to predict the soil temperatures before they were compared to another set of measured temperatures [7]. On the other hand, [PERSON] et al. (2013) used the principle of transient heat flow with assumptions of one-dimensional heat flow, homogeneous soil, and constant thermal diffusivity to predict the daily soil temperatures depending on depth and time. Their efforts resulted in establishing a model for soil temperature prediction as a function of depth [8]. [PERSON] et al. (2013) estimated the soil thermal diffusivity from the soil temperature profile using the amplitude, logarithmic, arctangent, and phase-shift methods. The estimated soil thermal diffusivities showed significant differences andvaried over the study period as a function of the volumetric soil water content [9]. Additionally, [PERSON] et al. (2014) used the harmonic method and the temperature integral method to determine soil heat storage and energy balance in arid and semiarid regions [10].  
Furthermore, the residual effects of dissimilar management on the temporal variability and covariance structure of the soil temperature was reported by [PERSON] et al. (2015) [11], and [PERSON] et al. (2016) [12] used the amplitude, phase-shift, conduction-convection, and harmonic methods to estimate the thermal diffusivity under different climatic conditions in the subsurface layers. [PERSON] et al. (2017) investigated the soil temperatures at different depths in several regions of Turkey. They used a sinusoidal prediction model for the soil temperatures based on the depth and time to describe the annual soil temperature variations in different regions of Turkey [13].  
The boundary conditions of open-field soil and the soil underneath a greenhouse are different. Evaluations of the open-field soil thermal diffusivity assume that the soil is a one-dimensional isotropic medium and that the average soil temperature is the same at all depths. Conversely, the soil temperature in a greenhouse always has a thermal gradient. In a greenhouse, the soil surface is enclosed, and its temperature is different from that of the outside air, although at a certain depth (i.e., the constant-temperature layer), the soil temperature underneath a greenhouse will be the same as that of the outdoor soil. In this research, we focused on estimating the local heat transfer in the soil underneath a greenhouse above the constant-temperature layer. Various methods were employed to estimate the greenhouse soil thermal diffusivity and to determine the soil temperature at various depths.