District-level rice yield forecasting in uttarakhand, India: A comparative study of regularization, kernel-based, tree-based and neural network models

Introduction

Global food production needs to double by 2050 in order to meet the demand of the rapidly growing population (Tilman et al., 2011; FAO, 2009) [12,41] . On the other hand, the current yield growth rates for the major cereals grown across the globe are not high enough to meet this target (Ray et al., 2013) [34] . Environmental changes, particularly global warming and climate variability, are key concerns that have a negative impact on agriculture (Rosenzweig et al., 2014) [36] . This may result in a decline in crop production (Lobell & Gourdji, 2012) [25] , making the world more food insecure. As the global population is projected to reach 9 billion people by 2050, governments all over the world need to be well prepared to deal with supply shocks of major cereals. The Food and Agriculture Organization (FAO) reports that the demand for and consumption of grains have grown significantly relative to production in developing nations such as India. From 1964 to 2030, there will have been a sustained increase in demand for rice, wheat, and other coarse grains (FAO, 2003) [11] . Cereal imports in developing countries increased significantly to meet rising demand, growing from 39 million tons annually in 1970 to 130 million tons annually by 1997-1999. These developing nations are predicted to import 265 million tons of grains by 2030, which represents approximately 14% of their total yearly consumption (FAO, 2003) [11] . Nations that do not take action to reduce their overall reliance on imports for conventional crops could suffer greatly as a result of these conditions. It is therefore a global challenge to make nations increasingly self-sufficient in meeting their food demands, which in turn requires accurate and timely forecasting of crop yields at a granular, sub-national level. Crop yield prediction is one of the most challenging tasks in precision agriculture. The ability to forecast crop yields enables the relevant authorities to make appropriate decisions to ensure food security. In addition to soil type, genotype, and management techniques, weather conditions exert a significant influence on crop yield (Singh et al., 2014) [39] . Approximately 30% of annual global crop production is lost due to unfavorable weather conditions (FAO, 2011) [13] . As a result, there is a critical demand for reliable pre-harvest yield prediction models that can be utilized by governments, policymakers, and farmers alike to plan food procurement, price stabilization, and agricultural input decisions in advance. Rice (Oryza sativa L.) is the foundational cereal crop of Uttarakhand, underpinning the food and nutritional security of millions of farming households across its diverse landscapesfrom the fertile Tarai plains to the terraced fields of the mid-and high-altitude Himalayan valleys. The state's agricultural system is increasingly vulnerable to the convergence of extreme topographic heterogeneity with the growing unpredictability of the southwest monsoon under a changing climate (Ministry of Agriculture and Farmers' Welfare, 2022) [29] . This creates a complex, high-risk environment where reliable, advance predictions of rice yield at the district level are no longer merely beneficial but are a critical operational necessity -for government agencies involved in procurement and relief, for commodity markets managing price volatility, and for farmers making crucial input decisions. Historically, yield forecasting in India has relied on a triad of methodologies: crop-cutting experiments, process-based crop simulation models such as DSSAT and ORYZA, and empirical statistical models. While crop simulation models offer valuable mechanistic insights into crop physiology, their operational scalability across diverse districts is constrained by the requirement for extensive, site-specific calibration data (Aggarwal et al., 2006) [1] . Traditional statistical approaches, such as weather-index-based regressions employed by the Indian Council of Agricultural Research (ICAR), often fall short in capturing the complex, non-linear interactions among multiple, often collinear, climatic drivers and the final yield outcome. Crop yield estimation via machine learning models therefore serves as a robust and scalable alternative. Over the past decade, the advent of machine learning (ML) has revolutionized predictive analytics in agriculture. ML algorithms excel at modeling complex non-linear relationships, handling high-dimensional feature spaces, and scaling across spatial units without the need for explicit mechanistic assumptions (Van Klompenburg et al., 2020) [42] . Every domain of modern lifefrom health-monitoring systems and marketing software to equipment maintenance and soil science -is being transformed by machine learning. Numerous studies across major riceproducing regions of Asia have demonstrated that ensemble methods, particularly Random Forest and Gradient Boosting, often outperform classical regression and even deep learning models in terms of predictive accuracy and robustness (Jeong et al., 2016; Cao et al., 2020) [4,20] .

Ensemble Methods: Random Forest and Gradient Boosting

Random Forest (RF), introduced by Breiman (2001) [3] , has emerged as a benchmark algorithm in agricultural prediction. Its robustness against overfitting, inherent feature selection capability, and adeptness at handling complex interactions among predictors make it particularly suitable for ecological and agricultural data. Studies by Jeong et al. (2016) [20] and Everingham et al. (2016) [10] validated RF's superior performance in predicting crop yields across climatically variable environments in Australia and South Korea. In the Indian context, Meena et al. (2021) [28] demonstrated that RF models could achieve validation R² values exceeding 0.80 for wheat yield forecasting in Madhya Pradesh, while Shahhosseini et al. (2021) [38] corroborated RF's consistent outperformance of other algorithms in heterogeneous growing environments. Gradient Boosting methods, particularly XGBoost (Chen & Guestrin, 2016) [6] , have gained prominence for their ability to achieve exceptional calibration accuracy through iterative tree building. XGBoost optimizes a regularized objective function, making it powerful but also susceptible to overfitting, especially with the small sample sizes common in district-level agricultural datasets. While Cao et al. (2020) [4] found XGBoost to be a top performer for rice yield prediction in China, they also noted its generalization limitations compared to RF. Research combining XGBoost with remote sensing data has demonstrated improved validation performance, highlighting its potential when integrated with richer feature sets (Ma et al., 2021) [26] .

1.2 Kernel-Based Methods: Support Vector Machines Support Vector Machines (SVM), grounded in statistical learning theory (Vapnik, 1995) [43] , offer a powerful alternative for handling small, high-dimensional datasets through kernel transformations. The kernel trick allows SVM to map input data into a higher-dimensional feature space where non-linear relationships become tractable. Early applications by Karimi et al. (2008) [21] in Iran showed SVM's comparable or superior performance over regression-based methods for wheat yield forecasting. In the context of rice, Peng et al. (2014) [31] highlighted that SVM with a radial basis function (RBF) kernel is particularly adept at modeling the non-linear yield-climate relationships prevalent in complex topographies -a finding directly relevant to the heterogeneous hill districts of Uttarakhand.

Regularized Regression: Elastic Net

Elastic Net (Zou & Hastie, 2005) [47] provides a robust linear alternative by combining L1 (LASSO) and L2 (Ridge) penalties. This dual regularization enables automatic feature selection while handling highly correlated predictors -a common issue with seasonal climatic variables. Das et al. (2022) developed multiple rice yield forecast models for fourteen districts on the west coast using ELNET alongside LASSO, SMLR, PCA-SMLR, PCA-ANN, and ANN based on weekly weather indices. Sridhara et al. (2023) similarly used LASSO, ENET, PCA, ANN, and SMLR techniques to forecast sorghum crop yield at the district level. While Elastic Net's predictive power may be surpassed by non-linear methods, it offers unparalleled interpretability and computational efficiency, making it a valuable benchmark and a practical choice for operational systems where transparency to stakeholders is paramount.

Neural Networks

Artificial Neural Networks (ANNs) have a long history in agricultural prediction, prized for their capacity to learn intricate non-linear patterns. Singh et al. (2014) [39] used the SMLR technique alongside ANN to develop wheat yield forecast models based on weekly weather indices for districts of Punjab, while Kaul et al. (2005) [22] demonstrated ANN's applicability for corn and soybean yield prediction. However, ANN performance is highly context-dependent and often constrained by the need for large training datasets. In data-sparse regions such as Uttarakhand, their performance must be rigorously benchmarked against simpler, more regularized approaches.

Deep learning adaptations such as LSTM and CNN networks have shown promise for spatiotemporal yield prediction (Wang et al., 2020; You et al., 2017) [44,46] , but their application in datalimited hill-state contexts remains challenging.

Research Gap and Objectives

Despite the rapidly growing body of literature on ML-based crop yield forecasting, a significant gap persists: a comprehensive, multi-model comparative evaluation specifically tailored to the unique agroclimatic and topographic context of an Indian hill state like Uttarakhand has not yet been conducted. The majority of existing research for this region relies on traditional statistical models, leaving the potential of modern ensemble and kernelbased methods largely unexplored. Therefore, the present study directly addresses this gap by conducting a systematic and rigorous comparison of five machine learning algorithms Random Forest (RF), Elastic Net (ELNET), Support Vector Machine (SVM), Extreme Gradient Boosting (XGBoost), and Artificial Neural Network (ANN) for district-level rice yield forecasting across all 13 districts of Uttarakhand. By leveraging a 25-year dataset of agrometeorological variables and historical yields and evaluating model performance across both calibration and chronological validation phases, this research aims to provide a definitive benchmark for the region. The findings are intended to guide the operational implementation of ML-based forecasting systems by state agricultural departments and national agencies, moving beyond a one-size-fits-all approach towards more accurate, localized pre-harvest predictions.

Materials and Methods

Study Area

The study was conducted across all 13 administrative districts of Uttarakhand, a hill state located in the northern part of India. The state lies between latitudes 28°43′-31°27′N and longitudes 77°34′-81°02′E, encompassing a geographical area of approximately 53,483 km² (Census of India, 2011) [5] . Uttarakhand shares international borders with China (Tibet) to the north and Nepal to the east and is bounded domestically by Himachal Pradesh to the northwest and the plains of Uttar Pradesh to the south. One of the defining characteristics of the state is its extreme topographic heterogeneity. Elevations range from approximately 200 m above mean sea level (amsl) in the southern Tarai-Bhabar belt to over 7,800 m above mean sea level in the Greater Himalayan ranges (Dobhal et al., 2013) [9] . This vertical gradient produces a spectrum of agroclimatic conditions: the southern districts of Udham Singh Nagar and Haridwar are characterized by a subtropical, semi-arid to sub-humid climate with fertile alluvial soils and access to canal irrigation, whereas the mid-Himalayan and high-altitude districts such as Chamoli, Pithoragarh, Rudraprayag, and Uttarkashi experience a cooler, wetter temperate to alpine climate, with agriculture confined largely to narrow river valleys and terraced fields (Rawat & Rawat, 2019; ICAR-VPKAS, 2020) [19,33] . [2] . The total rice-cultivated area in Uttarakhand ranges between approximately 3.0 and 3.5 lakh hectares annually (Ministry of Agriculture and Farmers' Welfare, 2022) [29] . Productivity is strongly altitude-dependent, varying from less than 1.0 t/ha in remote high-altitude districts to over 2.5 t/ha in the irrigated Tarai districts (Directorate of Agriculture, Uttarakhand, 2023) [8] . This wide inter-district variability in yield, climate, and farm management makes Uttarakhand an ideal and challenging natural laboratory for evaluating the generalizability and robustness of machine learning forecast models.

Data Sources and Pre-processing

Two primary data streams were compiled for the analysis period 1998-2023, yielding 26 annual observations per district.

Agrometeorological Data

Monthly gridded data for six agrometeorological variables were obtained from the NASA Prediction of Worldwide Energy Resources (NASA POWER) database (Stackhouse et al., 2019) [40] , a publicly accessible repository providing bias-corrected surface meteorological parameters at a 0.5° × 0.5° spatial resolution. The variables extracted were maximum temperature (Tmax, °C), minimum temperature (Tmin, °C), afternoon relative humidity (RH2%), total rainfall (RF, mm), soil surface wetness (SSW, dimensionless), and mean sunshine hours (SSH, hrs/day). District-level values were derived by spatially averaging the grid cells falling within each district boundary. The predictor window was restricted to the active rice growing season, spanning June through October, consistent with the kharif crop calendar of Uttarakhand.

Rice Yield Data

Historical district-level rice yield records (t/ha) for the period 1998-2023 were sourced from the Directorate of economics and statistics (Dacnet), Government of Uttarakhand. These records were independently cross verified against the Area, Production and Yield (APY) statistics published by the Ministry of Agriculture and Farmers' Welfare, Government of India (Ministry of Agriculture and Farmers' Welfare, 2022) [29] . Any discrepancies between the two sources were resolved by retaining the state directorate values as the primary record. Yield data were screened for outliers using the interquartile range (IQR) method; no observations were removed as all values fell within agronomically plausible bounds.

Feature Engineering

A structured feature matrix was constructed for each of the 13 districts. The base predictor set comprised 30 features, representing the six meteorological variables observed across the five growing-season months (June-October). To enrich the representation of crop-climate interactions and improve model learning, the feature space was further augmented through the following transformations:  Interaction Terms: Multiplicative cross-features between maximum temperature and afternoon relative humidity (Tmax × RH2) were constructed for each month to capture combined heat and moisture stress effects on crop phenology (Lobell et al., 2011) [25] .  Agrometeorological Index: Accumulated Growing Degree Days (GDD) were computed from the transplanting date to harvest using daily temperature data, providing a biologically meaningful measure of thermal accumulation during the crop cycle (McMaster & Wilhelm, 1997) [27] .  Trend Variable: A continuous 'Year' variable was included to account for non-climatic long-term yield trends attributable to technological change, improved cultivar adoption, and evolving crop management practices (Ray et al., 2013) [34] .  All predictor features were standardized to zero mean and unit variance (z-score normalization) prior to model fitting. This step is particularly critical for algorithms sensitive to feature scale, namely SVM and ANN, and also ensures numerical stability in the regularized regression framework of Elastic Net (Hastie et al., 2009) [17] .

Model Development and Hyperparameter Tuning

Five machine learning algorithms were implemented and systematically tuned following a consistent cross-validation framework. All models were developed in R (version 4.3.0) using the caret, randomForest, glmnet, xgboost, and nnet packages.

 Random Forest (RF): An ensemble of 500 decision trees (ntree = 500) was grown. The number of predictor variables randomly sampled at each node split (mtry) was selected via 5-fold cross-validation from a grid spanning 2 to (p/3), where p is the total number of features. Node size was set to 5 (Breiman, 2001) [3] .  Elastic Net (ELNET): The L1/L2 mixing parameter (α ∈ [0, 1]) and the regularization penalty (λ) were jointly selected via 10-fold cross-validation using the glmnet package, with the minimum cross-validation error criterion applied for λ selection (Zou & Hastie, 2005) [47] .  Support Vector Machine (SVM): A radial basis function (RBF) kernel was employed. The regularization cost parameter (C) and the kernel bandwidth (γ) were simultaneously optimized via a grid search (γ ∈ {0.001, 0.01, 0.1, 1}; C ∈ {0.1, 1, 10, 100}) under 5-fold crossvalidation (Vapnik, 1995) [43] .  Extreme Gradient Boosting (XGBoost): Key hyperparameters learning rate (η), maximum tree depth (max_depth), minimum child weight, subsample ratio, and colsample_bytree were tuned using a randomized grid search with 5-fold cross-validation, minimizing root mean square error (Chen & Guestrin, 2016) [6] .  Artificial Neural Network (ANN): A single hidden-layer feedforward network with a sigmoid activation function was trained using backpropagation. The number of hidden neurons was determined via cross-validation from the range {3, 5, 7, 10, 15}. An early stopping criterion (patience = 10 epochs) was applied to prevent overfitting. To reduce sensitivity to random weight initialization, final predictions were averaged across five independent runs with different random seeds (Kaul et al., 2005) [22] .

Model Training and Validation Strategy

To simulate a realistic pre-harvest operational forecasting scenario, a strictly chronological data split was applied independently for each district. [35] .

Hyperparameter tuning for all models was conducted exclusively within the calibration set using cross-validation, and the tuned models were applied only once to the validation set to generate final performance estimates. This two-stage evaluation prevents overfitting to the validation set and provides unbiased generalization metrics.

Performance Evaluation Metrics

The predictive performance of each model was assessed during both the calibration and validation phases using four complementary statistical metrics, enabling a comprehensive evaluation of accuracy, precision, and systematic bias: [45] .  Coefficient of Variation of RMSE (CV %): Expresses RMSE as a percentage of the mean observed yield (CV = RMSE / ȳ × 100). This dimensionless metric enables meaningful cross-district comparisons of relative forecast accuracy independent of yield magnitude.  Mean Bias Error (MBE, t/ha): Computed as the mean of (predicted -observed) residuals, MBE reveals the direction and magnitude of systematic prediction bias. A positive MBE indicates a tendency toward over-prediction, while a negative MBE indicates under-prediction (Loague & Green, 1991) [24] .

Together, these metrics provide a multi-faceted assessment that captures different aspects of model performance: R² reflects explanatory power, RMSE and CV reflect precision, and MBE reflects systematic deviation all of which are relevant to operational forecasting contexts.

Results and Discussion

Overview and Model Ranking

The analysis of calibration and validation performance across 13 districts reveals a clear and consistent hierarchy among the five machine learning algorithms evaluated. As expected, all models particularly XGBoost and RF achieved high calibration R² values, demonstrating strong capacity to learn the training data (see Table 1). However, validation results provide the true measure of generalizability (Friedman, 2001; Breiman, 2001) [3,14] . Across most districts, Random Forest (RF) emerged as the most robust model, balancing high predictive accuracy with low error metrics and minimal bias. XGBoost showed a strong tendency to overfit (Cao et al., 2020) [4] , while SVM demonstrated utility in specific high-altitude hill districts (Vapnik, 1995) [43] . ELNET provided a stable, interpretable baseline (Zou & Hastie, 2005) [47] , and ANN performance was highly variable, largely attributable to limited training sample sizes per district (Hochreiter & Schmidhuber, 1997) [18] .

Analysis of Model-Specific Performance 3.2.1 Random Forest (RF)-The Most Generalizable Model

RF demonstrated the most consistent and balanced performance across the state, with validation R² exceeding 0.55 in nine of 13 districts (Table 1). Its top performance in Nainital (R²=0.890), Udham Singh Nagar (R²=0.797), and Pauri (R²=0.796) highlights its robustness across diverse agroclimatic settings. The low coefficient of variation (CV%; often <15%) and mean bias error (MBE) values close to zero further confirm reliability. RF's inherent ensemble averaging and bootstrap aggregation effectively mitigate overfitting (Breiman, 2001) [3] , making it the ideal candidate for operational forecasting in Uttarakhand's diverse environments. Its performance was notably poor only in Champawat (R²=0.113), a district that proved challenging for most models, suggesting the presence of unique, unmodeled local micro-climatic factors.

XGBoost-The Overfitting Risk

XGBoost exhibited a stark performance dichotomy. While it achieved near-perfect calibration (R²>0.99, RMSE≈0), its validation R² was highly variable (Table 1). It showed strong validation skill in Tehri (R²=0.928) and Udham Singh Nagar (R²=0.851), but collapsed in high-altitude, data-sparse districts such as Chamoli (R²=0.113) and Champawat (R²=0.064). This is a classic symptom of overfitting, whereby the model memorizes noise in a small training set that does not generalize to the test period (Chen & Guestrin, 2016) [6] . As noted by Cao et al.

(2020) [4] , XGBoost's power can become a liability without rigorous regularization or a larger training sample. Its use is therefore recommended only with stringent cross-validation and potentially as a component within a larger ensemble.

SVM-

The District-Specific Specialist SVM's performance was highly district-specific, achieving the best validation R² in the complex, high-altitude districts of Chamoli (R²=0.837) and Champawat (R²=0.630) (Table 1). This suggests that the Radial Basis Function (RBF) kernel is adept at capturing localized, non-linear yield responses to orographic effects and microclimates in these regions patterns that treebased models may not fully capture (Vapnik, 1995; Schölkopf & Smola, 2002) [37,43] . However, its poor performance in Tarai and mid-hill districts such as Haridwar (R²=0.068) and Tehri (R²=0.083) reflects sensitivity to hyperparameter tuning and variable performance across data regimes. SVM serves as a valuable complementary model rather than a universal solution.

ELNET-The Stable Benchmark

Elastic Net provided the most stable, though moderate, predictions across the study area (Table 1). Its best performance was observed in Pauri (R²=0.936) and Nainital (R²=0.670), suggesting that in districts where the climate-yield relationship is more linear, a regularized linear model can be highly effective (Zou & Hastie, 2005) [47] . Its interpretability providing explicit coefficients for each climate predictor is a significant advantage for operational use where transparency and stakeholder communication are valued. While outperformed by non-linear models in many cases, its stable and unbiased predictions establish it as a reliable benchmark.

ANN-The Inconsistent Learner

The ANN model produced the most inconsistent results across the 13 districts (Table 1). While it achieved high validation R² in Almora (R²=0.827) and Pauri (R²=0.913), it performed poorly in most other districts, including catastrophic failures (R²≈0) in Haridwar and Tehri. This high variability is attributable primarily to the limited training sample size (n≈22 per district), which is insufficient for effectively training even a single hidden-layer network (LeCun et al., 2015) [23] . Sensitivity to random initialization and the difficulty of finding globally optimal hyperparameters with small datasets further contributed to its unreliability (Hochreiter & Schmidhuber, 1997) [18] .

District-Level Synthesis and Model Selection Strategy

Acknowledgement

AcknowledgementsThe authors gratefully acknowledge NASA POWER for providing district-level meteorological data (Stackhouse et al., 2019) [40] . Sincere thanks are extended to the Directorate of Economics and Statistics, Government of Uttarakhand, for access to rice yield statistics. The first author acknowledges the support of the Department of Agrometeorology, G.B. Pant University of Agriculture and Technology, Pantnagar. The authors declare no conflict of interest.

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