A Variational Method for Estimating Surface Fluxes with Mass Conservation Constraint

Abstract

n the basis of the similarity theory of the atmospheric surface layer and the mass conservation principle, a new scheme using a variational method is developed to estimate the surface momentum and sensible and latent heat fluxes. In this scheme, the mass conservation is introduced into the cost function as a weak physical constraint, which leads to an overdetermined system. For the variational method with mass conservation constraint, only the conventional meteorological observational data are taken into account. Data collected in the Yellow River Source Region Climate and Environment Observation and Research Station at Maqu, China, during 11?25 August 2010 are used to test this new scheme. Results indicate that this scheme is more reliable and accurate than both the flux-profile method and the variational method without mass conservation constraint. In addition, the effect of the weights in the cost function is examined. Sensitivity tests show that the fluxes estimated by the proposed scheme are insensitive to the stability functions explored in the cost function and measurement errors.