Indirect effect of diabatic heating on Mei-yu frontogenesis

Abstract

Mei-yu fronts are accompanied with the formation of frontal clouds. In addition to its direct effect on Mei-yu fronts through the modification of atmospheric temperature, diabatic heating related to clouds formation also influences frontogenesis indirectly by changing local atmospheric circulation. To quantify such indirect effects, piecewise potential vorticity (PV) inversion is adopted to decompose the process of deformation frontogenesis into several parts associated with distinct PV anomalies. The balanced flow associated with the interior-level diabatic PV anomaly emerges as the most stable and important contributor to the total deformation frontogenesis with the effect of local diabatic PV anomaly in the frontal zone outweighing the effect of remote diabatic PV anomaly. Lower-boundary thermal anomaly (i.e., surface cooling associated with frontal clouds formation) and mean flow provide weak negative and positive contributions to the deformation frontogenesis, respectively. The balanced flow associated with the upper-level PV perturbations is weak at lower-levels, especially in the vicinity of the front zone and thus has negligible contributions to the Mei-yu frontogenesis. The indirect effect of diabatic heating on Mei-yu frontogenesis is generally weaker in magnitude compared to the direct effect of temperature modification as well as the impact of moisture depletion that is also tied to clouds formation. The results presented here add further evidences about the importance of cloud feedback to the evolution of Mei-yu fronts and suggest the necessity of improved model representations of cloud processes in achieving a better simulation and prediction of Mei-yu rainfall.

Appendix

Based on the non-divergent approximation ($\mathrm{V}\approx {\mathrm{V}}_{\psi }=\mathrm{k}\times \nabla\Psi$), hydrostatic balance assumption ($\partial\Phi /\partial \pi =-\theta$) and a “full” linearization method (see Davis and Emanuel 1991; Davis 1992 for details), the perturbation equations to perform the piecewise PV inversion are:

$${\nabla }^{2}{\Phi }_{n}=\nabla \bullet (f\nabla\Psi )+\frac{2}{{a}^{4}{\mathrm{cos}}^{2}\varphi }\times \left({\frac{{\partial }^{2}{\Psi }^{*}}{\partial {\lambda }^{2}}\frac{{\partial }^{2}{\Psi }_{n}}{\partial {\varphi }^{2}}+\frac{{\partial }^{2}{\Psi }^{*}}{\partial {\varphi }^{2}}\frac{{\partial }^{2}{\Psi }_{n}}{\partial {\lambda }^{2}}-2\frac{{\partial }^{2}{\Psi }^{*}}{\partial \lambda \partial \varphi }\frac{{\partial }^{2}{\Psi }_{n}}{\partial \lambda \partial \varphi }}\right),$$

(8)

$${q}_{n}=\frac{g\kappa \pi }{p}\left[\left(f+{\nabla }^{2}{\Psi }^{*}\right)\frac{{\partial }^{2}{\Phi }_{n}}{\partial {\pi }^{2}}+\frac{{\partial }^{2}{\Phi }^{*}}{\partial {\pi }^{2}}{\nabla }^{2}{\Psi }_{n}-\frac{1}{{a}^{2}{\mathrm{cos}}^{2}\varphi }\left(\frac{{\partial }^{2}{\Psi }^{*}}{\partial \lambda \partial \pi }\frac{{\partial }^{2}{\Phi }_{n}}{\partial \lambda \partial \pi }+\frac{{\partial }^{2}{\Phi }^{*}}{\partial \lambda \partial \pi }\frac{{\partial }^{2}{\Psi }_{n}}{\partial \lambda \partial \pi }\right)-\frac{1}{{a}^{2}}\left(\frac{{\partial }^{2}{\Psi }^{*}}{\partial \varphi \partial \pi }\frac{{\partial }^{2}{\Phi }_{n}}{\partial \varphi \partial \pi }+\frac{{\partial }^{2}{\Phi }^{*}}{\partial \varphi \partial \pi }\frac{{\partial }^{2}{\Psi }_{n}}{\partial \varphi \partial \pi }\right)\right],$$

(9)

where ${q}_{n}$ is a specific PV anomaly; ${\Phi }_{n}$ the geopotential anomaly; ${\Psi }_{n}$ the non-divergent streamfunction anomaly; $f$ the Coriolis parameter; $a$ the radius of the Earth; $\varphi$ the latitude; $\lambda$ the longitude; $\pi ={{\mathrm{C}}_{p}(p/{p}_{0})}^{{\mathrm{C}}_{p}/R}$ is the Exner function. ${\Psi }^{*}$ and ${\Phi }^{*}$ are defined by the mean plus half of the total anomaly, i.e., ${\left[\right]}^{*}=\left[\stackrel{-}{}\right]+\frac{1}{2}{\sum }_{n=1}^{N}{\left[\right]}_{n}$. Given the three-dimensional distribution of ${q}_{n}$ and the boundary conditions (i.e., the Neumann conditions at lower and upper boundaries and Dirichlet conditions on the lateral boundaries), the two equations (i.e., 8, 9) with two unknowns (i.e., ${\Phi }_{n}$,${\Psi }_{n}$) can be solved through iteration.