Radiative–Convective Equilibrium over an Idealized Land Surface with Fixed Soil Moisture

Abstract Radiative–convective equilibrium (RCE) is an idealized model of the atmosphere in which surface fluxes exactly balance radiative cooling. While recent work has shown RCE over land is a reasonable first-order model of continental climate, previous RCE studies have mainly focused on ocean surfaces. Unlike the ocean, the land surface has limited water and a low heat capacity. Here, we use theory and simulations to understand RCE over an idealized land surface with fixed soil moisture, a logical next step in the land climate model hierarchy. The fixed soil moisture case is also relevant to irrigated areas, groundwater-fed ecosystems, and broader debates about potential evapotranspiration (PET), aridity, and their changes in a warming world. We derive a parsimonious gray gas theory that reproduces major aspects of cloud-permitting simulations of RCE over an idealized land surface and permits analytic solutions for several special cases. Over fixed dry surfaces, the theory shows that hydrological sensitivity follows Clausius–Clapeyron scaling, considerably greater than the typical 2%–3% K −1 over oceans. Over fixed saturated surfaces, the theory reconciles divergent explanations for hydrological sensitivity based on surface and atmospheric energy budgets, with changes in near-surface relative humidity playing a key role. Finally, the theory shows that PET primarily scales with surface net radiation, rather than temperature or vapor pressure deficit, in agreement with recent empirical findings. The predicted PET scaling implies only modest changes in global mean aridity with warming, rather than the large increases implied by some prior studies. Biological plant responses to increasing carbon dioxide (CO 2 ) are not essential to this explanation. Significance Statement Will global warming make the world more arid? There has been a lot of debate on this question, with some arguing it will drastically increase aridity. Answering it requires understanding changes in atmospheric water demand: the evapotranspiration that would occur if the land surface was always kept saturated. We use basic physics to understand climate over land surfaces in which soils are kept saturated—and, more broadly, fixed at any level of saturation, from wet to dry. Our results support the view that global warming will not drastically increase aridity, on average. We also show that rainfall increases with warming at a faster rate over fixed dry land surfaces than it does on Earth (where land surfaces change from dry to wet and back again).