A four‐layer model for the heat budget of homogeneous land surfaces

Abstract The model is an explicit solution of the equations which define the conservation of heat and water vapour in the system consisting of uniform vegetation and soil. The vegetation has two layers, the first extending from a reference height in the atmosphere to the virtual sink for momentum and the second from the virtual sink to the soil surface. Soil between the surface and the damping depth is divided into an upper, completely dry layer and a lower wet layer. Throughout the system, differences of potential per unit flux are specified by resistances, notably the conventional surface resistance governing the loss of vapour from foliage and a new soil resistance, assumed proportional to the accumulated loss of water by evaporation from the soil surface, which is proportional to the square root of elapsed time. Since the total energy available to the system is limited by absorption of radiation, the increase of transpiration from foliage as it expands decreases evaporation from the soil. Conversely, as soil dries, transpiration rate per unit of foliage area increases. This interaction of vapour fluxes is governed by the behaviour of the saturation vapour pressure deficit within the vegetation, identified as a major variable. General implications of the model are consistent with observations and estimates of evaporation rate from a stand of wheat grown in Arizona agree well with measurements from lysimeters. The model is applicable to a wide range of problems in agricultural meteorology and hydrology. With simplification, it could be used to obtain surface exchanges of sensible and latent heat in atmospheric general circulation models.