Resolution dependence in the Zhang-McFarlane deep convection parameterization and impact of CAPE calculation

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Description

Atmospheric models are particularly prone to errors introduced by resolution changes due to nonlinearities in convection and its semi-resolved nature. The issue is most prominent when the grid spacing impinges on the dynamical scale of clouds and more information than available within the local grid column is needed to properly represent the cloud effects. We analyzed the behavior of the Zhang-McFarlane deep convection parameterization to understand which variables and assumptions impact its resolution dependence. We specifically focused on the parameterization’s ability to mimic the vertical transport of moist static energy (w’h’) as simulated by two cloud-resolving models (CRM) with 2 km grid spacing. One model was configured with a doubly periodic, quasi-equilibrium scenario, and the other was configured with forced boundaries for a real-world case representing the Atmospheric Radiation Measurement (ARM) Madden-Julian Oscillation Investigation Experiment (AMIE) in the Indian Ocean. Using the 2 km simulations we constructed a series of coarser grids by averaging the 2 km results to grid spacings of 8 to 256 km. These coarser grid columns were then used to drive an offline version of the parameterization and its output compared to the 2 km CRM outputs, which were used as a proxy for realistic parameterization behavior. We found that the parameterization was unable to reproduce the CRM tendency of having smaller w’h’ at smaller grid spacings. Instead the parameterization only had this for the strongest convection, while it had opposite behavior for weak convection. Our analysis showed that this behavior could be explained by the behavior of the grid-scale convective available potential energy (CAPE) tendency used in the parameterization’s quasi-equilibrium based closure. We introduced a simple averaging algorithm that enabled consistent application of the convective quasi-equilibrium-based closure at high resolution and improved the resolution dependence of the Zhang-McFarlane–produced subgrid-scale transport significantly. We also found that the correlation between the CRM and parameterized w’h’ gradually worsened as the grid spacing shrank, with a correlation of 0.89 at 256 km grid spacing and only 0.54 at 8 km grid spacing. This was due, in part, to increased variability of the CRM results at fine resolution, which the parameterization did not reproduce. This pointed to the need for stochastic treatments to capture small-scale cloud variability.