**1. Introduction**

Air temperature (*Ta*) is an important proxy for energy exchange between land-surface and atmosphere, making *Ta* one of the most important parameters in climate research [1,2]. *Ta* is generally observed at a height of about 2 m above the land surface and it is considered as a critical parameter for glacio-hydrological studies because it controls the rate of melting of snow and ice and the proportion of form of precipitation [3,4]. In addition, it also regulates the evolution of flora and fauna in an area, ultimately controlling the evolution of the ecological niche [5]. *T<sup>a</sup>* is also important for determining the atmospheric water vapor saturation point and thus for the formation of fogs and clouds. The gradient between the air and ground temperature is relevant for estimating the sensible heat flux (i.e., the convective heat flux loss from surface to the air) for calculations of the surface energy balance [6]. The surface-to-air temperature difference is particularly important for evapotranspiration [7]. In other regions, such as the Arctic, the *T<sup>a</sup>* difference is taken as a critical parameter to monitor climate change [8]. Therefore, it is imperative to have accurate estimates of *T<sup>a</sup>* for various natural science disciplines including glaciology, hydrology, ecology, and climatology. The measurement of *T<sup>a</sup>* using in situ automatic meteorological stations is cost intensive due to involved instrumentation and maintenance which makes the spatial continuity of data sparse, particularly in remote environments. This spatially discontinuous nature of in situ *Ta* measurements adds uncertainty in geospatial modelling in mountainous terrain when the *T<sup>a</sup>* representing single data points are extrapolated to a continuous surface based on fixed lapse rates [9–11].

The land surface temperature (*Ts*) in a remote sensing perspective is the measure of how hot or cold the top canopy skin layer of the Earth at a particular location will feel when touched [12]. The measure of *T<sup>s</sup>* is largely dependent on net solar radiation, sensible heat flux, reflectance property of the surface, aerodynamic resistance, and the density of air [13]. Although the *T<sup>s</sup>* is closely related to *Ta*, it can be significantly influenced by the surface characteristics, buffering effects of vegetation and the periodicity of the shortwave radiation emitted from the sun [14]. Over the past decade, the remotely-sensed *T<sup>s</sup>* measurements have been used to map permafrost in different parts of the world [14–17]. There have been several attempts to estimate *T<sup>a</sup>* using remotely-sensed *T<sup>s</sup>* in different ecological systems [18–22]. The root mean square difference (RMSD) between *T<sup>a</sup>* from meteorological stations and *T<sup>s</sup>* from Moderate Resolution Imagining Spectroradiometer (MODIS) on Terra [23] and Aqua [24] satellites was estimated to be ±2.20 ◦C in Indo-Gangetic plain [25], ±1.33 ◦C in Portugal [18], ±5.48 ◦C in mountainous regions of Nevada, United states of America [19], ±2.97 to ±7.45 ◦C in northern Tibetan Plateau, China [26], ±4.09 to ±4.53 ◦C in a mountainous region of sub-Arctic Canada [27], and ±1.51 to ±3.74 ◦C over different ecosystems in Africa [22]. A recent study attempted to analyze the temperature trend using the 8-day *T<sup>s</sup>* corrected using the difference between *T<sup>s</sup>* and *T<sup>a</sup>* calculated for 87 meteorological stations in the Chinese part of Himalaya and Tibetan Plateau [28]. Most of these published studies have compared the *Ta* and *Ts* at monthly or 8-day scales while several prominently used ecological and glacio-hydrological models in Himalaya that require daily temperature data as input parameter [4,29]. Moreover, such comparative studies for high mountains of Central or Western parts of Himalaya are completely missing.

The observed temperatures in Himalaya are scarce and fragmented in spatiotemporal domain due to difficult terrain, inhospitable weather conditions, and logistic difficulties in setting-up the weather stations [29]. The Himalayan mountains serve as a source of fresh water supply [30,31] and hydropower generation [32] to the densely populated mountainous regions of Indian Subcontinent. The Himalayan rivers mainly consist of the meltwaters coming from snow and glaciers [30] and this runoff is largely dependent on the seasonal temperatures [4,33]. The glaciers in Himalaya are losing mass in general with a few exceptions [29,33]. However, the quantification of the changes evident in glacierized regions in Himalaya with respect to the changing temperatures are largely uncertain due to unavailability of well-distributed and spatiotemporally continuous network of meteorological stations [29]. Furthermore, the lack of a definite and abiding framework for mutual climatological data sharing among various research and academic organizations in Himalayan countries makes regional-scale glacio-hydro-climatological modelling and interpretations more uncertain [29]. In this respect, there are two significant research gaps: (i) the studies comparing *Ta* with *Ts* for a large spatial domain are completely missing for the Central and Western Himalaya, and (ii) owing to this research

gap, the glacio-hydrological community is further unsure of the significant role that spatiotemporally continuous satellite-derived surface temperatures can play as a substitute for spatially discontinuous *T<sup>a</sup>* observations. The land-surface temperature is more likely proxy of energy exchange between land-surface and atmosphere for phenomena which are more strongly linked to ground processes [27]. The main aim of the present study is to understand and quantify the statistically significant trends in *T<sup>s</sup>* − *T<sup>a</sup>* variation over a large spatiotemporal domain in Western Himalaya. Here, we start with providing a description of the study area, followed by data and used methods, and finally we discuss and conclude the main findings of the analyses. −
