Appendix A.1.1 Input Variables

T, P, S are three basic inputs of SRM.

The daily snowmelt depth is calculated by the number of degree-days, which is determined by the daily temperature. In order to run SRM for each elevation zone, daily temperature from Hotan station was extrapolated to the mean elevation of each zone based on the global lapse rate value of 6.5 ◦C/km.

The daily watershed-averaged precipitation was derived from the China Ground Rainfall Daily Value 0.5◦ × 0.5◦ Lattice Dataset by using the Thiessen polygon (TP) method, which was used for each elevation zone.

The daily SCA for each elevation zone was generated from the SCA of 8-day composite MOD10A2 satellite images by using linear interpolating.

#### Appendix A.1.2 Parameters

*Cs*, *Cr*, *a*, *Tc*, RCA, *K*, and time lag are the seven parameters to set up SRM, whose value are presented in Table 3.

The runoff coefficients *Cs* and *Cr*, account for the losses between the runoff contributed by snowmelt and rainfall to precipitation. *Cs* and *Cr* are time-varying parameters, affected by lots of controlling factors such as climatic conditions and land cover properties. They can vary over seasonal, monthly, or even daily scale, which are the primary candidates for tuning if a runoff simulation is not immediately successful [47].

The degree-day factor *a* (cm/ ◦C/day), converts the degree-days T (◦C day) into the daily snowmelt depth M (cm) by Equation (A2). *a* is related to snow properties. According to the research for degree-day factors in western China conducted by Zhang et al. [88], 0.3 is adopted in this study.

$$M = a \, \times T \tag{A2}$$

The critical temperature *Tc* is used to determine whether the precipitation is rainfall (*T* > *Tc*) or snowfall (*T* <*Tc*). The *Tc* values for June–August and September–May are set to 3 ◦C and 0 ◦C, respectively, As recommended by Martinec [47].

The rainfall contributing area RCA represents the way that how to treat the rainfall determined by *Tc* and it needs to be determined according to the basin characteristics beforehand. When RCA is set to be 0, it is assumed that the rain falling on the snowpack is retained by the snow which is dry and deep. In this situation, rainfall depth is reduced by the ratio snow-free area/zone area. RCA is set to be 1 when the snowpack is ripe, which means that rainfall from the entire area is added to snowmelt. In this study, the snowpack is assumed to be ripe during May–September when the temperature is above 0 ◦C.

The recession coefficient *K* indicates the decline of discharge in a period without snowmelt or rainfall, and (1 − *K*) presents the proportion of the meltwater production immediately appearing in the runoff. *K* is determined by Equation (A3) [47], in which parameters *x* and *y* can be obtained through linear regression analysis using the historical discharge data.

$$K\_{n+1} = \frac{Q\_{n+1}}{Q\_n} = \mathbf{x} \times Q\_n^{-y} \tag{A3}$$

There is a time lag (L) between the temperature cycle and the resulting discharge cycle in Equation (A1). In this study, a lag time of 18 h is adapted depending on the relation between L and basin size [16]. In the case of 18 h, temperature measured on the nth day corresponds to the discharge on the *n* + 1 day.

#### **References**


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