Environmental system dynamics analysis and prediction based on big climate data and differential equation models

Introduction Environmental systems are governed by complex interactions among climatic variables and ecological processes. Accurate analysis and prediction of these dynamics require the integration of observational data with mathematical models. In this study, a data-driven framework is proposed that combines large-scale climate data with differential equation modeling to analyze and forecast environmental system behavior in Zhengzhou, China. Methods Daily climate data from 2015 to 2025 were collected for Zhengzhou, including air temperature, relative humidity, wind speed, solar radiation, and precipitation. Descriptive and correlation analyses were performed to identify key relationships among variables. A differential equation model was formulated to represent the temporal evolution of the environmental system. Model parameters were estimated from the observed data, and numerical simulations were conducted to evaluate system dynamics. Model performance was assessed using root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (R 2 ). Forecasts were generated for the period 2026 to 2030. Results Descriptive analysis showed mean temperature and humidity values of approximately 10 °C and 60%, respectively, while mean solar radiation was about 200 kWh m –2 day –1 . Correlation analysis revealed a strong positive association between temperature and solar radiation (r ≈ 0.95), which indicated their dominant influence on environmental variability. Numerical simulations showed that the modeled environmental system state remained stable within the range 0.84 to 0.93, with a mean value of 0.89. Validation results demonstrated good predictive accuracy, with RMSE = 0.041, MAE = 0.032, and R 2 = 0.87. Forecasts indicated a gradual increase in environmental system values from 0.94 in 2026 to 0.98 in 2030. Discussion The results demonstrate that the integration of climate big data with differential equation models provides a reliable and interpretable approach for analyzing environmental dynamics and generating long-term forecasts. The strong predictive performance suggests that this framework can support environmental assessment and planning in regions affected by climate variability. The proposed methodology is readily transferable to other locations and environmental applications.