The Rasch/Kristjánsson scheme in HIRLAM
Viel Ødegaard, DNMI
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
email@example.com for further information.
The scheme is built of the following modules:
large scale condensation
cloud fraction parameterization
microphysics, precipitation processes
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, qs is specific
humidity in f (specific humidity at saturation) and qe is specific
humidity in 1-f. L is the latent heat of condensation/evaporation
and cp 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/
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.
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.,
Sundqvist, H., 1993: Parameterization of clouds in large-scale numerical models.
Aerosol-Cloud-Climate Interactions, P. V. Hobbs, Ed., Vol. 1. Academic
Last Modified: 12:40am GMT, April 6, 1999