Retrieval of eddy thermal conductivity in the weakly nonlinear Prandtl model for katabatic flows

Abstract

Because the nonlinearity of actual physical processes can be expressed more precisely by the introduction of a nonlinear term, the weakly nonlinear Prandtl model is one of the most effective ways to describe the pure katabatic flow (no background flow). Features of the weak nonlinearity are reflected by two factors: the small parameter e and the gradually varying eddy thermal conductivity. This paper first shows how to apply the Wentzel–Kramers–Brillouin (WKB) method for the approximate solution of the weakly nonlinear Prandtl model, and then describes the retrieval of gradually varying eddy thermal conductivity from observed wind speed and perturbed potential temperature. Gradually varying eddy thermal conductivity is generally derived from an empirical parameterization scheme. We utilize wind speed and potential temperature measurements, along with the variational assimilation technique, to derive this parameter. The objective function is constructed by the square of the differences between the observation and model value. The new method is validated by numerical experiments with simulated measurements, revealing that the order of the root mean squre error is 10–2 and thus confirming the method’s robustness. In addition, this method is capable of anti-interference, as it effectively reduces the influence of observation error.