Temperature modelling using machine learning model across Lucknow region

Introduction

Temperature is a key climatic parameter that influences environmental processes, crop growth, and human comfort (Zhao et al., 2024) [1] . In regions like Lucknow, which experience significant seasonal variations, accurate temperature prediction is essential for agricultural planning and climate risk management (Fraisse et al., 2006) [2] . Traditional statistical methods often fail to capture complex nonlinear relationships in climatic data, necessitating the use of advanced computational techniques. A basic physical quantity that expresses how hot or cold a substance or environment is called temperature. It is essential to many scientific fields, including as climate research, physics, environmental science, and agriculture (Aleixandre-Benavent et al., 2017) [3] . To put it simply, temperature affects many natural and manmade processes and establishes a system's thermal state. Temperature is one of the key factors utilized in environmental and climate studies to comprehend weather patterns, climate variability, and long-term climate changes (Thornton et al., 2014) [4] . Ecosystems, human health, water resources, and agricultural productivity are all directly impacted. In thermodynamics, temperature is a fundamental property that determines the direction of heat transfer between two systems. According to the zeroth law of thermodynamics, if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other (Ehrlich, 1981) [7] . This principle forms the basis for temperature measurement. Temperature also plays a key role in defining thermodynamic states (Lipka-Bartosik et al., 2023) [5] .

It is directly associated with internal energy, entropy, and other thermodynamic properties. In statistical mechanics, temperature is related to the distribution of energy among particles in a system. Machine learning (ML) has emerged as a powerful tool for modeling and predicting environmental variables due to its ability to learn patterns from large datasets (Hamdan et al., 2024) [6] . With the increasing availability of meteorological data, ML models can provide more accurate and reliable temperature forecasts (Singh et al., 2024) [8] . This study aims to develop and evaluate machine learning-based models for temperature prediction in the Lucknow region.

Study Area

Uttar Pradesh is a northern state of India situated between latitudes 23°52′N and 31°28′N and longitudes 77°3′E and 84°39′E. It is one of the most populous states in the country and exhibits diverse climatic and geographical conditions, making it suitable for various environmental and climatic studies. For the present study, Lucknow district has been selected as the study area due to its representative climatic conditions and availability of reliable meteorological data (Fig. 1). The study primarily focuses on the analysis of rainfall data collected from the district, which plays a significant role in understanding regional climate variability, water resource management, and agricultural planning. Lucknow, the capital city of Uttar Pradesh, India, lies in the Indo-Gangetic plain and experiences a subtropical climate with hot summers, cold winters, and moderate monsoon rainfall. The region is characterized by high temperature variability, making it suitable for temperature modeling studies. Lucknow, the capital city of Uttar Pradesh, is located in the central part of the state and serves as an important administrative, cultural, and economic center. Geographically, Lucknow lies approximately between latitudes 26°30′N and 27°10′N and longitudes 80°30′E and 81°13′E. The region experiences a subtropical climate characterized by hot summers, a monsoon season with moderate to heavy rainfall, and cool winters.

Data Sources

The meteorological data used in this study have been obtained from the NASA POWER (Prediction Of Worldwide Energy Resources) database. NASA POWER provides high-quality, satellite-based and model-derived climate data for research and analysis purposes. The dataset includes reliable and consistent long-term records of climatic parameters such as rainfall, temperature, humidity, wind speed, and solar radiation. These data are widely used in environmental and agricultural studies due to their global coverage, accessibility, and scientific accuracy. For the present study, the required data for the Lucknow district were extracted from the NASA POWER platform based on its geographical coordinates. The use of NASA POWER data ensures consistency, accuracy, and suitability for climate modeling and analysis.

Methodology

Random forest regression

The forest technique's versatility allows it to handle both supervised classification and regression tasks. The purpose of this section is to give a brief but precise mathematical explanation of the random forest (RF) creation algorithm. The fundamental framework is nonparametric regression estimation, where the goal is to predict the square-integrable random response Y ∈ R by estimating the regression function m(x)= E[Y| X= x]. This is accomplished by looking at an input random vector, X •X ÷ Rp. For this purpose, it was assumed that we have a training sample Dn = ((X1, Y1),., (Xn, Yn)) of randomly distributed variables, and that we have an independent prototype pair (X, Y). The goal is to use the information set Dn to estimate the function "m" (mn: X→R).

The regression function estimate "mn" is (mean squared error) consistent if E[mn(X) -m(X)]2→0 as n→∞ as the expectation is evaluated over "X" and consequently the sample Dn. An RF is a predictor composed of a collection of "M" randomized regression trees. mn(x; Ψj, Dn) represents the expected value at the query point 'x' for the tree j in the family, where Ψ1,., ΨM are independent random variables that are randomly distributed as both an independent variable of Dn and a generic stochastic variable .

In practice, the variable Ψ is utilized to resample the training set before individual trees are expanded and to choose the next splitting directions. The RF machine learner could be a meta-learner composed of several individual learners (trees).

The RF votes between numerous random tree classifications to choose an overall classification for the given set of inputs. Each machine learner vote typically has the same weight. In following work by Breiman (2001), this method was modified to allow for both weighted and unweighted voting. The category with the most votes is chosen by the forest.

Results and Discussion

The performance of the developed temperature modelling using Random Forest Regression was evaluated using statistical indicators such as the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error

Testing Sets

The testing set is a separate portion of the dataset used to evaluate the performance of the trained model. It contains unseen data that was not used during training, allowing us to check how well the model generalizes to new data. By comparing predicted values with actual values in the testing set, we can assess metrics like accuracy, error, and reliability. A good model performs well on both training and testing data, indicating that it is neither overfitting nor underfitting. This graph represents the testing dataset consisting of 20 samples. The blue line shows the actual temperature values, while the red line represents the simulated (model-predicted) temperature. Unlike the training set, this data was not used during model training, so it helps evaluate how well the model performs on unseen data. In the initial samples (1-5), there is slight variation between actual and simulated values, but the model still follows the general pattern of the data. As the sample number increases (from around 6 to 20), both lines show a gradual increasing trend, with temperatures rising from about 20°C to nearly 23.5°C. The simulated values closely track the actual values, although small deviations can be observed at a few points. Overall, the close alignment between the two lines indicates that the model has good generalization ability and performs well on the testing data, with only minor prediction errors. For the testing dataset, the model achieved an R² value of 0.799, demonstrating a strong predictive capability on unseen data. Although slightly lower than the training performance, this result indicates that the model generalizes well and does not suffer from significant overfitting. The RMSE and MAE values for the testing phase were found to be 0.471 and 0.397, respectively, which are within acceptable limits for temperature prediction studies. Overall, the results suggest that the Random Forest Regression model is effective in capturing the relationship between temperature and the selected climatic variables. The relatively high R² values and low error metrics for both training and testing datasets indicate that the model provides reliable and accurate predictions. Therefore, it can be concluded that the developed model is suitable for temperature modelling and can be used for further climate analysis and prediction.

Conclusion

This study demonstrates the effectiveness of machine learning techniques in temperature modeling for the Lucknow region. highlight that the prediction errors are small, further validating the accuracy and precision of the model. 9. There is no clear indication of overfitting or underfitting, as the model performs well on both training and testing datasets. This balance is essential for ensuring reliable predictions in practical applications. 10. Based on all graphical and statistical evaluations, it can be concluded that the developed machine learning model is stable, accurate, and suitable for temperature prediction, and it can be effectively applied in areas such as climate analysis, agricultural planning, and environmental monitoring.

References

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