The Rasch-Kristjánsson scheme for large scale condensation is now implemented and can be run in HIRLAM reference code (4.3) together with the Tiedtke mass flux scheme for convection. The code is available for HIRLAM researcher at FUJITSU, please contact viel.odegaard@dnmi.no for further information.

The scheme is built of the following modules:

The large scale condensation parameterization is built on Sundqvist (1975, 1993). The equation determining the condensation rate (Q-E) is

where the tendency in water vapour and temperature from dynamics and subgrid processes are contained in the variable M. f is cloud fraction, T is temperature, q is specific humidity, q_s is specific humidity in f (specific humidity at saturation) and q_e is specific humidity in 1-f. L is the latent heat of condensation/evaporation and c_p is the heat capacity at constant pressure. The closure assumption

states that the fraction of M operating within the cloudy part of the volume acts to condense/evaporate cloud water. The second closure assumption states that when the cloud is growing, the new cloud water increases to match that within the cloudy part of the grid box. Conversely, when the cloud is eroding, the cloud water goes to zero in that region:

where m is the specific cloud water and the tilde stands for the in-cloud value. By subtracting (2) and (3) from (1) ((Q-E)_cloudy+(Q-E)_clear=Q-E) it comes out that the fraction of M operating in the clear part of the grid box acts to change the water vapour amount in the grid volume and to increase the cloud fraction.

The procedure is to first determine M, the right side of (1) and next the change in cloud fraction multiplied by the incloud water content (right side of (3). When adding (2) and (3) one can readily solve for (Q-E).

Solving for (Q-E) gives

and from (5) it is clear that the condensation rate is quite sensitive to the formulation of cloud cover.

The microphysics module models the conversion of cloud water to precipitating water. Five processes are taking into account: autoconversion of cloud liquid water to rain, autoconversion of cloud ice to snow, rain collecting cloud water, snow collecting cloud water and snow collecting cloud ice.

The cloud fraction parameterization is based on Slingo (1987). Cloud fraction is diagnosed as a function of relative humidity. In addition the parameterization of low clouds takes into account omega. Rasch and Kristjánsson modifications to the Slingo scheme include taking detrainment rate in deep convective updrafts into account when determining convective cloud cover, and to let the marine stratocumulus depend on the mean stratification in the lower troposphere. Convective cloud cover could alternatively be taken from the convection scheme, but due to the argument in Rasch and Kristjánsson (1998) that the cloud fraction should be strongly correlated with local moistening for the condensation formulation to work (see also equation (5)) the Rasch/Kristjánsson method is chosen. Figure 1 shows the sensitivity to choice of convective cloud cover parameterization to mslp in a 24 hour forecast. Blue contours show result with Rasch/Kristjánsson convective cloud cover, red contours show result with Tiedtke convective cloud cover.

One should be aware that both the Rasch/Kristjánsson condensation formulation and the cloud fraction formulation use the vertical velocity fields from HIRLAM. The change in saturation vapour pressure with pressure multiplied by vertical velocity is contributing to M, the moistening term. It is not taken into account in the present version of the Rasch/ Kristjansson scheme.

The Rasch/Kristjánsson scheme has a simplified treatment of the ice phase compared to the Sundqvist scheme in HIRLAM. Cloud ice is diagnosed from grid point temperature with a probability distribution function. Cloud ice is then used as a parameter in the microphysical functions where it is needed. In addition the phase of grid point precipitation is diagnosed from grid point temperature; fraction of snow is 0 for temperatures above freezing level and 1 for temperature below freezing level. Melting of snow is similarly a function of grid point temperature only; all precipitation is assumed to melt in the first level where grid point temperature exceeds freezing level.

The impact of cloud microphysics on atmospheric circulation is mainly due to the spatial distribution and varying rates of latent heat transfer, redistribution of atmospheric water, and water loading. The contributions from ice phase microphysics are the additional heat of sublimation compared to condensation/ evaporation and the freezing and melting of water. In addition the formation of ice crystals triggers the growth of hydrometeors and release of precipitation. When ice particles (snow) is entering a cloud of supercooled water from above, the whole cloud will rapidly glaciate, and the precipitation process is significantly enhanced. In stratiform precipitation, melting of precipitation is concentrated to a shallow layer and frequently stable isothermal layers are produced. The melting layer is moving downwards as melting heat is consumed. A study of Matsuo and Sasyo (1981) indicates that wet-bulb temperature should be the melting criterion, because the snowflakes are chilled by evaporation from the surface while falling through subsaturated air.

It is suggested that the Rasch/Kristjánsson scheme is extended in accordance with what is written above. Additional benefits should be improved information about snow/rain (and eventually supercooled rain) from the forecasts. Surface temperature is a poor predictor for precipitation phase, and it is quite common that it is snowing up to one or two degrees above freezing level.

Testing of the scheme in parallel runs can start up as soon as the extensions due to ice phase are introduced. The first comparison should be done between the combination of Rasch/Kristjánsson and Tiedtke mass flux on one hand and the combination Sundqvist and Tiedtke mass flux scheme on the other. If the Rasch/Kristjánsson scheme represents an improvement compared to the Sundqvist code in HIRLAM, further testing should concentrate on finding the best convection scheme to combine it with; Tiedtke or Kain/Fritsch. Finally the preferred combination must be compared to STRACO.

References

Matsuo, T., and Y. Sasyo, 1981: Empirical formula for the melting rate of snowflakes. J. Meteor. Soc. Japan, 59, 1-9.

Rasch, P. J. and J. E. Kristjánsson, 1998: A comparison of the CCM3 model climate using diagnosed and predicted condensate parameterizations. J. Climate. 11, 1587-1614.

Slingo, J. M., 1987: The development and verification of a cloud prediction scheme for the ECMWF model. Quart. J. Roy. Meteor. Soc., 113, 899-927.

Sundqvist, H., 1978: A parameterization scheme for non-convective condensation including prediction of cloud water content. Quart. J. Roy. Meteor. Soc., 104, 677-690.

Sundqvist, H., 1993: Parameterization of clouds in large-scale numerical models. Aerosol-Cloud-Climate Interactions, P. V. Hobbs, Ed., Vol. 1. Academic Press, 175-203.

Last Modified: 12:40am GMT, April 6, 1999