Multivariate Time Series Models for Soil Nutrient and Yield Prediction in Site Specific Integrated Nutrient Management

In agriculture, precise prediction of soil nutrient dynamics and crop yield under Site-Specific Integrated Nutrient Management (SSNM) is essential for optimizing resource efficiency and enhancing sustainability. SSNM can be integrated with LSTM, ARIMA, or SARIMA models to optimize nutrients based on real-time or forecasted data. While SSNM focuses on personalized nutrient requirements for specific sites, these time series models, like LSTM (Long Short-Term Memory), ARIMA (AutoRegressive Integrated Moving Average), and SARIMA (Seasonal ARIMA), can be used to predict environmental factors such as weather patterns, crop growth conditions, and soil nutrient levels over time. This study applies advanced multivariate time series models, including Long Short-Term Memory (LSTM) networks, AutoRegressive Integrated Moving Average (ARIMA), and Seasonal ARIMA (SARIMA) to establish their complementary role in SSNM implementation. These models help to predict the dynamics of soil nutrients such as nitrogen (N), phosphorus (P), and potassium (K) along with crop yield over a 25-year (2025–2050). LSTM demonstrated superior predictive accuracy for soil nutrient dynamics (R² = 0.99), while ARIMA outperformed for crop yield predictions (R² = 0.58), effectively capturing temporal fluctuations. However, the modest performance of ARIMA for yield prediction due to exogenous variables, seasonal and structural trends. The results highlight the strengths of these models in supporting SSNM by enabling accurate forecasts of key parameters for data-driven decision-making. This research underscores the importance of integrating dynamic modeling approaches with SSNM to enhance agricultural productivity, improve resource use efficiency, and support sustainable crop management strategies.