https://orcid.org/0009-0009-7546-3791
Figures
Abstract
Reliable crop yield estimates at fine spatial resolution are essential for precision agriculture, food security planning, and insurance schemes. However, yield statistics are reported at coarser administrative levels, limiting their applicability for field-scale analysis. This study proposes a multi-stage hybridized framework that integrates deep learning (DL) models with geostatistical residual kriging to disaggregate village-level crop yield statistics to the pixel level. The proposed methodology is demonstrated using wheat and mustard crops as case study in the semi-arid districts, Haryana, India. The study identifies suitable data combination by evaluating multiple combinations of soil, weather, Sentinel-1, and Sentinel-2 bands data for yield disaggregation. Results show that datasets combining spectral and weather information consistently outperform other data combinations. Validation results showed that the strongest numerical accuracy was observed for machine learning algorithms, e.g., random forest, with an R2 of 0.9949, but it lacks spatial realism. On the other hand, DL models had comparable numerical accuracy and also produced smoother and more realistic spatial transitions but exhibited spatially structured residuals. To mitigate these spatial biases, residual kriging was applied to DL outputs, resulting in RMSE reduction of 35–45% and generating smoother pixel-level maps that preserved fine-scale heterogeneity and aligned with reported village yields. Moran’s I analysis confirmed significant residual spatial autocorrelation for DL models, justifying the use of geostatistical correction. Thus, the proposed hybridized framework emerged as best for balancing statistical accuracy with spatially realistic yield disaggregation. This study provides one of the first empirical demonstrations of village-to-pixel yield disaggregation using the identified weather and satellite band data combination.
Citation: R. S, Jain R, Singh VK, Bharadwaj A, Sehgal VK, Biswas A, et al. (2026) Hybridizing deep learning algorithms and geostatistical approaches for improved crop yield disaggregation. PLoS One 21(3): e0344081. https://doi.org/10.1371/journal.pone.0344081
Editor: Babak Mohammadi, Swedish Meteorological and Hydrological Institute, SWEDEN
Received: October 28, 2025; Accepted: February 16, 2026; Published: March 6, 2026
Copyright: © 2026 R. et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the manuscript and its Supporting Information files.
Funding: Part of the research was supported by a grant from the Bill & Melinda Gates Foundation (Grant No. OPP1215722) under the Zn Mainstreaming Project in India. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: No authors have competing interests.
Introduction
The need for crop yield disaggregation stems from the limitations of aggregated yield statistics, which mask significant local variations in agricultural productivity, risk, and management practices. In many countries, including India, official crop yield estimates are typically reported at coarse administrative levels such as districts or states [1]. Although such aggregated statistics are valuable for regional production monitoring, they are inadequate for applications including precision agriculture, farm-level advisory services, and crop insurance schemes that require spatially explicit localized insights [2–5]. When yield data are aggregated, localized yield losses or gains cannot be accurately captured, leading to inefficiencies in resource allocation and increased basis risk in insurance payouts. Policy schemes such as crop insurance, subsidies, and disaster compensation also require farm-level yield estimates to reduce basis risk and ensure timely and transparent payouts to farmers [5,6]. Precision agriculture depends on field-level information to optimize input use, improve resource efficiency, and enhance farm profitability [3].
Beyond farm management and policy making, finer-scale yield estimates are increasingly important for food security monitoring and climate adaptation studies [4,7]. Disaggregating yield data to smaller geographical units, such as villages or farmer’s field, provides a more granular and realistic understanding of agricultural performance. To address these diverse needs, many studies reported disaggregation methods that translate coarse level yield data (e.g., district) into finer-scale (e.g., field) estimates [8], often referred to as a downscaling approach in some studies [9]. These methods are conceptually linked to spatial interpolation techniques [10].
Existing yield disaggregation approaches can be broadly grouped into five categories (Fig 1). Geostatistical methods, particularly area-to-point kriging (ATPK), exploit spatial autocorrelation to interpolate fine-scale yield estimates from aggregated data [9,11]. However, ATPK cannot incorporate spectral or weather covariates, and the accuracy of kriging is highly sensitive to variogram specification [12] and sampling density [13,14]. Vegetation index (VI)-based allocation methods distribute aggregated yields across pixels with relative proportion [15]. While computationally simple and efficient, these methods assume linear proportionality between VIs and yield, often failing to capture temporal dynamics [16]. Regression-based frameworks relate yield variability to NDVI, climate, or biophysical covariates and have shown strong agreement with official statistics [17,18]. Nevertheless, regression approaches are typically linear, rarely account for nonlinear crop responses, and often ignore temporal variation within the growing season.
Recent advances in machine learning (ML) have enhanced the disaggregation of crop yield data by integrating multi-source environmental covariates and modeling complex nonlinear relationships. Ensemble ML models such as Random Forest (RF), Gradient Boosting (GB), and Extreme Gradient Boosting (XGB) have demonstrated strong performance in downscaling crop yields [19–21]. Although these models often achieve high numerical accuracy, they tend to produce spatial artifacts such as abrupt boundaries and block-like patterns due to the discrete nature of decision-tree structures, thereby limiting their spatial realism [22,23]. Here, spatial realism is defined as the model’s ability to capture and represent fine-scale heterogeneity and continuous spatial transitions in crop yield patterns.
As referred in previous paragraph, ML approaches significantly improve the accuracy of disaggregation, it is hypothesized that recently evolved Deep Learning (DL) approaches (e.g., Long Short-Term Memory (LSTM), Gated Recurrent Units (GRU)), having strong capability in capturing nonlinear temporal dependencies, should further improve disaggregated yield values [24–27]. These studies have reported the use of the DL based models for improved yield prediction, but to the best of our knowledge, their application in yield disaggregation remains unexplored.
Parallel efforts in related domains reinforce the potential of multi-source downscaling. Early applications include remote sensing-based drought monitoring [28] and spatial interpolation for soil property mapping [13]. More recently, Mahmood et al. [29] demonstrated the value of ML for downscaling biophysical parameters, refining soil water indices from 1 km to 100 m resolution. These studies highlight the potential of disaggregation approaches but also reveal the scarcity of applications specifically targeting crop yield disaggregation.
Wheat and mustard are two of the most important crops in the rice-wheat cropping system of India, sustaining both household consumption and national food security [30]. Wheat occupies about 35.2 million hectares with a production of 128.5 million tons, while mustard covers approximately 9.9 million hectares with a production of 14.3 million tons [1]. Together, these crops contribute substantially to India’s agricultural economy and rural livelihoods [31]. However, their productivity is highly sensitive to weather variability and climate change. Even modest temperature increases have been shown to reduce wheat yields in India by 2–4% per degree Celsius rise, while heat stress and rainfall deficits further exacerbate risks during grain filling and maturity stages [32]. Mustard, similarly, is vulnerable to late-season heat stress and water scarcity, which can reduce oil content and yields [33].
With the above background, the present study proposes a hybrid framework that integrate DL algorithms and geostatistical methods to disaggregate village-level crop yields to pixel-level estimates. The study systematically evaluates traditional, ML, DL, and hybrid approaches for yield disaggregation; identifies an optimal minimum dataset combination comprising satellite spectral bands and weather variables for accurate yield disaggregation; and it provides one of the first empirical demonstrations of village-to-pixel yield disaggregation for wheat and mustard crops in semi-arid regions of India, balancing numerical accuracy with spatial realism.
Study area
Haryana plays a central role in India’s food grain economy, ranking 2nd nationally in mustard yield (after Gujarat) and 4th in wheat production and area, while standing 3rd in wheat yield (after Punjab and Chandigarh) [1]. The state is among the leading producers of wheat, rice, and mustard in India, with extensive irrigation coverage and relatively uniform management practices that reduce variability unrelated to biophysical conditions. Moreover, the availability of high-resolution remote sensing data such as Sentinel‑1 (Synthetic Aperture Radar) and Sentinel‑2 (multispectral optical imagery), obtained from the European Space Agency (ESA), with spatial resolutions of 10 m and 20 m depending on the bands [34]. Administrative boundaries [35], secondary yield data and ground truth data support from Krishi Vigyan Kendra, Adampur, Chaudhary Charan Singh Haryana Agricultural University, Hisar, and Department of Agriculture and Farmers Welfare Haryana, facilitated conduct of this study. Haryana’s robust data systems, coupled with its ongoing challenges related to water scarcity and crop diversification, make it an ideal site to develop and validate yield disaggregation models.
The study was conducted in Hisar and Bhiwani districts, located in the arid and semi-arid region of Haryana [36], which together provide a representative landscape of wheat and mustard cropping systems. Hisar is predominantly wheat-growing, with approximately 210 thousand hectares under wheat and 108 thousand hectares under mustard, whereas Bhiwani is mustard-dominated, with approximately 170 thousand hectares under mustard and 90 thousand hectares under wheat (Table 1). Five-year records (2018–2023) confirm the stability of crop dominance in the study area, with mustard consistently higher in Bhiwani and wheat dominating in Hisar (Table 1). The region with average annual rainfall of 350–500 mm, temperature ranges from 2–45°C [37], sandy loam to loam soils of medium fertility [38], and irrigation supplied mainly through tube wells and canals [39], all of which contribute to spatial variability in crop yields across village fields.
Fig 2 illustrates the spatial distribution of wheat and mustard yields during the rabi season, classified into six categories for wheat (<35, 35–40, 40–45, 45–50, 50–55, > 55 quintals/ha) and mustard (<10, 10–15, 15–18, 18–20, 20–23, > 23 quintals/ha), highlighting the heterogeneity of yields across the landscape. This combination of temporal stability and spatial variability makes Hisar and Bhiwani ideal for evaluating village-to-pixel crop yield disaggregation approaches.
The spatial yield maps are author-generated outputs using QGIS. Village boundaries were obtained from Survey of India (SoI) village digital boundary shape files (Product Code: OVSF/-/10; https://onlinemaps.surveyofindia.gov.in/Digital_Product_Show.aspx; accessed Jan 2024).
Materials and methodology
This study developed a DL framework to disaggregate village-level crop yields into pixel-level estimates. The workflow comprised four sequential steps: (i) Dataset preparation, (ii) Regression and ML modelling for best inputs selection, (iii) DL modeling, and (iv) Geostatistical correction and validation. We used traditional disaggregation methods as benchmarking methods.
Dataset preparation
This study integrated multi-source datasets (Table 2) covering crop yields, crop mask, weather, soil, and satellite observations to enable village-to-pixel disaggregation. Village-level yield statistics for wheat and mustard were obtained from the Department of Agriculture and Farmers Welfare, Haryana, and manually harmonized with administrative boundaries through village ID, block ID mapping, and cleaning were done in QGIS. Missing or inconsistent entries were corrected by imputing block-level averages, while villages absent from the shape file were excluded from analysis. We generated a crop mask using Sentinel-1 and Sentinel-2 data and validated it with crop ground truth (GT) collected from Hisar and Bhiwani districts. The crop mask was used to isolate cultivated pixels and ensure that spectral, radar, and weather information was extracted only from relevant crop areas.
Optical, radar, weather, and soil were accessed and downloaded via the Google Earth Engine (GEE) platform [42]. GEE provides cloud-based access to curated satellite archives and supports scalable geospatial processing, making it suitable for handling temporal and multi-sensor datasets required for this study [43]. All outputs were exported in GeoTIFF format for local processing and analysis.
Sentinel-2 optical bands (B2-Blue, B3-Green, B4-Red, B8-Near Infrared, and B11-Shortwave Infrared) and Sentinel-1 radar bands (VV, VH) were utilized to capture crop growth dynamics. Data were acquired for November, December, and February, corresponding to key growth stages of wheat and mustard during the rabi season. January imagery was excluded from the analysis due to persistently high cloud cover during this period, which limited the availability of cloud-free optical observations. March was excluded because most mustard harvesting occurs by late February or early March, reducing the relevance of spectral signals for yield estimation. All scenes were clipped to the study area boundary, mosaicked for multiple acquisition dates within each month, and averaged to generate a monthly composite for subsequent analysis.
Six weather features were extracted from the ERA5-Land Hourly dataset [40], produced by the European Centre for Medium-Range Weather Forecasts (ECMWF). Hourly records were aggregated into monthly means for the rabi season (November to March). These values were matched to village boundaries. Given the coarse spatial resolution (~27 km), multiple villages shared identical weather values, limiting village-scale differentiation, but they remained valuable when combined with higher-resolution satellite features. Soil properties were obtained from SoilGrids250m [41], based on over 230,000 soil profiles and ML predictions. Ten properties were aggregated to the village level and treated as static predictors.
Village-level averages of weather, soil, and band information from GeoTIFF were extracted using a crop mask to isolate cultivated pixels and computed zonal statistics by using village boundaries. These feature extraction and aggregation were performed using Python-based geospatial libraries. The final analytical dataset consisted of 1,116 village-level samples (Fig 3). The dataset was randomly partitioned into training and validation subsets using an 80:20 split, resulting in 892 samples for model training and 224 samples for validation. The same data partitioning strategy was consistently applied across regression, ML, and DL models to ensure comparability of results. A schematic overview of the data preparation, feature extraction, and data partitioning workflow is presented in Fig 3, which also illustrates representative spatial layers including village boundaries, crop masks, satellite imagery, soil variables, and weather data.
The figure shows (from left to right) village administrative boundaries (Survey of India, Product Code: OVSF/-/10; https://onlinemaps.surveyofindia.gov.in/Digital_Product_Show.aspx; accessed Jan 2024) with yield, crop mask (wheat and mustard), Sentinel-2 RGB imagery, representative soil property raster’s (sand, silt, and clay), and selected weather raster’s (air temperature at 2 m, soil temperature level 1, and surface net solar radiation). The workflow diagram layout was created by the authors, and map visualizations were prepared in QGIS.
Various datasets have been used in previous studies for crop yield prediction and disaggregation, including climate, satellite-derived VIs, and soil properties [21,24]. Different combinations used in different studies: NDVI combined with climatic data [18]; climate with leaf area index (LAI) [26]; climate and soil [19]; temporal LAI sequences [8,25]; VIs alone [9,15,16]; and climate-only datasets [2]. To assess the significance of one or multiple types of inputs, systematically combined to form seven combinations are summarized in Table 3.
Algorithms
This study uses four categories of algorithms, namely traditional, regression, ML, DL, and hybrid, to assess the merits and demerits of each one (Table 4). Within each category, multiple algorithms have been used in this study. The algorithms have been used for various purposes like best dataset selection, model selection and visualization of the disaggregated yield values.
Fig 4, illustrates the hierarchical workflow of the proposed yield disaggregation framework. The first level corresponds to dataset and algorithm selection, where multiple feature combinations and predictive models are evaluated using quantitative performance metrics. The second level shows pixel-level yield prediction using selected ML and DL models. The third level depicts residual kriging, where spatial autocorrelation in model residuals is modeled using variogram analysis and in forth level applied to correct systematic spatial biases, resulting in the final disaggregated yield maps. In the final stage, corrected yields are aggregated to administrative units and model performance is evaluated.
The yield prediction, residual, and corrected yield maps of Hisar and Bhiwani shown in the figure are author-generated (Python) and visualized using QGIS are included to illustrate the methodological process.
Dataset selection using regression and ML models
The first stage of analysis employed regression and ML to identify the best dataset combination among all seven datasets (refer to Table 3, Fig 4). This stage was designed to screen input feature combinations and select a consistently performing dataset prior to DL based pixel-level yield modeling. Regression and ML models are well suited for capturing nonlinear interactions among spectral, weather, and soil variables at the village level while maintaining computational efficiency.
Linear regression (Linear) assumes linear dependence between predictors and yield [47]:
where 𝑦 is the predicted yield, 𝑥𝑖 are the features, 𝛽0 is the intercept, 𝛽𝑖 are the coefficients, and 𝜖 is the error term.
Ridge regression (Ridge) adds L2 regularization to handle multicollinearity [48]:
where 𝜆 is the regularization parameter controlling the penalty term. Ridge Regression shrinks the coefficients but does not set them exactly to zero.
Lasso regression (Lasso) extends linear regression with L1 regularization, which can shrink some coefficients to zero, thereby performing variable selection [49]:
Random Forest (RF) is an ensemble learning algorithm that builds multiple decision trees using bootstrap samples and averages their predictions to reduce variance [50].
where, ft (x) = prediction from the tth decision tree, T = total number of trees. Each tree ft is trained on a bootstrap sample of the data.
Gradient Boosting (GB) constructs an additive model by sequentially fitting decision trees to the residual errors of previous trees, minimizing a differentiable loss function via gradient descent [51].
where, T = total number of trees (boosting iterations), η = learning rate
Extreme Gradient Boosting (XGB) improves upon traditional gradient boosting by incorporating second-order derivatives in the optimization process and adding regularization terms to control model complexity [52].
Where F = space of all possible trees
Linear, Ridge, Lasso, RF, GB, and XGB models were trained using village-level yield observations. Model performance was evaluated using prediction error metrics, and the dataset-model combination yielding the lowest error was selected as the optimal input configuration for subsequent DL modeling. The best-performing regression and ML models were also retained for comparison with DL and hybrid DL-kriging approaches.
DL model
Using the optimal dataset combination identified in the previous stage, Recurrent Neural Networks (RNN) algorithm were implemented which capture temporal dependencies and generate pixel-level yield predictions. Two RNN architectures were implemented: Long Short-Term Memory (LSTM) [53] and Gated Recurrent Unit (GRU) [54]. Both models share the same architecture, differing only in the internal recurrent structure. The LSTM model comprised 25,889 trainable parameters, while the GRU model comprised 23,553 trainable parameters. This DL model integrates three types of inputs (Fig 5):
GRU and LSTM models share identical architectures, differing only in the recurrent cell type.
Bands inputs 𝑋bands ∈ 𝑅 𝑅1× 𝐹1: time-series (T1=3) of backscatter and spectral bands (F1=7).
Weather inputs 𝑋weather ∈ 𝑅𝑅2×𝐹2: time-series(T2=5) of weather variables (F2=6).
Static inputs 𝑋static ∈ 𝑅𝐹3: features such as soil or crop type (F3=1).
Each sequential input is processed through its own recurrent module (either GRU or LSTM) with 32 hidden units, followed by a Dense layer of 16 neurons activated by ReLU:
LSTM maintains long-term cell state 𝐶𝑡 and hidden state ℎ𝑡 via input, forget, and output gates. GRU architectures simplify recurrence with update and reset gates directly controlling hidden state transitions.
The static input branch bypasses temporal processing, preserving its spatial and categorical characteristics. Outputs from the bands, weather, and static branches are concatenated to form a unified feature vector . This merged representation is passed through three fully connected layers (128, 64, and 32 neurons) with ReLU activations to learn complex nonlinear relationships:
Where, W1, W2, and W3 denote the learnable weight matrices and b1, b2 and b3 represent the corresponding bias vectors of the successive fully connected layers, while ReLU is the nonlinear activation function applied at each layer.
Finally, a Softplus activation function is applied at the output layer to ensure non-negative yield predictions suitable for regression tasks [55].
Mean squared error was used as the optimization loss, while mean absolute error was monitored during training to assess convergence and model stability [56,57]. Regularization was achieved implicitly through limited network depth, early stopping, and an 80:20 training-validation split. Training was conducted for a maximum of 500 epochs with early stopping patience set to 25 and a batch size of 32.
Table 5 shows the hyper parameter setting for different ML and DL methods. All models were trained on village-level data, applied to pixel-level features for yield prediction, and aggregated back to village-level yields to estimate the residual for further geostatistical correction.
Geostatistical correction
Although regression, ML, and DL models captured feature-yield relationships, their residuals exhibited spatial autocorrelation. To address this, a robust regression-kriging framework [58] was applied to refine the results. Residuals for each village 𝑖 were computed as:
where 𝑦𝑖 is the observed village yield and is the predicted mean yield aggregated from ML/DL maps. Village polygons were converted to centroids, and semi-variograms [12] were fitted to model spatial dependence:
where ℎ is the separation distance, 𝑁(ℎ) is the number of point pairs at distance ℎ, and 𝑒(𝑠𝑖) is the residual at location 𝑠𝑖. Residuals were interpolated using kriging with the best-fitting variogram model (‘linear,’ ‘spherical,’ ‘Gaussian,’ or ‘exponential’) selected through cross-validation.
In kriging, residuals were modeled as a weighted sum of nearby observations [59]:
where 𝜆𝑖 are kriging weights assigned to each residual 𝑒(𝑠𝑖).
The weights depend on the variogram model: closer points (small 𝛾(ℎ)) get higher weights, while distant or weakly correlated points get smaller weights. 𝜆𝑖 are derived from solving this kriging matrix equation using γ(h).
γ(si – sj): semi variance between observed locations si and sj, γ(si – s0): semi variance between observed location si and the prediction location s0, μ: Lagrange multiplier enforcing unbiasedness.
The resulting kriging residual surface was then added back to the predicted raster. [58]:
where is the corrected yield at location 𝑠. This refinement improved fine-scale accuracy by combining feature-driven predictions with spatially dependent corrections. Block-level aggregations of corrected predictions were validated against reported statistics. Performance of DL- kriging was benchmarked against the best standalone DL and ML model under identical dataset combinations.
Traditional methods
The three commonly used traditional disaggregation methods, namely weight-based, percentile-based, and area-to-point kriging (ATPK), were implemented as benchmarking methods.
Weight-based disaggregation [15]: Pixel-wise yield was calculated as:
where NDVIₚ is the NDVI value for pixel p, P is the reported production for the administrative unit.
Percentile-based disaggregation [16]: Yield values were scaled as:
where MaxNDVI₉₅ and MinNDVI₅ are the 95th and 5th percentile NDVI values, respectively.
Area-to-Point Kriging: village-level yields were disaggregated to pixel scale without external covariates [11,59]. These methods were not part of the main workflow but served as external benchmarks against ML, DL, and residual kriging approaches.
Model evaluation
Model performance was assessed using the coefficient of determination (R2), adjusted coefficient of determination (adjusted R2), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). Additionally, the statistical significance of differences among different dataset models was assessed using the Friedman chi-square test, followed by post-hoc analysis.
The coefficient of determination (R2) [60] was computed as:
where yᵢ represents observed yield, ŷᵢ is the predicted yield, and ȳ is the mean of observed yields.
The adjusted coefficient of determination (adjusted R2) accounts for the number of predictors relative to the number of observations and penalizes model complexity. It was computed as [61]:
where n is the number of observations and p is the number of predictors.
The Root Mean Squared Error (RMSE) [56] was computed as:
where n is the number of observations. RMSE measures the average magnitude of prediction error, with lower values indicating better model performance.
The Mean Absolute Error (MAE) was computed as [56]:
MAE represents the average absolute difference between observed and predicted values, providing a straightforward measure of prediction accuracy.
The Mean Absolute Percentage Error (MAPE) was computed as [57]:
MAPE expresses prediction accuracy as a percentage, allowing for easier interpretation of model error relative to the magnitude of the observed values.
The Friedman chi-square test [62] was applied to assess whether performance differences among models were statistically significant across datasets. The test statistic is given by:
where 𝑁 is the number of dataset, 𝑘 is the number of model, and 𝑅𝑗 is the average rank of model 𝑗.
When significant differences were detected, pairwise comparisons were conducted using the Nemenyi post-hoc test [63]. The critical difference (CD) was computed as:
where qα is the critical value of the Studentized range statistic for significance level α, k is the number of models compared, and N is the number of datasets. If the average rank difference between two models exceeds CD, their performance difference is considered statistically significant.
Spatial autocorrelation in the predicted yield residuals was quantified using Moran’s I statistic [64]. Moran’s I was computed using a k-nearest neighbor spatial weights matrix (k = 8) constructed from pixel-level prediction locations in projected coordinate space. Positive Moran’s I values indicate spatial clustering of similar residuals, while values near zero indicate spatial randomness and negative values indicate spatial dispersion.
Software and computational environment
All spatial and statistical analyses were conducted in Anaconda Jupyter Notebook using a Python 3.8.20 environment on a workstation equipped with an NVIDIA RTX A5000 GPU (24 GB memory). This setup provided sufficient computational capacity for DL model training, geostatistical processing, and large raster handling.
Geospatial data preprocessing was performed with geopandas, rasterio, rasterstats, and shapely for handling vector and raster layers, including resampling and zonal aggregation. Regression and ML models were implemented with scikit-learn and xgboost, while DL models were built with TensorFlow and Keras. For geostatistical corrections, pykrige was used for variogram fitting and kriging, with pyproj handling coordinate reference systems and scikit-learn providing K-fold cross-validation. Visualization and statistical analyses were supported by matplotlib, seaborn, and scipy. stats, while scikit-posthocs enabled post-hoc significance testing.
Result and discussion
This section presents the outcome of the proposed hybrid village-to-pixel yield disaggregation methodology and its counterparts namely traditional, ML and DL. As a byproduct, the study also evaluates the use of various data sources combination and filters to the optimum dataset features for yield disaggregation. The first part present results of experiments related to the identification of the optimum dataset and algorithms for yield disaggregation. Then discusses disaggregation on a selected dataset across the algorithms and also presents the disaggregated results in the map.
Dataset selection
Fig 6 presents the performance metrics, namely R2, adjusted R2 and RMSE and in a 7 x 6 grid (datasets x model) across datasets and model. A horizontal bar at bottom represents the color scale with corresponding values. It is observed that the datasets band-weather, weather-only, and all-features produced the higher R2 and lower RMSE values across most of the models. However, adjusted R2 reveals a different pattern, it explicitly penalizes model complexity and redundant predictors. As a result, datasets with fewer but more informative variables are favored. In this context, the adjusted R2 values indicate that weather-only, band-only, and band-weather outperform the all-features dataset, highlighting the limited marginal benefit of including additional predictors when they do not contribute proportionally to explanatory power.
To further test whether the dataset results are significantly different, Friedman tests were conducted on values of RMSE (χ2 = 19.50; p = 0.0034) and R2 (χ2 = 19.68; p = 0.00315), confirming significant variation among datasets. Further Post-hoc analysis further identified that the soil-only dataset performed significantly worse (average rank difference < CD = 3.6772) than both band-weather and weather-only datasets. No other pairwise differences reached significance. These results are summarized in Table 6 and visually illustrated in Fig 7.
As shown in Fig 7a-b, the weather-only dataset yielded deceptively low RMSE and strong adjusted R2 values due to the coarse resolution of ERA5-Land weather data used in this study, which assigns identical weather values to many villages and fails to capture fine-scale heterogeneity. This artificially reduces prediction variance and inflates performance, and thus these results should not be interpreted as evidence that weather (weather-only) alone is sufficient. The soil-only dataset performed poorly (RMSE > 5.20 q/ha, R2 < 0.89 across models), as confirmed by post-hoc tests (Table 6), reflecting the limited explanatory power of static soil variables for intra-season yield variation.
In all features, when soil information was added to other predictors (weather and band), performance did not improve; in fact, accuracy slightly decreased compared with band-weather. A paired t-test between band-weather and all-features also confirmed no significant difference (p = 0.145). Integrating insights from adjusted R2, results indicate that while all-features achieves strong raw performance, it does so at the cost of increased complexity without commensurate gains in explanatory power. Although band-only achieved high adjusted R2, it lacks explicit meteorological information and did not perform RMSE or R2 well as compared to band-weather. Therefore, band-weather was selected as the final dataset combination for DL modeling and comparison.
Algorithm selection
The set of algorithms evaluated in this study was selected to represent a broad spectrum of modeling paradigms commonly used in yield prediction and spatial modeling studies. Linear regression, Ridge, and Lasso were included as baseline parametric models to assess the limits of linear relationships between predictors and yield. Tree-based ensemble methods, namely RF, GB, and XGB, were chosen due to their proven ability to model nonlinear interactions and handle multi-source remote sensing and environmental data. This diverse selection allows a systematic comparison of simple, regularized, and nonlinear ensemble models before advancing to DL and hybrid geostatistical approaches.
As per Fig 6, among the algorithms, RF performed particularly well, achieving RMSE below 4.69 q/ha while maintaining high R2 values (>0.91). XGB and GB also performed competitively, though RF remained more stable across datasets. In contrast, linear models (Linear, Ridge, Lasso) generally yielded higher RMSE values.
Friedman test RMSE across all six models (χ2 = 7.95; p = 0.159) revealed no statistically significant differences. Nevertheless, average ranks analysis (Fig 8) indicated that tree-based ensemble models XGB, RF, and GB outperformed the regression models. Considering both performance stability across dataset and relative ranking based on RMSE and adjusted R2, XGB and RF were selected for subsequent analysis. These models were retained as strong and widely used ML baselines for comparison with DL and kriging-based hybrid approaches.
DL model performance
Using the band-weather dataset, DL models were trained to capture yield dependencies on temporal values of weather and bands.
Fig 9 illustrates the training and validation MAE (left) and loss (right) curves for both models. The LSTM exhibited faster and more stable convergence, with MAE and loss stabilizing within the first 30–40 epochs, reflecting efficient learning and reduced overfitting. In contrast, the GRU model showed a delayed convergence pattern, requiring more epochs to reach optimal performance, though it eventually achieved comparable validation loss. This difference can be attributed to GRU’s simpler gating mechanism, which can sometimes require longer adaptation when handling complex temporal dependencies.
The LSTM model achieved an RMSE of 4.89 q/ha and an R2 of 0.9013, whereas the GRU model achieved a slightly better RMSE of 4.75 q/ha and R2 of 0.9024, indicating that both performed comparably with ensemble ML models.
Spatial visualization of disaggregated yield
This section presents a comparative visual assessment of the spatial patterns generated by different yield disaggregation approaches. Spatial visualization is used to evaluate the realism, continuity, and artifact behavior of the disaggregated yield maps beyond quantitative accuracy metrics. The analysis is organized to reflect the methodological workflow, progressing from pre-kriging results to residual kriging and post-kriging outcomes.
Traditional disaggregation
The traditional approaches were presented without any spatial correction to serve as baseline methods. The weight-based and percentile-based, showed limited ability to reproduce fine-scale spatial heterogeneity (Fig 10(a), 10(b), 10(d) and 10(e)). These methods rely on temporally aggregated average or a peak VI values for the season derived from different discrete acquisition periods. As a result, the generated yield maps exhibited spatially distinct yield zones driven by VI temporal grouping rather than true yield variability, thereby producing artificial partitions across the landscape [65]. Thus, we observed three sets of partitions in yield maps (left-light green, middle-orange, brown, and right-parrot green) corresponding to different VI acquisition periods. Area to Point Kriging of village level yields provided a smooth reference surface but lacked spatial realism, as it could not leverage spectral or weather covariates necessary to capture fine-scale yield variability (Fig 10(c) and 10(f)).
These maps are analytical raster outputs (Python).
ML and DL yield disaggregation
Spatial visualization of ML- and DL-based disaggregated yield maps revealed clear differences in spatial structure and realism (Fig 11). ML-based maps (Fig 11(a-b) and 11(e-f)) showed sharp contrasts and exaggerated block boundaries, resulting in spatial discontinuities and linear artifacts due to decision tree splits [22,23]. In contrast, the DL models (LSTM, GRU) generated visually smoother and more coherent yield patterns, better representing gradual yield transitions across the landscape (Fig 11(c-d) and 11(g-h)). Between these two DL models, GRU maps displayed stronger structural coherence and preserved within-village variability without over-smoothing.
These maps are analytical raster outputs (Python) produced in this study and visualized using QGIS.
Residual kriging and variogram model selection
To account for spatial dependence in model residuals, multiple variogram models (linear, spherical, Gaussian, and exponential) were evaluated using cross-validation. The cross-validation RMSE values and the corresponding selected variogram models are summarized in Table 7.
Results indicate that the optimal variogram model varied across crops, districts, and predictive approaches rather than a single model being universally applicable. For ML, linear variograms were most frequently selected, suggesting weak or near-linear residual spatial structure. In contrast, exponential variograms were more commonly selected for Bhiwani district across both ML and DL models, reflecting stronger short-range spatial autocorrelation under more heterogeneous agro-climatic conditions.
DL models (GRU and LSTM) predominantly favored spherical variogram models, particularly in Hisar district. This pattern suggests moderate and well-defined spatial dependence in DL residuals, consistent with the ability of RNN to capture large-scale temporal variability while retaining localized spatial structure in residual errors. Gaussian variograms were rarely selected, indicating that residual surfaces generally did not exhibit excessively smooth spatial behavior. These findings underscore the importance of adaptive, data-driven variogram selection for accurately modeling residual spatial dependence prior to kriging.
Residual spatial patterns after kriging
The effectiveness of residual kriging was further evaluated through spatial visualization and quantitative diagnostics. Fig 12 illustrates the spatial distribution of kriged residuals for wheat and mustard yields across Hisar and Bhiwani districts. The residual maps show smoother spatial transitions and a clear reduction in localized error clusters, indicating that kriging effectively corrects spatially structured biases present in the original model outputs.
These maps are analytical raster outputs (Python) produced in this study and visualized using QGIS.
Consistent with these visual patterns, Table 8 quantitatively compares the residual RMSE before and after kriging and reports Moran’s I statistics. The reported p-values correspond to Moran’s I and test the null hypothesis of spatial randomness, with values below 0.05 indicating statistically significant spatial autocorrelation. Results indicate that residual spatial autocorrelation is generally weak or insignificant for ML-based models, particularly for wheat, whereas DL-based models exhibit stronger and statistically significant clustering for both wheat and mustard. Accordingly, larger reductions in residual RMSE after kriging are observed for DL-based approaches, reflecting their greater reliance on spatial correction. These findings confirm that integrating geostatistical correction with DL-based yield predictions improves both numerical accuracy and spatial realism, as evidenced by reduced residual clustering and enhanced spatial coherence in the final yield maps.
Post-kriging ML and DL yield disaggregation
To enhance statistical accuracy and spatial realism, a hybrid method (DL-kriging) was developed. In DL methods, kriging correction effectively reduced systematic regional biases without destroying fine-scale heterogeneity (Fig 13(c-d, g-h)). In contrast, ML-kriging maps (RF-kriging, XGB-kriging) continued to exhibit exaggerated block boundaries, a residual effect of their categorical tree splits in both wheat and mustard maps (Figs 13(a-b, e-f)). Based on these visual inspection and residual behavior, the GRU-kriging approach demonstrated spatial smoothness with preservation of local variability. Consequently, GRU-kriging emerged as the most effective method for yield disaggregation using the band-weather dataset.
These maps are analytical raster outputs (Python) produced in this study and visualized using QGIS.
Validation
Due to the unavailability of pixel-level GT yield data, validation was performed using officially reported village-level and block-level crop yield statistics obtained from the Department of Agriculture and Farmers Welfare, Haryana. These statistics represent aggregated average yields compiled through crop-cutting experiments and administrative reporting, and therefore differ from pixel-level GT data, which would correspond to direct yield measurements at field or pixel scale. For validation, pixel-level predictions generated from each disaggregation approaches were spatially aggregated to the respective village and block level and then compared with reported yield statistics for Bhiwani and Hisar districts (Table 9). Table 9 shows the overall performance of the different disaggregation methodologies.
At the village level, performance exhibited greater variability due to limited training data and local heterogeneity in management. The traditional approaches performed reasonably (R2 = 0.832–0.858) but were less reliable, due to higher MAPE. The ML models achieved the highest accuracy, with R2 ranging from 0.909 to 0.916 and RMSE between 4.93–5.34 q/ha. Their ability to model nonlinear relationships between spectral and weather variables enabled stable and robust predictions even across heterogeneous agro-climatic zones. In contrast, DL models showed moderate performance (R2 = 0.867–0.876; RMSE = 5.67–5.98 q/ha), reflecting the challenge of learning long-term temporal dependencies from limited samples. Applying residual kriging to DL outputs improved their accuracy (R2 ≈ 0.885; RMSE ≈ 5.40 q/ha), demonstrating that even at coarse scales, this hybridization effectively mitigated systematic spatial bias.
At the block scale, where spatial aggregation reduced noise, all models achieved substantially better accuracy. The Weight-Based NDVI method produced plausible spatial patterns and reasonable accuracy (RMSE ≈ 3.09 q/ha; MAPE >11), demonstrating its utility as a simple and data-efficient baseline (Table 8). However, the Percentile-Based approach exhibited unstable behavior (RMSE > 5.60 q/ha, MAPE > 17), reflecting its sensitivity to outliers and its inability to capture temporal crop dynamics. Among all models, the ensemble ML approaches (XGB, RF) achieved the strongest numerical performance. RF (RMSE = 2.45 q/ha) slightly outperformed XGB (RMSE = 2.83 q/ha) in terms of RMSE. Their strength lies in capturing nonlinear interactions between spectral bands and weather variables, making them particularly effective for disaggregating village-level training data into fine-scale pixel predictions. In contrast, the DL models achieved moderate performance, with higher RMSE ≈ 3.06–3.57 q/ha compared to ensemble ML models. Applying residual kriging to the GRU and LSTM predictions reduced errors by approximately 35–45% while retaining the spatial continuity of the DL outputs. Specifically, for GRU the RMSE decreased from 3.07 to 1.85 q/ha (39.6%) and for LSTM from 3.56 to 1.96 q/ha (44.9%), confirming the effectiveness of the hybrid DL-kriging approach.
The performance of crop-specific comparison of traditional, ML, DL, and hybrid (DL-kriging) models for wheat and mustard is presented in Tables 10 and 11, respectively. For wheat (Table 10), DL-kriging hybrids clearly outperformed all others, achieving the lowest RMSE (≈ 1.8–1.9 q/ha) and MAPE (≈ 3.2–3.5%). This indicates that kriging correction effectively compensated for regional biases while retaining the fine-scale detail of DL predictions. For mustard (Table 11), absolute yields were lower and hence percentage errors were higher, but the relative pattern among models was consistent. Incorporating GRU-kriging achieved RMSE = 1.81 q/ha and MAPE = 9.43%, and similarly LSTM-kriging, achieved RMSE = 2.12 q/ha and MAPE = 9.82%.
The strong block-level performance of GRU-Kriging and LSTM-Kriging, demonstrated by low RMSE and MAPE values for both wheat and mustard, provides confidence in the accuracy of pixel-level predictions. As shown in Figs 11 and 13, based on visual comparison and statistical results (Table 9–11), indicate that the hybrid models effectively reduce systematic regional biases while retaining fine-scale spatial variability within village, resulting in smoother and more realistic yield patterns compared to non-kriged ML and DL approaches. Building on this quantitative validation, the spatial disaggregation maps highlighting the practical advantages of hybrid DL-kriging approaches in representing crop yield variability across the landscape.
Overall, The GRU-kriging combination offered the best balance by reducing artificial discontinuities, preserving local gradients. It also provides a robust combination of numerical accuracy and spatial realism, making it highly suitable for high-resolution yield disaggregation across multiple crops. This approach is particularly valuable for applications requiring smoother and spatially coherent outputs, such as precision agriculture, crop insurance, and extension services, while maintaining high predictive accuracy.
Model generalization, limitations, and transferability
The proposed yield disaggregation framework was evaluated using a single growing season and two major crops (wheat and mustard) due to the availability of consistent village-level yield statistics and supporting datasets. While the model was not explicitly validated across multiple years or additional crop types, several aspects of the framework support its potential generalization and transferability.
First, the input features Sentinel-1 SAR, Sentinel-2 optical data, weather variables, and soil properties are globally available and crop-agnostic, enabling application across different regions and cropping systems. Second, the DL component learns generalized temporal-spectral relationships rather than crop-specific empirical thresholds, while the residual kriging step adapts locally by exploiting spatial autocorrelation in prediction errors.
Furthermore, the adaptive variogram selection employed during residual kriging allows the spatial correction process to respond to varying agro-climatic and management conditions, which is essential for model transferability across regions with differing spatial structures. While crop-specific retraining would be required to account for phenological differences, the overall workflow remains unchanged and can be readily applied to other crops and growing seasons where aggregated yield statistics are available.
Future research should explore the integration of higher-resolution and temporally dynamic weather datasets to further reduce prediction uncertainty. In the current experiments, soil properties were treated as static inputs; incorporating temporally varying soil moisture and soil sensor data may improve representation of intra-seasonal yield dynamics. Extending the framework to additional crops, agro-ecological zones, and management systems would further strengthen its generalizability and support broader operational deployment.
Conclusion
In this study, we experimented with different spectral bands, weather data and soil data at pixel level and identified their contribution in disaggregation of macro level yield values to pixel level. This pixel level disaggregated yield data is useful to estimate household yield and avoid farmer specific response bias. Spectral bands from Sentinel-1 and Sentinel-2 along with weather features were identified as the best predictors for yield disaggregation using village yields. The experimental results in the study proved that the proposed integrated framework of geostatistical and DL methods improve the disaggregation performance comparison to non-integrated approach involving ML, DL and statistical models alone. The proposed DL-kriging framework reduced RMSE and MAPE by approximately 35–45% while generating spatially coherent yield maps that preserve within-village variability. Importantly, this framework explicitly separates the roles of data-driven learning and spatial correction: DL captures large-scale temporal and spectral relationships, while kriging exploits residual spatial autocorrelation to correct systematic regional biases. This complementary interaction makes the framework transferable and applicable to new crop or other regions where only aggregated yield statistics are available.
From a practical perspective, pixel-level yield estimates derived from the proposed framework can support household-level yield assessment while reducing farmer-specific response bias inherent in survey-based approaches. The generated fine-resolution yield maps are particularly relevant for agricultural monitoring, targeted resource allocation, and evidence-based policy planning in smallholder-dominated regions. Integration of this framework with crop insurance schemes and government monitoring platforms could further enable near-real-time yield loss assessment and transparent compensation mechanisms. To transfer the benefits of such disruptive technologies to the farmers, Government of India has initiated Digital Agriculture Mission which allows registration of farmers along with crop and land details in each season. The proposed methodology shall be useful in monitoring the farm fields and also take timely decisions regarding import/ export of a commodity based on unbiased advance estimates.
Supporting information
S1 File. Village-level observed and predicted crop yields across different modeling approaches.
The file provides village-level actual and predicted crop yields (quintal/ha) across proportional, machine-learning, deep learning, and hybrid DL-kriging approaches, along with associated performance metrics (RMSE, MAE, MAPE, and R2).
https://doi.org/10.1371/journal.pone.0344081.s001
(XLSX)
S2 File. Training input features used for model development.
The file contains training inputs derived from remote sensing, weather, and static variables, along with associated yield values used for model development.
https://doi.org/10.1371/journal.pone.0344081.s002
(XLSX)
Acknowledgments
The authors are grateful to the Director, ICAR-NIAP, for the necessary logistic and technical support in the conduct of the study. This manuscript is an output from an ongoing research project at ICAR-NIAP. Authors also acknowledge the Director ICAR-IASRI and the Director ICAR-IARI for facilitating technical resources and other necessary support for the study.
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