Jean-Christophe (Chris) Golaz: Publications

Peer-reviewed publications

1. Golaz, J.-C., J. D. Doyle and S. Wang, 2009: One-way nested large-eddy simulation over the Askervein Hill. J. Adv. Model. Earth Syst., 1, 6, 1-6, doi: 10.3894/JAMES.2009.1.6. (pdf, 418K)
   Abstract
   

   Large-eddy simulation (LES) models have been used extensively to study atmospheric boundary layer turbulence over flat surfaces; however, LES applications over topography are less common. We evaluate the ability of an existing model -- COAMPS(R)-LES -- to simulate flow over terrain using data from the Askervein Hill Project. A new approach is suggested for the treatment of the lateral boundaries using one-way grid nesting. LES wind profile and speed-up are compared with observations at various locations around the hill. The COAMPS-LES model performs generally well. This case could serve as a useful benchmark for evaluating LES models for applications over topography.

   
   
2. Klein, S. A., R. B. McCoy, H. Morrison, A. S. Ackerman, A. Avramov, G. de Boer, M. Chen, J. N. S. Cole, A. D. Del Genio, M. Falk, M. J. Foster, A. Fridlind, J.-C. Golaz, T. Hashino, J. Y. Harrington, C. Hoose, M. F. Khairoutdinov, V. E. Larson, X. Liu, Y. Luo, G. M. McFarquhar, S. Menon, R. A. J. Neggers, S. Park, M. R. Poellot, J. M. Schmidt, I. Sednev, B. J. Shipway, M. D. Shupe, D. A. Spangenberg, Y. C. Sud, D. D. Turner, D. E. Veron, K. von Salzen, G. K. Walker, Z. Wang, A. B. Wolf, S. Xie, K.-M. Xu, F. Yang and G. Zhang, 2009: Intercomparison of model simulations of mixed-phase clouds observed during the ARM Mixed-Phase Arctic Cloud Experiment. Part I: Single layer cloud. Quart. J. Roy. Meteor. Soc., 135, 979-1002. (pdf, 652K; doi: 10.1002/qj.416)
   Abstract
   

   Results are presented from an intercomparison of single-column and cloud-resolving model simulations of a cold-air outbreak mixed-phase stratocumulus cloud observed during the Atmospheric Radiation Measurement (ARM) programme's Mixed-Phase Arctic Cloud Experiment. The observed cloud occurred in a well-mixed boundary layer with a cloud-top temperature of -15 C. The average liquid water path of around 160 g m-2 was about two-thirds of the adiabatic value and far greater than the average mass of ice which when integrated from the surface to cloud top was around 15 g m-2 . Simulations of 17 single-column models (SCMs) and 9 cloud-resolving models (CRMs) are compared. While the simulated ice water path is generally consistent with observed values, the median SCM and CRM liquid water path is a factor-of-three smaller than observed. Results from a sensitivity study in which models removed ice microphysics suggest that in many models the interaction between liquid and ice-phase microphysics is responsible for the large model underestimate o f liquid water path. Despite this underestimate, the simulated liquid and ice water paths of several models are consistent with observed values. Furthermore, models with more sophisticated microphysics simulate liquid and ice water paths that are in better agreement with the observed values, although considerable scatter exists. Although no single factor guarantees a good simulation, these results emphasize the need for improvement in the model representation of mixed-phase microphysics.

   
   
3. Ackerman, A. S., M. C. vanZanten, B. Stevens, V. Savic-Jovcic, C. S. Bretherton, A. Chlond, J.-C. Golaz, H. Jiang, M. Khairoutdinov, S. K. Krueger, D. C. Lewellen, A. Lock, C.-H. Moeng, K. Nakamura, M. D. Petters, J. R. Snider, S. Weinbrecht, and M. Zulauf, 2009: Large-eddy simulations of a drizzling, stratocumulus-topped marine boundary layer Mon. Wea. Rev., 137, 1083-­1110. (pdf, 1.5M; doi: 10.1175/2008MWR2582.1)
   Abstract
   

   Cloud water sedimentation and drizzle in a stratocumulus-topped boundary layer are the focus of an intercomparison of large-eddy simulations. The context is an idealized case study of nocturnal stratocumulus under a dry inversion, with embedded pockets of heavily drizzling open cellular convection. Results from 11 groups are used. Two models resolve the size distributions of cloud particles, and the others parameterize cloud water sedimentation and drizzle. For the ensemble of simulations with drizzle and cloud water sedimentation, the mean liquid water path (LWP) is remarkably steady and consistent with the measurements, the mean entrainment rate is at the low end of the measured range, and the ensemble-average maximum vertical wind variance is roughly half that measured. On average, precipitation at the surface and at cloud base is smaller, and the rate of precipitation evaporation greater, than measured. Including drizzle in the simulations reduces convective intensity, increases boundary layer stratification, and decreases LWP for nearly all models. Including cloud water sedimentation substantially decreases entrainment, decreases convective intensity, and increases LWP for most models. In nearly all cases, LWP responds more strongly to cloud water sedimentation than to drizzle. The omission of cloud water sedimentation in simulations is strongly discouraged, regardless of whether or not precipitation is present below cloud base.

   
   
4. Haywood, J., L. Donner, A. Jones, and J.-C. Golaz, 2009: Global indirect radiative forcing caused by aerosols: IPPC (2007) and beyond. Clouds in the perturbed climate system: their relationship to energy balance, atmospheric dynamics, and precipitation. J. Heintzenberg and R. J. Charlson, Eds., MIT Press, 451­-467. (pdf, 1.4M)
   Abstract
   

   Anthropogenic aerosols are thought to exert a significant indirect radiative forcing because they act as cloud condensation nuclei in warm cloud-forming processes and ice nuclei in cold cloud-forming processes. Although many of the processes associated with the perturbation of cloud microphysics by anthropogenic aerosols were discussed, IPCC (2007) provided only an estimate of full quantification of the radiative forcing attributable to the first indirect effect (which they referred to as the cloud albedo effect). Here we explain that this approach is necessary if one is to compare the radiative forcing from the indirect effect of aerosols with those from other radiative forcing components such as that from changes in well-mixed greenhouse gases. We also highlight the problems in assessing the effect of anthropogenic aerosols upon clouds under the strict definitions of radiative forcing provided by the IPCC (2007). Although results from global climate models, at their current state of development, suggest that an analysis of indirect aerosol effects in terms of forcing and feedback is possible, a key rationale for the IPCC's definition of radiative forcing, a straightforward scaling between an agent's forcing and the temperature change it induces, is significantly compromised. Feedbacks from other radiative forcings are responses to radiative perturbations, whereas feedbacks from indirect aerosol effects are responses to both radiative and cloud microphysical perturbations. This inherent difference in forcing mechanism breaks down the consistency between forcing and temperature response. It is likely that additional characterization, such as climate efficacy, will be required when comparing indirect aerosol effects with other radiative forcings. We suggest using the radiative flux perturbation associated with a change from preindustrial to present-day composition, calculated in a global climate model using fixed sea surface temperature and sea ice, as a supplement to IPCC forcing.

   
   
5. Wang, S., J.-C. Golaz and Q. Wang, 2008: Effect of intense wind shear across the inversion on stratocumulus clouds Geophys. Res. Lett., 35, L15814, doi: 10.1029/2008GL033865. (pdf, 231K)
   Abstract
   

   A large-eddy simulation model is used to examine the impact of the intense cross-inversion wind shear on the stratocumulus cloud structure. The wind shear enhanced entrainment mixing effectively reduces the cloud water and thickens the inversion layer. It leads to a reduction of the turbulence kinetic energy (TKE) production in the cloud layer due to the weakened cloud-top radiative cooling and the formation of a turbulent and cloud free sublayer within the inversion. The thickness of the sublayer increases with the enhanced wind shear intensity. Under the condition of a weaker inversion, the enhanced shear mixing within the inversion layer even lowers the cloud-top height and reduces the entrainment velocity. Finally, increasing wind shear or reducing inversion strength tends to create an inversion layer with a constant bulk Richardson number (~0.3), suggesting that an equilibrium value of the Richardson number is reached.

   
   
6. Teixeira J., 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, 2008: Parameterization of the atmospheric boundary layer: A view from just above the inversion Bull. Amer. Meteor. Soc., 89, 453-­458. (pdf, 655K; doi: 10.1175/BAMS-89-4-453)
   
   
7. Golaz, J.-C, V. E. Larson, J. A. Hansen, D. P. Schanen, and B. M. Griffin, 2007: Elucidating model inadequacies in a cloud parameterization by use of an ensemble-based calibration framework Mon. Wea. Rev., 135, 4077-4096. (pdf, 2.1M; doi: 10.1175/2007MWR2008.1)
   Abstract
   

   Every cloud parameterization contains structural model errors. The source of these errors is difficult to pinpoint because cloud parameterizations contain nonlinearities and feedbacks. To elucidate these model inadequacies, this paper uses a general-purpose ensemble parameter estimation technique. In principle, the technique is applicable to any parameterization that contains a number of adjustable coefficients. It optimizes or calibrates parameter values by attempting to match predicted fields to reference datasets. Rather than striving to find the single best set of parameter values, the output is instead an ensemble of parameter sets. This ensemble provides a wealth of information. In particular, it can help uncover model deficiencies and structural errors that might not otherwise be easily revealed. The calibration technique is applied to an existing single-column model (SCM) that parameterizes boundary layer clouds. The SCM is a higher-order turbulence closure model. It is closed using a multivariate probability density function (PDF) that represents subgrid-scale variability. Reference datasets are provided by large-eddy simulations (LES) of a variety of cloudy boundary layers. The calibration technique locates some model errors in the SCM. As a result, empirical modifications are suggested. These modifications are evaluated with independent datasets and found to lead to an overall improvement in the SCM's performance.

   
   
8. Larson, V. E., A. J. Smith, M. J. Falk, K. E. Kotenberg, and J.-C. Golaz, 2006: What determines altocumulus dissipation time? J. Geophys. Res., 111, D19207, doi:10.1029/2005JD007002. (pdf, 726K)
   Abstract
   

   This paper asks what factors influence the dissipation time of altocumulus clouds. The question is addressed using three-dimensional, large-eddy simulations of a thin, midlevel cloud that was observed by aircraft. The cloud might be aptly described as "altostratocumulus" because it was overcast and contained radiatively driven turbulence. The simulations are used to construct a budget equation of cloud water. This equation allows one to directly compare the four processes that diminish liquid: diffusional growth of ice crystals, large-scale subsidence, radiative heating, and turbulent mixing of dry air into the cloud. Various sensitivity studies are used to find the "equivalent sensitivity" of cloud decay time to changes in various parameters. A change from no sunlight to direct overhead sunlight decreases the lifetime of our simulated cloud as much as increasing subsidence by 1.2 cm s-1, increasing ice number concentration by 780 m-3, or decreasing above-cloud total water mixing ratio by 0.60 g kg-1. Finally, interactions among the terms in the cloud water budget are summarized in a "budget term feedback matrix." It is able to diagnose, for instance, that in our particular simulations, the diffusional growth of ice is a negative feedback.

   
   
9. Beare, R. J., M. K. MacVean, A. A. M. Holtslag, J. Cuxart, I. Esau, J.-C. Golaz, M. A. Jimenez, M. Khairoutdinov, B. Kosovic, D. Lewellen, T. S. Lund, J. K. Lundquist, A. McCabe, A. F. Moene, Y. Noh, S. Raasch, and P. Sullivan, 2006: An intercomparison of large-eddy simulations of the stable boundary layer. Bound.-Layer Meteor., 118, 247-272. (pdf, 657K; doi: 10.1007/s10546-004-2820-6)
   Abstract
   

   Results are presented from the first intercomparison of large-eddy simulation (LES) models for the stable boundary layer (SBL), as part of the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study initiative. A moderately stable case is used, based on Arctic observations. All models produce successful simulations, in as much as they generate resolved turbulence and reflect many of the results from local scaling theory and observations. Simulations performed at 1-m and 2-m resolution show only small changes in the mean profiles compared to coarser resolutions. Also, sensitivity to subgrid models for individual models highlights their importance in SBL simulation at moderate resolution (6.25 m). Stability functions are derived from the LES using typical mixing lengths used in numerical weather prediction (NWP) and climate models. The functions have smaller values than those used in NWP. There is also support for the use of K-profile similarity in parametrizations. Thus, the results provide improved understanding and motivate future developments of the parametrization of the SBL.

   
   
10. Golaz, J.-C., S. Wang, J. D. Doyle, and J. M. Schmidt, 2005: COAMPS^® -LES: Model evaluation and analysis of second and third moment vertical velocity budgets. Bound.-Layer Meteor., 116, 487-517. (pdf, 975K; doi: 10.1007/s10546-004-7300-5)
    Abstract
    

    The Naval Research Laboratory Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS®) has been extended to perform as a large-eddy simulation (LES) model. It has been validated with a series of boundary-layer experiments spanning a range of cloud nighttime, and includes a nighttime stratocumulus case, a trade wind cumulus layer, shallow cumulus convection over land, and a mixed regime consisting of cumulus clouds under broken stratocumulus. COAMPS-LES results are in good agreement with other models for all the cases simulated. Exact numerical budgets for the vertical velocity second (w'2) and third moment (w'3) have been derived for the stratocumulus and trade wind cumulus cases. For the w'3 budget in the stratocumulus, the buoyancy contribution from the updraughts and downdraughts largely cancel each other due to their similar magnitudes but opposite signs. In contrast, for the cumulus layer, the negative buoyancy contribution from the environmental downdraughts is negligible and the positive contribution from the updraughts completely dominates due to the conditional instability in the environment. As a result, w'3 is significantly larger in the cumulus than in the stratocumulus layer.

    
    
11. Larson, V. E., J.-C. Golaz, H. Jiang, and W. R. Cotton, 2005: Supplying local microphysics parameterizations with information about subgrid variability: Latin hypercube sampling. J. Atmos. Sci., 62, 4010-4026. (pdf, 997K; doi: 10.1175/JAS3624.1)
    Abstract
    

    One problem in computing cloud microphysical processes in coarse-resolution numerical models is that many microphysical processes are nonlinear and small in scale. Consequently, there are inaccuracies if microphysics parameterizations are forced with grid box averages of model fields, such as liquid water content. Rather, the model needs to determine information about subgrid variability and input it into the microphysics parameterization. One possible solution is to assume the shape of the family of probability density functions (PDFs) associated with a grid box and sample it using the Monte Carlo method. In this method, the microphysics subroutine is called repeatedly, once with each sample point. In this way, the Monte Carlo method acts as an interface between the host model's dynamics and the microphysical parameterization. This avoids the need to rewrite the microphysics subroutines. A difficulty with the Monte Carlo method is that it introduces into the simulation statistical noise or variance, associated with the finite sample size. If the family of PDFs is tractable, one can sample solely from cloud, thereby improving estimates of in-cloud processes. If one wishes to mitigate the noise further, one needs a method for reduction of variance. One such method is Latin hypercube sampling, which reduces noise by spreading out the sample points in a quasi-random fashion. This paper formulates a sampling interface based on the Latin hypercube method. The associated family of PDFs is assumed to be a joint normal/lognormal (i.e., Gaussian/lognormal) mixture. This method of variance reduction has a couple of advantages. First, the method is general: the same interface can be used with a wide variety of microphysical parameterizations for various processes. Second, the method is flexible: one can arbitrarily specify the number of hydrometeor categories and the number of calls to the microphysics parameterization per grid box per time step. This paper performs a preliminary test of Latin hypercube sampling. As a prototypical microphysical formula, this paper uses the Kessler autoconversion formula. The PDFs that are sampled are extracted diagnostically from large-eddy simulations (LES). Both stratocumulus and cumulus boundary layer cases are tested. In this diagnostic test, the Latin hypercube can produce somewhat less noisy time-averaged estimates of Kessler autoconversion than a traditional Monte Carlo estimate, with no additional calls to the microphysics parameterization. However, the instantaneous estimates are no less noisy. This paper leaves unanswered the question of whether the Latin hypercube method will work well in a prognostic, interactive cloud model, but this question will be addressed in a future manuscript.

    
    
12. Larson, V. E. and J.-C. Golaz, 2005: Using probability density functions to derive consistent closure relationships among higher-order moments. Mon. Wea. Rev., 133, 1023-1042. (pdf, 621K; doi: 10.1175/MWR2902.1)
    Abstract
    

    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.

    
    
13. Stevens, B., C.-H. Moeng, A. S. Ackerman, C. S. Bretherton, A. Chlond, S. de Roode, J. Edwards, J.-C. Golaz, H. Jiang, M. Khairoutdinov, M. P. Kirkpatrick, D. C. Lewellen, A. Lock, F. Müller, D. E. Stevens, E. Whelan, and P. Zhu, 2005: Evaluation of large-eddy simulations via observations of nocturnal marine stratocumulus. Mon. Wea. Rev., 133, 1443-1462. (pdf, 869K; doi: 10.1175/MWR2930.1)
    Abstract
    

    Data from the first research flight (RF01) of the second Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) field study are used to evaluate the fidelity with which large-eddy simulations (LESs) can represent the turbulent structure of stratocumulus-topped boundary layers. The initial data and forcings for this case placed it in an interesting part of parameter space, near the boundary where cloud-top mixing is thought to render the cloud layer unstable on the one hand, or tending toward a decoupled structure on the other hand. The basis of this evaluation consists of sixteen 4-h simulations from 10 modeling centers over grids whose vertical spacing was 5 m at the cloud-top interface and whose horizontal spacing was 35 m. Extensive sensitivity studies of both the configuration of the case and the numerical setup also enhanced the analysis. Overall it was found that (i) if efforts are made to reduce spurious mixing at cloud top, either by refining the vertical grid or limiting the effects of the subgrid model in this region, then the observed turbulent and thermodynamic structure of the layer can be reproduced with some fidelity; (ii) the base, or native configuration of most simulations greatly overestimated mixing at cloud top, tending toward a decoupled layer in which cloud liquid water path and turbulent intensities were grossly underestimated; (iii) the sensitivity of the simulations to the representation of mixing at cloud top is, to a certain extent, amplified by particulars of this case. Overall the results suggest that the use of LESs to map out the behavior of the stratocumulus-topped boundary layer in this interesting region of parameter space requires a more compelling representation of processes at cloud top. In the absence of significant leaps in the understanding of subgrid-scale (SGS) physics, such a representation can only be achieved by a significant refinement in resolution--a refinement that, while conceivable given existing resources, is probably still beyond the reach of most centers.

    
    
14. Zhu, P., C. S. Bretherton, M. Köhler, A. Cheng, A. Chlond, Q.Geng, P. Austin, J.-C. Golaz, G. Lenderink, A. Lock, and B. Stevens, 2005: Intercomparison and interpretation of single-column model simulations of a nocturnal stratocumulus-topped marine boundary layer. Mon. Wea. Rev., 133, 2741-2758. (pdf, 1.3M; doi: 10.1175/MWR2997.1)
    Abstract
    

    Ten single-column models (SCMs) from eight groups are used to simulate a nocturnal nonprecipitating marine stratocumulus-topped mixed layer as part of an intercomparison organized by the Global Energy and Water Cycle Experiment Cloud System Study, Working Group 1. The case is idealized from observations from the Dynamics and Chemistry of Marine Stratocumulus II, Research Flight 1. SCM simulations with operational resolution are supplemented by high-resolution simulations and compared with observations and large-eddy simulations. All participating SCMs are able to maintain a sharp inversion and a mixed cloud-topped layer, although the moisture profiles show a slight gradient in the mixed layer and produce entrainment rates broadly consistent with observations, but the liquid water paths vary by a factor of 10 after only 1 h of simulation at both high and operational resolution. Sensitivity tests show insensitivity to activation of precipitation and shallow convection schemes in most models, as one would observationally expect for this case.

    
    
15. Cheng, A., K.-M. Xu, and J.-C. Golaz, 2004: The liquid water oscillation in modeling boundary layer cumuli with third-order turbulence closure models. J. Atmos. Sci., 61, 1621-1629. (pdf, 778K; doi: 10.1175/1520-0469(2004)061<1621:tlwoim>2.0.CO;2)
    Abstract
    

    A hierarchy of third-order turbulence closure models are used to simulate boundary layer cumuli in this study. An unrealistically strong liquid water oscillation (LWO) is found in the fully prognostic model, which predicts all third moments. The LWO propagates from cloud base to cloud top with a speed of 1 m s-1. The period of the oscillation is about 1000 s. Liquid water buoyancy (LWB) terms in the third-moment equations contribute to the LWO. The LWO mainly affects the vertical profiles of cloud fraction, mean liquid water mixing ratio, and the fluxes of liquid water potential temperature and total water, but has less impact on the vertical profiles of other second and third moments. In order to minimize the LWO, a moderately large diffusion coefficient and a large turbulent dissipation at its originating level are needed. However, this approach distorts the vertical distributions of cloud fraction and liquid water mixing ratio. A better approach is to parameterize LWB more reasonably. A minimally prognostic model, which diagnoses all third moments except for the vertical velocity, is shown to produce better results, compared to a fully prognostic model.

    
    
16. Larson, V. E., J.-C. Golaz, and W. R. Cotton, 2002: Small-scale and mesoscale variability in cloudy boundary layers: Joint probability density functions. J. Atmos. Sci., 59, 3519-3539. (pdf, 574K; doi: 10.1175/1520-0469(2002)059<3519:ssamvi>2.0.CO;2)
    Abstract
    

    The joint probability density function (PDF) of vertical velocity and conserved scalars is important for at least two reasons. First, the shape of the joint PDF determines the buoyancy flux in partly cloudy layers. Second, the PDF provides a wealth of information about subgrid variability and hence can serve as the foundation of a boundary layer cloud and turbulence parameterization. This paper analyzes PDFs of stratocumulus, cumulus, and clear boundar y layers obtained from both aircraft observations and large eddy simulations. The data are used to fit five families of PDFs: a double delta function, a single Gaussian, and three PDF families based on the sum of two Gaussians. Overall, the double Gaussian, that is binormal, PDFs perform better than the single Gaussian or double delta function PDFs. In cumulus layers with low cloud fraction, the improvement occurs because typical PDFs are highly skewed, and it is crucial to accurately represent the tail of the distribution, which is where cloud occurs. Since the double delta function has been shown in prior work to be the PDF underlying mass-flux schemes, the data analysis herein hints that mass-flux simulations may be improved upon by using a parameterization built upon a more realistic PDF.

    
    
17. Golaz, J.-C., V. E. Larson, and W. R. Cotton, 2002a: A PDF based model for boundary layer clouds. Part I: Method and model description. J. Atmos. Sci., 59, 3540-3551. (pdf, 195K; doi: 10.1175/1520-0469(2002)059<3540:apbmfb>2.0.CO;2)
    Abstract
    

    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.

    
    
18. Golaz, J.-C., V. E. Larson, and W. R. Cotton, 2002b: A PDF based model for boundary layer clouds. Part II: Model results. J. Atmos. Sci., 59, 3552-3571. (pdf, 662K; doi: 10.1175/1520-0469(2002)059<3552:apbmfb>2.0.CO;2)
    Abstract
    

    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.

    
    
19. Brown, A. R., R. T. Cederwall, A. Chlond, P. G. Duynkerke, J.-C. Golaz, M. Khairoutdinov, D. C. Lewellen, A. P. Lock, M. K. MacVean, C.-H. Moeng, R. A. J. Neggers, A. P. Siebesma, and B. Stevens, 2002: Large-eddy simulation of the diurnal cycle of shallow cumulus convection over land. Quart. J. Roy. Meteor. Soc., 128, 1075-1093. (pdf, 601K; doi: 10.1256/003590002320373210)
    Abstract
    

    Large-eddy simulations of the development of shallow cumulus convection over land are presented. Many characteristics of the cumulus layer previously found in simulations of quasi-steady convection over the sea are found to be reproduced in this more strongly forced, unsteady case. Furthermore, the results are shown to be encouragingly robust, with similar results obtained with eight independent models, and also across a range of numerical resolutions. The datasets produced are already being used in the development and evaluation of parametrizations used in numerical weather-prediction and climate models .

    
    
20. Golaz, J.-C., H. Jiang, and W. R. Cotton, 2001: A large-eddy simulation study of cumulus clouds over land and sensitivity to soil moisture. Atmos. Res., 59-60, 373-392. (pdf, 275K; doi: 10.1016/S0169-8095(01)00113-2)
    Abstract
    

    A series of large-eddy simulations (LES) of non-precipitating cumulus clouds over land was performed. These simulations were idealized from observed conditions at the Southern Great Plains ARM site on 21 June 1997 and were intended to investigate the effect of initial soil moisture on the structure of the cloudy boundary layer. The surface fluxes were either dominated by latent heat or sensible heat flux, with the transition between one regime and the other occurring over a very narrow soil moisture range. The effect on clouds was mixed. Cloud fraction was nearly identical throughout all experiments. Simulations with dominant sensible heat fluxes led to more turbulent boundary layers and higher cloud bases. Simulations dominated by latent heat flux tended to have fewer but stronger updrafts in the cloud layer.

    
    
21. Larson, V. E., R. Wood, P. R. Field, J.-C. Golaz, T. H. Vonder Haar, and W. R. Cotton, 2001a: Systematic biases in the microphysics and thermodynamics of numerical models that ignore subgrid-scale variability. J. Atmos. Sci., 58, 1117-1128. (pdf, 184K; doi: 10.1175/1520-0469(2001)058<1117:sbitma>2.0.CO;2)
    Abstract
    

    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.

    
    
22. Larson, V. E., R. Wood, P. R. Field, J.-C. Golaz, T. H. Vonder Haar, and W. R. Cotton, 2001b: Small-scale and mesoscale variability of scalars in cloudy boundary layers: One-dimensional probability density functions. J. Atmos. Sci., 58, 1978-1994. (pdf, 279K; doi: 10.1175/1520-0469(2001)058<1978:ssamvo>2.0.CO;2)
    Abstract
    

    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 obser vational 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.

    
    
23. Galli, G., F. Gygi, and J.-C. Golaz, 1998: Vibrational and electronic properties of neutral and negatively charged C₂₀ clusters. Physical Review B, 57, 1860-1867. (pdf, 161K; doi: 10.1103/PhysRevB.57.1860)
    Abstract