Vincent E. Larson

A PDF-Based Model for Boundary Layer Clouds. Part I: Method and Model Description

A new cloudy boundary layer single-column model is presented. It is designed to be flexible enough to represent a variety of cloudiness regimes—such as cumulus, stratocumulus, and clear regimes—without the need for case-specific adjustments. The methodology behind the model is the so-called assumed probability density function (PDF) method. The parameterization differs from higher-order closure or mass-flux schemes in that it achieves closure by the use of a relatively sophisticated joint PDF of vertical velocity, temperature, and moisture. A family of PDFs is chosen that is flexible enough to represent various cloudiness regimes. A double Gaussian family proposed by previous works is used. Predictive equations for grid box means and a number of higherorder turbulent moments are advanced in time. These moments are in turn used to select a particular member from the family of PDFs, for each time step and grid box. Once a PDF member has been selected, the scheme integrates over the PDF to close higher-order moments, buoyancy terms, and diagnose cloud fraction and liquid water. Since all the diagnosed moments for a given grid box and time step are derived from the same unique joint PDF, they are guaranteed to be consistent with one another. A companion paper presents simulations produced by the single-column model.

Observed Microphysical Structure of Midlevel, Mixed-Phase Clouds

Abstract This paper analyzes airborne measurements of six midlevel clouds observed over the Great Plains of the United States in late 1999 and early 2000 during the fifth of the Complex Layered-Cloud Experiments (CLEX-5). Data show that these innocuous-looking clouds display complicated microphysical and thermodynamic structures. Five of the six cases exhibit mixed-phase conditions in temperatures ranging from near 0° to −31°C, at altitudes of 2400 to 7200 m MSL. Four of the cases consist of a single cloud layer, while the other two are multilayered systems. In the thin, mixed-phase, single-layered clouds that the authors observed, there is an increase of liquid water content with altitude, whereas the ice water content maximizes in the mid- to lower part of the clouds. This contrasts the two multilayered systems the authors observed, in which significant amounts of ice occur in the top as well as the bottom of the individual layers of each system. A lack of significant temperature inversions or wind shea...

CGILS: Results from the First Phase of an International Project to Understand the Physical Mechanisms of Low Cloud Feedbacks in Single Column Models

CGILS—the CFMIP-GASS Intercomparison of Large Eddy Models (LESs) and single column models (SCMs)—investigates the mechanisms of cloud feedback in SCMs and LESs under idealized climate change perturbation. This paper describes the CGILS results from 15 SCMs and 8 LES models. Three cloud regimes over the subtropical oceans are studied: shallow cumulus, cumulus under stratocumulus, and well-mixed coastal stratus/stratocumulus. In the stratocumulus and coastal stratus regimes, SCMs without activated shallow convection generally simulated negative cloud feedbacks, while models with active shallow convection generally simulated positive cloud feedbacks. In the shallow cumulus alone regime, this relationship is less clear, likely due to the changes in cloud depth, lateral mixing, and precipitation or a combination of them. The majority of LES models simulated negative cloud feedback in the well-mixed coastal stratus/stratocumulus regime, and positive feedback in the shallow cumulus and stratocumulus regime. A general framework is provided to interpret SCM results: in a warmer climate, the moistening rate of the cloudy layer associated with the surface-based turbulence parameterization is enhanced; together with weaker large-scale subsidence, it causes negative cloud feedback. In contrast, in the warmer climate, the drying rate associated with the shallow convection scheme is enhanced. This causes positive cloud feedback. These mechanisms are summarized as the “NESTS” negative cloud feedback and the “SCOPE” positive cloud feedback (Negative feedback from Surface Turbulence under weaker Subsidence—Shallow Convection PositivE feedback) with the net cloud feedback depending on how the two opposing effects counteract each other. The LES results are consistent with these interpretations.

Systematic Biases in the Microphysics and Thermodynamics of Numerical Models That Ignore Subgrid-Scale Variability

A grid box in a numerical model that ignores subgrid variability has biases in certain microphysical and thermodynamic quantities relative to the values that would be obtained if subgrid-scale variability were taken into account. The biases are important because they are systematic and hence have cumulative effects. Several types of biases are discussed in this paper. Namely, numerical models that employ convex autoconversion formulas underpredict (or, more precisely, never overpredict) autoconversion rates, and numerical models that use convex functions to diagnose specific liquid water content and temperature underpredict these latter quantities. One may call these biases the ‘‘grid box average autoconversion bias,’’ ‘‘grid box average liquid water content bias,’’ and ‘‘grid box average temperature bias,’’ respectively, because the biases arise when grid box average values are substituted into formulas valid at a point, not over an extended volume. The existence of these biases can be derived from Jensen’s inequality. To assess the magnitude of the biases, the authors analyze observations of boundary layer clouds. Often the biases are small, but the observations demonstrate that the biases can be large in important cases. In addition, the authors prove that the average liquid water content and temperature of an isolated, partly cloudy, constant-pressure volume of air cannot increase, even temporarily. The proof assumes that liquid water content can be written as a convex function of conserved variables with equal diffusivities. The temperature decrease is due to evaporative cooling as cloudy and clear air mix. More generally, the authors prove that if an isolated volume of fluid contains conserved scalars with equal diffusivities, then the average of any convex, twice-differentiable function of the conserved scalars cannot increase.

Using Probability Density Functions to Derive Consistent Closure Relationships among Higher-Order Moments

Parameterizations of turbulence often predict several lower-order moments and make closure assumptions for higher-order moments. In principle, the low- and high-order moments share the same probability density function (PDF). One closure assumption, then, is the shape of this family of PDFs. When the higher-order moments involve both velocity and thermodynamic scalars, often the PDF shape has been assumed to be a double or triple delta function. This is equivalent to assuming a mass-flux model with no subplume variability. However, PDF families other than delta functions can be assumed. This is because the assumed PDF methodology is fairly general. This paper proposes closures for several third- and fourth-order moments. To derive the closures, the moments are assumed to be consistent with a particular PDF family, namely, a mixture of two trivariate Gaussians. (This PDF is also called a double Gaussian or binormal PDF by some authors.) Separately from the PDF assumption, the paper also proposes a simplified relationship between scalar and velocity skewnesses. This PDF family and skewness relationship are simple enough to yield simple, analytic closure formulas relating the moments. If certain conditions hold, this set of moments is specifically realizable. By this it is meant that the set of moments corresponds to a real Gaussian-mixture PDF, one that is normalized and nonnegative everywhere. This paper compares the new closure formulas with both large eddy simulations (LESs) and closures based on double and triple delta PDFs. This paper does not implement the closures in a single-column model and test them interactively. Rather, the comparisons are diagnostic; that is, low-order moments are extracted from the LES and treated as givens that are input into the closures. This isolates errors in the closures from errors in a single-column model. The test cases are three atmospheric boundary layers: a trade wind cumulus layer, a stratocumulus layer, and a clear convective case. The new closures have shortcomings, but nevertheless are superior to the double or triple delta closures in most of the cases tested.

Small-Scale and Mesoscale Variability of Scalars in Cloudy Boundary Layers: One-Dimensional Probability Density Functions

A key to parameterization of subgrid-scale processes is the probability density function (PDF) of conserved scalars. If the appropriate PDF is known, then grid box average cloud fraction, liquid water content, temperature, and autoconversion can be diagnosed. Despite the fundamental role of PDFs in parameterization, there have been few observational studies of conserved-scalar PDFs in clouds. The present work analyzes PDFs from boundary layers containing stratocumulus, cumulus, and cumulus-rising-into-stratocumulus clouds. Using observational aircraft data, the authors test eight different parameterizations of PDFs, including double delta function, gamma function, Gaussian, and double Gaussian shapes. The Gaussian parameterization, which depends on two parameters, fits most observed PDFs well but fails for large-scale PDFs of cumulus legs. In contrast, three-parameter parameterizations appear to be sufficiently general to model PDFs from a variety of cloudy boundary layers. If a numerical model ignores subgrid variability, the model has biases in diagnoses of grid box average liquid water content, temperature, and Kessler autoconversion, relative to the values it would obtain if subgrid variability were taken into account. The magnitude of such biases is assessed using observational data. The biases can be largely eliminated by three-parameter PDF parameterizations. Prior authors have suggested that boundary layer PDFs from short segments are approximately Gaussian. The present authors find that the hypothesis that PDFs of total specific water content are Gaussian can almost always be rejected for segments as small as 1 km.

A PDF-Based Model for Boundary Layer Clouds. Part II: Model Results

A new single-column model for the cloudy boundary layer, described in a companion paper, is tested for a variety of regimes. To represent the subgrid-scale variability, the model uses a joint probability density function (PDF) of vertical velocity, temperature, and moisture content. Results from four different cases are presented and contrasted with large eddy simulations (LES). The cases include a clear convective layer based on the Wangara experiment, a trade wind cumulus layer from the Barbados Oceanographic and Meteorological Experiment (BOMEX), a case of cumulus clouds over land, and a nocturnal marine stratocumulus boundary layer. Results from the Wangara experiment show that the model is capable of realistically predicting the diurnal growth of a dry convective layer. Compared to the LES, the layer produced is slightly less well mixed and entrainment is somewhat slower. The cloud cover in the cloudy cases varied widely, ranging from a few percent cloud cover to nearly overcast. In each of the cloudy cases, the parameterization predicted cloud fractions that agree reasonably well with the LES. Typically, cloud fraction values tended to be somewhat smaller in the parameterization, and cloud bases and tops were slightly underestimated. Liquid water content was generally within 40% of the LES-predicted values for a range of values spanning almost two orders of magnitude. This was accomplished without the use of any case-specific adjustments.

PDF Parameterization of Boundary Layer Clouds in Models with Horizontal Grid Spacings from 2 to 16 km

Many present-day numerical weather prediction (NWP) models are run at resolutions that permit deep convection. In these models, however, the boundary layer turbulence and boundary layer cloud features are still grossly underresolved. Underresolution is also present in climate models that use a multiscale modeling framework (MMF), in which a convection-permitting model is run in each grid column of a global general circulation model. To better represent boundary layer clouds and turbulence in convection-permitting models, a parameterization was developed that models the joint probability density function (PDF) of vertical velocity, heat, and moisture. Although PDF-based parameterizations are more complex and computationally expensive than many other parameterizations, in principle PDF parameterizations have several advantages. For instance, they ensure consistency of liquid (cloud) water and cloud fraction; they avoid using separate parameterizations for different cloud types such as cumulus and stratocumulus; and they have an appropriate formulation in the ‘‘terra incognita’’ in which updrafts are marginally resolved. In this paper, an implementation of a PDF parameterization is tested to see whether it improves the simulations of a state-of-the-art convection-permitting model. The PDF parameterization used is the Cloud LayersUnifiedBy Binormals (CLUBB)parameterization.The host cloud-resolving model usedis theSystem forAtmosphericModeling(SAM).SAMisrunbothwithandwithoutCLUBBimplementedinit.Simulations of two shallowcumulus(Cu)cases andtwo shallowstratocumulus(Sc)casesarerun ina 3D configurationat 2-, 4-, and 16-km horizontal grid spacings. Including CLUBB in the simulations improves some of the simulated fields—such as vertical velocity variance, horizontal wind fields, cloud water content, and drizzle water content—especially in the two Cu cases. Implementing CLUBB in SAM improves the simulations slightly at 2-km horizontal grid spacing, significantlyat4-kmgridspacing,andgreatlyat 16-kmgridspacing.Furthermore,thesimulationsthatinclude CLUBB exhibit a reduced sensitivity to horizontal grid spacing.

Higher-Order Turbulence Closure and Its Impact on Climate Simulations in the Community Atmosphere Model

AbstractThis paper describes climate simulations of the Community Atmosphere Model, version 5 (CAM5), coupled with a higher-order turbulence closure known as Cloud Layers Unified by Binormals (CLUBB). CLUBB is a unified parameterization of the planetary boundary layer (PBL) and shallow convection that is centered around a trivariate probability density function (PDF) and replaces the conventional PBL, shallow convection, and cloud macrophysics schemes in CAM5. CAM–CLUBB improves many aspects of the base state climate compared to CAM5. Chief among them is the transition of stratocumulus to trade wind cumulus regions in the subtropical oceans. In these regions, CAM–CLUBB provides a much more gradual transition that is in better agreement with observational analysis compared to CAM5, which is too abrupt. The improvement seen in CAM–CLUBB can be largely attributed to the gradual evolution of the simulated turbulence, which is in part a result of the unified nature of the parameterization, and to the general i...

An Analytic Longwave Radiation Formula for Liquid Layer Clouds

Abstract Many Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study (GCSS) intercomparisons of boundary layer clouds have used a convenient but idealized longwave radiation formula for clouds in their large-eddy simulations (LESs). Under what conditions is this formula justified? Can it be extended to midlevel layer clouds? This note first derives the GCSS formula using an alternative method to effective emissivity. A key simplifying assumption is that the cloud is isothermal in the vertical (and horizontal). However, this assumption does not turn out to be overly restrictive in practice. Then the GCSS formula is compared with a detailed numerical code, BugsRad. Sensitivity studies are performed in which cloud properties, cloud altitude, and thermodynamic profiles are modified. Here, the focus is primarily on midlevel, altostratocumulus layers. The results here show that the GCSS formula can be successfully extended to liquid (ice free), midlevel clouds. The GCSS formula produces remarkably ...