## Materials and Methods
### Study Area  
The study area (Figure 1) in which air and soil temperatures were measured is located on the Seward Peninsula, in Council, Alaska. The altitude is approximately 30 m, and the mean annual temperature and precipitation are \(-\)3.1 \({}^{\circ}\)C \(\pm\) 1.4 \({}^{\circ}\)C and 258 mm, respectively [39]. The sieve analysis of soil particles conducted by [PERSON] et al. [21] revealed that the ranges of clay, silt, and sand contents in this area are 6.4%-19.0%, 55.1%-70.0%, and 16.2%-38.5%, respectively, depending upon the sampling depth and location. The test sites were leased from the natives of Council Native Corporation, and there was restriction of moving soils out of the study area. Therefore, taking out of soil samples was possible for limited area, locations of M1, M2, M3, and M4. The sampled locations are not exactly the same of locations of soil temperature measurements because sampling at the same locations will influence soil temperature measurement. The soils of the site have colors of gray-brown, dark black, or reddish brown. The sieve analysis for these soils are summarized in Table 1. Although thermal properties were not measured, it is presumed that there exists spatial heterogeneity in soil particle size distribution or other thermal properties. The spatial heterogeneity may also influence the spatial variability of water content.  
The devices used to air and soil temperatures and soil water content were installed in the ground in Council, Alaska, as shown in Figure 2. The measurement sites had a plain topography. In the 100  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Location** & **No. of Samples** & **Sand (\%)** & **Silt (\%)** & **Clay (\%)** \\ \hline M1 & 1 & 36.0 & 56.6 & 7.4 \\ M2 & 1 & 38.5 & 55.1 & 6.4 \\ M3 & 2 & 16.8 & 64.2 & 19.0 \\ M4 & 2 & 16.2 & 70.0 & 13.8 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Composition ratios of averages of sand, silt, and clay.  
100 m\({}^{2}\) study area, seven measurement locations (P1-3 and M1-M4 in Figure 2) were selected. At each location, soil temperature was measured at depths of 5, 10, and 15 cm.  
Each measurement instrument consisted of a battery-powered sensor node and a flash memory interface circuit (sink node) that stored and remotely transmitted receiver data. The sensors used for soil temperature measurements (107 temperature probe, Campbell Scientific, Inc., Logan, UT, USA) had a temperature resolution of 0.01 \({}^{\circ}\)C. Air temperature measurements (TMC6-HD, Onset Computer, Bourne, MA, USA) were made at a 1.2-m height from the ground surface at the same time interval as soil temperatures (Figure 2).  
The soil water content was measured at a depth of 15 cm at the same points used for soil temperature measurements. The sensor used was a soil water content reflectometer (CS650, Campbell Scientific, Inc., Bourne, MA, USA). The measurement data of the soil water content sensors were stored in the same way as the soil temperatures were stored. Measurements were continuously taken for 160 days, from 10 May to 14 October in 2015. A model for estimating soil temperatures was developed based on the soil and air temperature and soil water content data at locations M1-M4 (Figure 2); the soil water content and soil temperature data at locations P1-P3 were used to validate the developed model.