A mathematical model is presented to assess the impact of climatic anomalies and convective behavior on climatic variability at the Earth's surface, focusing on soil-atmosphere interaction. This model is applied within a control volume covering the Hadley cell, allowing for the verification of convective coupling and prediction of the effects of the studied climatic variation. The mathematical analysis delves into the soil-atmosphere interaction within the control volume, quantifying variations in water evaporation levels in bodies of water and soil, water vapor content in clouds, adiabatic gradient in the atmosphere, relative humidity, and condensation, taking into account average solar radiation. This developed model is a robust foundation for reproducing convective climate effects, pinpointing coupling forces, and validating models in local climate studies.