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  • Author or Editor: A. M. Tompkins x
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F. Di Giuseppe and A. M. Tompkins

Abstract

To relate the error associated with 1D radiative calculations to the geometrical scales of cloud organization and/or in-cloud optical inhomogeneities, a new idealized methodology, based on a Fourier statistical technique, has been developed. Three-dimensional cloud fields with variability over a selected range of horizontal spatial scales and consistent vertical structure can be obtained and controlled by a small number of parameters, which relate directly to the dynamical and thermodynamical meteorology of the situation to be examined. This initial study deals with marine stratocumulus. Two experiments are conducted: an overcast situation and a broken cloud case with maximum cloud cover of 80%. For each experiment, five cloud fields are generated with the dominant organizational scale changing from 1.4 to 22 km, while all other quantities—such as cloud cover, cloud liquid water, and total water variance—remain constant. For each scene, three radiative calculations are performed for solar zenith angles of 0° and 60°: a plane parallel (PP) calculation, similar to that commonly implemented in general circulation models; an independent pixel approximation (IPA); and a full 3D calculation. The “PP bias” (IPA-PP) is used to assess cloud optical homogeneity approximation, while the “IPA bias” (3D-IPA) measures the impact of horizontal photon transport.

For the overcast scenes, the neglect of horizontal photon transport was found to be unimportant, and the IPA calculation gives accurate results. For the broken cloud case, this was only true for clouds with dominant horizontal spatial scales exceeding 10 km. With a scale of 2 km or less, the IPA bias in reflectivity, transmissivity, and absorption could exceed 5%. This indicates that even for shallow cloud systems, cloud geometry can play an important role. The sign of the bias depends critically on the solar angle, with IPA over- (under) estimating reflectivity for high (low) sun angles.

The PP bias in reflectivity was also found to be around 5% for both cases, comparable to the IPA bias, and smaller than previous estimates for this cloud type. Additional sensitivity tests prove this to be due to the vertical cloud structure. Vertically resolving the subcloud adiabatic liquid profile leads to a more opaque cloud upper boundary, reducing photon penetration into the cloud layer, and thus also PP biases. Additionally, for the broken cloud case it was found that changes in cloud fraction with height are translated by cloud overlap rules into effective horizontal variability in the liquid water path, further reducing biases. Taking a vertically uniform slab with identical integrated properties led to much larger PP biases comparable to previous estimates. Thus, models with sufficient vertical resolution are likely to suffer from smaller PP biases than previously estimated.

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F. Di Giuseppe and A. M. Tompkins

Abstract

Conflicting claims have been made concerning the magnitude of the bias in solar radiative transfer calculations when horizontal photon transport is neglected for deep convective scenarios. The difficulty of obtaining a realistic set of cloud scenes for situations of complex cloud geometry, while certain characteristics such as total cloud cover are systematically controlled, has hindered the attempt to reach a consensus. Here, a simple alternative approach is adopted. An ensemble of cloud scenes generated by a cloud resolving model are modified by an idealized function that progressively alters the cirrus anvil coverage without affecting the realism of the scene produced. Comparing three-dimensional radiative calculations with the independent column approximation for all cloud scenes, it is found that the bias in scene albedo can reach as much as 22% when the sun is overhead and 46% at low sun angles. The bias is an asymmetrical function of cloud cover with a maximum attained at cirrus anvil cloud cover of approximately 30%–40%. With a cloud cover of 15%, the bias is half its maximum value, while it is limited for coverage exceeding 80%. The position of the peak occurs at the cloud cover coinciding with the maximum number of independent clouds present in the scene. Increasing the cloud cover past this point produces a decrease in the number of isolated clouds because of cloud merging, with a consequential bias reduction.

With this systematic documentation of the biases as a function of total cloud cover, it is possible to identify two contributions to the total error: the geometrical consequences of the effective cloud cover increase at low sun angles and the true 3D scattering effect of photons deviating from the original path direction. An attempt to account for the former geometrical contribution to the 1D bias is made by performing a simple correction technique, whereby the field is sheared by the tangent of the solar zenith angle. It is found that this greatly reduces the 1D biases at low sun angles. Because of the small aspect ratio of the cirrus cloud deck, the remaining bias contribution is small in magnitude and almost independent of solar zenith angle.

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A. N. Ross, A. M. Tompkins, and D. J. Parker

Abstract

Gravity-current models have been used for many years to describe the cold pools of low-level air that are generated by cumulonimbus precipitation. More recently, it has been realized that surface fluxes of heat and water vapor can be important in modifying these flows, through turbulent mixing of buoyancy by convection, and through direct modification of the cold pool buoyancy. In this paper, simple models describing the role of surface fluxes in depleting the negative buoyancy of a gravity current and the consequences of this for the flow dynamics are discussed.

It is pointed out that the depletion of cold pool buoyancy by surface fluxes is analogous to the depletion of buoyancy in a turbidity current through particle sedimentation, and in one regime of parameter values the analogy is exact. This analogy allows one to use simple flow models that have been tested extensively against laboratory experiments on turbidity currents. A simple “box model” and a more sophisticated shallow water model are each developed. It is shown how these models can give relatively simple expressions for cold pool “runout length” and buoyancy distributions. These runout lengths compare well with maximum cold pool sizes previously observed in cloud-resolving model simulations of unorganized tropical deep convection.

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