*2.2. Observations*

The soil data used in this study, measured at the period of 2014–2016, are shared by Ma et al. [52] at the Science Data Bank (https://doi.org/10.11922/sciencedb.00103 (accessed on 26 August 2021), Ma et al. [52]), and the National Tibetan Plateau Data Center (https://doi.org/10.11888/Meteoro.tpdc.270910 (accessed on 26 August 2021)). The data were hourly values. The information of soil sensors used at each site is presented in Table 2. Note that at 2014 BJ the soil temperature and moisture were measured at the depths of 0.04 m, 0.10 m and 0.20 m, and 0.04 m and 0.20 m, respectively. Both the soil temperature and moisture were measured at the depths of 0.05 m, 0.10 m, and 0.20 m at 2015–2016 BJ.


**Table 2.** The sensors and observation information at each site.

The NDVI data were obtained from MYD13C2-v006, provided on a monthly basis, with a spatial resolution of 0.05◦ × 0.05◦ (https://giovanni.gsfc.nasa.gov/giovanni/, accessed on 15 April 2022).

### *2.3. The Method Used to Determine Soil Apparent Thermal Diffusivity*

Expanding the heat conduction equation presented by Van Wijk and De Vries [30], Gao et al. [23] presented the conduction and convection heat transfer equation with an assumption that the soil apparent thermal diffusivity was vertically homogenous, as follows:

$$\frac{\partial T}{\partial t} = k \frac{\partial^2 T}{\partial z^2} + W \frac{\partial T}{\partial z} \tag{1}$$

where *T* ( ◦C) is soil temperature, *t* (s) is the time, and *z* (m) is the vertical coordinate positive downward; *k* (m<sup>2</sup> s<sup>−</sup>1) is soil apparent thermal diffusivity, *W* (m s<sup>−</sup>1) is the apparent convection parameter. With a boundary condition described with the sine function of soil temperature, Gao et al. [23] obtained an analytical solution of this heat transfer equation, and derived the equations of k, as follows:

$$k = -\frac{(z\_1 - z\_2)^2 \omega \ln(A\_1 / A\_2)}{\left(\Phi\_1 - \Phi\_2\right) \left[\left(\Phi\_1 - \Phi\_2\right)^2 + \ln^2(A\_1 / A\_2)\right]}\tag{2}$$

where *z*1 (m) and *z*2 (m) are the measurement depths of soil temperature; *A*1 ( ◦C) and *A*2 ( ◦C) are soil temperature amplitude at the depths of *z*1 and *z*2, respectively, Φ1 (rad) and Φ2 (rad) are soil temperature phase at the depths of *z*1 and *z*2, respectively; *ω* (=2 π/P = 7.292 × 10−<sup>5</sup> rad−1) is the angular velocity of the Earth's rotation; and P (=24 × 3600 s) is the harmonic period of the soil temperature.

### *2.4. Data Processing*

Equation (2) is the conduction–convection method for determining k, which is the same equation derived by McCallum et al. [53] and Luce et al. [54] for saturated soil. In order to determine k at various timescales, we first derived hourly A and Φ of daily soil temperature at two depths using the DHR (See Appendix A) from the Captain toolbox [50,51], and then put them into Equation (2) to obtain hourly k. The daily and monthly values of k were obtained by averaging the hourly values.

To ensure the quality of k, the first 3 days of soil k data from the beginning and end of the data collection periods were discarded due to the edge effects of digital filtering with DHR [55,56]. Gordon et al. [57] suggested that data from any time series that have amplitudes below the sensor resolution should be treated with suspicion. To minimize the amount of suspicion, we deleted the data when the soil temperature amplitude at 0.20 m depth was below the values of 0.5 ◦C, 0.1 ◦C and 0.1 ◦C at BJ, QOMS and NADORS, respectively. After data deletions, approximately 95–100%, 96–100%, and 78–82% of the original data remained for analyses at BJ, QOMS and NADORS, respectively.

The soil moisture measured at the 0.10 m depth was used to represent the soil water status in the 0.0 m to 0.20 m layer. The θ measured at the 0.04 m depth was used as the soil water condition in the interest layer for 2014 BJ. For NADORS, the θ at the 0.10 m depth was calculated by the arithmetic mean of θ measured at the surface and the 0.20 m depth. Note that here θ indicates liquid water content in the soil, and the ice content is not measured. Ice content is qualitatively discussed based on soil temperature and initial soil liquid water content as described in the Section 4.2.
