*4.3. Seasonal Relationship*

The difference between mean monthly *T<sup>a</sup>* and *T<sup>s</sup>* (i.e., *T<sup>s</sup>* − *Ta*) for the entire period of study shows high inter-monthly variability for all the stations except for the stations in monsoon-dominated regions (Figures 5 and 6). The mean monthly *Ts* is lower in comparison to mean monthly *Ta* for southern slopes (Figure 6a) and increases with increasing latitudes (Figure 6c) except for the stations in westerlies dominated areas (Figure 6d). The magnitude of difference between mean monthly *T<sup>s</sup>* and mean monthly *Ta* is negative for the stations in monsoon-dominated areas and positive for the stations in precipitation

shadow and westerly-dominated regions. In the precipitation-transition zone, the difference is positive for summer months and negative for winter months except for Rakchham, the southernmost station of the transition zone (Figure 5). For Rakchham, the *T<sup>s</sup>* − *T<sup>a</sup>* values are negative throughout the year similar to the stations in monsoon-dominated areas (Figure 6b). This might be a result of the added effect of humidity in the near-surface atmosphere and presence of snow on land surface which moderates the difference between *T<sup>s</sup>* and *T<sup>a</sup>* [42] throughout the year in monsoon-dominated regions. In the precipitation-transition zone, the difference is partly moderated by the presence of snow during winter months and partly humidity during summer months, particularly for the southernmost stations of the zone (Rakchham and Kalpa) (Figures 5 and 6b) which receive enough precipitation through both monsoon and westerlies. *T<sup>s</sup>* − *T<sup>a</sup>* values for the stations in westerly-dominated region are regulated mainly by the presence of snow during winters (Figures 5 and 6d), which tends to cool the surface due to high albedo [42]. The *T<sup>s</sup>* − *T<sup>a</sup>* values for the stations in precipitation-shadow zone are significantly high and positive in magnitude throughout the year in comparison to all the other stations due to the perennial cold-arid atmospheric conditions (Figures 5 and 6c). This confirms the role of water cycle on this gradient and shows that in the absence of soil-atmosphere water cycle (dry conditions) the magnitude of the difference between *T<sup>s</sup>* − *T<sup>a</sup>* increases and is more positive. −

**Figure 6.** Graph showing the mean monthly difference between daily *T<sup>s</sup>* and *T<sup>a</sup>* for the entire period for which the data is available for stations in (**a**) monsoon-dominated areas, (**b**) transition zone, (**c**) precipitation shadow zone, and (**d**) westerlies-dominated areas. The observed *Ta* for Skardu for winter months was unavailable. The *T<sup>s</sup>* − *T<sup>a</sup>* values for the stations in the precipitation-shadow zone (**c**) are significantly higher and positive in magnitude, due to the perennial cold-arid atmospheric conditions.

The comparison of *Ts* and *Ta* showed high inter-monthly variability throughout the study period. Therefore, we performed an additional analysis where we estimated the seasonal effect of each month on the difference between *T<sup>s</sup>* and *T<sup>a</sup>* (Figure 7) in reference to a base month. For this multiple regression analysis, January was considered as the base month since the *T<sup>s</sup>* − *T<sup>a</sup>* values in January were least for all the stations in general (Figure 6). This analysis further corroborates the above-discussed aspect that the *T<sup>s</sup>* − *T<sup>a</sup>* coefficient values are larger in summer months in comparison to winter months (Figure 7). Additionally, the difference in coefficient and RMSD is high for stations in precipitation shadow regions (Kaza, Shiquanhe and Losar) in comparison to the stations in monsoon-dominated areas (Shimla and Mukteshwar) (Figures 6 and 7).

**Figure 7.** Graph showing the effect of each month on the *T<sup>a</sup>* in reference to the month of January for stations in (**a**) monsoon-dominated areas, (**b**) transition zone, (**c**) precipitation shadow zone, and (**d**) westerlies-dominated areas. The observed *Ta* for Skardu for winter months was unavailable.

To further corroborate the effect of seasonality and the presence of snow and humidity on the *T<sup>s</sup>* − *T<sup>a</sup>* values, we created monthly box and whisker plots of daily difference between *T<sup>s</sup>* and *T<sup>a</sup>* (Figure 8). The whisker for the stations in precipitation shadow zone and transition zone is longer showing the high monthly variability of the difference value in comparison to the stations in monsoon and westerlies-dominated areas. This is due to the presence of snow during the winter and humidity in the atmosphere in summer regulating the difference between *T<sup>s</sup>* and *T<sup>a</sup>* in the monsoon dominated areas. Additionally, the size of the boxes are smaller for the stations in monsoon and westerlies-dominated areas explaining the presence of maximum data points close to the median representing that throughout the year the difference between *T<sup>s</sup>* and *T<sup>a</sup>* is regulated by presence of snow or atmospheric moisture. On the contrary, the boxes for stations in precipitation shadow zones which receive significantly less precipitation throughout the year, are wider in size representing large variation in the difference between *Ts* and *Ta* throughout the year. The boxes for the stations in the southern part of the transition zone are smaller in summer and wider in winter showing the effect of humidity due to some influence of monsoon owing to their spatial closeness to the monsoon-dominated region. Besides, both the boxes and whiskers for the stations in north-eastern part of the transition zone, closer to the precipitation shadow zone, are wider in size showing the variability due to lack of both snow and humidity.

**Figure 8.** Box and whisker plots showing the monthly variation of daily difference between *T<sup>s</sup>* and *Ta* for the entire period for which the data is available for stations in (**a**) monsoon-dominated areas, (**b**) transition zone, (**c**) precipitation shadow zone, and (**d**) westerlies-dominated areas.

#### **5. Discussion**

The observed near-surface air temperature is one of the most important climate parameters used in different kinds of environmental studies particularly in Himalaya where the interaction between high elevation, climate, and cryosphere is highly significant and complex. It is extremely difficult to capture the spatial heterogeneity of the near-surface temperature [43] which is the primary forcing data for different glacio-hydrological models [3,4,44–46]. It is also used as primary data for climate change assessment [47,48], agro-climatic [40], ecological [49,50], and socio-economic [51,52] studies. Our results present a freely available substitute for station recorded *Ta* with high temporal and spatial resolution. Conclusively, the *T<sup>s</sup>* is highly correlated with *T<sup>a</sup>* throughout the study area at both daily and 8-day scales. The correlation is highest at the stations located at Southern slope (Shimla and Mukteshwar) with significantly low RMSD in comparison to the stations located in the Eastern part (Losar and Shiquanhe). Although, the degree of congruence between *Ts* and *Ta* is slightly higher in the 8-day dataset (R<sup>2</sup> > 0.77) in comparison to the daily dataset (R<sup>2</sup> > 0.69), the number of data points available for comparison is significantly low. The overall RMSD improved by 0.2 ◦C on an average by using the 8-day dataset. The largest improvement in RMSD was observed for Skardu (1.1 ◦C) but the number of data points available for correlation was significantly less than other stations. The overall SE improved by 0.38 ◦C except for Kalpa and Kaza for which it deteriorated by 0.02 and 0.08 ◦C, respectively. It is interesting to note that for Shiquanhe which is located in precipitation shadow zone and highest altitude among all the stations, shows largest improvement in SE (by 1.63 ◦C) and reduction in RMSD (0.2 ◦C).

− The difference between *T<sup>s</sup>* and *T<sup>a</sup>* is primarily controlled by elevation, the land surface cover characteristics, and near-surface humidity. At higher altitudes, the thinner atmosphere shows lesser water holding capacity and the atmosphere saturates faster, thus allowing for lesser evaporation/sublimation in a given pressure-temperature scenario [53]. This puts a constraint on the limit of specific humidity in the high elevations and the comparatively lesser number of available water molecules in the near-surface atmosphere cannot trap the same amount of heat as those at lower elevations. This can provide a basis for the observed high values of *T<sup>s</sup>* − *T<sup>a</sup>* at the higher altitudes. The

intercept of the regression between *T<sup>s</sup>* and *T<sup>a</sup>* shows increase for the stations in monsoon, transition, and westerlies-dominated areas. On the contrary, the stations in precipitation shadow zone show a sharp decrease in the intercept of the regression at high elevations (>3600 m). The slope of the regression between *T<sup>s</sup>* and *T<sup>a</sup>* is higher for stations in low elevation and precipitation-dominated areas (0.80–1.03) in comparison to the stations in high elevation and in transition-to-precipitation shadow zones (0.59–0.86). This observation is supported by a study which shows decrease in slope and degree of correlation in high elevation [54]. The high difference between *T<sup>s</sup>* and *T<sup>a</sup>* for the stations in dry atmosphere at high altitude may partially be due to the heat from the Sun and cooling of near-surface atmosphere due to heat exchange from surrounding air and temperature lapse rate [55]. The presence of more humidity moderates the difference between *T<sup>s</sup>* and *T<sup>a</sup>* in precipitation dominant areas. The difference between *T<sup>s</sup>* and *T<sup>a</sup>* is highest with positive magnitude when the land surface is snow-free and the near-surface atmosphere is dry. On the contrary, the *T<sup>s</sup>* and *T<sup>a</sup>* is negative and lower in magnitude when the land surface is covered by snow and/or atmosphere is more saturated with moisture regardless of high altitude. In addition to the elevation and precipitation regime, season was observed to have significant control over the difference between *T<sup>s</sup>* and *Ta*. The summer months were observed to have a significantly higher effect on *T<sup>a</sup>* in reference to January, in general for all the stations. The inter-monthly variability was observed to be very high for year-round humidity-deficient transition zones and precipitation shadow zones in comparison to the monsoon-dominated and westerlies-dominated regions. It can be interpreted that the energy exchange between the surface and near-surface atmosphere in the precipitation dominant areas is more efficient in comparison to the precipitation deficient areas.

The lower magnitude of RMSD between *T<sup>s</sup>* and *T<sup>a</sup>* represents lower gradient of temperature between the land surface and near-surface air due to the cold bias caused by snow cover which protects the surface from warming because of its high albedo [42]. A possible contributing factor to this seasonal disparity can be the reported perpetually melting seasonal snow in Himalayan mountains [55] under the changing regional climate. The causal mechanism for this relationship deserves a separate detailed investigation. However, a possible cause of such observations can be linked to the fact that the diurnal temperatures even in the mid-winter months often cross the freezing point causing a certain degree of melting to prevail [56]. This can start a cascading event where during the preliminary warming phase, the average snowpack temperature reaches and stays at 0 ◦C isotherm until the melting typically starts within the snowpack prior to the ripening phase as meltwater is retained within the snowpack [57]. This meltwater may subsequently refreeze owing to the diurnal cycles of temperature and the latent heat released during this process can additionally warm the snow surface and the surrounding air, further minimizing the temperature difference [56]. In addition to the seasonal change in the land cover characteristics, the variation in humidity in the near-surface atmosphere is an important factor controlling the difference between *T<sup>s</sup>* and *Ta*. It was recently proposed that the amount of moisture content on the land surface has a cooling effect on land surface temperature [40]. Thus, the precipitation regime in which a particular station is located can further provide us several clues regarding the observed variations in *T<sup>s</sup>* − *T<sup>a</sup>* values. These precipitation regimes have been previously characterized [34] and in the following discussion, we take a focused approach towards revisiting the *T<sup>s</sup>* − *T<sup>a</sup>* variations with respect to the respective precipitation scenarios.

All the statistical results and the regression equation between *T<sup>s</sup>* and *T<sup>a</sup>* have specific trends for particular climate setting and elevation which can be used to estimate *T<sup>a</sup>* using *T<sup>s</sup>* (Table 3) for glacio-hydrological and climate change studies in data-deficient Himalaya. For example, the RMSD ranges between 1.2–1.6, 2.6–5., 2.5–4.3, and 7.2–8.9 ◦C for the stations in monsoon-dominated, transition, westerlies-dominated, and precipitation shadow zones, respectively, for both daily and 8-day products. The slope and intercept of the regression equations between *Ts* and *Ta* are also similar for the stations in the same precipitation regime. The paper demonstrates different patterns of variation of *T<sup>s</sup>* − *T<sup>a</sup>* in different climate regimes within the region of study. Due to the inherent limitations of the available data, some of this analysis may be revised in the future by specific dedicated studies, in particular to

asses if the relationships hold on daily scales and with what error bar. Some possible error sources for this analysis may come from the scarcity of the data, and the fact that we compared data from different instrumentation accuracies and cadences. *T<sup>a</sup>* is measured by three different organizations and two calculation methods are used for daily mean air temperature during different observation periods. The correlation of the instantaneous observation of *Ta* in relation to satellite derived *Ts* can be investigated by analyzing the diurnal variation of *T<sup>a</sup>* in relation to the time of pass of the satellite [58]. There are different parameters like wind speed and fractional vegetation which have additional effects on the difference between *T<sup>s</sup>* and *Ta*, which have not been investigated in the present study [54,55] and can be interesting research questions for future investigations in the region.

#### **6. Conclusions**

Unavailability of reliable temperature observations with spatial continuity along with the extreme weather conditions and difficult terrain in the remoteness of Himalaya hampers our understanding of the cryosphere-climate coupling in these mountains. Here we attempt to compare remotely sensed *T<sup>s</sup>* with respect to in situ *T<sup>a</sup>* observations over different precipitation and altitudinal zones of the Western Himalaya. Although, there are several studies available from different parts of the globe attempting to estimate *Ta* using *Ts* or vice-versa using monthly or 8-day MODIS data, we provide an understanding of the spatiotemporal variability of the *T<sup>a</sup>* vs. *T<sup>s</sup>* relationship at diurnal scales. The results show a strong and statistically significant relationship between *T<sup>s</sup>* and *T<sup>a</sup>* in general with a spatiotemporal consistency, thus projecting satellite-derived *Ts* as a viable alternative to the in situ *Ta* for glacio-hydro-climatological studies. We also provide regression equations to facilitate modeling of gridded *T<sup>a</sup>* using corresponding *T<sup>s</sup>* for different regions of Western Himalaya. MODIS in combination with Sea and Land Surface Temperature Radiometer (SLSTR) onboard Sentinel-3 can provide better capability to overcome cloud gaps and ensuring spatiotemporal continuity for *T<sup>s</sup>* future studies in this direction.

**Author Contributions:** S.S. conceptualized and designed the research and wrote the manuscript. S.S., A.B., A.S., L.S., and M.S. performed statistical tests, and wrote the manuscript and methods section with inputs from all the co-authors. S.S., A.B., and A.S., performed raw data generation and analysis. F.J.M.-T. and M.-P.Z. helped in analyzing the results and correlating them with the different variables.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors would like to acknowledge National Snow and Ice Data Centre, USA and National Oceanic and Atmospheric Administration, USA for providing freely available MODIS satellite products and Global Historical Climatology Network station data, respectively. The authors are also grateful to India Meteorology Department (IMD), India, Bhakhra Beas Management Board (BBMB), India and Hendrik Wulf, University of Zurich, Switzerland for providing the station data. A.B. acknowledges the Swedish Research Council for supporting his research in Himalaya. M.S. acknowledges Director, Birbal Sahni Institute of Palaeosciences and Birbal Sahni Research Associate fellowship.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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*Article*
