Predicting Paddy Rice NDVI from Meteorological Variables Using Linear Regression

Technical Summary: Predicting Paddy Rice NDVI from Meteorological Variables Using Linear Regression

Problem Statement
Vegetation indices, particularly the Normalized Difference Vegetation Index (NDVI), are critical for monitoring crop growth and health. While satellite-derived NDVI offers extensive spatial coverage, it suffers from temporal resolution limitations due to weather conditions (e.g., clouds, precipitation) and observation cycles. Conversely, ground-based sensors provide high-frequency, in-situ data but lack spatial breadth. These limitations hinder timely resource allocation and decision-making in crop management. Although various machine learning (ML) approaches, including deep learning models like Long Short-Term Memory (LSTM), have been proposed to predict NDVI using climate data, they often require complex physical principles or large datasets and lack interpretability. This study addresses the need for a rapid, accurate, and interpretable NDVI prediction model for paddy rice that relies on meteorological data and ground-based spectral reflectance sensors, specifically tailored for agricultural environments where computational efficiency is paramount.

Methodology
The study developed and evaluated predictive models using meteorological variables to estimate the daily mean NDVI of paddy rice.

• Data Collection: Data were collected over five growing seasons (2020–2024) from a single paddy field in Sacheon-si, South Korea. Meteorological data (precipitation, humidity, solar radiation, temperature, wind speed) were recorded hourly by an ATMOS-41 automatic weather station. NDVI was measured hourly using a ground-based fixed spectral reflectance sensor (SRS).
• Input Variables: Eight features were considered: Daily Mean Temperature (MTEM), Accumulated Temperature (ATEM), Daily Solar Radiation (SOL), Accumulated Solar Radiation (ASOL), Daily Precipitation (DPR), Accumulated Precipitation (APR), 3-day Antecedent Precipitation (PPR), and Days After Transplanting (DAT).
• Model Configuration: The study generated 255 distinct models representing all possible combinations of the eight input variables. Two primary algorithms were employed:
  1. Multiple Linear Regression (MLR): Modeling linear relationships between dependent and independent variables.
  2. Polynomial Regression (PR): Extending linear regression to capture non-linear relationships using quadratic (PR2) and cubic (PR3) terms.
• Training and Validation: Models were trained using Stochastic Gradient Descent (SGD) with Elastic Net regularization to prevent overfitting. Hyperparameters were optimized via GridSearchCV with five-fold cross-validation.
• Evaluation Metrics: Performance was assessed using Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and the Coefficient of Determination ($R^2$).

Key Results

• Model Performance: The Polynomial Regression (PR) models significantly outperformed the Multiple Linear Regression (MLR) models. The best-performing PR3 model (C8-1, using all eight variables) achieved an $R^2$ of 0.754, compared to the best MLR model's $R^2$ of 0.528.
• Non-Linearity: The PR2 model demonstrated that capturing non-linear relationships was crucial. Notably, a single-variable PR2 model using only "Days After Transplanting" (DAT) achieved an $R^2$ of 0.582, outperforming multi-variable MLR models (e.g., the five-variable MLR model C5-2 had an $R^2$ of 0.528).
• Variable Importance:
  • High Influence: DAT, daily mean temperature, accumulated temperature, daily solar radiation, and accumulated solar radiation were the most influential predictors.
  • Cumulative vs. Daily: Cumulative variables (ATEM, ASOL) exhibited stronger explanatory power than their daily mean counterparts (MTEM, SOL), suggesting long-term climatic conditions drive crop vigor more than short-term fluctuations.
  • Low Influence: Precipitation-related variables (DPR, APR, PPR) showed relatively low predictive capability.
• Complexity vs. Accuracy: Increasing model complexity from PR2 to PR3 yielded negligible performance improvements (e.g., $R^2$ increased from 0.738 to 0.754 for the full-variable model). The study identified that models with four or more variables in PR2 (e.g., C4-60 with $R^2$ = 0.730) offered a practical balance between accuracy and simplicity.

Significance and Claims
The authors claim that linear regression-based models, specifically when enhanced with polynomial terms, offer a highly effective alternative to complex deep learning models (like LSTM) for agricultural NDVI prediction. The study highlights three main advantages:

1. Interpretability: Unlike "black-box" deep learning models, linear and polynomial regression models allow for clear identification of influential meteorological factors.
2. Computational Efficiency: These models are computationally lightweight, making them suitable for real-time decision-making in agricultural settings.
3. Robustness with Limited Data: The models demonstrated stable performance even with smaller datasets, which is often a constraint in specific agricultural field studies.

The paper concludes that while deep learning models excel at capturing long-term dependencies, the proposed linear regression approach provides comparable predictive accuracy with greater transparency and efficiency. The study suggests that for paddy rice monitoring, focusing on cumulative temperature and solar radiation alongside the growth stage (DAT) is more critical than precipitation data, particularly in the humid climate of the study area. The authors recommend future research into hybrid models that integrate the strengths of both linear and deep learning approaches, as well as investigations into model performance under extreme weather conditions and across different crop types.