Basic Convective and Mesoscale Research
Other Agency – Evaluation of Microphysical Parameterizations
Funding Agency: NSF and CIMMS Task I
Objectives
Explore the physical consistency of certain microphysical parameterizations
with the physical processes they are designed to represent.
Accomplishments
The equations which represent two microphysical processes, for which
total number concentration Nt should be conserved, are integrated over
sizes of hydrometeor diameters D for one- and two-moment methods. The
gamma distribution function is assumed and incorporates total mixing
ratio q, Nt, and mean diameter Dn, (inverse of the distribution slope
l). In all the methods, the slope intercept, no, is diagnosed or specified
but not predicted. The moment methods explored include:
- Scheme-A: the one-moment method where q is predicted, no is specified, and Nt and Dn are diagnosed;
- Scheme B: the one-moment method where q is predicted, Dn is specified, and Nt and no are diagnosed;
- Scheme E: the two-moment method where q and Dn are predicted, and Nt and no are diagnosed;
- Scheme F: the two-moment method where q and Nt are predicted, and no and Dn are diagnosed.
In order to more easily discern the strengths and weaknesses of each moment-method, two processes are considered: vapor diffusional growth and continuous collection growth, and in both cases there is no introduction of new particles (d Nt /Dt = 0). It is demonstrated for the processes examined that all of the schemes fail to conserve Nt and have other unphysical attributes, except the two-moment method where q and Nt are predicted.
In a separate paper, it is demonstrated mathematically why Nt is not conserved when it should be conserved for continuous collection growth. The results for vapor diffusional growth are qualitatively similar. The figure below shows a time series of the total number concentration for each of the schemes A-F listed above. It is clear that only Scheme F conserves Nt for continuous collection growth. Scheme-B has the most erroneous solution with regard to the conservation of Nt.
This project is ongoing.
Publications
Straka, J., M., K. M. Kanak, and M. S. Gilmore, 2006: The behavior of
number concentration tendencies for conservative microphysical growth
equations using bulk one-, and two-, moment schemes. 12th Conference
on Cloud Physics, Madison, WI, Amer. Meteor. Soc.
Straka, J., M., K. M. Kanak, and M. S. Gilmore, 2007: The behavior of number concentration tendencies for the continuous collection growth equation using one- and two-moment bulk parameterization schemes. J. Applied Meteor. Climatol., 46, 1264- 1274.
Time series up to 600 s. (a) N1 in units of (m-3) vs. time (s); (b) q in units of (kg kg-1) vs. time (s)