Calculation of radiative forcing from 3-D models is a relatively new endeavor. The history of this calculation began with one-dimensional models (e.g., Hansen et al., 1984a) that made use of the basic radiative-convective model approach initiated by Manabe and Wetherald (1967). Subsequent researchers expanded this calculation, using GCM output to describe atmospheric lapse rate, water vapor, and cloud cover and including latitudinal and seasonal changes (e.g., Pollack et al. 1993). Both the radiative perturbations from aircraft and the background radiative constituents (e.g., clouds, water vapor, albedo) vary with altitude, latitude, longitude, and time.
Three-dimensional modeling of radiative forcing introduces substantial complexity. The different modeling groups cited here have different approaches to calculating RF, involving choices in spatial and temporal domains.
All models report instantaneous values of radiative forcing at the top of the atmosphere and at the tropopause; in other words, these RF values have been calculated with no changes in atmospheric temperature. As discussed in Section 6.2.1, the most appropriate RF value includes allowance for stratospheric temperatures to readjust to radiative perturbation. Only two groups (Forster and Haywood, and Ponater and Sausen-see paragraphs below) have models that allow for such stratospheric adjustment. This correct, adjusted RF usually lies between the instantaneous values at the top of the atmosphere and the tropopause, and we correct the RF reported from other groups so that all RF values here refer to tropopause radiative forcing with stratospheric adjustment.
RF modeling results were contributed by P. Forster and J. Haywood (Forster and Shine, 1997), A. Grossman (Grossman et al., 1997), J. Haywood (Haywood and Ramaswamy, 1998), D. Rind (Rind and Lonergan, 1995), W.-C. Wang (Wang et al., 1995), and M. Ponater and R. Sausen (Ponater et al., 1998).
Forster and Haywood's radiation scheme has been previously used to calculate ozone and water vapor radiative forcings; it is described in Forster and Shine (1997). It employs a 10 cm-1 narrowband model (Shine, 1991) in the thermal infrared (IR) and a discrete-ordinate model (Stamnes et al., 1988) at solar wavelengths with 5-nm resolution in the ultraviolet (UV) and 10-nm resolution in the visible. As in Forster and Shine (1997), the fixed dynamic heating approximation (Ramanathan and Dickinson, 1979) is used to calculate stratospheric temperature perturbations. A zonally and annually averaged, 5� latitudinal resolution climatology was used as the basis for the forcing calculations. Temperature and humidity were derived largely from European Centre for Medium-range Weather Forecasts (ECMWF) analyses, averaged over the period 1980-91. In the upper stratosphere, temperatures were derived from Fleming et al. (1990). At pressures less than 300 hPA, humidity was based on a combination of Stratospheric Aerosol and Gas Experiment II (SAGE-II) and Halogen Occultation Experiment (HALOE) data. Surface albedos, cloud amounts, and optical depths were 7-year averages from International Satellite Cloud Climatology Project (ISCCP) (Rossow and Schiffer, 1991). Clouds were specified at three levels. The thermal infrared calculations included absorption by nitrous oxide, methane, and carbon dioxide. Ozone climatologies were taken from an observed climatology derived by Li and Shine (1995), a combination of SAGE-II, Solar Backscatter Ultraviolet (SBUV), Total Ozone Mapping Spectometer (TOMS), and ozonesonde data. To calculate forcing, the climatological profiles were perturbed by the absolute annual averages of ozone and water vapor changes.
Grossman (Grossman et al., 1997) uses a set of baseline annual and longitudinal average atmospheric profiles, resolved by 50 layers between 0 and 60 km, at latitudes of 60�N/S, 30�N/S, and at the Equator that are scaled to IS92A (IPCC, 1995) composition. Supersonic and subsonic aircraft O3 and H2O perturbation profiles were added to the baseline atmospheric profiles for RF calculations. The Lawrence Livermore National Laboratory (LLNL) 16-band solar radiation model (Grant and Grossman, 1998) and the LLNL 32-band IR radiation model (Chou and Suarez, 1994) were used to calculate instantaneous tropopause and top-of-atmosphere RFs at each latitude for the global average value for O3 and H2O.
Haywood's RF calculations for sulfate and black carbon aerosols were made following the method of Haywood and Ramaswamy (1998). The Geophysical Fluid Dynamics Laboratory (GFDL) R30 GCM incorporates a 26 band delta-Eddington solar radiative code (Ramaswamy and Freidenreich, 1997) and includes the cloud parameterization of Slingo (1989) and aerosol optical properties calculated using Mie theory. RF calculations are performed at the top of the atmosphere every day using mean solar zenith angle. No account is made for stratospheric adjustment, the effects of which are likely to be small for tropospheric aerosol in the solar spectrum.
Ponater and Sausen estimated instantaneous RF using the ECHAM4 GCM (Roeckner et al., 1996). Radiative transfer calculations (one radiative time step only) were performed for each grid point with and without local ozone perturbation, including the actual cloud profile. Several diurnal cycles were calculated for each calendar month, and the radiative flux change was determined for each individual grid point at the top of the atmosphere and at the tropopause. The annual global mean radiative forcing was obtained by averaging over all grid points and over the seasonal cycle. To calculate the stratosphere-adjusted, tropopause RF, a "second atmosphere" was implemented into the ECHAM4 GCM. Whereas the primary atmosphere of the GCM does not "feel" the perturbation of the greenhouse gas, the second atmosphere experiences an additional radiative heating above the tropopause, although dynamic heating is identical to that of the first, unperturbed atmosphere. In the troposphere, the primary and second atmospheres are not allowed to diverge. In this configuration, the model is run for one annual cycle.
Rind used the Goddard Institute for Space Studies (GISS) Global Climate Middle Atmosphere Model (Rind et al., 1988). The radiation scheme in the model is the correlated-k method for modeling non-gray gaseous absorption (Lacis and Oinas, 1991). The procedure involved keeping re-start files and full diagnostics for the first full day of each month from a control run. Radiation and all other routines were called each hour, so a full, diurnal average global response was calculated. Then the first day of each month was re-run with altered atmospheric composition (e.g., changes in ozone). The global net radiation at the top of the atmosphere was compared. The assumption is that with only 1 day of running time, temperatures would not adjust (even in the stratosphere) to the altered composition; hence, the results are instantaneous values.
Wang's RF calculations use the National Center for Atmospheric Research (NCAR) Community Climate Model 3 (CCM3) radiative model with monthly mean, latitude-by-longitude distributions of vertical temperature, moisture, clouds, and surface albedo simulated from the Atmospheric Model Intercomparison Project (AMIP). The year 1992 of the CCM3-AMIP simulations was used because the corresponding year was used to simulate ozone in the Oslo 3-D CTM (Isaksen et al., 1999). Because this State University of New York/ Albany version of CCM3 used the ozone climatology (Wang et al., 1995), CTM-simulated absolute ozone changes for 1992-2015 and 1992-2050 are mapped onto 1992 ozone climatology to calculate the RF. RFs are based on fixed temperature treatment rather than fixed dynamic heating treatment (Wang et al., 1993).
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