An Economical PDF-Based Turbulence Closure Model for Cloud-Resolving Models and Global Climate Models
Abstract
The representation of boundary layer clouds in GCMs has long been a challenge to climate modelers. The Multiscale Modeling Framework (MMF) embeds a coarse-grid 2D cloud-resolving model (CRM) in every GCM grid column. In MMF, the challenge becomes improving boundary layer cloud representation in coarse-grid CRMs in an economical way. Our solution has been to integrate several existing components: a prognostic SGS TKE equation, the assumed joint PDF method of Golaz et al. (2002), the diagnostic second-moment closure of Redelsperger and Sommeria (1986), the diagnostic closure for /line{w'w'w'} by Canuto et al. (2001), and a turbulence length scale related to the square root of subgrid-scale (SGS) turbulence kinetic energy (TKE) (Teixeira and Cheinet 2004) and eddy length scales. In comparison to the implementation of Golaz et al. (2002), our turbulence closure requires only one extra prognostic instead of seven. This makes our closure more economical, more portable, and better behaved. Our closure also uses a novel turbulence length scale that produces excellent scalablity with horizontal resolution. We implemented our approach in a CRM and and tested it against large-eddy simulation (LES) results. We also implemented it in a MMF and evaluated the results using global observations. The CRM that we used is SAM (System for Atmospheric Modeling) developed by Marat Khairoutdinov (Khairoutdinov and Randall 2003). SAM-PDF incorporates our new turbulence closure model. In SAM-PDF, the SGS TKE is prognosed, the turbulence length scale is related to the SGS TKE and eddy length scales, SGS condensation is diagnosed from the assumed joint PDF, the SGS buoyancy flux is diagnosed from the assumed joint PDF, and additional moments required by the PDF closure are diagnosed, so no additional prognostic equations are needed. The turbulence length scale is needed to parameterize the TKE dissipation rate and the eddy diffusivity. Cheng et al. (2010) showed that eddy diffusivity schemes function well if the profile of the SGS TKE is correct. Teixeira and Cheinet (2004) showed that a length scale proportional to a constant time scale and the square root of the TKE works well for the convective boundary layer. Several LES benchmark cases were used to test SAM-PDF in a 2D CRM configuration: clear convective boundary layer, trade-wind cumulus, precipitating shallow cumulus, continental shallow cumulus, a stratocumulus to cumulus transition, and deep oceanic convection (GATE "Giga-LES"). Our evaluations using LES results show that SAM-PDF can realistically represent many boundary layer cloud regimes in CRMs with horizontal grid sizes of 0.5 km or larger, with virtually no dependence on horizontal grid size. We also performed a test of our closure within a MMF. SPCAM (Super-Parameterized Community Atmospheric Model) and SPCAM-PDF were both run in a T42 configuration with 30 vertical levels. The horizontal grid size of the embedded CRMs was 4 km, and its vertical grid sizes were 200 to 300 m in the boundary layer. Our results are from a JJA simulation. In MMF-PDF, shallow cumulus were improved by the new turbulence model but subtropical stratocumulus were still severely under-represented, likely due to inadequate vertical resolution.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2011
- Bibcode:
- 2011AGUFM.A13D0334K
- Keywords:
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- 3307 ATMOSPHERIC PROCESSES / Boundary layer processes;
- 3311 ATMOSPHERIC PROCESSES / Clouds and aerosols;
- 3379 ATMOSPHERIC PROCESSES / Turbulence;
- 3365 ATMOSPHERIC PROCESSES / Subgrid-scale parameterization