Douglas K. Lilly

A proposed modification of the Germano subgrid‐scale closure method

The subgrid‐scale closure method developed by Germano et al. is modified by use of a least squares technique to minimize the difference between the closure assumption and the resolved stresses. This modification removes a source of singularity and is believed to improve the method’s applicability.

Dynamics and chemistry of marine stratocumulus - DYCOMS II

The second Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) field study is described. The field program consisted of nine flights in marine stratocumulus west-southwest of San Diego, California. The objective of the program was to better understand the physics a n d dynamics of marine stratocumulus. Toward this end special flight strategies, including predominantly nocturnal flights, were employed to optimize estimates of entrainment velocities at cloud-top, large-scale divergence within the boundary layer, drizzle processes in the cloud, cloud microstructure, and aerosol–cloud interactions. Cloud conditions during DYCOMS-II were excellent with almost every flight having uniformly overcast clouds topping a well-mixed boundary layer. Although the emphasis of the manuscript is on the goals and methodologies of DYCOMS-II, some preliminary findings are also presented—the most significant being that the cloud layers appear to entrain less and drizzle more than previous theoretical work led investigat...

Generalized Smagorinsky model for anisotropic grids

The Smagorinsky subgrid model is revised to properly account for grid anisotropy, using energy equilibrium considerations in isotropic turbulence. For moderate resolution anisotropies, Deardorff’s estimate involving an equivalent grid scale Δeq=(Δ1Δ2Δ3)1/3 is given a rigorous basis. For more general grid anisotropies, the Smagorinsky eddy viscosity is recast as νT=[csΔeqf(a1, a2)]2‖S‖, where f(a1,a2) is a function of the grid aspect ratios a1 and a2, and ‖S‖ is the resolved strain rate magnitude. The asymptotic behavior of νT at several limits of the aspect ratios are examined. Approximation formulas are developed so that f(a1,a2) can easily be evaluated in practice, for arbitrary values of a1 and a2. It is argued that these results should be used in conjunction with the dynamic model of Germano et al. whenever the anisotropy of the test‐filter differs significantly from that of the basic grid.

A comparison of two dynamic subgrid closure methods for turbulent thermal convection

Two dynamic subgrid‐scale (SGS) closure methods for turbulent thermal convection are described. The first method assumes the dissipation rate equals the SGS energy production rate that includes a troublesome buoyancy term, while the second method avoids this complication with a simplifying scale analysis. Tests with large‐eddy simulations (LES) of thermal convection reveal that the second method is computationally efficient, and produces results agreeing with direct numerical simulation (DNS) data, as well as values predicted by the inertial subrange theory. Within the LES, the SGS representation is locally and dynamically adjusted to match the statistical structure of the smallest resolvable eddies.

Some facets of the predictability problem for atmospheric mesoscales

The predictability of mesoscale weather differs from that of the larger scales in several ways, but perhaps most importantly through the greater intermittance of the small scales and the importance of relatively rare high amplitude events. For quiescent weather periods predictability is presumably roughly determinable from the structure of the velocity variance, as measured by, e.g., the energy spectrum or spatial covariance function. Recent measurements from radar and aircraft indicate that the kinetic energy spectrum follows a ‐5/3 power law for wave lengths between a few and a few hundred km. Two different explanations for this structure are discussed, one based on turbulence dynamics and the other assuming the dominance of internal gravity waves.Strongly energetic turbulent events, like buoyant convective storm systems, can be expected to have a shorter predictability time than quiescent weather. For a particularly important high energy convective storm type, the rotating ‘‘supercell’’ storms, evidenc...

Mesoscale Organization and Processes: Panel Report

The Panel on Mesoscale Organization and Processes consisted of 19 members (identified in the footnote) who either produced written responses to requests for review of Dr. Keith Browning’s paper (see Chapter 26a) or attended the panel meeting in Boston, or both. The reviewers of Browning’s paper agreed that it is well written and authoritative. We are deeply indebted to Dr. Browning for his untiring efforts in compiling his review and also recognize the unique perspective afforded by his distinguished career. The panel would also like to thank him for his gracious responses to requests for expansion and alteration of his review paper.

The Meteorological Development of Large Eddy Simulation

The development of what is now called large eddy simulation is traced from the early days of numerical weather prediction to Smagorinsky’s 1963 introduction of a first order subgrid scale closure, Lilly’s analysis of the technique and utilization in 2-dimensional simulations of convection, and Deardorff’s further development and exploitation through 3-dimensional simulations of boundary layer flows. Smagorinsky’s closure was originally based on an empirical smoothing device developed by von Neumann and Richtmyer for 1-dimensional shock wave calculations, extended to 2- and 3-dimensional flow by Charney and Phillips. In a series of papers from 1972–80, Deardorff largely developed and defined large eddy simulation, though not under that name. His work was aimed at elucidating the structure and behaviour of turbulent boundary layers at high Reynolds and low Mach numbers, and was interpersed with a series of laboratory simulations and theoretical analyses. He introduced or initially applied several modeling concepts and techniques which have been followed, and in most cases are still utilized in some form, by investigators in geophysical and engineering fluid dynamics. The sequence, methods and results are reviewed and reconsidered.

Application of a 3D delta-Eddington radiative transfer model to calculation of solar heating and photolysis rates in a stratocumulus cloud layer

A number of problems of aerosol/cloud and radiation/cloud interactions, as well as cloud chemistry, related to climate change study, which could be addressed with 3-D cloud structure models which incorporate a detailed `inventory of physical processes. Also, cloud remote sensing problems can be sensitive to the 3-D structure of clouds. Those problems motivate us to develop a 3-D Large Eddy Simulation model with explicit description of cloud microphysical processes. The model output contains fields of aerosol and drop size distributions, among other output parameters. Some results of recent model runs are presented. In order to study a 3-D radiance response of the system we derive a `two-stream approximation of radiative transfer for a 3-D inhomogeneous medium based on a 3-D delta- Eddington method. The basic equations of the method are derived and the solution method is outlined. Relevance of the model to investigation of arctic stratus layers is discussed.

Study of the effects of cloud microphysics on cloud optical depth parameterizations using an explicit cloud microphysical model

The impact of clouds on radiation fields is one of the most important. It is well known that clouds greatly affect the earths radiation budget, thus exerting a profound influence on the radiative driving force of the climate system. The clouds affect motions of all spatial scales resulting in the fact that atmospheric models need to include increasingly more and more sophisticated parameterizations of interactions with clouds. Examples range from general circulation models 1,2 large eddy simulations of the cloudy boundary layer 35,to relatively simple one-dimensional models of fog or boundary layer stratus. L5 Many studies demonstrate the importance of the detail microphysics. The correct determination of radiative iransfer and the total water budget requires information about the dropsize distribution function. Since these models only allow currently to detennine the liquid water content, they need to use pararneterization (albeit crude) to take into account implicitly some details of microphysics. It is important that those schemes should be capable of accounting for the radiative effects of clouds as accurate as possible. Regarding to the climate models most swdies describe the role of clouds in climate change problems generally assuming for the cloud radiative properties to be constant. It means that they consider either constant optical thickness or specify the bulk radiative properties such as the transmittance and reflectivity as fixed The climatic effects of clouds are restricted mostly to those that associated with changes in cloud amounts. For GCMs the siwation is not better and it is almost a standard practice to assign predetermined values to the relevant shortwave optical and radiative characteristics of clouds. This approach has suffered not only from the problem how to determine what quantities should be prescribed to these parameters, but from severe limitation, related to the fact that the radiative properties of clouds also change with both changing cloud character and changing sun elevation. Extensive observations apparently demonstrate (e.g., 910 ) that those predetermined cloud properties are often do not have good enough agreement with both observational and theoretical data. In addition theory and observations have shown strong dependence of cloud radiative characteristics from cloud microstrucwre. The swdies 1044 have examined the dependence of cloud shortwave properties on the dropsize distribution. It has been found that as the dropsize increases at constant liquid water content, there is a small increase in the absorption, and a larger increase in the scattering and albedo. This results from the larger optical thickness that arise from drop spectra composed of smaller droplets. tei& and Slingo and Schrecker14 showed thai. the distribution of heating in the cloud is also influenced by the drop size spectra. Radiative transfer depends on microphysics through the scattering and extinction functions which directly include the dropsize distribution. The complex interactions between different physical processes in cloud formation and evolution on a wide range of scales make the development of accurate cloud parameterizations for global climate and 0CM model a difficult task. We believe that high-resolution Sc model that explicitly formulates microphysical and radiative processes is a tool that can improve our understanding of the complex interactions between all these processes and serve as a basis for the development of more accurate parameterizations. The cloud optical thickness is one of the most important parameters used in determination and parameterization of cloud radiative properties. Based on the simulations with a 3-D large-eddy simulation model of marine cloud-topped boundary layer that includes explicit cloud physics formulation, we will evaluate in this paper the effect of spatial inhomogeneities in cloud macro and microstructure on the performance of two parameterizations of cloud optical depth