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## Abstract

The production, transport and distribution of ozone are simulated for a January with a global atmospheric general circulation model. In this model the ozone influences the radiational heating as well as the photochemical ozone production and destruction, the radiational heating influences the atmospheric circulation, and the circulation redistributes the ozone.

The model has fairly successfully simulated the synoptic and time-averaged observed large-scale fields of temperature, mass, and velocity in the troposphere and stratosphere, although there are some deficiencies. In particular, the simulated temperatures are too cold in the lower and middle stratosphere in the polar regions, the sea level pressure is too high in the Arctic and in the Antarctic circumpolar trough, and the flow field in the middle-latitude troposphere does not show the observed wavenumber 3.

Despite these shortcomings, the model has simulated the observed high correlation of synoptic and time-averaged total ozone with the tropospheric height field in middle latitudes, with the ozone maxima and minima, respectively, located at the troughs and ridges of the tropospheric waves. The deficiencies which are seen in the time-averaged O_{3} distribution are attributable to recognized deficiencies of the general circulation model.

In the tropics there is a vertically integrated transport of 0_{3}, from the summer to the winter hemisphere which is almost entirely produced by the mean-meridional circulation. In the middle latitudes, in both hemispheres, 0_{3} is transported toward the equator by the mean-meridional circulation and toward the poles by the zonal eddies; but the eddy transport dominates, so that the net 0_{3}, transport is poleward. In the high latitudes in both hemispheres, there is a reversal in the directions of the two components of the 0_{3}, transport; but here the transport by the mean-meridional circulation dominates, so that the net transport continues to be poleward.

In the individual latitudes, the zonally integrated vertical transport of ozone is dominated by the transport by the mean-meridional circulation; but integrated over the globe, the vertical O_{3} transport is dominated by the eddy transport. Between 20 and 31 km elevation, the globally integrated vertical 0_{3}, transport is a countergradient transport with respect to the globally integrated 0_{3}, mixing ratio.

The divergence of the 0_{3} transport maintains the ozone below its photochemical equilibrium concentration in the tropics and subtropics, and the convergence of the 0_{3} transport maintains the ozone above its photochemical equilibrium concentration in the middle and high latitudes of both hemispheres. In this way, both the atmospheric motions and the 0_{3} photochemistry determine the 0_{3}, sources and sinks.

The globally integrated photochemical production of ozone exhibits variations with periods of a day and less. These high-frequency oscillations are due to the quasi-stationary longitudinal variation in the ozone that is produced by the 0_{3} transports.

## Abstract

The production, transport and distribution of ozone are simulated for a January with a global atmospheric general circulation model. In this model the ozone influences the radiational heating as well as the photochemical ozone production and destruction, the radiational heating influences the atmospheric circulation, and the circulation redistributes the ozone.

The model has fairly successfully simulated the synoptic and time-averaged observed large-scale fields of temperature, mass, and velocity in the troposphere and stratosphere, although there are some deficiencies. In particular, the simulated temperatures are too cold in the lower and middle stratosphere in the polar regions, the sea level pressure is too high in the Arctic and in the Antarctic circumpolar trough, and the flow field in the middle-latitude troposphere does not show the observed wavenumber 3.

Despite these shortcomings, the model has simulated the observed high correlation of synoptic and time-averaged total ozone with the tropospheric height field in middle latitudes, with the ozone maxima and minima, respectively, located at the troughs and ridges of the tropospheric waves. The deficiencies which are seen in the time-averaged O_{3} distribution are attributable to recognized deficiencies of the general circulation model.

In the tropics there is a vertically integrated transport of 0_{3}, from the summer to the winter hemisphere which is almost entirely produced by the mean-meridional circulation. In the middle latitudes, in both hemispheres, 0_{3} is transported toward the equator by the mean-meridional circulation and toward the poles by the zonal eddies; but the eddy transport dominates, so that the net 0_{3}, transport is poleward. In the high latitudes in both hemispheres, there is a reversal in the directions of the two components of the 0_{3}, transport; but here the transport by the mean-meridional circulation dominates, so that the net transport continues to be poleward.

In the individual latitudes, the zonally integrated vertical transport of ozone is dominated by the transport by the mean-meridional circulation; but integrated over the globe, the vertical O_{3} transport is dominated by the eddy transport. Between 20 and 31 km elevation, the globally integrated vertical 0_{3}, transport is a countergradient transport with respect to the globally integrated 0_{3}, mixing ratio.

The divergence of the 0_{3} transport maintains the ozone below its photochemical equilibrium concentration in the tropics and subtropics, and the convergence of the 0_{3} transport maintains the ozone above its photochemical equilibrium concentration in the middle and high latitudes of both hemispheres. In this way, both the atmospheric motions and the 0_{3} photochemistry determine the 0_{3}, sources and sinks.

The globally integrated photochemical production of ozone exhibits variations with periods of a day and less. These high-frequency oscillations are due to the quasi-stationary longitudinal variation in the ozone that is produced by the 0_{3} transports.

## Abstract

Numerical experiments are conducted using the University of Illinois, Urbana–Champaign (UIUC), 11-layer atmospheric general circulation model (GCM) to investigate the dependence of the simulated tropical intraseasonal oscillation (TIO) on convection parameterization. Three convection parameterizations have been tested: 1) the UIUC GCM’s original cumulus–convection parameterization, which includes a modified version of the penetrative–convection parameterization and a middle-level convection parameterization, 2) the parameterization of , and (3) the moist convective adjustment parameterization of For each parameterization a relative humidity criterion (RH_{c}) for convection or convective heating to occur is used, as in many GCMs. Perpetual-March simulations with these convection parameterizations have been performed for different values of RH_{c}. It is found that the simulated TIO is highly dependent on RH_{c}. As RH_{c} increases, the oscillation in the simulations becomes stronger for all three parameterizations. This dependence of the amplitude of the simulated oscillation on RH_{c} appears to explain the differences in the TIO among previous simulations by different GCMs.

The analysis of the simulations suggests that a certain degree of nonlinear dependence of the condensational heating on large-scale moisture convergence is required to give a reasonable simulation of the TIO. When large values of RH_{c} are used, the triggering of convective activity requires the moist static energy in the lower troposphere to be accumulated to a certain amount through moisture convergence. This requirement of accumulation of the moist static energy to trigger convection leads to the weakening of the interaction between the circulation and the heating for perturbations of small amplitudes and small scales, and allows the initiation of the TIO to occur at lower frequencies. In the simulations that produce relatively strong intraseasonal oscillations, the frictional wave-CISK (conditional instability of the second kind) appears to contribute to the amplification of the TIO.

## Abstract

Numerical experiments are conducted using the University of Illinois, Urbana–Champaign (UIUC), 11-layer atmospheric general circulation model (GCM) to investigate the dependence of the simulated tropical intraseasonal oscillation (TIO) on convection parameterization. Three convection parameterizations have been tested: 1) the UIUC GCM’s original cumulus–convection parameterization, which includes a modified version of the penetrative–convection parameterization and a middle-level convection parameterization, 2) the parameterization of , and (3) the moist convective adjustment parameterization of For each parameterization a relative humidity criterion (RH_{c}) for convection or convective heating to occur is used, as in many GCMs. Perpetual-March simulations with these convection parameterizations have been performed for different values of RH_{c}. It is found that the simulated TIO is highly dependent on RH_{c}. As RH_{c} increases, the oscillation in the simulations becomes stronger for all three parameterizations. This dependence of the amplitude of the simulated oscillation on RH_{c} appears to explain the differences in the TIO among previous simulations by different GCMs.

The analysis of the simulations suggests that a certain degree of nonlinear dependence of the condensational heating on large-scale moisture convergence is required to give a reasonable simulation of the TIO. When large values of RH_{c} are used, the triggering of convective activity requires the moist static energy in the lower troposphere to be accumulated to a certain amount through moisture convergence. This requirement of accumulation of the moist static energy to trigger convection leads to the weakening of the interaction between the circulation and the heating for perturbations of small amplitudes and small scales, and allows the initiation of the TIO to occur at lower frequencies. In the simulations that produce relatively strong intraseasonal oscillations, the frictional wave-CISK (conditional instability of the second kind) appears to contribute to the amplification of the TIO.

## Abstract

A simple atmosphere-Ocean model is developed to represent the 20-year 1 × C0_{2} and 2 × C0_{2} simulations obtained with a coupled atmosphere-ocean general circulation model for the purpose of obtaining a new estimate of the characteristic response time of the climate system that accounts for oceanic upwelling.

The simple atmosphere-generalized ocean model consists of a zonally averaged energy balance climate model and a zonally averaged multilayer ocean model. The high latitudes of both hemispheres are combined into a single polar region, and the low and middle latitudes into a single nonpolar region. The atmosphere is treated as a single layer and the ocean as an arbitrary number of layers. The simple model includes the meridional transport of heat between the nonpolar and polar regions for both the atmosphere and each ocean layer. The ocean model includes the vertical advective heat transfer by the vertical velocity, the latter of which is prescribed and can vary with depth in both the polar and nonpolar regions. The unknown parameters of the simple model are the meridional heat fluxes between the nonpolar and polar regions, the coefficients of heat transfer within the ocean, the heat transfer coefficient between the ocean and atmosphere, an additional ocean-atmosphere heat transfer parameter, and the climate sensitivity parameter.

The parameters of the simple model are determined from the 1 × C0_{2} and 2 × CO_{2} simulations of the coupled atmosphere-ocean general circulation model. The simple atmosphere-ocean model is then used to project the response of the coupled atmosphere-ocean GCM from year 20 to year 100, and the resulting 2 × C0_{2}−1 × C0_{2} differences are normalized by the estimated equilibrium temperature changes. From these projections it is estimated that the characteristic response time is between 40 and 60 years, in close agreement with the estimates of Schlesinger et al.

## Abstract

A simple atmosphere-Ocean model is developed to represent the 20-year 1 × C0_{2} and 2 × C0_{2} simulations obtained with a coupled atmosphere-ocean general circulation model for the purpose of obtaining a new estimate of the characteristic response time of the climate system that accounts for oceanic upwelling.

The simple atmosphere-generalized ocean model consists of a zonally averaged energy balance climate model and a zonally averaged multilayer ocean model. The high latitudes of both hemispheres are combined into a single polar region, and the low and middle latitudes into a single nonpolar region. The atmosphere is treated as a single layer and the ocean as an arbitrary number of layers. The simple model includes the meridional transport of heat between the nonpolar and polar regions for both the atmosphere and each ocean layer. The ocean model includes the vertical advective heat transfer by the vertical velocity, the latter of which is prescribed and can vary with depth in both the polar and nonpolar regions. The unknown parameters of the simple model are the meridional heat fluxes between the nonpolar and polar regions, the coefficients of heat transfer within the ocean, the heat transfer coefficient between the ocean and atmosphere, an additional ocean-atmosphere heat transfer parameter, and the climate sensitivity parameter.

The parameters of the simple model are determined from the 1 × C0_{2} and 2 × CO_{2} simulations of the coupled atmosphere-ocean general circulation model. The simple atmosphere-ocean model is then used to project the response of the coupled atmosphere-ocean GCM from year 20 to year 100, and the resulting 2 × C0_{2}−1 × C0_{2} differences are normalized by the estimated equilibrium temperature changes. From these projections it is estimated that the characteristic response time is between 40 and 60 years, in close agreement with the estimates of Schlesinger et al.

## Abstract

The OSU global atmospheric general circulation model (AGCM) has been coupled to a 60-m deep mixed-layer ocean model to simulate the equilibrium seasonal climatic changes induced by a doubling of the CO_{2} concentration. Simulations with CO_{2} concentrations of 326 ppmv (1 × CO_{2}) and 652 ppmv (2 × CO_{2}) were performed using an accelerated integration procedure for 45 solar cycles followed by the normal unaccelerated integration procedure for 24 and 16 solar cycles (years), respectively. Averages were then obtained over the last 10 yr of each simulation and were analysed in terms of the annual-mean climate and the annual cycle of climate, the latter defined as the departure of the monthly or seasonal mean from the corresponding annual mean.

The 1 × CO_{2}/observed comparison shows that although the model is capable of simulating many features of the observed climate, it does not do so without error. Annual-mean errors are found in the geographical distributions of sea surface temperature, sea ice area, surface air temperature and precipitation rate, and annual-cycle errors are found in the geographical distribution of sea ice area and precipitation rate. Several of the simulation errors have occurred in previous simulations by the atmospheric GCM with the sea surface temperature and sea ice prescribed from observations. The remainder of the simulation errors occurred as a result of having made the sea surface temperature and sea ice prognostic variables of the model.

The 2 × CO_{2}/1 × CO_{2} comparison shows that not all quantities undergo a CO_{2}-induced change in both their annual mean and annual cycle. For the sea surface temperature there is a statistically significant increase everywhere in the annual mean, but the change in the annual cycle is negligible. There is a corresponding statistically significant increase in the annual-mean surface air temperature everywhere, but there are changes in the annual cycle only in the polar regions where the amplitude of the annual cycle is reduced. On the other hand, both the precipitation rate and soil water display increases and decreases in their annual means and annual cycles, but these changes are not statistically significant everywhere.

In comparison With CO_{2}-doubling simulations by the Geophysical Fluid Dynamics laboratory (GFDL), Goddard Institute for Space Studies (GISS), National Center for Atmospheric Research (NCAR), and United Kingdom Meteorological Office (UKMO) AGCM/mixed-layer ocean models, the OSU model simulates an annual-mean global-mean surface air temperature warming of 2.8°C compared to 3.5°–5.2°C, and an increase in the global-mean precipitation rate of 7.8% compared to 7.1°–11.0%. The OSU model also simulates a desiccation of the Northern Hemisphere continents almost everywhere in summer. This is in agreement with the GFDL and UKMO models, and to a lesser extent with the GISS model, but is in contrast to the results of the NCAR model.

## Abstract

The OSU global atmospheric general circulation model (AGCM) has been coupled to a 60-m deep mixed-layer ocean model to simulate the equilibrium seasonal climatic changes induced by a doubling of the CO_{2} concentration. Simulations with CO_{2} concentrations of 326 ppmv (1 × CO_{2}) and 652 ppmv (2 × CO_{2}) were performed using an accelerated integration procedure for 45 solar cycles followed by the normal unaccelerated integration procedure for 24 and 16 solar cycles (years), respectively. Averages were then obtained over the last 10 yr of each simulation and were analysed in terms of the annual-mean climate and the annual cycle of climate, the latter defined as the departure of the monthly or seasonal mean from the corresponding annual mean.

The 1 × CO_{2}/observed comparison shows that although the model is capable of simulating many features of the observed climate, it does not do so without error. Annual-mean errors are found in the geographical distributions of sea surface temperature, sea ice area, surface air temperature and precipitation rate, and annual-cycle errors are found in the geographical distribution of sea ice area and precipitation rate. Several of the simulation errors have occurred in previous simulations by the atmospheric GCM with the sea surface temperature and sea ice prescribed from observations. The remainder of the simulation errors occurred as a result of having made the sea surface temperature and sea ice prognostic variables of the model.

The 2 × CO_{2}/1 × CO_{2} comparison shows that not all quantities undergo a CO_{2}-induced change in both their annual mean and annual cycle. For the sea surface temperature there is a statistically significant increase everywhere in the annual mean, but the change in the annual cycle is negligible. There is a corresponding statistically significant increase in the annual-mean surface air temperature everywhere, but there are changes in the annual cycle only in the polar regions where the amplitude of the annual cycle is reduced. On the other hand, both the precipitation rate and soil water display increases and decreases in their annual means and annual cycles, but these changes are not statistically significant everywhere.

In comparison With CO_{2}-doubling simulations by the Geophysical Fluid Dynamics laboratory (GFDL), Goddard Institute for Space Studies (GISS), National Center for Atmospheric Research (NCAR), and United Kingdom Meteorological Office (UKMO) AGCM/mixed-layer ocean models, the OSU model simulates an annual-mean global-mean surface air temperature warming of 2.8°C compared to 3.5°–5.2°C, and an increase in the global-mean precipitation rate of 7.8% compared to 7.1°–11.0%. The OSU model also simulates a desiccation of the Northern Hemisphere continents almost everywhere in summer. This is in agreement with the GFDL and UKMO models, and to a lesser extent with the GISS model, but is in contrast to the results of the NCAR model.

## Abstract

The global distributions of selected climatic variables simulated by numerical integration of a two-level atmospheric general circulation model for January and July are presented in comparison with the corresponding observed climatological fields. The model has reproduced the observed large-scale patterns of sea-level pressure, lower tropospheric temperature and circulation with reasonable accuracy, although there are a number of systematic errors. In particular, the intensity of the semipermanent low-pressure centers in January in the Northern Hemisphere is overestimated, and the 400 mb temperature is too high in the tropics. Accompanying these errors are overestimates of the meridional temperature gradient and zonal westerlies in the mid-latitudes of the winter hemisphere. Although their global patterns resemble those observed, systematic amplitude errors are also present in the simulations of precipitation and evaporation (both of which the model overestimates by nearly a factor of 2 in January and July), in the simulated mean meridional circulation (in which the strength of the Hadley cells is overestimated and that of the Ferrel cells underestimated in both summer and winter), and in the cloudiness (which is underestimated by nearly a factor of 2 in the summer hemisphere). These errors have resulted in the simulation of too vigorous a hydrologic cycle, and distortions in the total meridional transports of heat and moisture, especially in the subtropics of the summer hemisphere.

In spite of these shortcomings, the model has successfully simulated the principal features of the observed heat and energy balances, at least in the zonal average. The characteristic meridional structure of the observed evaporation-precipitation difference is reproduced (but with values that are slightly too negative), the interhemispheric gradient of the net radiation of the top of the atmosphere and at the surface is nearly correct (but with excessive net radiation in the higher latitudes of the summer hemisphere), and the observed meridional distribution of the net heating of the earth-atmosphere system is simulated with good overall accuracy (but is too high in high latitudes during summer and too low in the subtropics during winter).

Comparison of the separate January and July simulators shows that the model has reproduced the observed seasonal shifts of the heat and energy balance, as well as that of the principal climate variables themselves, such as the pressure, temperature, wind and precipitation. Except for the precipitation and the mean meridional circulation in the lower latitudes, these changes are generally comparable to those found from models with higher vertical resolution. With improved parameterizations of subgrid-scale processes, especially in the tropics, it is believed that the two-level model can be substantially improved, and will prove useful in the further simulation of climate and climatic change.

## Abstract

The global distributions of selected climatic variables simulated by numerical integration of a two-level atmospheric general circulation model for January and July are presented in comparison with the corresponding observed climatological fields. The model has reproduced the observed large-scale patterns of sea-level pressure, lower tropospheric temperature and circulation with reasonable accuracy, although there are a number of systematic errors. In particular, the intensity of the semipermanent low-pressure centers in January in the Northern Hemisphere is overestimated, and the 400 mb temperature is too high in the tropics. Accompanying these errors are overestimates of the meridional temperature gradient and zonal westerlies in the mid-latitudes of the winter hemisphere. Although their global patterns resemble those observed, systematic amplitude errors are also present in the simulations of precipitation and evaporation (both of which the model overestimates by nearly a factor of 2 in January and July), in the simulated mean meridional circulation (in which the strength of the Hadley cells is overestimated and that of the Ferrel cells underestimated in both summer and winter), and in the cloudiness (which is underestimated by nearly a factor of 2 in the summer hemisphere). These errors have resulted in the simulation of too vigorous a hydrologic cycle, and distortions in the total meridional transports of heat and moisture, especially in the subtropics of the summer hemisphere.

In spite of these shortcomings, the model has successfully simulated the principal features of the observed heat and energy balances, at least in the zonal average. The characteristic meridional structure of the observed evaporation-precipitation difference is reproduced (but with values that are slightly too negative), the interhemispheric gradient of the net radiation of the top of the atmosphere and at the surface is nearly correct (but with excessive net radiation in the higher latitudes of the summer hemisphere), and the observed meridional distribution of the net heating of the earth-atmosphere system is simulated with good overall accuracy (but is too high in high latitudes during summer and too low in the subtropics during winter).

Comparison of the separate January and July simulators shows that the model has reproduced the observed seasonal shifts of the heat and energy balance, as well as that of the principal climate variables themselves, such as the pressure, temperature, wind and precipitation. Except for the precipitation and the mean meridional circulation in the lower latitudes, these changes are generally comparable to those found from models with higher vertical resolution. With improved parameterizations of subgrid-scale processes, especially in the tropics, it is believed that the two-level model can be substantially improved, and will prove useful in the further simulation of climate and climatic change.

## Abstract

A modified version of the two-level atmospheric general circulation model has been developed and used in the simulation of January and July global climates. The overall physical and numerical formulation of this Oregon State University (OSU) model is the same as that described previously by Gates and Schlesinger (1977), but in the new version water vapor at the upper level has been made a prognostic variable, the parameterizations of cumulus convection, large-scale condensation and evaporation, clouds and radiative-transfer have been changed, the surface snow mass and ground temperature have been made prognostic variables, and the treatment of the surface boundary layer has been revised. Modifications have also been made in the numerical solution procedure (which have increased the model’s speed by nearly a factor of 2), and in the prescribed distributions of topography, sea surface temperature and sea ice. The surface albedo is now a function of the prescribed surface type and of the predicted surface snow cover.

The model simulates most features of the large-scale distributions of observed January and July climate more accurately than before, including the primary variables of pressure, temperature, wind, cloudiness and precipitation. In addition, the simulated meridional transports of zonal momentum, heat and water vapor are closer to those observed than heretofore, as are the elements of the associated heat and hydrologic balances. The energy cycle is also simulated with greater accuracy, although the zonal potential and kinetic energies are still somewhat overestimated by the model while the eddy kinetic energy is underestimated. The markedly improved simulations of precipitation, evaporation, 400 mb temperature and surface sensible heat flux in the tropics are shown to be due to the revisions in the new model’s boundary-layer parameterization.

## Abstract

A modified version of the two-level atmospheric general circulation model has been developed and used in the simulation of January and July global climates. The overall physical and numerical formulation of this Oregon State University (OSU) model is the same as that described previously by Gates and Schlesinger (1977), but in the new version water vapor at the upper level has been made a prognostic variable, the parameterizations of cumulus convection, large-scale condensation and evaporation, clouds and radiative-transfer have been changed, the surface snow mass and ground temperature have been made prognostic variables, and the treatment of the surface boundary layer has been revised. Modifications have also been made in the numerical solution procedure (which have increased the model’s speed by nearly a factor of 2), and in the prescribed distributions of topography, sea surface temperature and sea ice. The surface albedo is now a function of the prescribed surface type and of the predicted surface snow cover.

The model simulates most features of the large-scale distributions of observed January and July climate more accurately than before, including the primary variables of pressure, temperature, wind, cloudiness and precipitation. In addition, the simulated meridional transports of zonal momentum, heat and water vapor are closer to those observed than heretofore, as are the elements of the associated heat and hydrologic balances. The energy cycle is also simulated with greater accuracy, although the zonal potential and kinetic energies are still somewhat overestimated by the model while the eddy kinetic energy is underestimated. The markedly improved simulations of precipitation, evaporation, 400 mb temperature and surface sensible heat flux in the tropics are shown to be due to the revisions in the new model’s boundary-layer parameterization.

## Abstract

A 3D hybrid (H) transport scheme has been developed that consists of the Prather (P) scheme for vertical transport and a semi-Lagrangian (SL) scheme for horizontal transport on a spherical surface. Two tests have also been developed to permit evaluation of the performance of any numerical transport scheme for flows similar to those found in the earth’s atmosphere. In the first test, the 2D distributions of the wind field and the 3D distribution of the chemical species concentration are prescribed analytically and the consistent analytical expression for the species sources and sinks is determined from the constituent continuity equation. The analytical expressions for the winds and source and sink are then used by a numerical scheme to calculate the 3D distribution of the species concentration. Comparison of the numerical distribution with the analytical distribution then allows evaluation of the performance of the numerical scheme. This test has been used to compare the P, SL, and H schemes. The test shows that the SL scheme produces errors up to 6% in species concentration. The P scheme has high accuracy (about 1%) but requires substantial amounts of computer CPU time and memory. The accuracy of the H scheme is higher (better than 1.6%) than that of the SL scheme and is close to that of the P scheme. The H scheme is about nine times faster than the P scheme but does require about three times more memory than the SL scheme. In another test, the P, H, and SL schemes are tested for 2D zonally averaged transport of the conservative species “cloud” by analytically calculated wind velocities. Comparison of the results shows that the H scheme is superior to the SL scheme. It is concluded that the H scheme is a computationally efficient, accurate scheme for simulating the 3D global transport of both conservative and nonconservative species.

## Abstract

A 3D hybrid (H) transport scheme has been developed that consists of the Prather (P) scheme for vertical transport and a semi-Lagrangian (SL) scheme for horizontal transport on a spherical surface. Two tests have also been developed to permit evaluation of the performance of any numerical transport scheme for flows similar to those found in the earth’s atmosphere. In the first test, the 2D distributions of the wind field and the 3D distribution of the chemical species concentration are prescribed analytically and the consistent analytical expression for the species sources and sinks is determined from the constituent continuity equation. The analytical expressions for the winds and source and sink are then used by a numerical scheme to calculate the 3D distribution of the species concentration. Comparison of the numerical distribution with the analytical distribution then allows evaluation of the performance of the numerical scheme. This test has been used to compare the P, SL, and H schemes. The test shows that the SL scheme produces errors up to 6% in species concentration. The P scheme has high accuracy (about 1%) but requires substantial amounts of computer CPU time and memory. The accuracy of the H scheme is higher (better than 1.6%) than that of the SL scheme and is close to that of the P scheme. The H scheme is about nine times faster than the P scheme but does require about three times more memory than the SL scheme. In another test, the P, H, and SL schemes are tested for 2D zonally averaged transport of the conservative species “cloud” by analytically calculated wind velocities. Comparison of the results shows that the H scheme is superior to the SL scheme. It is concluded that the H scheme is a computationally efficient, accurate scheme for simulating the 3D global transport of both conservative and nonconservative species.

## Abstract

The adjoint method of sensitivity analysis is demonstrated on a radiative-convective climate model. A single adjoint calculation, which requires about the same computation time as the original model suffices to calculate sensitivities of surface air temperature to all 312 model parameters. The uses of these sensitivities are discussed and illustrated. The sensitivities accurately predict the effect on surface air temperature of small variations in the model parameters. Relative sensitivities are used to rank the importance of all the parameters. Several of the sensitivities to parameters customarily considered in previous works (e.g., solar constant, surface albedo, relative humidity, CO_{2} concentration) are reproduced, but the largest sensitivities are to constants used to compute the saturation vapor pressure of water. The uncertainties in the model results are expressed formally in terms of all the sensitivities and parameter covariances. For results that cannot readily be compared with observation (for example, the results of a CO_{2} doubling experiment), this method of uncertainty analysis is the only systematic way to estimate the reliability of model results.

The radiative-convective model contains complex nonlinear processes of the type found in general circulation models. Therefore, the fact that the adjoint method works successfully and efficiently for the radiative-convective model provides valuable information about subsequent application of the method to general circulation models.

## Abstract

The adjoint method of sensitivity analysis is demonstrated on a radiative-convective climate model. A single adjoint calculation, which requires about the same computation time as the original model suffices to calculate sensitivities of surface air temperature to all 312 model parameters. The uses of these sensitivities are discussed and illustrated. The sensitivities accurately predict the effect on surface air temperature of small variations in the model parameters. Relative sensitivities are used to rank the importance of all the parameters. Several of the sensitivities to parameters customarily considered in previous works (e.g., solar constant, surface albedo, relative humidity, CO_{2} concentration) are reproduced, but the largest sensitivities are to constants used to compute the saturation vapor pressure of water. The uncertainties in the model results are expressed formally in terms of all the sensitivities and parameter covariances. For results that cannot readily be compared with observation (for example, the results of a CO_{2} doubling experiment), this method of uncertainty analysis is the only systematic way to estimate the reliability of model results.

The radiative-convective model contains complex nonlinear processes of the type found in general circulation models. Therefore, the fact that the adjoint method works successfully and efficiently for the radiative-convective model provides valuable information about subsequent application of the method to general circulation models.

## Abstract

An accelerated integration procedure (AIP) is developed for the OSU atmospheric GCM/mixed-layer ocean model. In this AIP the depth of the mixed-layer ocean is reduced by an acceleration factor *f _{e}*=12 from 60 m to 5 m and the length of a solar cycle is correspondingly reduced to eliminate the increase in the amplitude of the annual cycle of oceanic temperature which would otherwise occur. Furthermore, the ground bulk heat capacity, ground water field capacity and heat of fusion for sea ice and for snow on sea ice are reduced by

*f*to accelerate the equilibration of the ground temperature, soil water and sea ice, respectively.

_{a}The AIP was used for 1 × CO_{2} and 2 × CO_{2} simulations with the OSU AGCM/mixed-layer Oman model. The AIP attained the equilibrium climates in these simulations with the computer-time equivalent of about 2.5 unaccelerated solar cycles, but after the switch from the AIP to the normal unaccelerated integration procedure (NIP), the temperatures increased to new equilibrium values. Although additional computer time was required to achieve these new equilibria, the overall 1 × CO_{2} and 2 × CO_{2} simulations with the AIP/NIP required respectively only 55% and 28% of the computer time which would have been required with the NIP alone. Thus the AIP was successful in saying a significant amount of computer time.

The success of the AIP notwithstanding, an analysis was undertakes to determine the cause of the change in the equilibrium climate following the AIP/NIP switch. Diagnosis of the 1 × CO_{2} simulation by the OSU AGCM/mixed-layer. ocean model and tests with a latitudinally dependent energy balance model show that it is the increase in the amplitude of the annual cycle of atmospheric temperature from the AIP to the NIP which, acting through the ice-albedo/temperature feedback mechanism, causes the change in the equilibrium climate following the AIP/NIP switch.

It is therefore concluded that while the AIP can save a significant amount of computer time in achieving equilibrium with an AGCM/mixed-layer ocean model, caution in its use is warranted.

## Abstract

An accelerated integration procedure (AIP) is developed for the OSU atmospheric GCM/mixed-layer ocean model. In this AIP the depth of the mixed-layer ocean is reduced by an acceleration factor *f _{e}*=12 from 60 m to 5 m and the length of a solar cycle is correspondingly reduced to eliminate the increase in the amplitude of the annual cycle of oceanic temperature which would otherwise occur. Furthermore, the ground bulk heat capacity, ground water field capacity and heat of fusion for sea ice and for snow on sea ice are reduced by

*f*to accelerate the equilibration of the ground temperature, soil water and sea ice, respectively.

_{a}The AIP was used for 1 × CO_{2} and 2 × CO_{2} simulations with the OSU AGCM/mixed-layer Oman model. The AIP attained the equilibrium climates in these simulations with the computer-time equivalent of about 2.5 unaccelerated solar cycles, but after the switch from the AIP to the normal unaccelerated integration procedure (NIP), the temperatures increased to new equilibrium values. Although additional computer time was required to achieve these new equilibria, the overall 1 × CO_{2} and 2 × CO_{2} simulations with the AIP/NIP required respectively only 55% and 28% of the computer time which would have been required with the NIP alone. Thus the AIP was successful in saying a significant amount of computer time.

The success of the AIP notwithstanding, an analysis was undertakes to determine the cause of the change in the equilibrium climate following the AIP/NIP switch. Diagnosis of the 1 × CO_{2} simulation by the OSU AGCM/mixed-layer. ocean model and tests with a latitudinally dependent energy balance model show that it is the increase in the amplitude of the annual cycle of atmospheric temperature from the AIP to the NIP which, acting through the ice-albedo/temperature feedback mechanism, causes the change in the equilibrium climate following the AIP/NIP switch.

It is therefore concluded that while the AIP can save a significant amount of computer time in achieving equilibrium with an AGCM/mixed-layer ocean model, caution in its use is warranted.

## Abstract

In this study we develop theoretical expressions for the rainfall rate, *P*(*z*), and the total evaporation rate from cloud base to a level *z* below cloud base, *E*(*z*). The resultant parameterization for the total evaporation is given by *E*(*z*) = *CP*
^{α}(0)Ψ(*z*), where *P*(0) is the rainfall rate at cloud base, α and *C* are undetermined parameters, and Ψ(*z*) is a function of *z*. The latter is determined for the cases of constant relative humidity and constant absolute humidity below cloud base which correspond approximately to stratiform and cumuloform clouds, respectively. The parameters α and *C* are determined from radar observations of the rain failing from continental convective cells in central South Africa. The resultant values are α = 0.606 and *C* = 2.63 × 10^{−2} for *P*(0) and *E*(*z*) in millimeters per hour. Subsequent analyses of other radar observations utilizing the method developed in this study are needed to obtain corresponding evaporation parameterizations for cumuloform precipitation in other climatic regimes and for stratiform precipitation.

## Abstract

In this study we develop theoretical expressions for the rainfall rate, *P*(*z*), and the total evaporation rate from cloud base to a level *z* below cloud base, *E*(*z*). The resultant parameterization for the total evaporation is given by *E*(*z*) = *CP*
^{α}(0)Ψ(*z*), where *P*(0) is the rainfall rate at cloud base, α and *C* are undetermined parameters, and Ψ(*z*) is a function of *z*. The latter is determined for the cases of constant relative humidity and constant absolute humidity below cloud base which correspond approximately to stratiform and cumuloform clouds, respectively. The parameters α and *C* are determined from radar observations of the rain failing from continental convective cells in central South Africa. The resultant values are α = 0.606 and *C* = 2.63 × 10^{−2} for *P*(0) and *E*(*z*) in millimeters per hour. Subsequent analyses of other radar observations utilizing the method developed in this study are needed to obtain corresponding evaporation parameterizations for cumuloform precipitation in other climatic regimes and for stratiform precipitation.