Numerical modeling of heat and water vapor transport through the interfacial boundary layer into a turbulent atmosphere

A stochastic numerical model is developed to simulate heat and water vapor transfer from a rough surface through a boundary layer into the fully turbulent atmosphere. The so-called interfacial boundary layer is conceptualized as a semistagnant layer of air in the roughness cavities at the surface into which the smallest eddies penetrate to random approach distances and with random inter-arrival times, carrying away energy, molecules, or any other scalar admixture. The model makes use of the one-dimensional transient heat conduction equation where the boundary conditions are updated in time and space by random deviates from a general gamma distribution. The one-dimensional transfer equation is solved by the implicit finite difference method which allows conversion to a standard tridiagonal matrix equation. The algorithm is simple to implement and allows generation of large ensembles for statistical analysis in short periods of time. The simulations were used to compare and contrast earlier results obtained for heat and mass transfer through Earth surface-air interfaces. It is shown that even small increases in boundary-layer thickness may significantly enlarge the inverse Stanton roughness number St kappa(-1) reducing heat transfer from the surface. Review of experimental work suggests an updated relation for the heat transfer coefficient from bare soils into the atmosphere. Work is under way to incorporate the results into the atmospheric and remote sensing research related to the determination of the Earth's sensible and latent heat fluxes.