Multiscale analysis of satellite-derived climatic parameters over Himalayan foothills in view of climate change scenarios

1 Introduction

Precipitation is one of the most critical climatic variables, significantly influencing ecosystem productivity, vegetation dynamics, and soil moisture conditions. Large-scale climatic phenomena, such as monsoons and global warming, modulate vegetation dynamics and ecosystems (Yadav, 2022; Mamgain et al., 2023). Additionally, anthropogenically induced climate change affects vegetation, agriculture, and in turn, food security (Saleem et al., 2025). Regional climate change impacts hydrological processes, i.e., soil moisture and surface energy exchange (Huryna and Pokorný, 2016; Ougahi et al., 2022). The High Himalaya is sensitive to precipitation and air temperature at various spatial and temporal scales (Rawat et al., 2025). High-altitude climate is affected by dynamics of atmospheric circulation that play a significant role in shaping vegetation dynamics and biomass production (Poonia et al., 2022; Anand and Garg, 2024; Zhang et al., 2022; Liu et al., 2025). Land surface temperature plays an important role in influencing the variability of snow cover and vegetation dynamics significantly in climate at regional to global scales (Kydyrova et al., 2025; Masson et al., 2020). Regional precipitation changes can intensify or reduce the consequences of global warming, leading to widespread glacier retreat and impacts on hydrological cycles (Yadav et al., 2021). Vegetation index trends have been affected by climatic drivers, solar radiation, evapotranspiration (ET), and surface energy exchange processes, which makes NDVI a good indicator for assessing vegetation–climate interactions and environmental change, particularly in high- ecosystems (Satti et al., 2026; Lamchin et al., 2020). Satellite-derived observations have become essential tools to monitor climate change based on climatic indices that provide relationships between climate and vegetation (Joshi et al., 2024). Climatic variability, anthropogenic pressure, land-use and land-cover change, and environmental feedback mechanisms can be measured by remote sensing (Gao et al., 2022). Moreover, topography and vegetation significantly affect the distribution of LST through their effects on radiation absorption, surface roughness, moisture availability, and energy exchange processes (Feldman et al., 2023). NDVI is closely related to LST and soil water availability, which directly impacts climate variability. Regional-scale observations of LST and precipitation indicate climate variability, and are used in modeling surface energy balance and in the assessment of climate change impacts, especially in mountainous regions (Liu et al., 2022; Li et al., 2023; Taheri et al., 2022). Over the past few decades, the Indian Himalayan region has experienced substantial environmental challenges such as changes in precipitation patterns and a gradual decrease in seasonal snowfall (Negi et al., 2017). The Himalayas, due to their complex topography, elevation gradients, and seasonal weather patterns, have a strong influence on atmospheric circulation, making them highly vulnerable (Thapliyal et al., 2024). Climate change, accompanied by increasing anthropogenic activities in the mountainous regions, leads to serious challenges for sustainable ecosystems. In the Himalayan foothill areas, the southwest monsoon is the primary factor controlling the climate, especially in the Doon Valley. The Arabian Sea and Bay of Bengal bring moisture-laden winds that bring most of the precipitation (Saxena et al., 2024). Fluctuations in precipitation and temperature have significant impacts on vegetation dynamics, hydrology, and the productivity and growth of vegetation related to accumulated temperature above a specific threshold and moisture availability (Sharma et al., 2025). There is an urgent need to study the climate change issue based on the multi-scale interactions among orographic interaction with precipitation, vegetation, and Land Surface Temperature (Dhupper et al., 2023; Asam et al., 2018; Ivanyshyn and Kasiyanchuk, 2024). Physics-based climatic models can represent large-scale surface energy balance processes and are valuable for understanding how these processes drive climate variability and change (Shepherd et al., 2018). Physical models can be used to gain insight into climate system processes that can help to detect hidden patterns or long-term trends in climatic data (Kimothi et al., 2019; Kumar et al., 2023; Zhang et al., 2021). Satellite-derived remote-sensing products such as NDVI, LST, and PPT are especially useful for understanding the effects of climate change on terrestrial ecosystems. On the other hand, NDVI is a vegetation index that is very sensitive to regional temperature and precipitation. Thus, NDVI has been extensively applied to assess vegetation responses to climate change and climate variability, and long-term change (Kimothi et al., 2023; Mehmood et al., 2024; Carreño-Conde et al., 2021). To comprehend the climatic variability in the Himalayan foothills, this study seeks to integrate statistical and physical analyses with climate time-series data. Multi-Scale Event Synchronization (MSES), fractal analysis, and statistical trend assessment are employed to investigate temporal synchronization, persistence characteristics, and complexity of climatic interactions among precipitation–vegetation–temperature dynamics in the foothill region, which are lacking despite the abundance of research on climatic trends in the Himalayas.

2 Study area

Himalayan foothill regions mostly experience heavy rainfall during the monsoon, and the humid subtropical climate varies owing to the influence of the medium- to low-range Siwalik Hills. The study area, lying between latitude/longitude (30.3165°N/78.0322°E), spans roughly 308 sq. km and is occupied by the Ganges and Yamuna rivers. Figure 1 shows the digital elevation map of the Doon Valley, lying in the foothills of the Uttarakhand Himalaya, India.

The study area (Doon Valley) is an ideal setting for studying climate-vegetation interactions because of its topography and monsoon-driven climate. Because of its topography, it is particularly vulnerable to significant precipitation during the Southwest Monsoon, when rainfall is triggered by moist winds from the Arabian Sea and Bay of Bengal. The valley also suffers from isolated thunderstorms during the pre-monsoon season, while western disturbances in the winter deliver moderate rainfall.

2.1 Climate variation in foothills of the central Himalaya

The experimental site, with an elevation ranging from approximately 450 to 2,260 m above mean sea level, and exhibits complex topographic characteristics that influence local climatic conditions. The foothill region traps cool air during winter and retains warm air in summer, resulting in pronounced seasonal temperature variability, and also receives precipitation from Mediterranean-origin western disturbances (Tyagi and Veer, 2016; Barde et al., 2020; Jeelani et al., 2025). It has two main seasons: dry and wet, and the southwest monsoon is the main source of the annual rainfall. Summers are generally warm, 25⁰ to 45⁰, and the monsoon season features moderately humid conditions and moderate temperatures (Rajeevan et al., 2022). These seasonal climatic changes have a significant impact on vegetation growth, hydrological processes, and ecosystem dynamics in the region. During summer, intense surface heating promotes rapid uplift of warm air masses, leading to the formation of cumulonimbus clouds that often produce short-duration but intense rainfall accompanied by thunderstorms and hailstorms (Mohanty et al., 2024). Understanding the interactions among climatic parameters is essential for assessing climate variability, ecosystem dynamics, and environmental risks (Rani et al., 2019).

3 Materials and methods

Hydro-meteorological variability and climatic indices that are responsible for climate change at the local level were analyzed through different statistical and physical-based approaches. The temporal variability and intercorrelation between the variables were evaluated using OLS regression, Fractal analysis, Hurst exponent, Entropy, and MSES tests. Hurst exponent (H) assesses the long-term memory, persistence, and mean-reverting tendencies of a time series. The OLS regression measures the strength and statistical significance of the relationships among the climatic variables. The MSES was used to obtain synchronization patterns among climatic indices across several temporal scales. Hence, the long-term temporal distribution of climatic indices for different time scales has been analyzed over the foothill region of the Himalaya. The abovementioned approaches and analytical tools aid in investigating temporal synchronization, persistent characteristics, and statistical correlations, and may provide a comprehensive understanding of climate–vegetation interactions. Figure 2 illustrates a flow chart of the data processing steps undertaken in the methodology through physical approaches. The spatiotemporal data sources are diverse, and the research approach comprises three main phases, i.e., data collection, processing, and analysis.

Several space-borne satellite platforms, such as the moderate resolution imaging spectroradiometer (MODIS), and atmospheric reanalysis datasets, such as the European centre for medium-range weather forecasts (ECMWF) ERA5, provide hydro-meteorological datasets through the Google Earth Engine Platform (GEE). The normalized vegetation index (NDVI), land surface temperature (LST), and precipitation (PPT) averaged point datasets were collected over a 22-year period (2001–2022) using MODIS and ERA-5, respectively. All reanalyzed data product time series were processed in Python software. The monthly time scale and spatially inconsistent datasets were clipped to the extent of the study area. Table 1 provides detailed descriptions of the hydro-meteorological datasets used in the study.

Table 1. Characteristics of total precipitation, normalized difference vegetation index, and land surface temperature layers.

3.1 Dataset

Through historical observations, particularly satellite data, ERA5 offers hourly estimates of atmospheric variables at a higher spatial–temporal resolution in sophisticated data assimilation and modeling systems to estimate more precise atmospheric conditions. It has a total of 137 model layers of 0.01 hPa (approximately 80 km from the surface) and fine spatiotemporal resolution with a horizontal resolution of 31 km. This study obtained daily ERA5 precipitation and land surface temperature data on a regular latitude–longitude grid with 0.25° × 0.25° 0.25° × 0.25° resolution from 2001 to 2022. While MODIS NDVI products are gridded raster data (images/arrays) covering spatial resolutions of 250 m (MOD13Q1) or 1 km, and each data file contains a matrix of pixels representing a geographic region.

3.1.1 Normalized difference vegetation index (NDVI)

Vegetation indices (NDVI) are critical tools for assessing and monitoring vegetation using satellite datasets (Honeck et al., 2018). The NDVI is commonly used due to its ease of estimation, availability at various resolutions, and ability to mask clouds (Zhu and Helmer, 2018; Thomas et al., 2024; Bhowmik and Bhatt, 2024). A vegetation index derived from remote sensing using NIR and red bands shows that NDVI values mirror changes in vegetation cover, making it valuable for assessing ecosystem health globally. The NDVI can be determined by the absorption of chlorophyll and the high reflection of near-infrared by leaf structure (Rees et al., 2020). NDVI, linked to vegetation health, responds to temperature and precipitation, thereby reflecting changes in plant cover (Naga Rajesh et al., 2023). NDVI values are normalized to a range from −1 to +1. NDVI values range from −1 to +1, where values below 0 generally represent water bodies and snow; between −1 and 0.3 indicate non-vegetation or built-up areas; values between 0.3 and 0.5 represent shrubs; values between 0.5 and 0.6 indicate low-density forest; and values greater than 0.6 correspond to high-density forest. These thresholds facilitate the interpretation of vegetation condition and land surface characteristics, and the formula is given below:

NDVI = ρ nir − ρ red ρ nir + ρ red

Where,

ρ nir = near infra − red band reflectance value

ρ red = RED band reflectance value

3.1.2 Precipitation (PPT)

Hydrometrological parameters, i.e., precipitation, are influenced by different atmospheric parameters such as air temperature, atmospheric moisture content, relative humidity, wind circulation, and large-scale weather circulation (Saini and Attada, 2024). Temperatures increase evaporation and atmospheric moisture-holding capacity, while moisture transport controls cloud formation and precipitation intensity (Gupta et al., 2024). In mountainous regions, moist air masses force condensation and rainfall, and the interaction of these atmospheric processes needs to be determined to understand the temporal and spatial variability of precipitation (Kumar and Singh, 2024; Kalfas et al., 2024). Monitoring precipitation globally is vital, especially for changing weather conditions (Levizzani and Cattani, 2019). ERA5 time series datasets are widely used for monitoring extra-tropical precipitation (Lavers et al., 2022).

3.1.3 Land surface temperature (LST)

Land surface temperature (LST) is a crucial factor in various environmental studies such as energy balance, climate change, and Earth’s processes (Trenberth and Cheng, 2022). LST reflects surface energy changes, influenced by solar radiation, atmosphere, and land cover (Jiang et al., 2022). LST can increase evapotranspiration (ET) and affect local precipitation; conversely, increased cloud cover and PPT can reduce LST and impact soil moisture and surface heat fluxes. Prior knowledge of land surface emissivity is essential for using methods to estimate LST from satellite images (Zhang et al., 2023; Kafer et al., 2019).

L TOA , i = [ ε i β i ( T s ) − ( 1 − ε i ) ] L hem , i ↓ ] τ i + L atm , i ↑

Where,

L TOA , i = top of atmosphere radiance

ε i = surface emissivity

B(T_S) = blackbody radiance at LST

β i − spectral radiance

L hem , i ↓ − hemispheric downwelling radiance

L atm , i ↑ − atmospheric upwelling radiance

τ i − atmospheric transmitty

L TOA , i = 0.0003342 ∗ DN + 0.1

DN − the digital number ( DN ) measured from both TIR bands to radiance

LST = k 2 log k 1 B i + 1

Where,

k 1 & k 2 − different assigned values for band 10

3.2 Different approaches used

3.2.1 Ordinary least squares (OLS) analysis

Ordinary least squares (Pearson’s) correlation used to measure the time series variability and interrelationship strength (Garai et al., 2022). The accuracy of satellite, model, and reanalysis data is assessed using RMSE against ground-truth measurements, guiding model refinement for improved reliability (Julien et al., 2011; Hulley et al., 2012).

3.2.2 Fractal analysis (Hurst exponent analysis)

The Hurst exponent (H) of a time series shows an exponential growth scaling relation:

<R ( μ ) S ( μ )> = Z μ^H as ‘μ’ approaches infinity

μ − numberofdata points in timeseries

R ( μ ) − range of the first n cumulative deviations from the mean

S ( μ ) − standatrd deviation

Z − indicates constant ,

angular brackets 〈 … .. 〉 implies that anticipating values

The time series is { a 1 , a 2 , a 3 … … … … . a n }

R ( n ) = max { a 1 , a 2 , a 3 … … … … . a n } − min { a 1 , a 2 , a 3 … … … … . a n }

Hurst coeffient define interms of fractal analysis

H = 2 − D , where H − Hurst coefficient and D − fractal dimension

where D lying between 1.0 to 2.0

Now the pridictibility indicesis given as :

PI = 2 ∣ D − 1.5 ∣

PI = 2 ∣ 0.5 − H ∣ , the data series is predictable for values close to 1.

3.2.3 Entropy and multi-scale event synchronization (MSE)

In time series analysis, entropy measures disorder and information contributions based on data points, reflecting complexity and predictability such as daily temperature data (Tang et al., 2015). The entropy of the time series may be calculated through different steps:

If the length of data set of original time seriesz ( 1 ) , z ( 2 ) … … … … z ( n )

( i ) dimension vector z ( i ) = [ z ( p ) , z ( p + 1 ) , … … .. z ( p + m − 1 ) ]

Where i = 1 , 2 , … … .. n − m + 1

( ii ) define the distance d [ Z ( p ) , Z ( j ) ] as follows

d [ Z ( p ) , Z ( j ) ] = max [ z ( p + k ) − z ( j + k ) ]

Where k = 0 , 1 , 2 , … … . m − 1 ,

calculate the distance d [ Z ( p ) , Z ( j ) ] betweenZ ( p ) and other vector Z ( j )

Where j = 1 , 2 … … … .. n − m + 1 , but j ≠ p

( iii ) Count the d [ Z ( p ) , Z ( j ) ] that are less small than a given threshold r .

The ratio of this number to the total number n − m as:

μ i m ( r ) = { the number of d [ Z ( p ) , Z ( j ) ] < r } n − m

p = 1 , 2 , … … n − m + 1

( iv ) find the average μ p m ( r ) for all i as follows

μ p m ( r ) = ∑ μ p m ( r ) n − m + 1 , p = 1 , 2 … … n − m + 1

( v ) add one to the number of dimension of all the vectors ,

yield in d + 1 dimension repeat step i to iv yielding μ m + 1 ( r )

The theortical sample entropy of the time series is given as :

SampEn ( m , , r , , n ) = − log [ μ m + 1 ( r ) μ m ( r ) ]

MSE measures entropy at different time scales in climate systems, indicating complexity and predictability. Now, the multi-scale entropy procedure is:

y j τ = ∑ x ( p ) τ , where p = ( j − 1 ) τ + 1 , … … … . j ( τ ) , j = 1 , 2 … … .. n τ

where , τ − scale factor and y j τ − sample entropy

Studying climate processes at one timescale does not uncover all mechanisms due to limitations of the event synchronization method, which captures non-linear interactions at a single scale (Agarwal et al., 2017). The events are synchronized with a time lag ± τ lm xy, which is defined as:

τ lm pq = min { τ l + 1 p − τ l p , τ l p − τ l − 1 , p τ m + 1 q − τ m q , τ m q , τ m q − τ m − 1 q } 2

The time lag defines independent events and counts how many times an event occurs in a signal with the help of β ( p ∣ q ):

β ( p ∣ q ) = ∑ l = 1 S p ∑ m = 1 S q J p , q

And also

J pq = { 1 if 0 < t l p − t m q < τ lm pq 1 2 if t l p = t m q 0 else

The event synchronization strength between two signals Q pq is the measurement of strength, which is calculated as:

Q pq = β ( p ∣ q ) + β ( q ∣ p ) ( S p − 2 ) S q − 2 )

Synchronize events at different scales 0, 1, 2, 3, 4, 5, 6……… λ simultaneously to assess synchronization strength.

Q pλ , qλ pq = β ( p ∣ q λ ) + β ( q λ ∣ p λ ) ( S p λ − 2 ) S q λ − 2 )

4 Results and discussion

4.1 Monthly variation

Precipitation is significantly affected by seasonality (monsoonal) and increases in July and August and decreases in winter. Figure 3 illustrates the LST, indicating an increasing trend starting from January, a maximum in May–June and then a decrease during the monsoon season. NDVI is relatively low from January to April, but increases rapidly during the monsoon season reaching its maximum in September and October. The time lag between the peak in PPT and the peak in NDVI reflects the lag time in vegetation response to moisture availability. Overall, a strong seasonal link is obtained between PPT, LST, and NDVI in the foothills of the Himalayas. The mean trends in climate data reveal warming temperatures over decades and varying seasonal precipitation patterns.

4.2 Seasonal variation

The statistical characteristics of seasonal variability and interrelationship among PPT, LST, and NDVI are presented in Table 2 and Figure 4. The results revealed seasonal differences among all climatic parameters. However, PPT has strong seasonal variability. Maximum PPT (144.62 mm) was observed in the monsoon season, and the minimum value was observed in the autumn season (0.78 mm). The seasonal mean precipitation (55.87 mm) was recorded during the monsoon season, and the minimum was in autumn (3.45 mm), demonstrating that monsoon rainfall is dominant in the region’s hydrological regime.

Table 2. Statistical analysis of the seasonal variation of LST, NDVI, and PPT.

The seasonal mean LST ranged from 17.43 °C (winter) to 30.94 °C (summer), with significant seasonal temperature variations. The LST decrease during the monsoon is likely related to an increase in both cloud cover and precipitation, as well as increased evaporative cooling. The maximum NDVI (0.75) was recorded during the monsoon season, and the highest seasonal mean (0.64) was recorded during autumn, and the lowest seasonal mean (0.43) was recorded during the summer season. The seasonal relationships shown in Figure 4 suggest a tight link between precipitation and vegetation, with higher moisture levels leading to vegetation greening (higher NDVI). By contrast, precipitation has an inverse relationship with LST during the monsoon season, which is due to the cooling influence of rainfall and greenness. These results indicate that the seasonal climate variability plays an important role in controlling vegetation productivity and surface temperature of the foothill environment of the Himalayas.

4.3 Annual variation

The annual variations in PPT, LST, and NDVI over the study area from 2001 to 2022 are shown in Figure 5. Annual PPT is highly variable from 1 year to the next, with reduced amounts during the early period and increasing generally after 2009 but showing significant variations throughout the period. LST shows less variability and less changes inter-annually, which signifies that LST remains stable over time, while NDVI has significant interannual variability and trends downward slightly. The temporal variation in NDVI indicates an increasing trend in the first few years, followed by periodic fluctuations and a decreasing trend in NDVI values in recent years. Such temporal changes indicate that vegetation dynamics have been influenced by changes in PPT and LST. Overall, the annual trends are affected by both PPT and LST, and the effects of PPT are more important in controlling the annual variability of the ecosystem of the foothill region of the Himalayas.

4.4 Parametric linkages analysis

The seasonal analysis indicated that the interactions among PPT, LST, and NDVI are highly dynamic and controlled by seasonal climatic variability in the Himalayan foothill region.

Figure 6 and Table 3 present the seasonal correlations and variations, and their interactions, among LST, PPT, and NDVI. The correlation between PPT and NDVI was negative when calculated during winter, summer, and monsoon, with an r value of −0.319, −0.009, and −0.327, respectively, while autumn was positive r = 0.212. The significant negative correlation in winter and monsoon indicates that more precipitation does not always lead to more vegetation activity. This may be attributed to high rainfall, cloud cover, and seasonal environmental conditions that can negatively affect photosynthesis. The correlation in the summer was not statistically significant and was very small, which indicates that PPT had little effect on the NDVI. Similarly, in winter (−0.264), summer (−0.146), and monsoon (−0.282) were negative, indicating that higher LST was associated with more water in the soils and evaporative cooling. Autumn, on the other hand, showed a strong positive correlation (r = 0.498), indicating a seasonal trend: warmer surface temperatures were correlated with less but more fluctuating, moisture. Seasonal variability was also observed for the relationship between LST and NDVI, weak and statistically insignificant positive correlation was observed during winter (r = 0.046), a strong positive correlation was observed in summer (r = 0.667) suggesting a positive association between increasing temperatures but the LST and NDVI had significant negative correlation during the monsoon period (r = −0.368), which indicates the reduction in the LST due to dense vegetation and moisture. This strong positive correlation between vegetation activity and residual soil moisture (r = 0.542) was observed in the autumn, thus reaffirming the influence of residual soil moisture and optimal thermal conditions on vegetation activity.

Table 3. Seasonal variation and correlation coefficient (r) for PPT, LST, and NDVI.

4.5 Annual correlation

Figure 7 illustrates the Pearson’s correlation (r) between PPT, LST, and NDVI data for each year. The annual correlation matrix shows generally low correlations among these three climatic variables, implying that the vegetation dynamics in the foothill region of the Himalayas are driven by a variety of interacting climatic factors rather than by any one climatic variable. The correlation between PPT and NDVI is low and negative, indicating that a positive change in annual rainfall is not necessarily accompanied by a positive change in annual NDVI. The weak inverse correlation could be explained by the interplay among the distribution of PPT, soil moisture, topographic variability, and vegetation responses across different seasons. The observed variations in NDVI cannot be totally explained by annual precipitation alone. Similarly, the relationship between PPT and LST is very weakly negative, with higher rainfall years having slightly lower LST. The correlation between NDVI and LST is positive but weak, suggesting that annual vegetation is correlated with annual LST. This analysis suggests that precipitation, temperature, topography, soil moisture availability, and local environmental conditions are all factors affecting vegetation dynamics in the Himalayan region, not just temperature. The annual correlation analysis between PPT, LST, and NDVI is not very strong on an annual level. The findings indicated that there may be complex relationships between climatic and hydrometeorological factors in influencing ecosystem response in the foothill region of the Himalayas. Thus, it is essential to integrate multiple climatic variables, seasonal variations, and land surface processes to improve understanding of vegetation dynamics, climate variability, drought assessment, and sustainable management of ecosystem services in mountainous areas.

4.6 Climatic indices (H, FD, PI)

Fractal analysis (FD) is very important for the development of climate models and is used to identify interdependencies and improve predictions, all of which are crucial for understanding the cascading effects of climate change. The estimates are checked for randomness by the Hurst coefficient (randomness analysis). Climate systems are complex and dynamic, with linkages between parameters, such as temperature, humidity, PPT, wind speed, and solar radiation. A powerful technique within the field of climate science, fractal analysis is used to reveal hidden patterns through concepts such as fractal properties and self-similarity. Table 4 shows the fractal dimension (FD), Hurst exponent (H), and predictability index (PI) for the NDVI, precipitation (PPT), and land surface temperature (LST) time series during the study period. Long-term persistence and predictability of each climatic variable were assessed through the classical rescaled range (R/S) analysis method, which yielded the Hurst exponent. The results from the NDVI time series yielded a Hurst exponent of 0.5578, indicating that the time series was persistent (H > 0.5). This means the vegetation dynamics are weakly persistent over time, implying that previous patterns are likely to continue. The fractal dimension is moderately high (1.4422), reflecting a relatively high level of complexity in the temporal structure, and the predictability index (0.1156) indicates a relatively high but still measurable level of predictability in vegetation dynamics. The Hurst exponent for the time series of precipitation (PPT) was 0.4780, which is close to the value of 0.5, suggesting the presence of only weak anti-persistence. This indicates a low level of long-term dependence in precipitation and that the primary controlling factors are short-term climatic fluctuations. A relatively high level of temporal complexity is indicated by the corresponding fractal dimension (1.5220), while the low predictability index (0.0440) suggests that PPT may be the least predictable of the three variables. The Hurst exponent of the LST time series was 0.2874, which is less than 0.5, suggesting anti-persistence. This suggests frequent sign changes, or temporal reversals, and poor long-term persistence in surface temperature change, implying that more warming tends to be followed by more cooling, and vice versa. The fractal dimension (1.7126) indicates greater temporal complexity than NDVI and PPT, but the predictability index (0.4253) is relatively high, even though the temperature series is anti-persistent.

Table 4. Annual variation and correlation coefficient (r) for PPT, LST, and NDVI.

4.6.1 Validation

Table 4 shows the analyses of climatic indices which indicates the long-term trends and forecasts of climatic variables and the results reveal unique characteristics in the time series of NDVI, PPT, and LST. The NDVI’s Hurst exponent of 0.5578 is indicative of a persistent behavior (H > 0.5), which shows persistent trends. However, the value of the Hurst exponent for the PPTs of 0.4780, which lies close to 0.5, indicates that the PPTs behave almost randomly with limited anti-persistence and very limited long-term dependence. The land surface temperature (LST) time series has a Hurst exponent of 0.2874, which is less than 0.5, indicating anti-persistent behavior (H < 0.5). Higher LST is followed by lower LST, and vice versa, resulting in higher temporal variability. The fractal dimensions also reveal some distinct differences in the temporal complexity of the three variables. The fractal dimension value of NDVI was 1.4422, while PPT and LST were 1.5220 and 1.7126, respectively, indicating that the fractal dimension value of LST is highest, resulting in the highest temporal complexity. The predictability indices for NDVI, PPT, and LST were 0.1156, 0.0440, and 0.4253, respectively, with PPT having the lowest and LST the highest. The climatic indices (H, FD, PI) validate the long-range temporal dependence in vegetation dynamics, near-randomness in PPT characteristics, and anti-persistent characteristics in LST of the foothill region of the Himalayas, providing valuable insights into the long-term climatic variability over the Himalaya foothill region.

4.6.2 Multi-scale entropy and multi-scale event synchronization (MSES)

The MSE and MSES analysis of the PPT time series are shown in Figure 8. The scale-to-scale variability of entropy indicates high climatic complexity at different scales. It indicates that entropy is higher at lower to intermediate scales; the irregularity and variability in the PPT dynamics increase, while the lowest entropies occur at the largest scales, indicating that the dynamics are relatively more organized and predictable. The MSES analyses reveal that as scale increases, synchronization also increases, indicating that as more time is considered, the precipitation events become more coherent. Persistent climatic processes that drive long-term precipitation variability over the Himalayan foothill region are suggested by high synchronization at longer scales, while smaller scales indicate the effect of meteorological fluctuations at local and short-term scales. The significance-level analysis also indicates that several scales have high power values, suggesting statistically significant precipitation signals across multiple temporal scales. The high entropy, along with the growing event synchronization, implies that precipitation variability is controlled by complex interactions among climatic drivers at both local and regional scales. The findings reveal that, climatically, there is significant multiscale variability, highlighting the scale-dependency of climatic processes in assessing climate change impacts, hydrological responses, and ecosystem dynamics in the higher- to lower-altitude region of the Himalayas.

Table 5 demonstrates the comparative analysis of different approaches used to analyze the whole time series and decadal datasets of the studied parameters. Upon comparing decadal time series of climatic parameters, i.e., regression values (r²), Hurst Coefficient values (H), and Monte Carlo (P). The r² values for LST were 0.62 in decade I and 0.59 in decade II, while for PPT they were 0.64 and 0.61, respectively. The Hurst coefficient for LST was 1.3 in decade I and 0.94 in decade II, whereas for PPT it was 0.74 and 0.72, respectively. Significance levels for LST were 0.61 in decade I and 0.56 in decade II, and for PPT, 0.66 and 0.64, respectively. Monte Carlo simulation results showed NDVI had the highest significance (p = 0.856), followed by precipitation (p = 0.653) during 2001–2022, and extreme temperatures across the dataset. In contrast, LST had the lowest significance (p = 0.585).

Table 5. Regression values, Hurst coefficient values, and Monte Carlo values for whole and decadal time series.

4.7 Discussion and recommendations

Comprehensive Correlation analysis reveals high dependencies between PPT, LST, and NDVI, indicating high collective interaction of environmental factors in the system rather than a single climatic variable. The response of vegetation is influenced by seasonality, topography, soil moisture, land use, and rainfall distribution. There are stronger positive temperature responses in summer and weaker or negative monsoon relationships, as seen in the seasonal analyses, due to cloud cover and cooling in summer. These results highlight the seasonal climatic changes in the dynamics of foothill ecosystems of the Himalayas. NDVI is persistent, while precipitation and temperature exhibited anti-persistence behavior. Multi-Scale Entropy and Event Synchronization signify climate coherence at larger scales. These findings show consistent with studies from different mountain ecosystems worldwide and demonstrate that precipitation is the primary driver of vegetation dynamics, while temperature regulates seasonal and long-term ecosystem responses. Similar relationships observed in the Alps, Carpathians, Andes, and Balkan Mountains indicate that vegetation productivity and phenology are strongly influenced by hydroclimatic variability. These studies suggest that climate-driven changes in precipitation and temperature significantly affect ecosystem functioning, although the magnitude and timing of vegetation responses vary with regional climatic and topographic conditions. These studies collectively suggest that precipitation is a primary regulator of vegetation variability across many mountain environments, although the magnitude and timing of vegetation responses vary with regional climatic and topographic characteristics. Longer observations are a good fit to better analyze climatic variability over a longer time period but here the time period is limited (2001–2022). Besides, the analytical framework mainly analyzes the interaction among the variables and does not consider other climatic variables. Future research synthesizing higher-resolution datasets, extended time series, and other climatic variables would further improve the analysis of the interaction among the climate variables in the foothills of the Himalayas.

5 Conclusion

Findings of this study demonstrate that precipitation, land surface temperature, seasonal variation, and topography are more influential factors in determining vegetation dynamics. Annual Pearson correlation revealed that PPT, LST, and NDVI had a complex response of vegetation in the foothills of the Himalayas. Seasonal analysis revealed that strong climatic variability has been observed in recent decades. Climatic indices (H, FD, PI) reveal that persistent vegetation dynamics were observed in 2001–2010, but after 2011, more variability and less persistent indicators were observed; LST and PPT were mostly anti-persistent. Multi-Scale Entropy and Event Synchronization indicated a decrease in climatic complexity at higher temporal scales and increased synchronization at higher temporal scales. A comprehensive understanding of climate–vegetation interaction in the study region is mostly based on data sets derived from satellites. This study has multivariate limitations and large-scale climatic oscillations and extreme weather events to better understand the climate variability in this climate-sensitive region. In addition, the study demonstrates the feasibility of satellite remote sensing and multi-scale analytical methods to provide monitoring of environmental change in a climate-sensitive mountainous area. The outcomes of these results do not simulate flood or landslide events, but they show long-term variations in climatic indices that are important environmental indicators of hydro-meteorological hazards; therefore, it may be helpful to the climate adaptation strategy, ecosystem management and sustainable resource planning in the Himalayan region. Further studies are needed to examine the impacts of large-scale climatic oscillations and extreme events on climatic variability and vegetation responses in various Himalayan ecosystems.

Generative AI statement

The author(s) declared that Generative AI was not used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Footnotes

Edited by: Suraj A. Yadav, Mississippi State University, United States

Reviewed by: Dmytro Kasiyanchuk, Ivano-Frankivsk National Technical University of Oil and Gas, Ukraine

Shivaji Singh Patel, National Centre for Medium Range Weather Forecasting, India

Jyoti Sharma, India Meteorological Department, India