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A. P. Siebesma and A. A. M. Holtslag

Abstract

A mass flux parameterization scheme for shallow cumulus convection is evaluated for a case based on observations and large eddy simulation (LES) results for the Barbados Oceanographic and Meteorological Experiment (BOMEX). The mass flux scheme is embedded in a one-column model with prescribed large-scale forcings. Comparing the findings of the latter with the LES results, it is found that the mass flux scheme is too active. As a result, the scheme is mixing too much heat and moisture between the cloud layer and the inversion layer, giving rise to erroneous moisture and temperature profiles for the trade wind region. This is due to an underestimation of the lateral exchange rates. LES results show that for shallow cumulus cloud ensembles (lateral) entrainment and detrainment rates are typically one order of magnitude larger than values used in most operational parameterization schemes and that the detrainment rate is systematically larger than the entrainment rate. When adapting them enhanced rates, the mass flux scheme produces realistic mass fluxes and cloud excess values for moisture and heat and is therefore capable of maintaining the stationary state as observed during BOMEX.

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R. A. J. Neggers and A. P. Siebesma

Abstract

This study explores the opportunities created by subjecting a system of interacting fast-acting parameterizations to long-term single-column model evaluation against multiple independent measurements at a permanent meteorological site. It is argued that constraining the system at multiple key points facilitates the tracing and identification of compensating errors between individual parametric components. The extended time range of the evaluation helps to enhance the statistical significance and representativeness of the single-column model result, which facilitates the attribution of model behavior as diagnosed in a general circulation model to its subgrid parameterizations. At the same time, the high model transparency and computational efficiency typical of single-column modeling is preserved.

The method is illustrated by investigating the impact of a model change in the Regional Atmospheric Climate Model (RACMO) on the representation of the coupled boundary layer–soil system at the Cabauw meteorological site in the Netherlands. A set of 12 relevant variables is defined that covers all involved processes, including cloud structure and amplitude, radiative transfer, the surface energy budget, and the thermodynamic state of the soil and various heights of the lower atmosphere. These variables are either routinely measured at the Cabauw site or are obtained from continuous large-eddy simulation at that site. This 12-point check proves effective in revealing the existence of a compensating error between cloud structure and radiative transfer, residing in the cloud overlap assumption. In this exercise, the application of conditional sampling proves a valuable tool in establishing which cloud regime exhibits the biggest impact.

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A. P. Siebesma and J. W. M. Cuijpers

Abstract

A large-eddy simulation (LES) model has been utilized to study nonprecipitating Shallow Convective clouds such as observed during the undisturbed BOMEX period in the trade wind areas. By choosing a realistic large-scale forcing the authors have been able to simulate shallow convective clouds under quasi-steady-state conditions over a long period of 7 hours. This is a necessary condition to investigate diagnostic cumulus parameterization schemes since such schemes usually assume steady-state conditions. The response of the model to the applied large-scale forcing compares well with budget study results of BOMEX. In addition, the LES model delivers detailed information concerning the dynamics of shallow convective clouds. This is used to verify basic parameterizations of turbulent fluxes and entrainment and detrainment rates used in large-scale models. The most important conclusions are (i) the fractional entrainment and detrainment rates used in present large-scale atmospheric models are one order of magnitude too small, confirming previous results obtained by Esbensen, and (ii) estimates of turbulent fluxes by bulk cloud updrafts and environmental downdrafts give an underestimation of 20% to 50% depending on the variable that is transported. Implications of these results for cumulus parameterizations will be discussed.

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R. A. J. Neggers, A. P. Siebesma, and T. Heus

Uncertainties in numerical predictions of weather and climate are often linked to the representation of unresolved processes that act relatively quickly compared to the resolved general circulation. These processes include turbulence, convection, clouds, and radiation. Single‐column model (SCM) simulation of idealized cases and the subsequent evaluation against large-eddy simulation (LES) results has become an often used and relied on method to obtain insight at process level into the behavior of such parameterization schemes; benefits of SCM simulation are the enhanced model transparency and the high computational efficiency. Although this approach has achieved demonstrable success, some shortcomings have been identified; among these, i) the statistical significance and relevance of single idealized case studies might be questioned and ii) the use of observational datasets has been relatively limited. A recently initiated project named the Royal Netherlands Meteorological Institute (KNMI) Parameterization Testbed (KPT) is part of a general move toward a more statistically significant process-level evaluation, with the purpose of optimizing the identification of problems in general circulation models that are related to parameterization schemes. The main strategy of KPT is to apply continuous long-term SCM simulation and LES at various permanent meteorological sites, in combination with comprehensive evaluation against observations at multiple time scales. We argue that this strategy enables the reproduction of typical long-term mean behavior of fast physics in large-scale models, but it still preserves the benefits of single-case studies (such as model transparency). This facilitates the tracing and understanding of errors in parameterization schemes, which should eventually lead to a reduction of related uncertainties in numerical predictions of weather and climate.

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R. A. J. Neggers, A. P. Siebesma, G. Lenderink, and A. A. M. Holtslag

Abstract

Three closure methods for the mass flux at cloud base in shallow cumulus convection are critically examined for the difficult case of a diurnal cycle over land. The closure methods are first evaluated against large-eddy simulations (LESs) by diagnosing all parameters appearing in the closure equations during simulations of two different observed diurnal cycles of shallow cumulus. This reveals the characteristic behavior of each closure mechanism purely as a result of its core structure. With these results in hand the impact of each closure on the development of the cloudy boundary layer is then studied by its implementation in an offline single-column model of a regional atmospheric climate model. The LES results show that the boundary layer quasi-equilibrium closure typically overestimates the cloud-base mass flux after cloud onset, due to the neglect of significant moisture and temperature tendencies in the subcloud layer. The convective available potential energy (CAPE) adjustment closure is compromised by its limitation to compensating subsidence as the only CAPE breakdown mechanism and the use of a constant adjustment time scale. The closure method using the subcloud convective vertical velocity scale gives the best results, as it catches the time development of the cloud-base mass flux as diagnosed in LES.

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R. A. J. Neggers, A. P. Siebesma, and H. J. J. Jonker

Abstract

A new parameterization for cumulus convection is formulated, that consists of an ensemble of small, rising parcels. Large eddy simulation (LES) results are used to parameterize the lateral mixing of such a parcel: for the mixing process a relaxation timescale is defined and its value is determined by investigating individual LES clouds. The timescale is found to be nearly independent of cloud depth, which implies that the entrainment rate is inversely proportional to the vertical velocity. As a consequence, a dynamical feedback mechanism is established: the parcel dynamics influence the mixing rate, which, together with the environmental properties, feeds back on the parcel properties and therefore on the parcel dynamics.

The multiparcel model is validated with LES fields. The characteristics of the buoyant part of the clouds are reproduced: the decreasing fractional cover and increasing liquid water content with height, the vertical dynamics and mass flux, and the conserved properties and the marginally buoyant state. The model also produces the variability typical for shallow cumulus.

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R. A. J. Neggers, H. J. J. Jonker, and A. P. Siebesma

Abstract

Cloud size distributions of shallow cumulus cloud populations are calculated using the large-eddy simulation (LES) approach. A range of different cases is simulated, and the results are compared to observations of real cloud populations. Accordingly, the same algorithm is applied as in observational studies using high-altitude photography or remote sensing.

The cloud size density of the simulated cloud populations is described well by a power law at the smaller sizes. This scaling covers roughly one order of magnitude of cloud sizes, with a power-law exponent of −1.70, which is comparable to exponents found in observational studies. A sensitivity test for the resolution suggests that the scaling continues at sizes smaller than the standard grid spacing. In contrast, on the other end, the scaling region is bounded by a distinct scale break. When the cloud size is nondimensionalized by the scale break size, the cloud size densities of all cases collapse. This corroborates the idea of a universal description for the whole cloud size density, with the scale break size as the only variable. The intermediate dominating size in the cloud fraction and mass flux decompositions is directly related to the presence of the scale break in the cloud size density. Despite their large number, the smallest clouds contribute very little to the total vertical mass transport. The intermediate size of the dominating clouds in the cloud fraction and mass flux is insensitive to the resolution of LES.

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J. J. van der Dussen, S. R. de Roode, and A. P. Siebesma

Abstract

The relationship between the inversion stability and the liquid water path (LWP) tendency of a vertically well-mixed, adiabatic stratocumulus cloud layer is investigated in this study through the analysis of the budget equation for the LWP. The LWP budget is mainly determined by the turbulent fluxes of heat and moisture at the top and the base of the cloud layer, as well as by the source terms due to radiation and precipitation. Through substitution of the inversion stability parameter κ into the budget equation, it immediately follows that the LWP tendency will become negative for increasing values of κ due to the entrainment of increasingly dry air. Large κ values are therefore associated with strong cloud thinning. Using the steady-state solution for the LWP, an equilibrium value κ eq is formulated, beyond which the stratocumulus cloud will thin. The Second Dynamics and Chemistry of Marine Stratocumulus field study (DYCOMS-II) is used to illustrate that, depending mainly on the magnitude of the moisture flux at cloud base, stratocumulus clouds can persist well within the buoyancy reversal regime.

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J. Teixeira, B. Stevens, C. S. Bretherton, R. Cederwall, J. D. Doyle, J. C . Golaz, A. A. M. Holtslag, S. A . Klein, J. K. Lundquist, D. A. Randall, A. P. Siebesma, and P. M. M. Soares
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C.-H. Moeng, W. R. Cotton, C. Bretherton, A. Chlond, M. Khairoutdinov, S. Krueger, W. S. Lewellen, M. K. MacVean, J. R. M. Pasquier, H. A. Rand, A. P. Siebesma, B. Stevens, and R. I. Sykes

This paper reports an intercomparison study of a stratocumulus-topped planetary boundary layer (PBL) generated from ten 3D large eddy simulation (LES) codes and four 2D cloud-resolving models (CRMs). These models vary in the numerics, the parameterizations of the subgrid-scale (SGS) turbulence and condensation processes, and the calculation of longwave radiative cooling. Cloud-top radiative cooling is often the major source of buoyant production of turbulent kinetic energy in the stratocumulus-topped PBL. An idealized nocturnal stratocumulus case was selected for this study. It featured a statistically horizontally homogeneous and nearly solid cloud deck with no drizzle, no solar radiation, little wind shear, and little surface heating.

Results of the two-hour simulations showed that the overall cloud structure, including cloud-top height, cloud fraction, and the vertical distributions of many turbulence statistics, compared well among all LESs despite the code variations. However, the entrainment rate was found to differ significantly among the simulations. Among the model uncertainties due to numerics, SGS turbulence, SGS condensation, and radiation, none could be identified to explain such differences. Therefore, a follow-up study will focus on simulating the entrainment process. The liquid water mixing ratio profiles also varied significantly among the simulations; these profiles are sensitive to the algorithm used for computing the saturation mixing ratio.

Despite the obvious differences in eddy structure in two- and three-dimensional simulations, the cloud structure predicted by the 2D CRMs was similar to that obtained by the 3D LESs, even though the momentum fluxes, the vertical and horizontal velocity variances, and the turbulence kinetic energy profiles predicted by the 2D CRMs all differ significantly from those of the LESs.

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