A. Short wave (solar) heating

The driving force behind all atmospheric motions relative to the Earth's surface is the differential latitudinal heating due to absorption of radiation from the sun. The sun's emission spectrum peaks in the visible band at the relatively short wavelength end of the electromagnetic spectrum and is therefore termed short wave radiation. Because the sun's rays are not vertical at all latitudes, there is a strong variation in solar heating over the globe. The presence of clouds in the atmosphere also strongly modulates the absorption of solar radiation. Clouds scatter short wave radiation as well, and, as such, are responsible for a substantial fraction of the planetary albedo in regions that are not covered by ice.

The short wave radiation formulation is that of Lacis and Hansen (1974) as modified by Davies (1982). It includes atmospheric heating due to the absorption of solar radiation by water vapor and ozone. The ozone concentration is specified (rather than predicted) from a zonal mean climatology described in section VII (C). Since cloudiness has a major impact upon the amount of solar radiation that is scattered and absorbed, the predicted cloudiness is used in the calculation of short wave radiation. In typical climate simulations, the short wave heating is calculated each hour of simulated time. The short wave heating is temporally smoothed by linearly interpolation between calculations to the current time step.

B. Long wave heating

Balancing the absorption of solar radiation, the Earth emits radiation to space resulting in a conservation of energy for the Earth/atmosphere system in the time and global mean. The terrestrial radiation to space, which peaks in the infrared band is called outgoing long wave radiation. Long wave emission from the Earth's surface may be absorbed by constituents in the atmosphere, and it may be re-emitted as well. The distribution of surface emissions as well as absorbing and emitting species and clouds is not uniform over the globe, so the long wave heating is not equally distributed. The unequal distribution of short wave and long wave heating induces pressure gradients that give rise to atmospheric motions.

The long wave heating is a broad band parameterization formulated for fast computation by Harshvardhan et al. (1987). It includes atmospheric heating due to the absorption of terrestrial radiation by water vapor (predicted), carbon dioxide (specified), and clouds (predicted), as well as other less important species. The water vapor mixing ratio is computed from the specific humidity and virtual temperature that are carried as prognostic variables in the model equations. The cloud amount is predicted according to the scheme described in section II (C). The species that are radiatively active in the terrestrial wavelength band are described in section VII (C). In typical climate simulations, the long wave heating is computed at least every three hours of simulated time in order to adequately resolve the diurnal cycle of terrestrial radiation.

C. Cloud radiation interaction

As described above, the short wave and long wave heating parameterizations are substantially affected by the presence of clouds. Formerly, the COLA GCM included specified clouds from a zonal mean GFDL cloud climatology (Kinter et al., 1988), but this approach has been supplanted in most GCMs by predicted clouds. Our motivation is that predicted clouds alter the energy balance and may provide a considerably greater reservoir of available potential energy to drive atmospheric motions than the zonally symmetric clouds (Hou, 1990). As such, predicted clouds are employed in the model using a scheme that is a hybrid of the scheme implemented by Hou (1990) and the scheme employed in the National Center for Atmospheric Research (NCAR) Community Climate Model (CCM2; Kiehl et al., 1994). Hou’s scheme is further described by DeWitt (1996) and is based on the work of Slingo (1987). Following is a brief summary of the Hou (1990) scheme and a description of how it was changed to include beneficial features of the NCAR CCM2 scheme.

In the COLA GCM, clouds are divided into supersaturation and convective types (sections V - A and V - B). Supersaturation clouds are further divided according to the pressure level at which the cloud occurs. Supersaturation clouds are classified as low clouds if they occur between a pressure of 1000 and 700 millibars; middle clouds if they occur between a pressure of 700 and 400 millibars; and high clouds if they occur above 400 millibars. Formation of the supersaturation clouds is according to the equation:

where C_k is the fractional cloud cover which is bounded by 0 and 1, RH _k is the relative humidity within layer k, and RH_c is the critical relative humidity which is a function of cloud type (Smagorinsky, 1960). The values of RH_c are 0.8 for low and middle clouds and 0.9 for high clouds. If the relative humidity within a layer is less than the critical relative humidity for that layer then no supersaturation cloud will form. The low clouds are further modified by the vertical velocity of the layer in which they occur. The modification of the low supersaturated clouds due to vertical velocity is according to:

and w is the vertical pressure velocity in centibars per second.

In addition to the formation of low clouds by the above formula, low clouds are also allowed to form if a temperature inversion of sufficient strength is diagnosed. The formation of the inversion cloud is further modified by the relative humidity at the base of the inversion. The inversion clouds form according to the formula:

where RH_b is the relative humidity at the inversion base and dq _c/dp is the critical lapse rate which is used to determine the presence of an inversion. When low clouds form, they are prescribed to be two layers thick since the lower layers in the GCM are quite thin. If more than one layer within the same supersaturation cloud domain (i.e. low, middle, high) has a prescribed cloud amount, only the layer with the highest cloud amount is kept for that domain. For the purposes of computing the radiative effect of clouds, all clouds are treated as randomly overlapping.

Convective cloud is diagnosed according to the three hour mean precipitation rate using the formula:

where a and b are prescribed constants as in Slingo (1987) and P is the cumulative mean convective precipitation rate in units of mm day^-1. This cloud amount is assigned to every layer in between the base and top of the diagnosed convection. The convective cloud fraction is constrained to be smaller than 0.8. If the convective cloud fraction is diagnosed to be greater than 0.4 for some time step and the convection extends above 400 millibars, then an anvil cloud is diagnosed at the top level of convection according to the formula:

The prescription of the optical properties of the clouds follows Harshvardhan et al. (1989). The approximation of cloud pressure optical thickness in the short wave spectrum is according to:

The variable T_c in this formula is the mean cloud temperature (in ° C) and D p_c is the pressure thickness of the cloud (in hPa). The formula for long wave cloud emissivity is specified as:

The Hou (1990) formulation, especially in the short wave band, was found by DeWitt and Schneider (1996) to be at variance with the top of the atmosphere fluxes observed in the Earth Radiation Budget Experiment (ERBE; Barkstrom, 1984; Barkstrom et al., 1989; data set documented by Hurrell and Campbell, 1992). DeWitt and Schneider (1996) implemented a revised formulation of cloud radiation interaction that incorporated some of the favorable aspects of the NCAR CCM2 cloud scheme. One important aspect of the resulting hybrid scheme is that convective cloud amount is first determined for the entire depth of the cloud, and then the amount at each model level within the cloud is determined as a function of the total. The total convective cloud amount is specified as

The total convective cloud amount C_cont is, as in Hou (1990), constrained to be less than 0.8. In each layer between the cloud base and cloud top, the convective cloud amount is defined as C_con = 1 – (1–C_cont)^1/N where N is the number of layers between the convective cloud base and top. If the cloud top occurs above the 400 mb level, then an anvil cloud associated with the deep convection is assigned to the level above the cloud top. The anvil fraction is set to C_anvil = 2 C_cont. In addition to the clouds associated with deep convection, shallow convective clouds are diagnosed if the model’s shallow convection scheme is invoked. The total amount of shallow convective cloud is set to 0.3 and the cloud amount assigned to each layer between the shallow convective cloud base and cloud top is 1 – 0.7 ^1/M where M is the number of such layers.

In contrast to the Hou (1990) scheme, supersaturation clouds are assigned a cloud fraction as:

where RH is relative humidity. The low level inversion clouds are diagnosed using:

where dq /dp is the lapse rate of potential temperature and dq _c/dp is the critical value of the lapse rate that must be exceeded in order for inversion clouds to be diagnosed. RHF is the relative humidity function defined above, as in Hou (1990).

The total cloud fraction in any layer is defined as

where

C_conh = C_con + C_shal + C_anvil (34)

and