Mathematical Modelling of Wheat Yield in Ranchi, Jharkhand Using Rainfall and Temperature Data

Abstract

This work integrates long-term climate records (1975–2024) with district wheat production data (2003–2024) to develop a mathematical model to assess the effects of temperature and rainfall on wheat crop output in Ranchi, Jharkhand. We suggested a model that incorporates effective rainfall and accumulated thermal time (degree days) into a logistic growth framework. With wheat yield showing greater sensitivity to GDD (elasticity 0.65) than to rainfall (elasticity 0.35), the model described approximately 72% of yield variability by estimating accumulated growing degree days (GDD) and integrating rainfall into a logistic growth framework (R2 = 0.72). The findings show that accumulated thermal time is the main factor influencing wheat productivity in this area, even though sufficient rainfall supports soil moisture availability. The RMSE of around 300 kg/ha and R2 of 0.72 were attained using the suggested model. This study emphasizes the potential yield changes under anticipated climate scenarios and the significance of climatic factors in wheat productivity. Adaptive management in changing climatic conditions can benefit from these insights.

Introduction

Wheat, a major rabi crop in eastern India, particularly in Ranchi district, benefits from favorable post-monsoon soil moisture and cool temperatures but remains highly sensitive to climate variability, especially rainfall and temperature changes. While global studies have used temperature-based degree-day concepts to assess crop development, integrated mathematical models combining both rainfall and temperature for wheat growth are rare in eastern India.

This study develops a mathematical model for wheat yield in Ranchi by incorporating cumulative temperature (growing degree days, GDD) and rainfall into a logistic growth framework. The model relates wheat yield growth rate to climatic factors through sensitivity coefficients and thresholds, using long-term data from 1975-2024 (climate) and 2003-2024 (yield). Statistical methods including nonlinear least squares and residual normality tests ensure robust parameter estimation and model validation.

Results show that Ranchi has stable seasonal temperatures (~23.8°C) but highly variable rainfall (845–1690 mm annually). Wheat yield averages 2.54 t/ha with similar variability to rainfall, indicating precipitation’s key role in yield fluctuations. Correlation analysis reveals a strong positive relationship between wheat yield and GDD (r=0.68), and a moderate positive relationship with rainfall (r=0.43), confirming the importance of both heat accumulation and moisture for crop productivity.

The logistic model calibrated with these variables achieved a good fit (R²=0.72, RMSE=0.31 t/ha), effectively capturing the influence of climate on wheat yield. Stability analysis identified optimal conditions for yield stability—rainfall between 1000-1400 mm and GDD above 2600. The study highlights that integrating thermal and moisture data via logistic growth models provides valuable forecasts and insights for managing wheat production under climate variability in eastern India.

Conclusion

This study created a climate-integrated mathematical model that effectively represented the main factors influencing Ranchi\'s wheat production fluctuation over a 22-year period. With elasticities of roughly 0.65 and 0.35, respectively with GDD and rainfall, the results showed that accumulated growing degree days (GDD) have a greater impact on wheat yields than annual rainfall. With a strong R2 value of 0.72, the logistic model structure aligns well with accepted physiologic and agronomic concepts and supports past findings. The random residual patterns of predicted wheat yield and Shapiro-Wilk test support model robustness. This study underscores the primary role of accumulated temperature in wheat productivity, while rainfall ensures moisture sufficiency up to a saturation point, beyond which additional rain offers diminishing returns. Yield improvements with rising temperature are feasible but bounded by physiological limits. The model warns against over-reliance on rainfall due to its plateauing effect beyond a threshold. In order to enhance resilient agricultural planning for eastern India, future research could improve this strategy by adding cultivar-specific characteristics, soil moisture dynamics, and climate projections.

References

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Copyright

Copyright © 2025 Chandan Kumar Pandit, Shilpa Mahapatra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.