A 2026 study found that simple linear regression predicts sunshine duration in Jammu and Kashmir more accurately than complex machine-learning models, challenging the assumption that advanced algorithms always yield better climate estimates.
SRINAGAR: Simple statistical relationships between temperature, humidity and atmospheric pressure can predict sunshine duration in Jammu and Kashmir more reliably than several complex machine-learning models, according to a new study analysing more than five decades of meteorological records.
The research found that a linear regression model outperformed Random Forest, Gradient Boosting, XGBoost, and a neural network, explaining about 57 per cent of the variation in sunshine duration in its test data. The findings could help improve sunshine estimates for locations with incomplete observations and support solar-energy forecasting in the Himalayan region.
The study, A machine learning framework and Granger causal links of climatic variables over Jammu & Kashmir (1972–2024), was authored by Preeti of the Meteorological Centre, Lucknow, India Meteorological Department (IMD), Ministry of Earth Sciences, Uttar Pradesh, and Shashi Kant of the India Meteorological Department, Ministry of Earth Sciences, New Delhi.
Published in Next Sustainability, Elsevier Ltd. released the research online on August 10, 2026. It examined meteorological records spanning 1972–2024 to investigate relationships among sunshine, rainfall, temperature, humidity, atmospheric pressure and large-scale climate patterns.
PHOTO BY BILAL BAHADUR
Key Findings
The researchers reported that linear regression achieved a test-set R² score of 0.5696, with a root mean square error of 2.2023. Its average R² score across five rounds of time-series cross-validation was 0.6535, indicating relatively stable performance when tested on different portions of the historical record.
In simple terms, the model accounted for approximately 57 per cent of the variation in the sunshine observations used for testing. The R² score measures how much of the variation in observed values a model can explain; it does not mean that 57 per cent of individual forecasts were correct.
The study found that Gradient Boosting and Random Forest performed less effectively on the test data, recording R² scores of 0.5447 and 0.5307, respectively. XGBoost scored 0.4606, while the multi-layer perceptron neural network scored 0.1572. Two conventional forecasting approaches based on persistence and seasonal time-series modelling performed poorly.
The findings challenge the assumption that increasingly complex algorithms necessarily produce better climate estimates. In this case, a comparatively straightforward model captured the principal relationships more consistently.
Data Sources
The researchers analysed daily meteorological observations from Srinagar, Gulmarg and Qazigund for 1972–2024, while records for Jammu covered 1982–2024. The data were obtained from the India Meteorological Department in Pune.
The variables included maximum and minimum temperatures, rainfall, sunshine duration, low-level cloud cover and relative humidity. The researchers also calculated the difference between daily maximum and minimum temperatures, a measure known as the diurnal temperature range.
Additional datasets were used to examine atmospheric pressure and wind interactions, evaporation patterns and large-scale climate influences. These included half-hourly aviation weather observations from Srinagar and Jammu airports for 2015-2024, elevation data from the Shuttle Radar Topography Mission dataset, evaporation data from the Copernicus Climate Change Service, and outgoing longwave radiation observations maintained by the US National Oceanic and Atmospheric Administration.
The study used records from four stations to account for the region’s varied terrain, ranging from the relatively low-lying Jammu plains to the higher-altitude Gulmarg observatory. This variation matters because elevation, slope, valley location and exposure to sunlight can influence cloud formation, fog and the number of sunshine hours recorded at a station.
The researchers also addressed gaps in the historical records. The dataset contained a complete missing year, 1990, along with smaller gaps affecting approximately two to three per cent of observations in other years. These gaps were filled using climatological averages, or values based on typical conditions for the corresponding period.
Weather Drivers
The analysis identified the difference between daytime and night-time temperatures, relative humidity and mean sea-level pressure as important variables for estimating sunshine duration.
The diurnal temperature range, or DTR, is the difference between the maximum and minimum temperatures recorded during a day. A relatively large difference can indicate clearer conditions, as stronger daytime heating and greater night-time cooling often occur when cloud cover is limited.
Cloud cover and rainfall, by contrast, generally reduce the amount of sunlight reaching the ground. The study found that rainfall on the preceding day had a statistically significant negative relationship with subsequent sunshine, while cloud cover also exerted a strong suppressive influence.
The researchers found that minimum temperature, maximum temperature and recent sunshine observations contributed to predictions in different ways. Minimum temperature and rainfall showed important short-term relationships, while maximum temperature continued to influence sunshine estimates over longer intervals.
The role of humidity was more complicated. Although it contributed to some machine-learning predictions, the statistical tests did not establish it as a strong independent causal driver. The researchers attributed this difference partly to humidity’s relationship with rainfall and cloud cover.
The study also found that sunshine duration had a degree of persistence: recent sunshine observations helped estimate sunshine over the following days. However, the poor performance of the persistence and seasonal autoregressive models suggested that simply extending past patterns forward was insufficient.
Causal Links
To investigate whether changes in one weather variable could help predict another, the authors used a statistical technique called Granger causality.
Unlike a simple correlation, which shows whether two variables move together, a Granger causality test examines whether past observations of one variable provide additional information for predicting another. It establishes predictive precedence, not necessarily proof of a direct physical cause.
The researchers used this method to identify relevant predictors before training their sunshine-estimation models. They then tested the models using time-series cross-validation, a procedure that preserves the chronological order of observations rather than randomly mixing past and future data.
The study also used SHAP, a method that estimates how much individual variables contribute to a model’s predictions, and partial dependence analysis, which examines how predicted outcomes change as a particular variable changes.
Together, these techniques helped the researchers distinguish variables that were useful for prediction from those that showed stronger independent predictive relationships.
The authors concluded that sunshine variability in the Himalayan setting was governed largely by relatively straightforward meteorological relationships rather than by complex nonlinear patterns that required more sophisticated machine-learning models.
Terrain Effects
The study found substantial differences in sunshine conditions among the four stations, highlighting the influence of local geography.
Jammu, at an altitude of 367 metres, was identified as the sunniest location in the group. Its lower elevation and relatively open terrain favour longer periods of sunshine and less cloud formation than at the higher mountain stations.
Srinagar, at 1,587 metres, provided a useful reference point for the Kashmir Valley, balancing periods of clear skies with episodes of fog and cloud.
Qazigund, at 1,690 metres, experienced intermediate conditions, with its valley setting and north-northeast orientation affecting direct solar exposure. Gulmarg, at 2,652 metres, recorded the lowest sunshine duration among the stations. Although higher elevations can receive strong solar radiation, the researchers noted that increased cloud, fog and snowfall can reduce the number of hours of effective sunshine.
The findings underline why sunshine estimates cannot be transferred uncritically from one location to another. Mountainous terrain creates local variations in weather that may not be adequately represented by regional averages.
Seasonal Patterns
Beyond sunshine prediction, the study examined the relationship between atmospheric pressure and wind using half-hourly observations from Jammu and Srinagar airports for 2015–2024.
The researchers found that these relationships changed with the seasons. During winter, atmospheric pressure changes at Jammu provided predictive information about wind variations at Srinagar. During the pre-monsoon period, the relationship operated in both directions, with pressure helping predict wind and wind providing information about subsequent pressure changes.
During the monsoon, the statistical tests found no significant predictive influence in either direction. In the post-monsoon period, wind variations provided predictive information about subsequent pressure changes.
The analysis indicated a lead time of approximately 15 hours during the pre-monsoon season and about one day during the post-monsoon period. These results suggest that the relationships between pressure and wind are not constant throughout the year.
The authors argued that accounting for seasonal differences could improve atmospheric analysis compared with approaches that treat the entire year as a uniform system.
Rainfall Links
The researchers also investigated whether atmospheric momentum flux could help predict rainfall and other local climate variables.
Momentum flux describes the transport of momentum by atmospheric disturbances and is used to study large-scale circulation patterns. The study estimated this quantity using atmospheric pressure data and tested its relationship with rainfall, temperature, sunshine and the difference between daytime and night-time temperatures.
The results did not support a strong direct short-term predictive role for this flux in rainfall variability at lags of one to three time steps in the principal analysis. Across the wider set of station-level tests, predictive relationships were limited, although Qazigund showed a weak signal at one lag.
Rolling cross-correlation analysis, which examines how the relationship between two variables changes over time, found that associations between momentum flux and rainfall varied across decades. Stronger positive relationships appeared during some monsoon-active periods, including the late 1970s and early 2000s, while weaker or negative associations occurred during other periods.
The researchers concluded that the influence of atmospheric momentum transport on local rainfall was more apparent over longer periods or in association with large-scale climate variability than at short forecasting intervals.
Global Influences
The paper also examined the influence of two large-scale climate patterns: the El Niño–Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO).
ENSO is a recurring pattern of changes in tropical Pacific Ocean temperatures and atmospheric circulation, encompassing El Niño and La Niña phases. The NAO describes variations in atmospheric pressure over the North Atlantic that can influence weather patterns over wider regions.
Using outgoing longwave radiation data as an indicator of atmospheric and tropical-convection conditions, the researchers compared the predictive influence of these climate patterns across selected event periods between 1975 and 2020.
They found that ENSO and NAO did not exert uniform influence across all events. Strong El Niño or La Niña episodes sometimes produced marked changes in the statistical distribution of radiation observations, while the NAO provided significant predictive information during selected periods.
The study highlighted 1997-98 as a period in which ENSO produced a particularly distinct radiation-distribution pattern, although the NAO showed a significant short-term predictive relationship at one lag. In 2019-20, when ENSO was neutral, the NAO also showed predictive influence in the analysis.
The authors used Kullback–Leibler divergence, a statistical measure of how different two probability distributions are, to quantify these changes. In plain language, the method helped determine whether the distribution of radiation observations during a climate event differed substantially from the comparison pattern.
The results showed that large-scale climate patterns can alter atmospheric conditions, but their predictive influence depends on the particular event and the time interval being examined.
Solar Potential
The study identified potential applications in renewable energy, particularly solar power, where reliable estimates of sunshine duration can help assess the availability of sunlight for electricity generation.
The authors suggested that the framework could be used to estimate sunshine duration at locations where direct observations are unavailable or incomplete. Such estimates could help support solar-resource assessments and improve the understanding of how cloud cover, temperature and local terrain influence solar-energy potential.
However, the study did not directly measure solar electricity generation or establish the amount of additional power that could be produced using its method. The potential benefits for energy forecasting would require further testing against actual solar-radiation and power-generation observations.
Further Research
The researchers concluded that the combination of statistical causality tests and machine-learning models offers a useful framework for analysing climate variability in mountainous regions.
They called for further research into the physical mechanisms linking atmospheric momentum flux with local climate conditions and suggested extending the approach to additional meteorological variables.
The study also acknowledged that more work is needed to understand the relationship between sunshine duration, cloud cover and solar-energy production in hilly areas.
