## 3 Results  
### Field Measurements of Air and Soil Temperatures and Soil Water Content  
Figure 3 shows the air temperatures continuously measured for 160 days from 10 May to 14 October of 2015 and the soil temperatures measured at locations of M1-M4 during the same period. The air temperature measured at point \(x\) fluctuated from the beginning and reached a maximum value of 24.1 \({}^{\circ}\)C around the 42 nd day. It continued fluctuating until the 131 st day, when it fell below 0 \({}^{\circ}\)C, but then fluctuated again until the 157 th day, when it once again fell below 0 \({}^{\circ}\)C (three days before the end of the study period). During the measurement period, air temperature was generally \(>\) 0 \({}^{\circ}\)C, except for a few days (days 131-136, 144-145, and 157-160). During the same period, the soil temperatures at depths of 5-15 cm were \(>\) 0 \({}^{\circ}\)C. This appears to be due to the snow accumulated on the ground surface acting as an effective insulator, thereby causing a difference between the soil and air temperatures [40; 41]. Figure 2: Sensor locations (P1–P3; M1–M4) for air and soil temperature measurements. The red “x” marks the location of above-ground temperature measurements. The air temperature measured at point \(x\) and the soil temperatures measured at locations M1-M4 during the same period showed a tendency to slowly increase at the beginning and then gradually decrease after reaching the maximum values on approximately the 45 th day. In Figure 3, the maximum soil temperature at location M1 is shown to be 15.4 \({}^{\circ}\)C. The maximum soil temperatures at locations M2, M3, and M4 were 23.5 \({}^{\circ}\)C, 23.1 \({}^{\circ}\)C, and 16.0 \({}^{\circ}\)C, respectively. These maximum temperatures are indicative of summer in Alaska. The soil temperatures at locations M1-M4 differed, even at the same depth. This appears to be because of the differences in the soil properties with depth and in the heat transfer of soil. In particular, the amplitude of the daily mean soil temperature changed more drastically as the depth was shallowed when compared to a depth of 15 cm due to the heat from the surface moving toward deeper positions and thus shallower depths were more affected by the heat from the surface. The changes in soil temperatures showed a tendency to decrease as the depth increased, and the maximum soil temperature decreased as the depth increased. Additionally, the soil temperatures of M2 and M4 at a depth of 15 cm showed different patterns of variation, as compared to those of M1 and M3, and temperature changes at other depths (Figure 3). The reason for this difference may be that there are different thermal properties between the soil and water contents due to spatial heterogeneity in the soil layering and particle size distribution. Moreover, slight time delays between the maximum air temperature and the maximum soil temperature were observed from a depth of 5 cm. According to the observed temperature data during the same period, soil temperature changed from positive to negative values in October and increased to positive values in April-May, even though air temperature had changed significantly. Figure 4 shows the relationships between air temperature (\(AT_{i}\)) and soil temperatures (\(ST_{i,t}\)) at depths of 5, 10, and 15 cm; subscripts \(i\) and \(t\) represent the depth from surface and number of days from the start of the study period, respectively. As air temperatures increased, the soil temperatures also showed a tendency to increase. The fitting line equations in Figure 4 were represented to show of different correlation degrees of soil temperature with air temperature with increasing soil depth. The decrease of gradient of the fitting equation with increasing soil depth in Figure 4 indicate decrease of correlation between soil temperature and air temperature with increasing depth. The intercept  
Figure 3: Observed soil temperature variations at sites: (**a**) M1; (**b**) M2; (**c**) M3; (**d**) M4.