Stochastic Convective Parameterization Development and Method Validation
Todd Jones
1. Motivation
The goal of cumulus parameterization is to realize changes in the simulated large-scale
environment as a function of the collective influence of multiple cumulus clouds that cannot be
explicitly resolved on atmospheric general circulation model (GCM) grids, which are on the
order of 100 km2. There is an attempt to thereby gain computational efficiency over atmospheric
simulations using cloud-resolving scale resolution with a minimal loss of accuracy in the final
solution produced by the GCM. As noted by Lin and Neelin (2002), many general circulation
and numerical weather prediction models use convective parameterizations that only aim to
simulate the first order moment of convection based on a local equilibrium hypothesis. The
equilibrium assumption can only be exactly true, however, in the limit of averaging over an
infinite number of clouds. Its validity, in part, relies on the not-at-all-real existence of a scale
separation between the large-scale environment and the clouds themselves.
In the real atmosphere, there is a contribution to the variability of convection that arises
inherently from small-scale motions and that deviates from the expected response of the
atmosphere to given large-scale temperature, momentum, and moisture fields. Knowledge of
these motions has prompted recognition of the fact that while such a balance is certain in a timeaveraged sense, it is actually only statistical (Randall et al. 1994).
Hence, the assumed
equilibrium as presented above is more correctly referred to as convective “quasi-equilibrium”
(QE). Further, nonlinear interactions between these small-scale fluctuations have been shown
(e.g., Randall et al. 1994) to produce spontaneous large-scale temporal variability that occur on
both short and long timescales. These are features that are absent from GCM simulations
employing a conventional convective parameterization. Fluctuations about the equilibrium state
present in cloud-resolving model (CRM) ensembles and observations, and the extent to which
deterministic and diagnostic convective parameterizations used in large-scale (mesoscale)
simulations fail to capture those statistical fluctuations have been noted by many authors,
including, Shutts and Palmer (2007), Craig and Cohen (2006), and Xu and Arakawa (1992).
Additionally, work in progress by Jones and Randall (ongoing) using results from a set of
2-km horizontal resolution, deep convection-resolving 3D model (Jung and Arakawa 2008)
simulations has produced further quantification and characterization of convective variability.
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The work sought to determine how the statistical fluctuations departing from QE are dependant
upon how quickly a supplied large-scale forcing (destabilization of the atmosphere) varied with
time and also how it depends on the size of the domain being studied. Succinctly, results have
shown that convective variability in response to a large-scale forcing increases with more rapidly
changing large-scale forcings and with decreasing domain size and that it is also variable with
dependence upon the presence of mesoscale organization.
In response to the problem of lacking convective variability in GCMs, authors have used
analysis of the statistical fluctuations (e.g., Lin and Neelin 2002; Teixeira and Reynolds 2008;
Shutts and Palmer 2007; and Plant and Craig 2008) and other statistical methods (e.g., Buizza et
al. 1999; Lin and Neelin 2002; Song et al. 2007; and Bright and Mullen 2002) to add the
convective variability observed in CRMs into the GCM in the form of an enhanced stochastic
(physically or unphysically constrained randomness in time) parameterization. These methods
have been shown to improve the representation of the variability seen in GCM simulation in
comparison to observations in an efficient manner. Unlike these studies, the work of Jones and
Randall (ongoing) has resulted in a dataset describing changes in variability in a number of
convective parameters in response to both changes in the large-scale variability time scale and
the size of the domain. Therefore, the statistical properties gleaned from their research may be
applied to a wide range of atmospheric conditions and can be adapted to be useful for a wide
range of domain sizes (i.e. grid cell sizes), which has not been the case in most of the previous
studies.
The former is clearly important in all simulations, and the latter is becoming
increasingly important as GCM grid cell sizes become smaller with increasing computing
capabilities. The smaller the grid sizes in a GCM become, the more relevant the deviation from
QE becomes in the simulation.
2. Proposition and Methods
Since previous application of convective variability statistics to GCMs has shown a
significant improvement in the GCM statistics, it is promising that the statistics compiled by
Jones and Randall (ongoing) should produce similar improvements, if not greater improvements
due their wider applicability. In spite of all of this, there is no guarantee of the degree to which
any of the CRM-computed statistics agree with observations. It is proposed that a program of
research be undertaken to 1) validate the CRM-computed statistics against observational datasets
and 2) develop a stochastic add-on component to an existing cumulus parameterization based on
the results of item 1. In accomplishing these proposed tasks, the proposed research will be
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relevant to promoting the goals of CMMAP by providing an increased understanding of the
physical cloud processes in a statistical sense and by adding to the general mission of CMMAP,
which is to develop an improved method with which to include the effects of clouds on the largescale atmosphere in a large-scale model.
Item 1 would likely require the analysis of a number of operational data sets to create
similar statistics as to what have been presented by Jones and Randall (ongoing). A candidate
source for the observed cloud and precipitation fields required for computation of the statistics is
the satellite CloudSat. CloudSat provides cloud profiling radar reflectivity, a cloud detection
mask, measures of cloud type and precipitation occurrence and type.
Additionally, a
corresponding relatively dense 3D wind and moisture fields would be required. The most
reliable data set for these fields is likely a reanalysis (TBD). By obtaining observations over a
variety of computed large-scale forcings, statistics could be computed relative to the forcing
magnitude and rate of change for an array of domain sizes for comparison with the CRM-derived
statistics to assess their validity.
Item 2 is the development of a stochastic convective parameterization. This will require
the application of the findings of item 1 to an existing conventional convective parameterization.
A likely candidate for this initial test would be the Zhang and McFarlane (1995)
parameterization as employed in the Community Atmosphere Model (CAM). Comparison of its
statistics of convective variability prior to and following the application of the new stochastic
parameterization will determine its usefulness. Additionally, it may be useful to test the new
stochastic parameterization in models used in previous studies to gauge improvement over past
techniques.
This project is to span three years, requiring funding for one graduate student for a year
and one professor for one month. One new computer will be required in addition to at least three
to six terabytes of local storage space. In the first year, the main focus will be on selecting the
correct data sets, obtaining those data sets, and analyzing those data sets as set forth in item 1.
The comparison to the CRM-derived statistics would also be started in this year, and it would
likely carry on into year 2. The second year will further consist of the development of the
stochastic convective parameterization, including all testing, selection of parameterization to
alter, and selection of model for testing.
Year three will be spent implementing the new
convective parameterization and analyzing the statistics of the modified model.
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References
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