An Analytic Theory of Near-Surface Relative Humidity over Land

Abstract

Abstract There is no simple explanation for the spatial structure of near-surface relative humidity over land. We present a diagnostic theory for zonally and temporally averaged near-surface relative humidity (RH) over land based on energy budgets of an atmospheric column in radiative–convective equilibrium. The theory analytically relates RH to the surface evaporative fraction (EF), has no calibrated parameters, and is quantitatively accurate when compared with RH from a reanalysis, and with cloud-permitting simulations over an idealized land surface. The theory is used to answer two basic questions. First, why is RH never especially low (e.g., 1%)? The theory shows that established lower bounds on EF over land and ocean are equivalent to lower bounds on RH that preclude particularly low values, at least for conditions typical of the modern Earth. Second, why is the latitudinal profile of RH over land shaped like the letter W, when both specific humidity and saturation specific humidity essentially decline monotonically from the equator to the poles? The theory predicts that the latitudinal profile of RH should look more like that of water stored in the soil (which also exhibits a W-shaped profile) than in the air (which does not).