A. Lower Boundary Conditions

In order to represent atmospheric processes on climate time scales of one month and longer, the conditions at the Earth's surface that most significantly affect the atmosphere must be allowed to vary with time. These fields include surface temperature over land and ocean, including both open water and sea ice; soil moisture over land; surface albedo; and snow depth. Of these fields, the land surface temperature, sea ice temperature, and snow depth vary so quickly with time that they are treated as prognostic variables in the model and are coupled with the atmospheric equations. The remaining fields could also become prognostic fields as well but vary slowly enough that they can be specified as boundary conditions for the model, being allowed to vary independently in time. By doing so, the atmospheric response to these fields can be determined without taking into account the storage residual in each of these fields. As knowledge of these fields and the corresponding atmospheric response increases, they may be also become prognostic variables.

The sea surface temperature (SST) is determined on a daily basis in the model by linear interpolation between means on monthly, weekly or other intervals. These fields are read in from data sets, whose preparation is discussed below. The observed value of SST is modified at each gridpoint of the model by a time invariant correction to account for the non-zero elevation introduced at some ocean points by the spectral truncation of the model orography. The correction is computed as the product of the orography and a constant lapse rate of 6.5° K km^-1. The monthly mean value from such a data set gives the model field value assumed to be valid instantaneously in the middle of the month. A field value for a day in the first half of the month is obtained by linear interpolation from the monthly means for the previous month and the current month. Similarly, a model field value for a day in the last half of the month is obtained from the monthly means for the current and the subsequent month. In this way a field which is smoothly varying in time can be constructed. Note that this can introduce a smoothing which is not observed and may inaccurately represent the monthly mean fields (Killworth, 1996).

For SST, a distinction is needed between open water and sea ice points, and possible transitions from open water to sea ice (and vice-versa) must be taken into account. In the model, this distinction is made when the sea surface is above or below the freezing temperature of sea water (-2° C). With sea ice points for a given month in the monthly sea surface temperature data set assigned to -3° C so that transition between open sea water and sea ice points can be arrived at by the linear interpolation method, each point is checked for its interpolated temperature value. If below -2° C, it is assumed to be a sea ice point, and the temperature at that point is treated as a prognostic variable whose initial value is -3° C. Once it is above -2° C, the time interpolated sea surface temperature is used at that point. The transition from open water to sea ice is done when the time interpolated temperature at a point falls below -2° C. The point remains a sea ice point until the time interpolated sea surface temperature rises above -2° C. The point is then set to the time interpolated sea surface temperature and the previously predicted sea ice temperature valid at the time is ignored.

The surface albedo is obtained differently over land and ocean points. Over ocean points, albedo is specified as a function of solar zenith angle:

where g = sin(q ) and q is the solar zenith angle.

The land surface biosphere model, SSiB, predicts albedo (see section IIIB).

The snow depth is applied as an initial condition, and carried as a prognostic variable in the model (see section IIIB). The initial snow depth can be based on the time interpolated surface albedo on the initial date of the model run. The surface albedo normally used to initiate a model integration is a climatological value based on Posey and Clapp (1954). The data are specified on the model Gaussian grid. The initial snow depth is specified as follows:

For ice points (both land and sea) 3000 kg m^-2

For points where 69%< albedo <75% 20 kg m^-2

For points where 49%< albedo <69% 10 kg m^-2

For points where 40%< albedo <49% 5 kg m^-2

The high value over ice points is so that a full account of ice melting or accumulation can be done during a long integration. The initial snow depth is set using an offline program. For boreal summer runs, the ice points alone can be set. It is also possible to use data sets of observed snow depth for particular periods to initialize the model.

Soil moisture is specified initially since the land surface model predicts the soil wetness in each of three layers. The data sets that are used were obtained from the water budget analyses of Willmott et al. (1985), either for climatological monthly means, or for means for a specific calendar month (e.g., April, 1987). The data are available on a 1° by 1° grid, and are interpolated to the model Gaussian grid. The soil moisture data are converted to soil wetness, and distributed over the three soil moisture storage layers maintained within the model as explained in Sato et al. (1989b). A scheme for estimating the initial values of the three soil moisture reservoirs from other soil moisture analyses (e.g., from the European Centre for Medium Range Weather Forecasts) has also been developed (Fennessy and Shukla, 1996).

General Preparation. All SST data sets used by the COLA AGCM require interpolation to the model Gaussian grid. Currently, areal interpolation is used separately on the SST and sea ice. When a location has an area average sea ice of 50% or more, that location is assigned as a sea ice point with a value of 270.2 K (-3°C). Non sea ice locations have a value of the interpolated SST or 271.4 K, whichever is larger. Due to Gibbs aliasing, SST at locations near land frequently will not be interpreted as originating at sea level. Instead, the SST will be seen as if it were on a surface corresponding to the surface spectral topography transformed to the model Gaussian grid space. This can "raise" the SST to elevations of 3 km or more. To avoid spurious heating, the SST (sea ice points excluded) is adjusted by the model back-transformed surface topography using the standard atmospheric lapse rate of -6.5 K km^-1.

Monthly data sets. Two types of monthly data sets can be processed by the model: 12 month cyclic sequential data or continuous direct access data. The 12 month cyclic data set consists of 13 records the first of which is no longer used, but remains for backward compatibility. The last 12 records are January through December values of SST assumed to be valid at the center of the month. Data can be climatological or observed. If observed, the data need not align with a calendar year but can start with any month and continue into the following year up to the month corresponding to the calendar month preceding the starting month. Data from each calendar month used, regardless of year, must be in the same data set position as used for a calendar year, i.e., all January data are the second data set record, all February data are the third data set record, until the December data as the thirteenth data set record. Multi-year simulations can be done with this type of data set provided data sets are changed every 10 months to allow for time interpolation. Continuous direct access data sets can contain any number of records of two or more. This avoids the need for changing data sets, but requires the user to indicate the data set start time in the model NAMELIST. This type of data set is not well suited for climatological data.

Weekly data sets: At present, only one weekly data set is available for use with the COLA AGCM.

B. Upper Boundary Conditions

The upper boundary condition is the kinematic constraint that vertical velocity through the top of the model atmosphere be zero everywhere (to satisfy mass conservation). This constraint is built into the solution through the vertical differencing in s coordinates.

C. Interior (fixed species)

The concentration of ozone is specified by interpolation from a table which gives the ozone mixing ratio for each of the model s levels, for each five degree latitude interval and for each of the four seasons (MRF88). Carbon dioxide, which is a radiatively active gas, is assumed to be well mixed throughout the entire atmosphere with a constant (default) value of 345 ppm (or as specified by the user).