Global Ground Validation of β in the Radiative-Convective Equilibrium Energy Budget Theory for Land Relative Humidity

The near-surface relative humidity (RH) over land, as a key parameter of land-atmosphere interaction, is crucial for the surface energy balance, water cycle, and ecosystem functions. McColl et al. present a diagnostic theory for zonally and temporally averaged near-surface relative humidity (RH) over land based on the energy budgets of an atmospheric column in radiative–convective equilibrium. In this theory, the core parameter β is theoretically approximately constant 4, but its applicability in measured data has not been fully verified. This study utilized the measured data from global FIUXNET sites to comprehensively examine the applicability of β in this theory.It analyzed the influences of latitude, dry and wet climate conditions, and distance from the seaside on β, and explored the stability and applicable scope of β at different time scales. The results show that β under the measured data has significant spatiotemporal variability and systematically deviates from the theoretical value of 4. β is significantly positively correlated with latitude and the dry-wet index (AI) : in high-latitude regions and more humid conditions, the value of β tends to increase, is less affected by the distance from the sea, and β can also be applied on smaller time scales (weekly scale and monthly scale). This study reveals the empirical characteristics and limitations of β in the Radiative-Convective Equilibrium Energy Budget Theory for Land Relative Humidity, providing a key basis for improving the terrestrial RH theoretical model and guiding the time scale of RH analysis.