*3.1. Air Temperature (Ta)*

The *Ta* is generally observed at a height of about 2 m above the land surface. *Ta* data observed at 11 different stations was used in the present study (Table 1). The data for five stations from Global Historical Climatology Network (GHCN) which was acquired from National Centre for Environmental Information (NCEI), NOAA web portal (https://www.ncei.noaa.gov/) [35] had observed daily mean *T<sup>a</sup>* estimated using hourly or 6-hourly observations (Version 3). For the other six stations of Bhakra Beas Management Board (BBMB) and India Meteorology Department (IMD), the *T<sup>a</sup>* was calculated using the daily maximum and minimum observations due to unavailability of daily mean *Ta*. This method of averaging the daily maximum and minimum temperatures for calculation daily mean temperature is widely used due to the instrumentation, logistic, and computational simplicity [36]. Although the method produces bias in the output due to inability to track the diurnal asymmetry [37], it has been used by considerable number of studies to make acceptable estimates requiring *T<sup>a</sup>* [36]. In order to understand the degree of bias for our study area, we compared the given daily mean *T<sup>a</sup>* with mean of daily maximum and minimum *T<sup>a</sup>* for the five stations of GHCN for which all the three parameters were available. The analysis showed that the RMSD was less than 1.62 ◦C with a very high correlation (R <sup>2</sup> > 0.96) for all the stations. In addition to the daily *Ta*, we also calculated 8-day mean *T<sup>a</sup>* for comparison with the corresponding 8-day *T<sup>s</sup>* explained in next section. The observations were carefully checked for systematic and random errors before using it for further comparison. The stations used in the present study are distributed broadly over four different precipitation zones (Table 1, Figure 1). The precipitation varies significantly in these precipitation zones. The monsoon dominated, transition zone, westerlies dominated, and precipitation shadow zone receive >1500, 200–800, 600–800, and <150 mm total annual precipitation on an average, respectively.

#### *3.2. MODIS Data*

The daily, and 8-day night- and day-time *T<sup>s</sup>* from MODIS satellites on Terra (MOD11A1 and MOD11A2 available from February, 2000) and Aqua (MYD11A1 and MYD11A2 available from July, 2002) satellites [23,24] was downloaded from NASA Earthdata portal (https://earthdata.nasa.gov/) [38] and was used to calculate average of daily and 8-day *T<sup>s</sup>* (Table 2). The remotely-sensed *T<sup>s</sup>* from MODIS (version 006) has been observed to have RMSD of less than 0.5 K in comparison to the

in situ measurements of the *T<sup>s</sup>* [39] and therefore has been widely used for multiple scientific applications [18,19,22,25–28,40].


**Table 2.** Details of Moderate Resolution Imagining Spectroradiometer (MODIS) data used in the present study.

The local time for the pass over the study area for Terra is around 10:30 and 22:30 and for Aqua is around 13:30 and 01:30 during day and night, respectively. The 8-day land surface temperature data MOD11A2 and MYD11A2 is a simple pixel wise average of all the respective MOD11A1 and MYD11A2 data collected during the 8-day period. The days with all the four observations, including the day and night-time measurements available from both Terra and Aqua were included in the comparison at both daily and 8-day scale. Equation (1) was used to compute the average of four MODIS observations during a day or 32 MODIS observations during an 8-day period (referred as *T<sup>s</sup>* in ◦C) from the pixel value corresponding to every station given in Table 1.

$$T\_s = \frac{T\_d^T + T\_n^T + T\_d^A + T\_n^A}{4} - c\_\prime \tag{1}$$

where,

*T T d* = Terra day-time observation

*T T <sup>n</sup>* = Terra night-time observation

*T A d* = Aqua day-time observation

*T A <sup>n</sup>* = Aqua night-time observation

*c* = Constant for conversion from kelvin to Celsius (273.15)

For every data point of daily and 8-day *Ts* , two night-time and two day-time satellite observations were used. It moderated the calculated daily *T<sup>s</sup>* for further comparison with *Ta*. Therefore, every data point of daily *Ts* is average of four MODIS observations during that day and 8-day *Ts* is average of 32 MODIS observations during that 8-day period. Since, the satellite observation from MODIS is unavailable in cloud cover condition and the calculated daily *T<sup>s</sup>* for comparison with *T<sup>a</sup>* can have large data gaps, we decided to also include MODIS 8-day *T<sup>s</sup>* in the analyses. For 8-day *T<sup>s</sup>* , the data available is comparatively more continuous due to correction of cloud contamination [39]. Although, the 8-day MODIS observations are more efficient in terms of temporal continuity, it compromises with the temporal resolution. Additionally, the number of data points available for comparison for 8-day average is significantly less than the dataset available for daily average. Thus, the average *Ts* used in our analyses, and referred to hereafter, is essentially the average of four-times daily and 8-day MODIS *T<sup>s</sup>* observations and all the results should be considered accordingly. Therefore, based on these data limitations, we finally compared the average of four-times daily and 8-day MODIS *T<sup>s</sup>* observations with observed daily mean *Ta* for five GHCN stations and with the average of observed daily maximum and minimum temperatures for the remaining six stations.
