Under this grant, we continued development and evaluation of the updraft downdraft model for cumulus parameterization. The model includes the mass, rainwater and vertical momentum budget equations for both updrafts and downdrafts. The rainwater generated in an updraft falls partly inside and partly outside the updraft. Two types of stationary solutions are identified for the coupled rainwater budget and vertical momentum equations: (1) solutions for small tilting angles, which are unstable; (2) solutions for large tilting angles, which are stable. In practical applications, we select the smallest stable tilting angle as an optimum value. The model has been incorporated into the Arakawa-Schubert (A-S) cumulus parameterization. The results of semi-prognostic and single-column prognostic tests of the revised A-S parameterization show drastic improvement in predicting the humidity field. Cheng and Arakawa presents the rationale and basic design of the updraft-downdraft model, together with these test results. Cheng and Arakawa, on the other hand gives technical details of the model as implemented in current version of the UCLA GCM

Arakawa, Akio

Mechoso, Carlos R.

English

NASA Technical Reports Server

NASA-CR-205076
Numerical Modeling of the Global Atmosphere
Summary of Research
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P.I. Akio Arakawa Co-P.I. Carlos R. Mechoso
Period covered by the report: 5/15/94 - 12/31/96
University of California, Los Angeles
405 Hilgard Ave., Los Angeles, CA 90095
Grant number: NAG 5-2591
This report summarizes the research we performed under the grant NAG 5-
2591, which consisted of the following topics:
(a) Development and evaluation of parameterization of convective-scale
downdrafts
Under this grant, we continued development and evaluation of the updraft-
downdraft model for cumulus parameterization. The model includes the mass,
rainwater and vertical momentum budget equations for both updrafts and
downdrafts. The rainwater generated in an updraft falls partly inside and partly
outside the updraft. Two types of stationary solutions are identified for the coupled
rainwater budget and vertical momentum equations: (1) solutions for small tilting
angles, which are unstable; (2) solutions for large tilting angles, which are stable. In
practical applications, we select the smallest stable tilting angle as an optimum
value. The model has been incorporated into the Arakawa-Schubert (A-S) cumulus
parameterization. The results of semi-prognostic and single-column prognostic
tests of the revised A-S parameterization show drastic improvement in predicting
the humidity field. Cheng and Arakawa (1997a) presents the rationale and basic
design of the updraft-downdraft model, together with these test results. Cheng and
Arakawa (1997b), on the other hand gives technical details of the model as
implemented in the current version of the UCLA GCM.
(b) Analysis of cloud properties simulated by a cloud ensemble model
We used a 2-D numerical cloud-resolving model (CRM) developed earlier for
studying cumulus entrainment and associate processes. First, we analyzed the
simulated data following the methods commonly used in observational studies on
cumulus entrainment and confirmed that the characteristic results from
observational studies can be produced using the simulated data. Second, through
extensive trajectory analysis, we investigated entrainment sources and the dilution
effect of entrainment on the bulk properties of each cumulus subensemble, which is
identified by the stratification of simulated saturated updrafts according to their
eventual heights. Then the total cloud mass flux and mean moist static energy are
https://ntrs.nasa.gov/search.jsp?R=19980211542 2020-06-15T23:57:31+00:00Z
calculated for each subensemble, and entrainment characteristics are inferred from
the cloud mass flux and in-cloud moist static energy. It was found that different
subensembles do have distinguishable entrainment characteristics. All
subensembles, however, are subject to the most significant dilution effect at levels
immediately above cloud base. All of these results are discussed in the paper by Lin
and Arakawa (1997 a, b).
(c) Statistical analysis of large-scale observed data and development of an
empirical cumulus parameterization
A cumulus parameterization generally combines a cloud model with a closure
assumption. The choice of a cloud model represents the "physical" aspect of the
problem while the choice of a closure assumption represents the "logical" aspect.
With this in mind, we performed statistical analysis of observed large-scale data to
study the macroscopic behavior of moist convection. Using the method of rotated
EOF (REOF) analysis applied to the vertical profiles of cumulus heating (Qi) and
cumulus drying (Q2) diagnosed from observed large-scale heat and moisture
budgets, we empirically classified cloud regimes and determined the characteristic
normalized vertical distributions of Q1 and Q2 for each cloud regime. Then, for
each cloud regime, we defined an empirical cloud work function, which is a
combination of (the vertical profiles of) thermodynamic state variables and their
vertical gradients that is strongly constrained to be near constant in observed time
sequences. We constructed an empirical cumulus parameterization in this way
using observations over the tropical Asian continent (Liu 1995). The
parameterization is then applied to the GATE situations for verification with very
encouraging results.
(d) Development and evaluation of a parameterization of orographic gravity
waves
We developed a new parameterization of orographic gravity waves that takes
into account the drag enhancement due to the formation of nonlinear critical layer
at the lee side of mountains. The development was guided by a number of
experiments performed with a numerical mesoscale model applied to a variety of
orographic conditions. Based on statistical measures of the subgrid-scale orography,
given as inputs additional to the mean and standard deviation of the surface height,
the parameterization selectively enhances drags at the reference-level and at lower-
tropospheric levels above when a nonlinear critical layer is expected to form. The
basis and description of the parameterization scheme are presented by Kim and
Arakawa (1995). The parameterization was then extensively evaluated in the UCLA
GCM (Kim 1996). Tests of the parameterization were also made with models at
other institutions such as those at CSU, NCEP, LLNL and CCSR/UT in Japan.
(e) Improved formulations of cloud-top processes in the UCLA GCM for better
2
simulation of starts cloud incidence and surface evaporation.
While the PBL parameterization used in the UCLA GCM can explicitly predict
the starts sub layer within the PBL, the standard version of the GCM generally the
starts cloud incidence almost everywhere, including the eastern subtropical Pacific
of both hemispheres. This indicates that the simulated PBL is not sufficiently moist.
The simulated surface evaporation, however, is not too small; in fact it is too large
compared to observation. These two deficiencies strongly suggest that the PBL of the
model is subject to too much drying, presumably due to the entrainment of drier air
from above. Even when the rate of mass entrainment is known, however, the rate
of moisture entrainment is sensitive to the way in which the humidity of
entraining air is specified. This is true particularly in models with relatively coarse
vertical resolution. As reported by IL and Arakawa (1997), we found that the
simulation of starts cloud incidence can be drastically improved by using a
specification of the humidity based on a downward extrapolation from the levels in
the free atmosphere to the PBL top.
(fl Research on the vertical discretization problem in atmospheric modeling and
development of a model based on a generalized vertical coordinate
When the standard Lorenz vertical grid is used, a vertical computational mode
characterized by a zigzag vertical profile of the potential temperature appears in
simulated results. In addition, the grid is subject to spurious baroclinic growth of
short waves. Using the Charney-Phillips grid, we have constructed a new vertically
discrete model based on a hybrid sigma-p coordinate, which is free from this
problem while maintaining most of the advantages of the Lorenz grid such as
maintaining the total energy conservation (Arakawa and Donor 1996). The paper
includes a comparison between results from the new model and a model based on
the standard Lorenz grid in view of the vertical propagation of gravity waves and
the baroclinic growth of middle-latitude cyclones from initially-random
disturbances.
g . Development of a model based on a generalized vertical coordinate
We have developed a model based on a generalized vertical coordinate, which
is identical to the isentropic coordinate model of Hs and Arakawa (1990) if the
coordinate is chosen to be the potential temperature everywhere. The model can be
used, however, as a hybrid-coordinate model in which the coordinate is essentially
sigma near the surface and wherever the stratification is unstable, and it is
essentially the potential temperature for the rest of the domain with a smooth
transition. The model was successfully tested in view of the growth of middle-
latitude cyclones and associated fronts on a middle-latitude beta-plane. The key to
the success is in the derivation and solution of the vertical mass flux equation to
maintain hydrostatic consistency in the discrete model, which guarantees that the
coordinate variable is single-valued and monatomic in the vertical. The design and
test of the model are presented in Donor and Arakawa (1997).
3
1.4 Publications
Refereed articles
Kim, Y. J., and A. Arakawa, 1995: Improvement of orographic gravity wave
parameterization using a mesoscale gravity wave model. J. Atmos. Sci., 52,
1875-1902.
Arakawa, A., and C. S. Donor, 1996: Vertical of the primitive equations based on the
Charney-Phillips grid in hybrid a-p vertical coordinates. Mon. Wea. Rev. 124,
511-528
Kim, Y.-J., 1996: Representation of subgrid-scale orographic effects in a general
circulation model: Part I Impact of the dynamics of simulated January climate.
J. Climate, 2698-2717
Lin, C.-C., and A. Arakawa, 1997a: The macroscopic entrainment processes of
simulated cumulus ensemble. Part I. Effective sources of entrainment. J.
Atmos. Sci., 54, 1027-1043.
Lin, C.-C., and A. Arakawa, 1997b: The macroscopic entrainment processes of
simulated cumulus ensemble. Part II. Testing the entraining-plume model. J.
Atmos. Sci., 54, 1044-1053.
Arakawa A., 1997: Adjustment mechanisms in atmospheric models. J. Met. Soc.
Japan, 75, No. 1B, 155-179.
Cheng, M.-D., and A. Arakawa, 1997a: Inclusion of rainwater budget and convective
downdrafts in the Arakawa-Schubert cumulus parameterization. J. Atmos.
Sci., 54, 1359-1378.
Konor, C. S., and A. Arakawa, 1997: Design of an atmospheric model based on a
generalized vertical coordinate. Mon. Wea. Rev., 125, 1649-1673.
Selected conference papers
Lin, C.-C., and A. Arakawa, 1995: Cumulus entrainment simulated by a cloud-
resolving model. Twenty-First Conference on Hurricane and Tropical
Meteorology, 9-13 April 1995, Miami, American Meteorological Society, 63-65.
Konor, C. S., and A. Arakawa, 1996: Development of a generalized vertical
coordinate model. Eleventh Conference on Numerical Weather Prediction,
August 19-23, 1996, Norfolk, Virginia, American Meteorological Society, 203-
205.
Kim, Young-Joon, C. R. Mechoso and A. Arakawa, 1996: Impact of gravity-wave drag
and envelope orography in climate simulated by a general circulation model.
Eleventh Conference on Numerical Weather Prediction, August 19-23, 1996,
Norfolk, Virginia, American Meteorological Society, 319-321.
Li, J.-L. F, and A. Arakawa. 1997: Improved simulation of PBL moist processes with
the UCLA GCM. 7th Conference on Climate Variations, February, 2-7, 1997,
Long Beach, California, American Meteorological Society, 35-40.
Arakawa, A., 1997: Cumulus parameterization: an ever-challenging problem in
4
tropical meteorology and climate modeling. 22nd Conference on Hurricanes
and Tropical Meteorology, 19-23 May 1997, Ft. Collins, Colorado, American
Meteorological Society, 7-12.
Lin, C.-C., and A. Arakawa, 1997c: Some bulk properties of simulated cumulus
ensemble. 22nd Conference on Hurricanes and Tropical Meteorology, 19-23
May 1997, Ft. Collins, Colorado, American Meteorological Society, 478-479.
Technical Report
Cheng, M.-D., and A. Arakawa, 1997b: Computational procedures for the Arakawa-
Schubert cumulus parameterization. Tech. Report 101, General Circulation
Modeling Group, Department of Atmospheric Sciences, UCLA, 50 pp.
Ph.D. dissertations
Liu, Y.-Z., 1995: The representation of the macroscopic behavior of observed moist-
convective processes. 227pp.
5


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