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Kuan-Man Xu

Abstract

Simulated data from the UCLA cumulus ensemble model are used to investigate the quasi-universal validity of closure assumptions used in existing cumulus parameterizations. A closure assumption is quasi-universally valid if it is sensitive neither to convective cloud regimes nor to horizontal resolutions of large-scale/mesoscale models. The dependency of three types of closure assumptions, as classified by Arakawa and Chen, on the horizontal resolution is addressed in this study. Type I is the constraint on the coupling of the time tendencies of large-scale temperature and water vapor mixing ratio. Type II is the constraint on the coupling of cumulus heating and cumulus drying. Type III is a direct constraint on the intensity of a cumulus ensemble.

The macroscopic behavior of simulated cumulus convection is first compared with the observed behavior in view of Type I and Type II closure assumptions using “quick-look” and canonical correlation analyses. It is found that they are statistically similar to each other. The three types of closure assumptions are further examined with simulated data averaged over selected subdomain sizes ranging from 64 to 512 km. It is found that the dependency of Type I and Type II closure assumptions on the horizontal resolution is very weak and that Type III closure assumption is somewhat dependent upon the horizontal resolution. The influences of convective and mesoscale processes on the closure assumptions are also addressed by comparing the structures of canonical components with the corresponding vertical profiles in the convective and stratiform regions of cumulus ensembles analyzed directly from simulated data. The implication of these results for cumulus parameterization is discussed.

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Kuan-Man Xu

Abstract

This study presents an approach that converts the vertical profiles of grid-averaged cloud properties from large-scale models to probability density functions (pdfs) of subgrid-cell cloud physical properties measured at satellite footprints. Cloud physical and radiative properties, rather than just cloud and precipitation occurrences, of assimilated cloud systems by the European Centre for Medium-Range Weather Forecasts (ECMWF) operational analysis (EOA) and 40-yr ECMWF Re-Analysis (ERA-40) are validated against those obtained from Earth Observing System satellite cloud object data for the January–August 1998 and March 2000 periods. These properties include the ice water path (IWP), cloud-top height and temperature, cloud optical depth, and solar and infrared radiative fluxes. Each cloud object, a contiguous region with similar cloud physical properties, is temporally and spatially matched with EOA and ERA-40 data. Results indicate that most pdfs of EOA and ERA-40 cloud physical and radiative properties agree with those of satellite observations of the tropical deep convective cloud object type for the January–August 1998 period. There are, however, significant discrepancies in selected ranges of the cloud property pdfs such as the upper range of EOA cloud-top height. A major discrepancy is that the dependence of the pdfs on the cloud object size for both EOA and ERA-40 is not as strong as in the observations. Modifications to the cloud parameterization in ECMWF that occurred in October 1999 eliminate the clouds near the tropopause but shift power of the pdf to lower cloud-top heights and greatly reduce the ranges of IWP and cloud optical depth pdfs. These features persist in ERA-40 due to the use of the same cloud parameterizations. The less sophisticated data assimilation technique and the lack of snow water content information in ERA-40, not the larger horizontal grid spacing, are also responsible for the disagreements with observed pdfs of cloud physical properties, although the detection rates of cloud object occurrence are improved for small-size categories. A possible improvement to the convective parameterization is to introduce a stronger dependence of updraft penetration heights on grid-cell dynamics.

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Kuan-Man Xu

Abstract

Simulated data from the UCLA Cumulus Ensemble Model (CEM) are analyzed to partition mass, heat, and moisture budgets of cumulus ensembles into convective and stratiform components. A method based primarily on the horizontal distribution of maximum cloud draft strength below the melting level in a CEM grid column has been developed for this analysis. The stratiform region includes both precipitating and nonprecipitating anvils.

The convective and stratiform components of mass, heat, and moisture budgets are distinctly different, in qualitative agreement with previous observational and modeling studies. In the heat and moisture budgets, the difference is due mainly to that in the phase change processes. In general, condensation/deposition dominate evaporation/sublimation in the convective region. All of these processes are more or less equally important in the stratiform region. Freezing occurs only in the convective region. Sublimation from snow/graupel in the stratiform region is much more important than in the convective region. Radiative effects in the stratiform component of the heat budget are as important as effects of phase changes, while radiative effects in the convective component are far less significant.

The importance of the convergences of eddy fluxes, especially in the moisture budget, is confirmed. The convergences in the stratiform component are found to be parameterizable only if the vertical motions and the properties of both mesoscale updrafts and mesoscale downdrafts are known. The horizontal inhomogeneity within mesoscale updrafts/downdrafts is of secondary importance for parameterizing the convergences of eddy fluxes in the stratiform component.

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Kuan-Man Xu

Abstract

This study examines the sensitivity of diagnosed radiative fluxes and heating rates to different treatments of cloud microphysics among cloud-resolving models (CRMs). The domain-averaged CRM outputs are used in this calculation. The impacts of the cloud overlap and uniform hydrometeor assumptions are examined using outputs having spatially varying cloud fields from a single CRM. It is found that the cloud overlap assumption impacts the diagnosis more significantly than the uniform hydrometeor assumption for all radiative fluxes. This is also the case for the longwave radiative cooling rate except for a layer above 7 km where it is more significantly impacted by the uniform hydrometeor assumption. The radiative cooling above upper-tropospheric anvils and the warming below these clouds are overestimated by about 0.5 K day−1 using the domain-averaged outputs. These results are used to further quantify intermodel differences in radiative properties due to different treatments of cloud microphysics among 10 CRMs. The magnitudes of the intermodel differences, as measured by the deviations from the consensus of 10 CRMs, are found to be smaller than those due to the cloud overlap assumption and comparable to those due to the uniform hydrometeor assumption for most shortwave radiative fluxes and the net radiative fluxes at the top of the atmosphere (TOA) and at the surface. For all longwave radiative fluxes, they are smaller than those due to cloud overlap and uniform hydrometeor assumptions. The consensus of all diagnosed radiative fluxes except for the surface downward shortwave flux agrees with observations to a degree that is close to the uncertainties of satellite- and ground-based measurements.

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Kuan-Man Xu

Abstract

A new method is proposed to compare statistical differences between summary histograms, which are the histograms summed over a large ensemble of individual histograms. It consists of choosing a distance statistic for measuring the difference between summary histograms and using a bootstrap procedure to calculate the statistical significance level. Bootstrapping is an approach to statistical inference that makes few assumptions about the underlying probability distribution that describes the data. Three distance statistics are compared in this study. They are the Euclidean distance, the Jeffries–Matusita distance, and the Kuiper distance.

The data used in testing the bootstrap method are satellite measurements of cloud systems called “cloud objects.” Each cloud object is defined as a contiguous region/patch composed of individual footprints or fields of view. A histogram of measured values over footprints is generated for each parameter of each cloud object, and then summary histograms are accumulated over all individual histograms in a given cloud-object size category. The results of statistical hypothesis tests using all three distances as test statistics are generally similar, indicating the validity of the proposed method. The Euclidean distance is determined to be most suitable after comparing the statistical tests of several parameters with distinct probability distributions among three cloud-object size categories. Impacts on the statistical significance levels resulting from differences in the total lengths of satellite footprint data between two size categories are also discussed.

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Anning Cheng and Kuan-Man Xu

Abstract

An analysis of simulated cloud regime transitions along a transect from the subtropical California coast to the tropics for the northern summer season (June–August) is presented in this study. The Community Atmosphere Model, version 5 (CAM5), superparameterized CAM (SPCAM), and an upgraded SPCAM with intermediately prognostic higher-order closure (SPCAM-IPHOC) are used to perform global simulations by imposing climatological sea surface temperature and sea ice distributions. The seasonal-mean properties are compared with recent observations of clouds, radiation, and precipitation and with multimodel intercomparison results. There are qualitative agreements in the characteristics of cloud regimes along the transect among the three models. CAM5 simulates precipitation and shortwave radiative fluxes well but the stratocumulus-to-cumulus transition occurs too close to the coast of California. SPCAM-IPHOC simulates longwave radiative fluxes and precipitable water well, but with systematic biases in shortwave radiative fluxes. The broad, stronger ascending band in SPCAM is related to the large biases in the convective region but the characteristics of the stratocumulus region are still more realistic and the transition occurs slightly farther away from the coast than in CAM5. Even though SPCAM-IPHOC produces the most realistic seasonal-mean transition, it underestimates the mean gradient in low-cloud cover (LCC) across the mean transition location because of an overestimate of LCC in the transition and convective regions that shifts the transition locations farther from the coast. Analysis of two decoupling measures shows consistency in the mean location and the histogram of decoupling locations with those of LCC transition. CAM5, however, lacks such a consistency, suggesting a need for further refinement of its boundary layer cloud parameterization.

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Kuan-Man Xu and Anning Cheng

Abstract

The eastern Pacific is a climatologically important region. Conventional coupled atmosphere–ocean general circulation models produce positive sea surface temperature biases of 2–5 K in this region because of insufficient stratocumulus clouds. In this study, a global multiscale modeling framework (MMF), which replaces traditional cloud parameterizations with a 2D cloud-resolving model (CRM) in each atmospheric column, is used to examine the seasonal variations of this Pacific region. The CRM component contains an advanced third-order turbulence closure, helping it to better simulate boundary layer turbulence and low-level clouds. Compared to available satellite observations of cloud amount, liquid water path, cloud radiative effects, and precipitation, this MMF produces realistic seasonal variations of the eastern Pacific region, although there are some disagreements in the exact location of maximum cloudiness centers in the Peruvian region and the intensity of ITCZ precipitation. Analyses of profile- and subcloud-based decoupling measures reveal very small amplitudes of seasonal variations in the decoupling strength in the subtropics except for those regions off the subtropical coasts where the decoupling measures suggest that the boundary layers should be well coupled in all four seasons. In the Peruvian and Californian regions, the seasonal variations of low clouds are related to those in the boundary layer height and the strength of inversion. Factors that influence the boundary layer and the inversion, such as solar incident radiation, subcloud-layer turbulent mixing, and large-scale subsidence, can collectively explain the seasonal variations of low clouds rather than the deepening–warming mechanism of Bretherton and Wyant cited in earlier studies.

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Kuan-Man Xu and Anning Cheng

Abstract

The multiscale modeling framework, which replaces traditional cloud parameterizations with a 2D cloud-resolving model (CRM) in each atmospheric column, is a promising approach to climate modeling. The CRM component contains an advanced third-order turbulence closure, helping it to better simulate low-level clouds. In this study, two simulations are performed with 1.9° × 2.5° grid spacing but they differ in the vertical resolution. The number of model layers below 700 hPa increases from 6 in one simulation (IP-6L) to 12 in another (IP-12L) to better resolve the boundary layer. The low-cloud horizontal distribution and vertical structures in IP-12L are more realistic and its global mean is higher than in IP-6L and closer to that of CloudSat/Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) observations. The spatial patterns of tropical precipitation are significantly improved; for example, a single intertropical convergence zone (ITCZ) in the Pacific, instead of double ITCZs in an earlier study that used coarser horizontal resolution and a different dynamical core in its host general circulation model (GCM), and the intensity of the South Pacific convergence zone (SPCZ), and the ITCZ in the Atlantic is more realistic. Many aspects of the global seasonal climatology agree well with observations except for excessive precipitation in the tropics. In terms of spatial correlations and patterns in the tropical/subtropical regions, most surface/vertically integrated properties show greater improvement over the earlier simulation than that with lower vertical resolution. The relationships between low-cloud amount and several large-scale properties are consistent with those observed in five low-cloud regions. There is an imbalance in the surface energy budget, which is an aspect of the model that needs to be improved in the future.

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Anning Cheng and Kuan-Man Xu

Abstract

Formulating the contribution of subgrid-scale (SGS) variability to microphysical processes in boundary layer and deep convective cloud parameterizations is a challenging task because of the complexity of microphysical processes and the lack of subgrid-scale information. In this study, a warm-rain microphysics parameterization that is based on a joint double-Gaussian distribution of vertical velocity, liquid water potential temperature, total water mixing ratio, and perturbation of rainwater mixing ratio is developed to simulate drizzling boundary layer clouds with a single column model (SCM). The probability distribution function (PDF) is assumed, but its parameters evolve according to equations that invoke higher-order turbulence closure. These parameters are determined from the first-, second-, and third-order moments and are then used to derive analytical expressions for autoconversion, collection, and evaporation rates. The analytical expressions show that correlation between rainwater and liquid water mixing ratios of the Gaussians enhances the collection rate whereas that between saturation deficit and rainwater mixing ratios of the Gaussians enhances the evaporation rate. Cases of drizzling shallow cumulus and stratocumulus are simulated with large-eddy simulation (LES) and SCM runs (SCM-CNTL and SCM-M): LES explicitly resolves SGS variability, SCM-CNTL parameterizes SGS variability with the PDF-based scheme, but SCM-M uses the grid-mean profiles to calculate the conversion rates of microphysical processes. SCM-CNTL can well reproduce the autoconversion, collection, and evaporation rates from LES. Comparisons between the two SCM experiments showed improvements in mean profiles of potential temperature, total water mixing ratio, liquid water, and cloud amount in the simulations considering SGS variability. A 3-week integration using the PDF-based microphysics scheme indicates that the scheme is stable for long-term simulations.

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Kuan-Man Xu and Akio Arakawa

Abstract

The Arakawa-Schubert (A-S) cumulus parameterization is evaluated by performing semiprognostic tests against data simulated by a cumulus ensemble model (CEM). The CEM is a two-dimensional cloud model for simulating the formation of an ensemble of cumulus clouds under prescribed large-scale conditions. Three simulations, two with vertical wind shear and one without, are performed with identical (time-varying) large-scale advective effects.

The semiprognostic tests follow a procedure similar to that used by Lord except that simulated data averaged over the entire domain or selected subdomains of the CEM provide the “observed” large-scale conditions. Detailed comparisons were made between the results of simulation and parameterization. The results include comparisons of surface precipitation rate, apparent heat source, apparent moisture sink, updraft mass flux, and downdraft mass flux. Two different sets of tests were performed. One is the standard A-S parameterization with the cloud work function (CWF) quasi equilibrium, and the other allows CWF nonequilibrium by taking into account the simulated time change of the CWF. The tests show that the A-S parameterization is basically valid in spite of the existence of mesoscale organization in cumulus convection. In particular, the assumption of CWF quasi equilibrium is more accurate for inputs averaged over smaller subdomain sizes that resolve some mesoscale processes. On the other hand, errors due to the nondiagnostic aspect of cumulus convection are more significant for inputs averaged over larger subdomain sizes. Errors due to the inherent nondeterministic aspect of cumulus convection appear to be more significant for inputs averaged over smaller subdomain sizes.

A modified A-S parameterization with a convective-scale downdraft formulation was also tested against the simulated data. The inclusion of downdrafts slightly improves the results of semiprognostic tests. The impact of downdrafts on the subcloud layer may depend significantly on the subdomain size.

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