A Numerical Investigation of the Criterion for Cloud-Top Entrainment Instability

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  • 1 Meteorological Office, Bracknell, Berkshire, United Kingdom
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Abstract

An investigation of cloud-top entrainment instability (CTEI) has been carried out using a fine-resolution two-dimensional numerical model. Initial conditions having specified values of R = cpΔθe/LΔqt were used. Here, Δθe, and Δqt, are the jumps in equivalent potential temperature and total water mixing ratio across cloud top. In order to isolate the effects of entrainment across cloud top, cloud microphysics and surface fluxes were excluded from all the integrations. Radiative processes were generally also excluded, although a number of runs with longwave radiative cooling were performed. Integrations were carried out for specified values of R, using various subgrid models, including several constant values of eddy viscosity. Because the crucial process underlying CTEI is small-scale mixing, which must be parameterized in this model, only those results that are not critically dependent on the precise form of the subgrid model are likely to have any general validity. Fortunately, significant conclusions can still be drawn from the study. At values of R greater than the critical value of about 0.7 recently derived by MacVean and Mason, the cloud layer breaks up and evaporates completely within 1–2 h. On the other hand, for values of R greater than and close to the critical value of about 0.23 derived by earlier authors, no tendency for rapid dissipation of the cloud is observed. The results from the integrations that included longwave cooling at cloud top suggest that the inclusion of this process does not fundamentally modify these conclusions. Furthermore, analysis suggests that the entrainment rate in the simulations is likely to be realistic. It is concluded that CTEI may be an important mechanism governing the rapid dissipation of stratocumulus, although only at much larger values of R than earlier theoretical work had suggested. This conclusion is shown to be consistent with most of the limited, available observational data. These simulations provide strong support for the CTEI criterion proposed by MacVean and Mason. This support is, however, not unequivocal because the model is two-dimensional and, of necessity, employs a subgrid parameterization and because of the continuously increasing potential source of turbulent kinetic energy from buoyancy reversal above R = 0.23.

Abstract

An investigation of cloud-top entrainment instability (CTEI) has been carried out using a fine-resolution two-dimensional numerical model. Initial conditions having specified values of R = cpΔθe/LΔqt were used. Here, Δθe, and Δqt, are the jumps in equivalent potential temperature and total water mixing ratio across cloud top. In order to isolate the effects of entrainment across cloud top, cloud microphysics and surface fluxes were excluded from all the integrations. Radiative processes were generally also excluded, although a number of runs with longwave radiative cooling were performed. Integrations were carried out for specified values of R, using various subgrid models, including several constant values of eddy viscosity. Because the crucial process underlying CTEI is small-scale mixing, which must be parameterized in this model, only those results that are not critically dependent on the precise form of the subgrid model are likely to have any general validity. Fortunately, significant conclusions can still be drawn from the study. At values of R greater than the critical value of about 0.7 recently derived by MacVean and Mason, the cloud layer breaks up and evaporates completely within 1–2 h. On the other hand, for values of R greater than and close to the critical value of about 0.23 derived by earlier authors, no tendency for rapid dissipation of the cloud is observed. The results from the integrations that included longwave cooling at cloud top suggest that the inclusion of this process does not fundamentally modify these conclusions. Furthermore, analysis suggests that the entrainment rate in the simulations is likely to be realistic. It is concluded that CTEI may be an important mechanism governing the rapid dissipation of stratocumulus, although only at much larger values of R than earlier theoretical work had suggested. This conclusion is shown to be consistent with most of the limited, available observational data. These simulations provide strong support for the CTEI criterion proposed by MacVean and Mason. This support is, however, not unequivocal because the model is two-dimensional and, of necessity, employs a subgrid parameterization and because of the continuously increasing potential source of turbulent kinetic energy from buoyancy reversal above R = 0.23.

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