Global warming is a long-term increase in the average temperature of the Earth (Mikhaylov et al., 2020; Hansen et al., 2022). Though this warming trend has been going on for a long time (Tokarska et al., 2020), its pace has significantly increased in the last hundred years due to the burning of fossil fuels leading to the increase in air, sea temperature and land surface temperature (LST) (Zhou et al., 2021). The reliable estimation of temperature increase is highly crucial (Mu et al., 2023), however, obtaining temperature data in extreme locations is difficult due to challenges in establishment of a weather station and extrapolation of empirical data can be misleading (Vela et al., 2023). This problem can be effectively dealt with satellite-based observational data pertaining Land Surface Temperature (LST) that is a proxy for the energy exchange balance between the earth and the atmosphere (Zhengming and Dozier 1989; Aguilar-Lome et al., 2019). LTS estimation has been in by the researchers since very log for climatic studies (Prata et al., 1995; Weng, 2009; Ozelkan, 2014). Vázquez et al., 1997, used LST data for explaining climatic conditions using AVHRR datasets. LST has been employed for purposes such as inferring surface air temperatures, other temperature dynamics such as relationships between land use/landcover and LSY in studies conducted by Xu et al. (2019), Rohde and Hausfather (2020), Sekertekin and Bonafoni (2020), Jamal et al. (2023), and Khan et al. (2023a). Additionally, LST has been instrumental in identifying rapid temperature changes, as noted by Li et al. (2022), and in tracking shifts in urban heat islands (Hu and Jia, 2010). Furthermore, LST assessments have been utilized for long-term temperature trend analyses, as seen in the work of Saini and Tiwari (1998), Gaffen and Ross (1999), and Neteler (2010). For long-term analysis of temperature, time series analysis has been extensively employed on LST products such as on MODIS, Landsat, and AVHRR (Otgonbayar et al., 2019; Firoozi et al., 2020). Tahooni et al., 2023 applied time series to ascertain the impact of albedo on LST while Khan et al., 2023 explained the relationship between biophysical factors and LST using time series. However, the use of LST in earlier research has been confined to analysing data available from past and present times, without projecting or predicting future LST trends. Some scholars used time series methods such as simple moving average, an easy-to-use method to predict LST, rainfall occurrence, and for exploring the relationship between LST and elevation (Khan et al., 2020; Das et al., 2020; Yudianto et al., 2021). However, these studies short of employing the time series for forecasting future scenarios of LST to intuit warming trends in spatial context.

Researchers like Panwar et al., 2018; Haq et al., 2020; and Saher et al., 2021, have concentrated on analysing LST trends using methods like Sen’s slope, while Haq et al., 2020 utilized the Mann-Kendall method for assessing LST warming trends in Himachal Pradesh, India. However, it is noteworthy that these studies primarily focus on localized areas and do not extensively apply forecasting techniques, indicating a potential gap in fully leveraging these methods for broader, predictive applications. Apart from the above methods, parametric statistical techniques, including the t-test and z-test that offer considerable utility in analysing climatic data, remained underutilized by researchers in the field. Murugan et al., 2012 employed this approach to ascertain the significance of the seasonal trend in Sen's slope but the application of this test was rudimentary, lacking the establishment of statistical power of test. Moreover, the direct application of these tests on climatic data has been almost negligible.

In the Himalayas, often referred to as the 'Third Pole' due to their extensive ice fields and glaciers such region-specific studies inferring information about future LST, rate of change in LST with statistical significance can be very crucial (Khan et al., 2023a; Khan et al., 2023b). Given the challenging terrain and the scarcity of weather stations in the Himalayas, satellite-based LST data has become an indispensable tool for assessing regional warming patterns (Pepin et al., 2019). These datasets offer valuable insights into temperature trends over time, especially in remote and inaccessible areas (Guo et al., 2020).

The proposed research aims to forecast LST dynamics in the Kumaun Himalayan region exploiting Landsat data, leveraging the Simple Moving Average (SMA) for temporal data smoothing, and emphasizing long-term climatic trajectories. Complementing this, Sen’s slope estimator will quantify LST trends, offering robustness against outliers and skewed distributions characteristic of environmental datasets (Barnett, 2005). A pivotal element of this research is the granular examination of seasonal temperature shifts, dissecting autumnal, winter, summer, and spring mean temperatures from 1990 to 2030. Such analysis is vital for discerning season-specific climatic impacts and differential temperature progression rates. Enhancing methodological rigor, z-statistics is used to ascertain the statistical significance of observed trends, comparing Long-term mean LST against forecasted LST. This approach is essential in climate research for substantiating statistical significance of temperature variation, thus informing predictive models, and shaping policy frameworks. z-statistics is not only applied to quantify the change in long-term mean and future LST means but also to intricately understand statistical significance of seasonal temperature variances highlighting pronounced seasonal warming.

The multifaceted methodology adopted in this paper is pivotal for developing innovative and practical applications of time series analysis in spatial contexts, where each pixel is meticulously analysed. This research paves the way for groundbreaking opportunities in integrating time series data with spatial analysis, enhancing our understanding and capabilities in this domain. Furthermore, the research opens-up prospects of parametric test in the analysis of climate change.