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Cloud parameterization and variability: is an important subject because clouds are too small to be resolved by numerical weather forecast models, even with the most powerful of presentday computers. Hence forecasts need to account for the smallscale cloud variability that they cannot represent explicitly.
2001: ``Systematic Biases in the Microphysics and Thermodynamics of Numerical Models that Ignore Subgrid Variability." V. E. Larson, R. Wood, P. R. Field, J.C. Golaz, T. H. Vonder Haar, W. R. Cotton. J. Atmos. Sci., 58, 11171128. (See also slides 812 of the following presentation, and this short conference paper.)
The paper above explores some systematic biases related to cloud processes. A systematic bias is a particular kind of error, namely one that always has the same sign. A systematic bias is more harmful than a series of ordinary errors, because a systematic bias can never partially selfcancel when averaged over space or time.
If a numerical model ignores variability on scales smaller than the grid box size, then a systematic bias can sometimes occur. These biases are associated with convex functions. One can find systematic biases by use of a theorem known as Jensen's inequality.
2001: ``Smallscale and Mesoscale Variability of Scalars in Cloudy Boundary Layers: Onedimensional Probability Density Functions." V. E. Larson, R. Wood, P. R. Field, J.C. Golaz, and T. H. Vonder Haar. J. Atmos. Sci., 58, 19781994. (See also the following short conference paper.)
The systematic biases mentioned above can be removed if a model can predict the appropriate probability density function (PDF). A PDF is essentially a histogram. It indicates the probability of finding a particular value of specific humidity, for instance, in a computational grid box. This paper examines PDFs of clouds. Some look quite complicated, with a long tail on the right or the left. However, the level of complexity is manageable (we hope!).
2002: ``SmallScale and Mesoscale Variability in Cloudy Boundary Layers: Joint Probability Density Functions." V. E. Larson, J.C. Golaz, W. R. Cotton. J. Atmos. Sci., 59, 35193539. (See also the following short conference paper.)
Whereas the prior paper discusses onedimensional PDFs of cloud water and humidity, this paper discusses joint PDFs that include the vertical velocity. Joint PDFs allow us to diagnose the buoyancy flux, which is the means by which convection generates turbulence. Joint PDFs also allow us to diagnose fluxes of heat and moisture. Therefore, joint PDFs can serve as the foundation of cloud and turbulence parameterizations in numerical models, as proposed and explored in the two following papers.
2002: ``A PDFBased Model for Boundary Layer Clouds. Part I: Method and Model Description." J.C. Golaz, V. E. Larson, W. R. Cotton. J. Atmos. Sci., 59, 35403551.
2002: ``A PDFBased Model for Boundary Layer Clouds. Part II: Model Results." J.C. Golaz, V. E. Larson, W. R. Cotton. J. Atmos. Sci., 59, 35523571.
(See also slides 1335 of the following presentation, and this short conference paper.)
Traditionally, cloud parameterization has been viewed as a multiplicity of tasks. Such tasks include the prediction of heat flux, moisture flux, cloud fraction, and liquid water. In contrast, the papers above adopt the alternative viewpoint that the goal of parameterization consists largely of a single task: the prediction of the joint PDF of vertical velocity, heat, and moisture. Once the PDF is given, the fluxes, cloud fraction, and liquid water can be diagnosed.
The above papers present a parameterization that can model both stratocumulus and cumulus clouds without casespecific adjustments. This avoids the difficulty of having to construct a ``trigger function" that determines which cloud type should be modeled under which meteorological conditions.
2005: ``Using Probability Density Functions to Derive Consistent Closure Relationships among HigherOrder Moments." V. E. Larson and J.C. Golaz. Mon. Wea. Rev., 133, 10231042. (See also slides 2627 of the following presentation.)
The aforementioned papers show that if we choose an accurate PDF family, then we can solve for many of the unknowns in our onedimensional cloud parameterization. For some of these unknown terms, the present paper lists simple, analytic approximations. All approximated formulas are based on the same PDF and hence are consistent with each other.
A PDF may be constructed from a set of means, variances, and other moments of velocity, moisture, and temperature. It is possible that a particular set of moments does not correspond to any real PDF in the family. We call such a set of moments ``specifically unrealizable." For instance, a set that includes asymmetric moments is specifically unrealizable with respect a PDF family of symmetric, bellshaped curves. This is because the bell shape family is too restrictive to include asymmetric moments. We show that a broad class of moments is specifically realizable with respect to our PDF family. That is, our PDF family is not restrictive.
2012: ``PDF Parameterization of boundary layer clouds in models with horizontal grid spacings from 2 to 16 km." V. E. Larson, D. P. Schanen, M. Wang, M. Ovchinnikov, and S. Ghan. Mon. Wea. Rev., 140, 285306.
This paper implements CLUBB in a
convectionpermitting model, SAM. The use of CLUBB in SAM is
tested for various boundarylayer cloud cases. We introduce a
simple, scaleaware method for damping CLUBB's effects at high
resolution, thereby reducing undesirable sensitivities to horizontal
grid spacing. We find that the use of CLUBB can improve the
simulations for grid spacings of 4 km or greater.
2013: ``Highorder turbulence closure and its impact on climate simulations in the Community Atmosphere Model." P. A. Bogenschutz, A. Gettelman, H. Morrison, Vincent E. Larson, C. Craig, and D. P. Schanen. J Climate.
In this paper, CLUBB is implemented and
tested in a global climate model, CAM. CLUBB is used in these
simulations to parameterize all shallow (stratocumulus and cumulus)
clouds. The resulting model, CAMCLUBB, is competitive with the
standard version of CAM, CAM5.
2013:
``Analytic upscaling of a local microphysics scheme. Part I: Derivation."
V. E. Larson and B. M. Griffin. Quart. J. Roy. Meteor. Soc., 139, 4657.
2013:
``Analytic upscaling of a local microphysics scheme. Part II: Simulations."
B. M. Griffin and V. E. Larson. Quart. J. Roy. Meteor. Soc., 139, 5869.
2005: ``Supplying local microphysics parameterizations with information about subgrid variability: Latin hypercube sampling." V. E. Larson, J.C. Golaz, H. Jiang, and W. R. Cotton. J. Atmos. Sci., 62, 40104026. (See also slides 3660 of the following presentation.)
The most accurate way to drive microphysics using a PDF is to integrate the relevant microphysical formulas analytically over the PDF. However, this may be intractable for some microphysics schemes or may require rewriting the microphysics code. To avoid this, one may draw sample points from the PDF and input them into the microphysics code one at a time. This allows the use of existing microphysics codes, but it also introduces statistical noise due to imperfect sampling. To reduce the noise, this paper proposes spreading out the sample points in a quasirandom fashion using "Latin hypercube sampling."
2007: ``From Cloud Overlap to PDF Overlap." V. E. Larson. Q. J. R. Meteorol. Soc., 133, 18771891. (See also the following presentation.)
Cloud overlap occurs when cloud layers at different altitudes are colocated horizontally. Because cloud overlap influences radiative transfer, it is desirable to parameterize overlap in climate models.
Even when two cloud layers are entirely overcast, it may still be beneficial to parameterize how liquid water contents in the two layers overlap. This is an example of "PDF overlap" (where “PDF” denotes probability density function).
Some climate models predict a separate PDF at each grid level, but this does not, in itself, tell us how the PDFs or clouds overlap in the vertical. To handle PDF overlap, we propose a new algorithm. It generalizes the separate PDFs at each level into a single, joint PDF that represents the entire grid column. An advantage of the algorithm is that it allows us to represent the joint overlap of more than one field, such as moisture or temperature.
In order to drive microphysics using
subgrid variability, we need to know the correlations between
hydrometeor species. For instance, the correlation between cloud
water and rain water influences the rate of accretion of cloud droplets
by rain drops. If cloud and rain are correlated, then cloud and
rain coexist, and accretion occurs rapidly. This paper proposes
a method to diagnose correlations based on information that is
typically available in cloud models.
2007: ``A singlecolumn model intercomparison of a heavily drizzling stratocumulustopped boundary layer." M. C. Wyant and CoAuthors. J. Geophys. Res., 112, D24204, doi:10.1029/2007JD008536.
This paper compared the output from numerous singlecolumn model that were all set up identically to simulate a cloud layer observed during the DYCOMSII field experiment. Part of the challenge was simulating drizzle. In order to couple drizzle to the cloud fields, instead of drawing sample points from the PDF using the Latin hypercube method discussed above, we analytically integrated over the PDF. This avoids the statistical noise inherent in Monte Carlo methods such a Latin hypercube sampling. However, the analytic integration can be performed only if the drizzle equations are simple enough.
2009: ``Intercomparison of model simulations of mixedphase clouds observed during the ARM MixedPhase Arctic Cloud Experiment. Part I: Single layer cloud." S. A. Klein and Coauthors (including V. E. Larson). Quart. J. Royal Met. Soc., 135, 9791002.
2009: ``Intercomparison of model simulations of mixedphase clouds observed during the ARM MixedPhase Arctic Cloud Experiment. Part II: Multilayer cloud." H. Morrison and Coauthors (including V. E. Larson). Quart. J. Royal Met. Soc., 135, 10031019.
Clouds in the Arctic are often mixedphase: that is, they often contain both liquid and ice. Longlived mixedphase clouds are difficult to simulate because ice naturally tends to grow at the expense of liquid. Models may overdeplete liquid unless the ice particles are limited in number and sediment out of cloud base rapidly enough. Our cloud parameterization, CLUBB, was used to simulate mixedphase clouds during the MPACE experiment. CLUBB was able to maintain liquid water in these clouds, as was observed.
2013: ``A singlecolumn model ensemble approach applied to the TWPICE experiment." L. A. Davies and Coauthors (including V. E. Larson). J. Geophys. Res., 118, 65446563.
2007: ``Elucidating model inadequacies in a cloud parameterization by use of an ensemblebased calibration framework." J.C. Golaz, V. E. Larson, J. A. Hansen, D. P. Schanen, and B. M. Griffin. Mon. Wea. Rev., 135, 40774096. (See also the following oral presentation or slides, and this conference paper.)
It is often easy to see when an atmospheric model disagrees with data. It is usually much harder to locate the ultimate sources of model error.
It is particularly difficult to diagnose errors in a model's structure, that is, errors in the functional form of the model equations. One technique that may help is parameter estimation, that is, the optimization of model parameter values. Typically, parameter estimation is used solely to improve the fit between a model and observational data. In the process, however, parameter estimation may cover up structural model errors.
In a quite opposite application, parameter estimation may be used to uncover the ways in which a model is wrong. The basic idea is to separately optimize model parameters to two different data sets, and then identify parameter values that differ between the two optimizations. When no single value of a particular parameter fits both datasets, then there must exist a related structural error.
2004: ``Prognostic equations for cloud fraction and liquid water, and their relation to filtered density functions." V. E. Larson. J. Atmos. Sci., 61, 338351. (See also slides 2932 of the following presentation, and this short conference paper.)
This paper derives equations for cloud fraction and liquid water content. Such equations are used in numerical models that cannot resolve all variability in wind, heat, and moisture because their grid boxes are too large (e.g., Tiedtke 1993). The derivations show that closure of these equations requires information about the PDF of vertical velocity, heat, and moisture.
Carbon cycle: is important for climate studies because not all the carbon dioxide that is emitted by humans remains in the atmosphere. Rather, some CO_{2} is taken up by vegetation or dissolved in the oceans.
2008: ``An idealized model of the onedimensional carbon dioxide rectifier effect." V. E. Larson and H. Volkmer. Tellus B, 60B, 525536. (See also this shorter conference paper.)
The net flux of carbon dioxide (CO_{2}) from the land surface into the atmospheric boundary layer has a diurnal cycle. Drawdown of CO_{2} occurs during daytime photosynthesis, and return of CO_{2} to the atmosphere occurs during night. Even when the net diurnalaverage surface flux vanishes, the diurnalaverage profile of atmospheric CO_{2} mixing ratio is usually not vertically uniform. This is because of the diurnal rectifier effect, by which atmospheric vertical transport and the surface flux conspire to produce a surplus of CO_{2} near the ground and a deficit aloft.
This paper constructs an idealized, 1D, eddydiffusivity model of the rectifier effect and provides an analytic series solution. When nondimensionalized, the intensity of the rectifier effect is related solely to a single ‘rectifier parameter’.
Alto clouds: could be called the ``forgotten clouds" of meteorology because they are less studied than other cloud types. But we think they are well worth remembering!
2002: ``Observed microphysical structure of midlevel, mixedphase clouds." R. P. Fleishauer, V. E. Larson, and T. H. Vonder Haar. J. Atmos. Sci., 59, 17791804. (See also this related presentation.)
Altostratocumulus (ASc) clouds are not merely very high stratocumulus clouds. ASc are distinctive because they are often mixedphase and also because they are often decoupled from surface fluxes of heat, moisture, and momentum. This paper presents some observations from the CLEX5 field experiment. In most cases we examined, there were weak temperature inversions and wind shears at cloud top. This contrasts with many observations of lowlevel stratocumulus clouds. We conjecture that the differences are related to the fact that ASc clouds are usually not sustained by surface moisture fluxes, and they are usually not frictionally coupled to the ground by turbulent updrafts and downdrafts.
CLEX5 frequently encountered alto clouds containing both liquid and ice. In the thin, singlelayer clouds that we observed, we found that near cloud top, where the cloud is coldest, liquid predominates over ice. Near cloud bottom, where the cloud is warmest, ice predominates. Prior authors have found the same vertical structure. Presumably it is due to gravitational settling of the ice crystals. 2001: ``The death of an altocumulus cloud." V. E. Larson, R. P. Fleishauer, J. A. Kankiewicz, D. L. Reinke, and T. H. Vonder Haar. Geophys. Res. Lett., 28, 26092612. This is a case study of an altostratocumulus cloud that ``died," or dissipated, as an aircraft observed it. There are four mechanisms that can cause an ASc to die: solar heating, incorporation into the cloud of dry air from outside, heating induced by largescale subsidence of air, and precipitation. In this particular case, subsidence seemed to be the major culprit. Solar radiative heating was weak because the cloud formed over Montana in November.
2006: ``What determines altocumulus dissipation time?" V. E. Larson, A. J. Smith, M. J. Falk, K. E. Kotenberg, and J.C. Golaz. J. Geophys. Res., 111, D19207, doi:10.1029/2005JD007002. (See also the following two animations, courtesy of David Schanen. The first shows dissipation of liquid water, with redder colors representing higher amounts of liquid; notice the strong turbulence. The second movie shows the evolution of cloud top and cloud base surfaces; notice that although the cloud base rises, the cloud remains overcast (100% cloud cover) until near the end of the simulation.)
This paper further investigates the causes of altostratocumulus death using numerical simulations. A particular subject of study is feedbacks or interactions between the 4 aforementioned processes: solar heating, incorporation into the cloud of dry air from outside, heating induced by largescale subsidence of air, and precipitation of ice. To quantify these, we construct a "budget term feedback matrix." It shows that precipitation of ice is a negative feedback on the other processes. For instance, if solar heating dissipates the cloud, precipitation of ice dissipates the cloud less than it would have otherwise, thereby diminishing the effectiveness of solar heating on cloud dissipation rate.
2009: ``Processes that generate and deplete liquid water and snow in midlevel, mixedphase clouds" A. J. Smith, V. E. Larson, J. Niu, J. A. Kankiewicz, L. D. Carey. J. Geophys. Res., 114, D12203, doi:10.1029/2008JD011531.
This paper extends the study of Larson et al. (2006) by adding simulations of two new observed mixedphase altostratocumulus cases and by constructing budgets of snow. As before, the new clouds, in both observations and simulations, consist of a mixedphase layer with a quasiadiabatic profile of liquid, and a virga layer below that consists of snow. The snow budgets show that snow grows by deposition in and below the liquid (mixedphase) layer, and sublimates in the remainder of the virga region below. The deposition and sublimation are balanced primarily by sedimentation, which transports the snow from the growth region to the sublimation region below.
2009: ``An analytic scaling law for glaciation rate in mixedphase layer clouds." V. E. Larson and A. J. Smith. J. Atmos. Sci., 66, 26202639. In various practical problems, such as assessing the threat of aircraft icing or calculating radiative transfer, it is important to know whether or not mixedphase clouds contain significant liquid water content. Some mixedphase clouds remain predominantly liquid for an extended time, and others glaciate, or become converted to ice, quickly. The glaciation rate of mixedphase layer clouds is thought to depend on various factors. This paper attempts to quantify some of these factors by deriving scaling laws (i.e.~power laws) for the amount of snow at cloud base. The scaling laws are derived from the governing equation for snow concentration. The scaling laws agree adequately with highresolution simulations over one order of magnitude for snow flux and over two orders of magnitude for snow mixing ratio. They indicate, for instance, that cloud base snow amount increases faster than linearly with increasing cloud thickness and supersaturation with respect to ice. By varying the exponents and prefactors of the scaling laws, one may explore the sensitivity of glaciation rate to ice particle shape. The relationship is complex, but for our cloud cases, dendrites tend to glaciate cloud more rapidly than plates.
2007: ``What causes partial cloudiness to form in multilayered midlevel clouds? A simulated case study." M. J. Falk and V. E. Larson. J. Geophys. Res., 112, D12206, doi:10.1029/2006JD007666. (See also the following short conference paper.)
At first glance, one might expect that a lower cloud layer would be little affected by a separated upper cloud layer that does not deposit snow or other quantities into it. However, we find that the cloud fraction of such a lower layer can increase from 15% to 100% if the upper layer is removed. The reason is that the removal of the upper layer allows cloudtop radiative cooling in the lower layer, thereby stabilizing it.
2007: ``An analytic longwave radiation formula for liquid layer clouds." V. E. Larson, K. E. Kotenberg, and N. B. Wood. M. Wea. Rev., 135, 689699. (See also the following short conference paper.)
This paper discusses an idealized longwave radiative transfer parameterization that is used in two papers above, Falk and Larson (2007) and Larson et al. (2006). This radiation parameterization is easy to implement in a numerical model, rendering it especially useful for numerical model intercomparisons. Dry atmospheres in radiativeconvective equilibrium: The goal of the two papers below is to move theory one step away from RayleighBenard convection, which has proved so fruitful for understanding of buoyant fluids, and one step closer to atmospheric convection. The problem considered here adds infrared radiation to the classical problem of fluid flow between two plates, the lower being heated and the upper being cooled. When radiation is added, the stability properties do not change qualitatively as long as one substitutes a radiative Rayleigh number for the classical Rayleigh number. However, when fluid motion occurs, the turbulent heat flux does change because the heat flux is strongly constrained by radiation.
(The following article has been made available by the permission of Dynamics of Atmospheres and Oceans. Single copies of the following article can be downloaded and printed for the reader's personal research and study.) 2001: ``The effects of thermal radiation on dry convective instability.'' V. E. Larson. Dynamics of Atmospheres and Oceans, 34, 4571. 2000: “Stability properties of and scaling laws for a dry radiativeconvective atmosphere.” V. E. Larson. Q. J. R. Meteorol. Soc., 126, 145171.
1999: “The relationship between the transilient matrix and the Green’s function for the advectiondiffusion equation.” V. E. Larson. J. Atmos. Sci., 56, 24472453. (See also slide 7 of the following presentation.)
The point of this paper is that if a singlecolumn model contains information only about horizontal averages, it discards crucial information about horizontal structure. For instance, a singlecolumn model may predict the average concentration of a pollutant at some altitude perfectly. But a model that only predicts averages doesn't know whether the pollutant resides in an updraft or downdraft. Hence the model doesn't know whether to transport the pollutant up or down at the next time step. Therefore, the transport prediction degrades rapidly. This problem was termed ``convective structure memory" by Roland Stull. It can be quantified using Green's function theory. This problem is part of the motivation for the papers below on probability density functions (PDFs). PDFs do contain information beyond the horizontal averages.
