## 4 Validation and Discussion

Table 7: Values of parameters for additional model validation. Figure 13: Measured and predicted temperatures for additional (model validation) data of a depth of 15 cm with increasing time, excluding the first 40 data points: (**a**) P1 and (**b**) P3. and 0.804 in Figure 12c] of the data including the first 40 points and those [0.702 in Figure 14a and 0.734 in Figure 14b], the model prediction of the data including the first 40 data points was the better that that excluding the first 40 data points. However, it was concluded that the prediction model implemented in this study reasonably predicts shallow depth soil temperatures based on air temperature and water content. When developing models, long-term data, such as daily mean temperatures from spring to autumn, are used to reduce the biases of predictions and the variability of temperatures caused by climatic and ground factors, as proposed by [PERSON] et al. [53], and because studies predicting future global soil temperatures have been conducted for spring, summer, autumn, and winter [24; 54]. Moreover, compared to the models for predicting soil temperatures on a monthly basis [55; 56], the temperatures predicted on a daily basis are important for studies on sea ice [57; 58] and crop growth [35], which are highly temperature-sensitive. In this study, experimental validation and regression analysis were conducted using long-term data, and important results for the suitability and utility of the proposed soil temperature model were obtained. In northern, high-latitude permafrost regions (e.g., central-northern Alaska), changes in soil temperatures may have serious impacts on the long-term stability of infrastructure, even though they do not present an immediate threat to natural or human systems [35]. Therefore, the model here can be utilized in various ways and applied to areas where temperatures must be rapidly predicted. An effective and practical shallow-depth soil temperature model was developed, and its use makes it possible to estimate soil temperatures for adjacent areas and ground layers if the air temperature and \(\mathrm{w_{SD}}\) are available for a given location. In previous studies, the measurement of soil temperature has required many parameters [22; 25], including environmental conditions (e.g., solar radiation, air temperature, and albedo) and soil characteristics (e.g., thermal conductivity, diffusivity, and soil properties), or long analytical periods, such as that used in the Weather Research Forecast model. In contrast, our newly developed model enables rapid analysis with fewer parameters and has a high degree of accuracy for estimating soil temperatures. Predicting the spatial and temporal patterns of soil temperatures is important because it can promote the understanding of the physical and biological processes of plants, the properties of permafrost and sea ice, and CO\({}_{2}\) and NH\({}_{4}\) emission patterns [20; 21]. Additionally, the model proposed  
Figure 14: Comparison between measured and predicted temperatures at a depth of 15 cm, excluding the first 40 data points: (**a**) P1 and (**b**) P3. her is able to determine the most suitable period, work timing, and productivity for field work related to soil heat flux, as well as the heat energy from the geothermal system, biomass, crop flowering time, and appropriate drought monitoring procedures by predicting the soil temperatures of adjacent areas in a rapid and reasonable manner [59]. As the wSD is an important factor for determining the model parameters, the application of the wSD must not be neglected in the estimation of soil temperature. The developed model has several limitations, despite its simplicity and user-friendliness. Although the mathematical procedure is independent of the measurement locations, at least three standard deviations of soil water content values are required at the target location to determine the three model fitting parameters, \(\alpha\), \(\beta\), and \(CSTRCAT_{15,mnax}\).