## GEWEX Cloud System Study: Working Group 3

### CLOUD-RESOLVING MODEL OUTPUTS

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Revision: Jan 10, 1996 - Main New Additions/p>

The utilization of cloud-resolving model (CRM) outputs to parameterize cloud effects in GCMs is one of the main components in the GCSS strategy for GCM cloud parameterization development. A list of CRM large-scale diagnostics have been suggested by GCM and CRM modellers for this purpose. This list of large-scale impact diagnostics and details of their calculations are given in the following.

A section on the definition and calculation of precipitation efficiency will be contributed by Brian Ryan. Please send additional suggestions or comments to Kit Szeto.

**A. CRM Large-scale impact diagnostics:**

Over subregions of the CRM with dimensions similar to those of a typical GCM grid box (~300x300 kmē x 500 m) and over a time interval representative of the typical time step used in a GCM integration, the following statistics (as functions of height and time) can be generated from the CRM outputs:

*Mean and variance of temperature**Mean and variance of mixing ratios of various water substance, layer liquid water content, layer liquid water path, layer optical depth and surface precipitation rate**Cloud coverage statistics**Mean long (short) wave fluxes**Fluctuations in the velocity fields and associated eddy fluxes of heat, moisture and momentum**Apparent heat, moisture and momentum sources/sinks**Precipitation efficiency*

Calculations over subdomains with and without embedded convection (and/or CSI) would be useful. It is also understood that (2) and (3) will be calculated for the cloud types resolved by the model only.

**B. Definitions and calculations:**

- Sample FORTRAN codes for some of the following calculations are available.
- Let
*x, y, z*and*t*be the grid-lengths and time step used in the CRM and*X, Y, Z, T*be the typical grid-lengths and time step used in a GCM (*X, Y*~ 300 km,*Z ~*500 m,*T*~ 30 min), then the mean value of a CRM prognostic variable*p*can be defined by:

where the summation is performed over all the grid points within a subdomain of size*X Y Z*within the CRM and over a time interval*T*. Likewise, the variance of*p*can be defined by:

- The optical depth is defined as:

img SRC="eqn3.gif" alt="Equation 3" WIDTH="239" HEIGHT="70">

The first integral is over the cloud depth h and the second integral is over the cloud droplet radius*r*.*f(r)*is the spectral density of droplets of radius*r*while*Qe*is the extinction factor (ratio of extinction to the cross-sectional area of cloud droplets) as a function of the size parameter*s*and refractive index*n*at wavelength . The functional form of*f(r)*and*Qe*typically varies from CRM to CRM. A good approximation in the calculation of is given by:

where*w*(*i*)= density of water (ice),*h*= cloud depth,*Nc*= cloud particle concentration and*rc*(*ri*)= mixing ratio of cloud water (ice). - The liquid (ice) water path
*W*is defined as the integrated liquid water (ice) through a cloud of depth h:

- The cloud coverage fraction can be calculated if we specify the threshold value of cloud water (plus cloud ice) mixing ratio to be 0.001 g/kg. This should allow for cirrus. The cloud fraction () can then be calculated by:

where the summation is over all grid points where the cloud mixing ratios exceed the respective threshold mixing ratios. - It would be of interest to calculate the fractional coverage of convective clouds if moist convection is resolved explicitly in the model. This can be done if we specify a threshold convective cloud water (plus cloud ice) mixing ratio. There is no precise value for this threshold and it will undoubtedly vary with case anyway. For many of our Canadian cases, a value of say 0.2 g/kg is reasonable for instance. Another condition that might be added is that the in-cloud updraft speed be greater than 0.4 m/s.
- For the purpose of comparing model cloud coverage to satellite data (eg. ISCCP), the cloud coverage can also be defined as the area where the column visible optical thickness be greater than 0.1.
- The fluctuations for
*p*are defined by:

- The eddy fluxes of momentum, heat and moisture associated
*ui"*are:

where <> denotes horizontal averages over the model domain, is potential temperature and*q*is the water vapor mixing ratio. - The apparent heat and moisture sources/sinks are defined as:

where*(P/Poo)(Rd/Cp), Cp*= heat capacity of dry air,*P*= pressure and*Poo*= reference pressure,*Rd*= gas constant for dry air.*L*= latent heat of vaporization,*Q*= total heating rate,*Qv*= heating rate associated with the phase change of water vapour only, and*DQi*denotes subgrid scale diffusions. - The apparent sources/sinks of the
*i*-component horizontal momentum can be defined as:

**C. Other useful CRM outputs**

The development of a physically-based cloud scheme requires the knowledge of the relationships between the large-scale effects and the physical features occurring on the mesoscale (e.g. frontal features). As such, archives of all the CRM variables within selected vertical columns will be useful.

**D. CRM diagnostic results**

Several CRM groups (e.g. Katzfey and Ryan; Rasmussen et al.; Szeto et al.) have presented preliminary CRM large-scale diagnostic results at the WG3 workshop in New York City (Nov, 1995). Further studies such as inter-comparisons of the large-scale effects for different types of cloud systems will be needed. If you have any large-scale diagnostic results that you want to pose on this home page, please contact Kit Szeto.

**D. Archives of large-scale computations**

Archival format for the large-scale diagnostic calculations will be finalized during Spring of 1996. We are soliciting suggestions on the archive format, archive site, model and case-specific informations that should accompany the diagnostic results. Please send you suggestions to Kit Szeto and he will summarize the ideas and pose the guidelines for the archival format here.