In the semi-implicit treatment of the moisture equation (5), the contributions to the moisture tendency are further split into two groups. First, the moisture tendency due to advection, surface fluxes and diffusion is computed, and a preliminary calculation of the moisture field at the next time step is made based on this tendency. Second, the moisture sources and sinks due to changes of phase are computed and a final determination of moisture at the next time is made. Changes of phase of water rank highly among the important processes affecting the dynamics and thermodynamics of the atmosphere. In the COLA GCM, we include the processes of large scale condensation, deep convection and shallow convection.

A. Large scale condensation

The change of phase of water is one of the very important processes that affect both the dynamics and thermodynamics of the atmosphere. As an air parcel containing water vapor is cooled, its capacity to retain water is reduced until the parcel is saturated (100% relative humidity). If the parcel is cooled any further, water vapor will change phase to liquid, releasing its latent heat of evaporation and forming a cloud. While this is a complex process involving the availability of cloud condensation nuclei, it is treated quite simply in the COLA GCM. Whenever the predicted moisture content in a given volume exceeds the saturation value, the excess water vapor is assumed to condense to liquid and precipitate out. The calculation is carried out from the topmost layer of the model to the bottom, including the possibility that liquid water may evaporate at intermediate model levels as described in MRF88 (chapter 5).

B. Deep convection

Not all condensation takes place simply by supersaturation of gridbox size volumes; most of the mass of water that is condensed in the atmosphere does so in relatively small scale convective clouds. A number of convection parameterizations have been tested with the COLA GCM including a modified Kuo scheme (Kuo, 1965; Anthes 1977; MRF88), the Betts-Miller scheme (Betts and Miller, 1986; 1993), and the relaxed Arakawa-Schubert scheme (RAS; Moorthi and Suarez, 1992). Both the Kuo-based and RAS schemes are available with the COLA GCM. The RAS scheme is currently considered the most suitable for climate simulations with the COLA GCM (DeWitt, 1996).

Heating and moistening due to deep convective clouds can be represented in the COLA GCM using the Kuo (1965) scheme, as modified by Anthes (1977). Deep convection in the Kuo scheme is active in the presence of a conditionally unstable column and a positive moisture source due to the sum of convergence of moisture into the column and evaporation into the column. The sum of the moisture converging into the column and the evaporation into the column is known as the moisture accession.

In those columns for which deep convection is diagnosed, the moisture accession is partitioned into a heat producing (rain producing) portion and a moistening portion based on the column integrated relative humidity. The vertical distribution of the heating and moistening of the environment is based on the vertical distribution of temperature and specific humidity differences between the cloud and the environment.

The cloud temperature and specific humidity are determined by lifting an air parcel from the lowest model layer dry adiabatically up to the lifting condensation level (cloud base) and then moist adiabatically up to the level where the cloud temperature is equal to the temperature of the environment (cloud top). If the lifting condensation level for the near surface air is not within 0.35 times the surface pressure, then no deep convection is allowed to occur. The moisture accession is determined by computing the change in specific humidity over the leapfrog time step for all levels. The presence of deep convection is further restricted by the following criteria:

• Deep convection only occurs for columns in which the cloud thickness is equal to 30 percent of the surface pressure. For a surface pressure of 1000 mb this would restrict deep convection to those columns which had convective clouds at least 300 mb thick.

• The moisture accession in the layers below s = 0.46 must exceed 2 mm day^-1 on any particular time step in order for deep convection to occur.

An alternative to the Kuo scheme in the COLA GCM is the relaxed Arakawa-Schubert (RAS) scheme of Moorthi and Suarez (1992). This scheme differs from the common implementation of the Arakawa and Schubert (1974) scheme following Lord et al. (1982) in two ways. First, the normalized mass flux that is an exponential function of height in the original formulation is replaced by a linear function of height. Second, the parameterization relaxes the large scale atmosphere toward quasi-equilibrium instead of requiring quasi-equilibrium each time the cumulus convection subroutine is called.

The implementation of RAS in the COLA GCM assumes the sub-cloud layer is composed of a mass weighted average of the two lowest model levels. Each time the cumulus convection is called, all levels above the sub-cloud layer are checked for the possibility of convection. Clouds with the same specified cloud base but different detrainment levels (cloud tops) are known as different cloud types. In the RAS scheme, cumulus convection occurs for those cloud types for which the cloud work function exceeds an empirically determined critical value. The cloud work function is an integrated measure of the difference between the moist static energy in the cloud and that in the environment. For those cloud types for which the cloud work function exceeds the critical cloud work function, the cloud base mass flux needed to restore the cloud work function to its critical value is diagnosed. This mass flux is used to solve equations for the grid scale effect of convection on the temperature and specific humidity. In the implementation of RAS in the COLA model, the convective rainfall re-evaporates back into the environment following a modified version of Sud and Molod (1988).

C. Shallow convection

In regions where the atmospheric column is conditionally unstable near the surface, vertical overturning on sub-grid scales may be induced. The resultant shallow cumulus clouds do not necessarily produce precipitation, but act to transport heat and moisture upward. In regions where the atmospheric column is conditionally unstable near the surface but deep convection does not occur, shallow cumulus clouds may act to mix the temperature and moisture between cloud base and cloud top. This shallow convection is parameterized following Tiedtke (1983). In the Tiedtke (1983) scheme, the effects of shallow convection on temperature and specific humidity are modeled using an eddy diffusivity approach with fixed coefficients. The occurrence of shallow convection is not dependent on the presence of moisture accession into the column. The following restrictions on the shallow convection apply when the deep convection scheme is Kuo:

• Cloud base is determined using the lifting condensation level from the deep convection subroutine, which is called first.
• Shallow convection is not allowed in columns in which deep convection has occurred in the current time step.
• The shallow convective cloud top is restricted to s levels between 0.7 and 1.0. Shallow convective cloud tops that exceed this value are set to the highest layer that meets this criterion.
• The shallow convection cloud base must occur between s levels 0.7 and 1.0.