Sorption-based atmospheric water harvesting (SAWH) driven by photovoltaic (PV) waste heat offers a promising pathway for decentralized water-electricity co-production, especially in regions facing concurrent water and energy scarcity. However, most existing studies evaluate reported sorbents under fixed operating conditions, and a quantitative framework that links adsorption characteristics to climate-driven system performance is still lacking. This study develops an adsorption-potential-based parametric framework to optimize idealized water adsorption isotherms under realistic climatic forcing by maximizing cumulative water yield. The framework explicitly quantifies optimal isotherm parameters, their sensitivities, and tolerance ranges across different climates. The results reveal that step-shaped adsorption behaviors are broadly favored across diverse climatic conditions, with the optimal adsorption-potential step position exhibiting pronounced spatial and seasonal variability governed by the local diurnal adsorption-potential window. Humid climates are capacity-controlled, with system performance governed by maximum uptake (sensitivity >90 %), a low optimal adsorption-potential step position of 1200 J mol(-1), and broad tolerance bands reaching 800 J mol(-1). In contrast, arid climates or climates with pronounced seasonal variability are step-controlled, where step-related parameters show sensitivities exceeding 60%, the optimal step position shifts to 1.5 times higher values, and the tolerance band narrows by 37.5%, requiring precise alignment with the climatic driving window. Furthermore, a regime dominance index (R) is introduced to quantitatively characterize the governing mechanism. For regions with pronounced climatic variability, monthly optimization outperforms annual optimization, delivering additional water-yield improvements of up to 18.57%. These results establish a unified framework for climate-driven optimization and the design of idealized sorbents in PV- SAWH systems.