Asian Journal of Pure and Applied Mathematics

This study addresses the research on calibrating Lorenz system parameters to represent regional temperature and rainfall dynamics in the Arid and Semi-Arid Lands (ASALs) of Kenya. Beginning from the governing equations of atmospheric convection, the classical Lorenz (1963) system and its stochastic extension are formulated as a mathematical framework for representing climate variability in ASAL environments. A systematic calibration framework is developed to relate the three Lorenz parameters (σ, ρ, β) to physically meaningful atmospheric processes corresponding to heat diffusion, thermal forcing, and geometric decay, respectively. Parameter estimation is achieved through penalised nonlinear least-squares optimisation using observed monthly temperature and rainfall climatologies from eight representative ASAL meteorological stations (Garissa, Wajir, Mandera, Turkana, Marsabit, Isiolo, Moyale, and Lodwar), covering the two principal rainfall seasons. Model outputs are mapped to observed climate variables through linear transformation functions, while calibration performance is evaluated using standard statistical measures including the Nash–Sutcliffe Efficiency (NSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Pearson correlation coefficient, and Percent Bias (PBIAS). The calibrated Lorenz parameters reproduce the observed seasonal temperature and rainfall patterns with good agreement, demonstrating that the Lorenz system provides a mathematically consistent and physically interpretable framework for representing the essential climate dynamics of Kenya’s ASAL regions. These findings establish a robust foundation for subsequent investigations into climate predictability, regime transitions, and early-warning applications based on the calibrated Lorenz framework.