Analytical asymptotic solutions to determine interactions between the planetary boundary layer and the Earth's surface

Abstract

This study derives an asymptotic analytical solution to calculate land skin temperature, planetary boundary layer (PBL) temperature, and turbulent heat fluxes over arid and wet ground surfaces. Applying the analytical solution to field data, the turbulent heat fluxes and the daytime canopy resistance (which are difficult to measure directly) can be easily determined on the basis of solar radiation and atmospheric radiation measurements, as well as other commonly available meteorological data. The results can be compared with a Lagrangian soil-plant-atmosphere model. Using the derived canopy resistance as input for the Lagrangian model, the simulated PBL temperature has a higher correlation coefficient with the real data than two other canopy schemes. The analytical solution proves that the mean skin temperature is slightly higher than the mean PBL temperature, and its amplitude is always larger than that of PBL temperature in general. An equation for determining the half-life of either PBL temperature or skin temperature is derived. The half-life is the time needed for the initial temperatures of the PBL or a land surface to decay to 50%. Note that the temperatures will alter in response to variations in the meteorological conditions such as changes in solar radiation. Over bare ground, vegetation, snow or ice, the half-lives are similar to8 hours. For a body of water, it is 1.4 months with a thermocline depth of 100 m. Although the algorithm of determining canopy resistance is verified in an urban area in Taiwan, it is likely to be valid worldwide.