radiative forcing by well-mixed greenhouse...

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. ???, XXXX, DOI:10.1029/,

Radiative forcing by well-mixed greenhouse gases:1

Estimates from climate models in the IPCC AR42

W. D. Collins,1

V. Ramaswamy,2

M. D. Schwarzkopf,2

Y. Sun,3

R. W. Portmann,3

Q. Fu,4

S. E. B. Casanova,5

J.-L. Dufresne,6

D. W. Fillmore,1

P. M. D. Forster,5

V. Y. Galin,7

L. K. Gohar,5

W. J. Ingram,8

D. P. Kratz,9

M.-P. Lefebvre,6

J. Li,10

P. Marquet,11

V. Oinas,12

Y. Tsushima,13

T. Uchiyama14

and W. Y. Zhong15

D R A F T July 7, 2005, 4:01pm D R A F T

X - 2 COLLINS ET AL.: GREENHOUSE FORCING BY AOGCM RADIATION CODES

W. D. Collins and D. W. Fillmore, Climate and Global Dynamics Division, National Center

for Atmospheric Research, P.O. Box 3000, Boulder, Colorado 80307, USA. ([email protected]

and [email protected])

V. Ramaswamy and M. D. Schwarzkopf, Geophysical Fluid Dynamics Laboratory,

201 Forrestal Road, Princeton, New Jersey 08542, USA. ([email protected] and

[email protected])

Y. Sun and R. W. Portmann, NOAA Aeronomy Laboratory, 325 Broadway, David

Skaggs Research Center, Boulder, Colorado 80305, USA. ([email protected] and

[email protected])

Q. Fu, Department of Atmospheric Sciences, University of Washington, 408 ATG Building,

P.O. Box 351640, Seattle, Washington 98195, USA. ([email protected])

S. E. B. Casanova,, P. M. D. Forster, and L. K. Gohar, Department of Meteorology, University

of Reading, Earley Gate, P.O. Box 243, Reading RG6 6BB, UK. ([email protected],

[email protected], and [email protected])

J.-L. Dufresne and M.-P. Lefebvre, Laboratoire de Meteorologie Dynamique (LMD/IPSL),

Tour 45–55, 3eme, Jussieu, CNRS/UPMC – Boite 99, F–75252 Paris Cedex 05, France.

([email protected] and [email protected])

V. Y. Galin, Institute of Numerical Mathematics, Academy of Sciences, 8 Gubkina St.,

Moscow 117333, Russian Federation. ([email protected])

W. J. Ingram, Atmospheric, Oceanic and Planetary Physics, Clarendon Laboratory, Parks


COLLINS ET AL.: GREENHOUSE FORCING BY AOGCM RADIATION CODES X - 3

Abstract. The radiative effects from increased concentrations of well-3

mixed greenhouse gases (WMGHGs) represent the most significant anthro-4

pogenic forcing of the climate system. The most comprehensive tools for sim-5

ulating past and future climates influenced by WMGHGs are fully coupled6

atmosphere-ocean general circulation models (AOGCMs). Because of the im-7

Road, Oxford, OX1 3PU, UK. ([email protected])

D. P. Kratz, Radiation and Aerosols Branch, NASA Langley Research Center, Mail Stop 420,

21 Langley Boulevard, Hampton, Virginia 23681, USA. ([email protected])

J. Li, Canadian Centre for Climate Modelling and Analysis, University of Victoria,

P.O. Box 1700, STN CSC, Victoria, British Columbia, V8W 2Y2, Canada.

([email protected])

P. Marquet, Meteo-France CNRM, 42 av. G. Coriolis, 31057 Toulouse Cedex 01, France

([email protected])

V. Oinas, NASA Goddard Institute for Space Studies, 2880 Broadway, New York, New

York 10025, USA. ([email protected])

Y. Tsushima, Frontier Research System for Global Change, Institute for Global Change Re-

search, 3173–25 Showa-machi, Kanazawa-ku,Yokohama 236–0001, Japan. ([email protected])

T. Uchiyama, Meteorological Research Institute, 1–1 Nagamine, Tsukuba-shi, Ibaraki-ken 305–

0052, Japan. ([email protected])

W. Y. Zhong, Space and Atmospheric Physics Group, Physics Department, Imperial College,

Blackett Laboratory, Prince Consort Road, London SW7 2BW, UK. ([email protected])

1National Center for Atmospheric Research, Boulder, Colorado, USA.



portance of WMGHGs as forcing agents, it is essential that AOGCMs com-8

pute the radiative forcing by these gases as accurately as possible. We present9

the results of an intercomparison between the forcings computed by AOGCMs10

and by benchmark line-by-line (LBL) radiative transfer codes. The compar-11

ison is focused on forcing by CO2, CH4, N2O, CFC-11, CFC-12, and the in-12

2Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey, USA.

3NOAA Aeronomy Laboratory, Boulder, Colorado, USA.

4Department of Atmospheric Sciences, University of Washington, Seattle, Washington, USA.

5Department of Meteorology, University of Reading, Reading, UK.

6Laboratoire de Meteorologie Dynamique, Paris, France.

7Institute of Numerical Mathematics, Academy of Sciences, Moscow, Russian Federation.

8Atmospheric, Oceanic and Planetary Physics, Clarendon Laboratory, Oxford, UK.

9NASA Langley Research Center, Hampton, Virginia, USA.

10Canadian Centre for Climate Modelling and Analysis, University of Victoria, Victoria,

Canada.

11Meteo-France CNRM, Toulouse, France.

12NASA Goddard Institute for Space Studies, New York, New York, USA.

13Frontier Research System for Global Change, Institute for Global Change Research,

Yokohama, Japan.

14Meteorological Research Institute, Ibaraki-ken, Japan.

15Physics Department, Imperial College, London, UK.



creased H2O expected in warmer climates. The models included in the in-13

tercomparison include representatives from most of the modeling groups par-14

ticipating in the IPCC 4th Assessment Report (AR4) and from a number15

of the principal groups developing LBL codes. The results indicate that there16

are still substantial discrepancies between AOGCMs and LBL models for forc-17

ings by CH4, N2O, and CO2. We quantify these differences and discuss the18

implications for interpreting variations in forcing and response across the multi-19

model ensemble of AOGCM simulations assembled for the IPCC AR4.20



1. Introduction

One of the major factors underlying recent climate change is radiative forcing. Ra-21

diative forcing is an externally imposed change in the radiative energy budget of the22

Earth’s climate system [IPCC , 2001]. The energy budget is characterized by an approxi-23

mate balance between shortwave absorption and longwave emission by the climate system24

[e.g., Kiehl and Trenberth, 1997]. Radiative forcing can affect either the shortwave or25

longwave components of the radiative budget. The changes can be caused by a number of26

factors including variations in solar insolation, alteration in surface boundary conditions27

related to land-use change and desertification, or natural and anthropogenic perturba-28

tions to the radiatively active species in the atmosphere. Perhaps the most basic and29

most important forcings are related to anthropogenic increases in the well-mixed green-30

house gases (WMGHGs) CO2, CH4, N2O, and the halocarbons. The WMGHGs enhance31

the absorption of radiation in the atmosphere through excitation of molecular rotational32

and rotational-vibrational modes by near-infrared and infrared photons. Despite contin-33

uing uncertainty regarding the magnitude of aerosol radiative forcing [Anderson et al.,34

2003], it is likely that the net anthropogenic radiative forcing of the climate system is35

positive because of the effects of WMGHGs [Boucher and Haywood , 2001]. The increased36

concentrations of CO2, CH4, and N2O between 1750 and 1998 have produced forcings of37

1.48, 0.48, and 0.15 Wm−2, respectively [IPCC , 2001]. The introduction of halocarbons38

in the mid-20th century has contributed an additional 0.34 Wm−2, for a total forcing by39

WMGHGs of 2.45 Wm−2 with a 15% margin of uncertainty.40



Coupled atmosphere-ocean general circulation models (AOGCMs) [Trenberth, 1992;41

Randall , 2000] represent the most comprehensive systems for simulating the response42

of the climate to radiative forcings. AOGCMs have been used extensively to simulate43

change in response to WMGHGs and other agents since pioneering studies by Manabe and44

Wetherald [1975] and other modeling groups. In the current fourth Assessment Report45

(AR4) of the Intergovernmental Panel on Climate Change (IPCC), sixteen international46

groups are submitting simulations from twenty-three different AOGCMs. These simu-47

lations are used to project climate change in the recent past and in the future under a48

variety of emissions scenarios for WMGHGs and other radiative species [Nakicenovic and49

Swart , 2000].50

Because of the intrinsic complexity of the numerous processes included in these models51

and the computational demands of climate-change simulation, it is frequently necessary52

to approximate the various processes using simplified representations called parameteriza-53

tions. Such approximations are necessary both for processes grounded in first-principles54

theory (e.g., radiative transfer) and for elements of the climate system which are less55

well understood (e.g., clouds). The lack of stringent observational or theoretical con-56

straints on the second class of processes has resulted in a diversity of parameterizations57

for many components of the climate system. The diversity reflects the uncertainty in the58

physics governing those components. Through interactions with the rest of the model59

physics, these uncertainties can have significant effects on climate simulations. The use60

of a multi-model ensemble in the IPCC reports is an attempt to characterize the impact61

of parameterization uncertainty on climate-change predictions.62



However, calculating the interaction of visible and infrared radiation with an (idealized)63

atmosphere free of clouds and aerosols is essentially a solved problem. The remaining64

uncertainties are related primarily to the spectroscopy of the WMGHGs and other atmo-65

spheric constituents and to the treatment of broadband continuum absorption by H2O and66

CO2. Very accurate line-by-line (LBL) codes can solve the basic equations of radiative67

transfer [Liou, 1992] for each quantum transition, or “line”, registered for each radia-68

tively active molecular constituent in the atmosphere. In carefully controlled comparisons69

against field data, LBL results agree with observed spectra to within observational uncer-70

tainty [e.g., Tjemkes et al., 2003]. Kratz et al. [2005] have shown that a collection of LBL71

models produce far-infrared radiances and fluxes that differ by roughly 0.5% when applied72

to identical atmospheric profiles. The results from LBL codes represent a rigorous set of73

benchmark calculations for development and evaluation of radiation codes in AOGCMs74

[Clough and Iacono, 1995].75

There have been several efforts to evaluate the accuracy of radiative parameterizations76

in AOGCMs relative to LBL calculations. The major projects include the Intercompar-77

ison of Radiation Codes in Climate Models (ICRCCM) [Ellingson and Fouquart , 1991;78

Ellingson et al., 1991; Fouquart et al., 1991], the GCM-reality Intercomparison Project79

for SPARC (GRIPS) [Pawson et al., 2000], and an assessment of treatments for unre-80

solved clouds [Barker et al., 2003]. Heating rates have been previously evaluated by Fels81

et al. [1991]. Analysis of radiative forcing by WMGHGs derived from earlier generations82

of AOGCMs has uncovered large discrepancies relative to LBL calculations, for example83

in the forcing from doubling atmospheric concentrations of CO2 [Cess et al., 1993]. The84

problems encountered in the Cess et al. [1993] study include omission of minor CO2 ab-85



sorption bands, errors in the overlap of absorption by H2O and CO2, and unresolved issues86

with the formulation of longwave radiative transfer. Analyses of the radiative forcing by87

sulfate aerosols has also demonstrated large differences among models [Boucher et al.,88

1998].89

In this study, we update the earlier intercomparions by evaluating many of the AOGCMs90

included in the IPCC AR4 against a representative set of current LBL codes. The goals91

of this exercise are to evaluate the fidelity of AOGCMs included in the IPCC AR4 and to92

establish new benchmark calculations for this purpose. The chief objective is to determine93

the differences in WMGHG forcing caused by the use of different radiation codes in the94

AOGCMs used for IPCC climate change simulations. Unlike some of the previous studies,95

the emphasis here is on the accuracy of radiative forcing rather than radiative flux. While96

the effects of increasing WMGHGs represent only part of the forcing applied to the climate97

system, a comprehensive evaluation of all the forcing agents in AOGCMs is beyond the98

scope of this work.99

The Radiative Transfer Model Intercomparison Project (RTMIP) and the participat-100

ing models are described in section 2. Results for the radiative forcings at the top of101

model (TOM), 200 mb (a surrogate for the tropopause), and surface are presented in102

section 3.1. A comparison of the corresponding changes in atmospheric heating rates is103

given in section 3.2. Discussion and conclusions are presented in section 4.104

2. Experimental configuration

2.1. Clear-sky forcing calculations

The specific goal of this study is to quantify the differences in instantaneous radiative105

forcing calculated from AOGCM and LBL radiation codes. Based upon experience from106



previous intercomparisons, the calculations requested from the participants in RTMIP are107

not sufficient for detailed explanation of the differences. On the other hand, minimizing108

the number of required calculations has helped insure nearly unanimous participation by109

the AOGCM groups.110

The calculations are performed offline by applying the LBL codes and radiative pa-111

rameterizations from the AOGCMs to a specified atmospheric profile. The results are112

therefore not affected by differences among the atmospheric climatologies produced by113

the various AOGCMs. The radiatively active species included in this evaluation are the114

WMGHGs CO2, CH4, N2O, and the chlorofluorocarbons CFC-11 and CFC-12. The in-115

tercomparison is based upon calculations of the instantaneous changes in clear-sky fluxes116

when concentrations of these WMGHGs are perturbed. While the relevant quantity for117

climate change is all-sky forcing, the introduction of clouds would greatly complicate the118

intercomparison exercise.119

In addition, the calculations omit the effects of stratospheric thermal adjustment to120

forcing derived using Fixed Dynamical Heating (FDH) [Manabe and Wetherald , 1967].121

This omission facilitates comparison of fluxes from LBL codes and AOGCM parameteri-122

zations, and it excludes discrepancies arising from differences in dynamical heating rates123

from various AOGCMs. For the purposes of this intercomparison, “flux” is defined as124

“flux for clear-sky and aerosol-free conditions” and “forcing” is defined as “instantaneous125

changes in fluxes without stratospheric adjustment”. It should be noted that our omission126

of FDH means that the results in this study are not directly comparable to the estimates127

of forcing in the IPCC [2001] reports, since the latter include the effects of adjustment.128



The effects of adjustment on forcing are approximately 2% for CH4, 4% for N2O, 5% for129

CFC-11, 8% for CFC-12, and 13% for CO2 [IPCC , 1995; Hansen et al., 1997].130

The specifications for each of the calculations requested from the LBL and AOGCM131

groups are given in Table 1. The concentrations of WMGHGs in calculations 3a and Table 1132

3b correspond to conditions in the years 1860 AD and 2000 AD, respectively. Differ-133

ences among these calculations cover several standard forcing scenarios performed by all134

AOGCMs included in the AR4:135

1. Forcing for changes in CO2 concentrations;136

(i) From 1860 to 2000 values (case 2a−1a);137

(ii) From 1860 to double 1860 values (case 2b−1a)138

2. Forcing for changes in WMGHGs from 1860 to 2000 values (case 3b−3a); and139

3. The effect of changes in H2O on forcing by CO2 (case 4a−2b).140

In addition to the four forcing experiments listed above, there are three additional141

forcing experiments for combinations of CH4, N2O, and CFC-11 and CFC-12. The changes142

in WMGHGs and H2O in these seven forcing experiments are given in Table 2. Table 2143

The quantities requested from each participating group include:144

1. Net shortwave and longwave clear-sky flux at the top of the model;145

2. Net shortwave and longwave clear-sky flux at 200 mb;146

3. Net shortwave and longwave clear-sky flux at the surface; and (optionally)147

4. Net shortwave and longwave clear-sky fluxes at each layer interface in the profile.148

The reason for performing calculations at 200 mb rather than the tropopause is to149

insure consistency with the radiative quantities requested from the climate-change simu-150



lations. Since not all modeling groups are prepared to compute fluxes at a time-evolving151

tropopause, the Working Group on Coupled Modeling (WGCM) of the World Climate152

Research Programme (WCRP) and the IPCC have requested fluxes at a surrogate for the153

tropopause at the 200 mb pressure surface. The precise choice of tropopause can affect154

forcings by up to 10% [Myhre and Stordal , 1997].155

In order to establish a common baseline, the background atmospheric state for all156

the calculations is the AFGL mid-latitude summer (MLS) atmospheric profile [Anderson157

et al., 1986]. Therefore all the calculations are performed using the same vertical profiles158

of temperature and the volume-mixing ratio of O3. The profile of specific humidity is also159

held fixed except for calculation 4a (Table 1). The concentrations of WMGHGs are set160

to a constant volume mixing ratio with respect to dry air throughout the column. The161

standard MLS profile has been interpolated to 40 levels for the AOGCM groups and 459162

levels for the LBL groups. As shown in Table 3, the comparison of forcings from AOGCM Table 3163

and LBL codes is not affected by the difference in resolution. Increasing resolution from 40164

to 459 levels changes the longwave forcings at TOM and surface by less than approximately165

0.01 Wm−2. Changing the methods of temperature interpolation within each layer in the166

LBL calculations changes the longwave forcings by less than 0.02 Wm−2.167

The radiative calculations include only the effects of molecular Rayleigh scattering and168

the absorption by the WMGHGs, H2O, and O3. The forcing calculations should not be169

appreciably affected by the red and near-infrared (A, B, and γ) bands of O2, collisionally-170

induced rotation bands in N2 at approximately 100 cm−1, quadrupole transitions in the171

fundamental vibration band of N2 at 2330 cm−1, the forbidden transitions of O2 in the172

vibration-rotation band, or the collision complexes O2·O2 and O2·N2. For example, the173



effect of the A, B, and γ bands of O2 on the shortwave forcing is less than 0.001 Wm−2174

(Table 3). The inclusion or omission of these absorption bands has been left to the175

discretion of the individual AOGCM and LBL modelers. The LBL groups have used176

spectral ranges of 100 to 2500 cm−1 for the longwave and 2000 to ≥50000 cm−1 for177

the shortwave. Some of the LBL groups have provided their spectrally resolved fluxes178

corresponding to their broadband calculations. The AOGCM groups have been asked to179

use the standard spectral ranges for their respective radiative parameterizations.180

For the shortwave calculations, the surface is a Lambertian reflector with a spectrally181

flat albedo of 0.1. At the TOM, the solar radiation is set to 1360 Wm−2 incident at a182

zenith angle of 53 degrees. The value for TOM solar insolation is the difference between183

a broadband solar constant of 1367 Wm−2 and the 6.33 Wm−2 of solar radiation in the184

wavenumber range 0 and 2000 cm−1 excluded from the calculations [Labs and Neckel ,185

1970]. For the longwave calculations, the surface is assumed to have a spectrally flat186

emissivity equal to 1 and a thermodynamic temperature of 294 K.187

2.2. General circulation and line-by-line models

The AOGCM groups and models contributing calculations to RTMIP are listed in Ta-188

ble 41 and Table 5. There are sixteen groups submitting simulations to the IPCC AR4, Table 4

Table 5

189

and fourteen of these are participating in RTMIP. The groups have submitted simula-190

tions from twenty-three models to the IPCC data archive, and calculations representing191

twenty of these are included in our intercomparison. It should be noted that a number of192

the AOGCMs share similar or identical radiative parameterizations. The two AOGCMs193

developed by CCCma, CCSR/NIES/FRCGC, GFDL, and GISS each share common ra-194

diation codes. In addition, the models BCCR-BCM2.0 and CNRM-CM3 have identical195



parameterizations, and the treatments of trace gases in CCSM3, FGOALS-g1.0 and PCM196

are essentially the same. The characteristics of the radiative parameterizations used in197

many of these AOGCMs are described in detail in Fu and Ramaswamy (manuscript in198

preparation)2.199

The LBL groups contributing calculations to RTMIP are listed in Table 5 and Table 6. Table 6200

The details of the calculations performed with each LBL code are given in Table 73. The Table 7201

five participating LBL groups have each performed the longwave calculations, and four202

have performed the shortwave calculations. The LBL models are all based upon the same203

Hitran line database for radiatively active species [Rothman et al., 2003], although three of204

the models include additional corrections to that database. Because of the heterogeneity205

of LBL configurations shown in Table 7, the agreement among the absolute fluxes from206

these codes is not as good as the agreement that can be achieved in more rigorously207

controlled intercomparisons [e.g., Kratz et al., 2005]. However, the objective in RTMIP is208

to derive accurate forcings, and the set of LBL calculations is adequate for that application209

(section 3). For example, consider the 200 mb longwave fluxes F200(LW ) for calculations210

1a and 2a. The difference between these fluxes is the longwave forcing at 200 mb caused211

by an increase in CO2 from 287 to 369 ppmv (Table 2). For both of the calculations 1a212

and 2a, the standard deviation of the LBL estimates of F200(LW ) is 1.25 Wm−2. However,213

the standard deviation of the forcing (the difference between calculations 1a and 2a) is214

just 0.02 Wm−2. This example illustrates that discrepancies among radiative codes that215

affect the calculation of fluxes need not appreciably affect the calculation of forcings.216

Sample infrared forcing calculations with the RFM code are shown in Figure 14. The Figure 1217

ratio of the net infrared flux at 200mb to the infrared flux from the surface is plotted in218



Figure 1a. Values close to 1 indicate that the absorption by tropospheric gases is relatively219

weak at those wavelengths, while values close to 0 indicate that the absorption is quite220

strong. The four prominent features are the strong H2O band at 6.7 µm, the mid-infrared221

“window” between 8 and 12 µm, the CO2 band at 15 µm, and the far-infrared rotation222

bands of H2O. The spectral infrared forcings for four of the experiments in Table 2 are223

plotted in Figure 1b. As this figure illustrates, the largest forcings generally occur outside224

the band centers of the major absorbing species. For example, the largest CO2 forcings225

appear in the wings of the 15-µm band. Similarly, the largest H2O forcings occur in the226

mid-infrared window and the far-infrared, not in the 6.7µm H2O band. The reason is227

that the absorption in the band centers is effectively saturated, and therefore increases in228

radiatively active species have minimal effects at those wavelengths.229

Corresponding visible and near-infrared forcing calculations are shown in Figure 2. The Figure 2230

ratio of the net surface flux to the TOM solar radiation is plotted in Figure 2a. At231

wavelengths where the ratio is close to 1, the atmosphere transmits most of the incident232

flux to the surface. Where the ratio is close to 0, the incident flux is largely absorbed233

by trace gases and water vapor along the ray path from the top of atmosphere to the234

surface. The major features in the transmission spectrum are the extremely strong O3235

bands at wavelengths below 0.26 µm, the visible atmospheric “window” between 0.3 and236

0.7 µm, the CO2 bands at 2.7 and 4.3 µm, and the primary and overtone bands of H2O.237

The spectral near-infrared forcings for four of the experiments in Table 2 are plotted in238

Figure 2b. Due to saturation effects, there is virtually no forcing near the CO2 and H2O239

band centers at 2.7 µm or the middle of the CO2 band at 4.3 µm. However, in other240

near-infrared bands of H2O and the WMGHGs, the line strengths are sufficiently weak241



that forcing can occur near the band centers. An example is the forcing by H2O in its242

overtone bands at wavelengths below 2 µm. It is also evident from comparison of the243

ordinates in Figures 1b and 2b that the forcings by WMGHGs in the near-infrared are244

generally weaker than the forcings in the infrared.245

3. Comparion of calculations from AOGCMs and LBL models

3.1. Forcings from AOGCMs and LBL models

The statistical summaries of the forcing intercomparison are given in Table 8 for the Table 8246

longwave and Table 9 for the shortwave. For each level, the tables list the mean and Table 9247

standard deviation of the AOGCM and LBL results, the difference between the means,248

and the probability from the Student t-test that the AOGCM and LBL distributions of249

forcings have the same mean. There are sixteen members of the distribution of forcings250

from AOGCMs (Table 4), and therefore the uncertainty in the mean AOGCM forcings251

is a factor of√

16 = 4 smaller than the standard deviations shown in Tables 8 and 9.252

For the LBL models, there are five members of the longwave forcing ensemble and four253

members of the shortwave forcing ensemble.254

The results from each of the forcing experiments are shown in Figure 3 through Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

255

Figure 9. The upper and lower panels in each figure display the longwave and shortwave

Figure 8

Figure 9

256

forcing statistics, respectively. The data from AOGCMS are shown with box-and-whisker257

diagrams [Tukey , 1977] for the three mandatory levels in the intercomparison. Since there258

are fewer LBL models, only the minimum, median, and maximum LBL values are plotted259

for each level. In many cases, the range of LBL estimates is so small compared to the260

scale of the abscissa that it is not visible in the plot, for example in the graph of shortwave261

forcing from doubling CO2 (Figure 4b).262



Perhaps the most basic result of the intercomparison is that all the mean forcings263

calculated from the AOGCMs have the correct sign. With one single exception, the forcing264

values from individual AOGCMs also have the correct sign. The exception occurs for one265

of the AOGCMs in the increased H2O experiment (case 4a−2b) in the shortwave band266

at the 200mb level. The longwave forcings are uniformly positive for all mandatory levels267

and for all experiments. The effect of increased WMGHGs and H2O is to reduce the net268

upward longwave flux from the the atmosphere and surface below. The shortwave forcings269

are positive or zero at the TOM and uniformly negative at the surface. This implies that270

WMGHGs and H2O enhance the absorption of solar radiation by the surface-atmosphere271

column. However, since the additional absorption occurs in the atmosphere and primarily272

affects the downwelling direct-beam radiation, the higher absorption also reduces the net273

surface insolation.274

The forcing applied to the climate from increases in WMGHGs between 1860 and 2000275

is shown in Figure 6. In the longwave, the differences between the forcings calculated with276

AOGCMs and LBL models are not statistically significant at the three surfaces included277

in the intercomparison (Table 8). As the analysis of individual gases will show, this278

agreement results in part from compensating errors in the AOGCM codes. Nonetheless,279

this is perhaps the most important test for the accuracy of the forcing applied to the280

AOGCMs in simulations of the recent past. In the shortwave, the AOGCMs systematically281

underestimate the magnitude of the forcings at the three mandatory surfaces, and the282

differences are highly significant (Table 9). As the analysis of individual gases will show,283

the discrepancies are caused by the omission of CH4 and N2O from all of the AOGCM284

radiative parameterizations.285



The forcing by increased CO2 is the most important component of the total forcing of286

the climate in the recent past. The model estimates for the shortwave and longwave effects287

from the observed increase and from doubling CO2 are shown in Figures 3 and 4. The288

AOGCMs tend to underestimate the longwave forcing at the three mandatory levels. The289

biases relative to LBL codes, while not large in relative terms, are statistically significant290

(Table 8). The relative differences in the mean forcings are less than 8% for the pseudo-291

tropopause at 200 mb, but increase to approximately 13% at the TOM and to 33% at the292

surface. The small errors at 200 mb may reflect earlier efforts to improve the accuracy293

of AOGCM calculations near the tropopause in order to produce reasonable estimates of294

radiative forcing. In general, the mean shortwave forcings from the LBL and AOGCM295

codes are in good agreement at all three mandatory surfaces. This implies the differences296

between the mean shortwave forcings for increased WMGHGs from 1860 to 2000 are not297

related to errors in the treatment of CO2. However, the range in shortwave forcing at the298

surface from individual AOGCMs is quite large. The ratios of the standard deviations299

to mean forcings for the two cases are 0.94 and 0.95 (Table 9). In addition, one of the300

AOGCM shortwave parameterizations does not include the effects of CO2 on shortwave301

fluxes and heating rates. The omission explains why the box-and-whisker diagrams for the302

multi-AOGCM ensemble of shortwave calculations in Figures 3 and 4 intersect the zero303

forcing value on the abscissas. This particular model only computes a non-zero shortwave304

forcing in case 4a−2b for increased H2O.305

The combined effects of increasing CH4 and N2O from 0 ppbv to the concentrations of306

these gases at 1860 are plotted in Figure 5. The forcings from increasing N2O and CFCs307

from concentrations at 1860 to 2000 are shown in Figure 7, and the corresponding forcings308



from increasing CH4 and CFCs are shown in Figure 8. The absorption by CFC-11 and309

CFC-12 occurs almost entirely between 450 and 2000 cm−1 [e.g., Christidis et al., 1997] and310

therefore shortwave forcing by these compounds may be neglected. Combinations of these311

cases provide sufficient information to diagnose potential errors in both the AOGCM and312

LBL codes. As the figures clearly show, all of the AOGCM codes in this intercomparison313

omit the effects of CH4 and N2O on shortwave fluxes and forcings. While the omission314

of N2O does not introduce a large absolute error in the forcings, recent increases in CH4315

produce decreases of up to −0.5 Wm−2 in the net shortwave fluxes at the surface in the316

LBL calculations [Ramaswamy et al (manuscript in preparation)].5 The AOGCMs also317

tend to overestimate the longwave forcing at the surface by both N2O and CH4, and these318

differences are statistically significant (Table 8). There is also evidence in Figures 7 and 8319

that the range of longwave forcings from the LBL models is larger than expected. When320

CH4 and N2O are paired with CFC-11 and CFC-12, the spread in LBL longwave forcings321

at each of the mandatory levels is larger by at least 2× than the corresponding range in322

the LBL calculation with CH4 and N2O alone (Table 8). In addition, the spread in the323

LBL results for N2O combined with the CFCs is nearly identical to the spread for CH4324

combined with the CFCs. These results suggest that the divergence among LBL codes is325

related to the introduction of chlorofluorocarbons in the longwave calculations. While the326

discrepancy has been traced to one of the LBL codes in the intercomparison, the cause of327

the discrepancy has not been determined at this time. The authors and LBL developers328

are continuing to investigate this issue.329

The longwave forcing from increasing H2O is quite well simulated with the AOGCM330

codes (Figure 9). The differences relative to the LBL calculations at the three standard331



levels are not statistically significant. In the shortwave, the only significant difference332

between the AOGCM and LBL calculations occurs at the surface, where the AOGCMs333

tend to underestimate the magnitude of the reduction in insolation. The fact that the334

surface forcing from the H2O feedback is larger than the surface forcing by the WMGHGs335

is consistent with earlier modeling studies of the interactions of the hydrological cycle and336

anthropogenic climate change [Ramanathan, 1981].337

3.2. Heating rates from AOGCMs and LBL models

The perturbations to the heating rates by increases in WMGHGs and H2O are rela-

tively small. The first law of thermodynamics applied to just the radiative processes in a

vertically stratified atmosphere is:

ρ cp

∂T

∂t= −∂F

∂z(1)

where ρ is the density of the atmosphere, cp is the specific heat of air at constant pressure,

T is the atmospheric temperature, F is a radiative flux (positive upward), t is time, and

z is the vertical coordinate. The radiative heating rates Q are equal to ∂T/∂t with time

expressed in days. Integrating this equation over the depth of a standard atmosphere and

denoting the mass-weighted heating rate by Q gives

Q ' ∆F

120(2)

with Q expressed in units of K/day and the radiative flux divergence ∆F expressed in338

Wm−2. This same relationship applies when Q and ∆F are perturbed by changes in atmo-339

spheric composition, e.g., increases in WMGHGs. In the RTMIP calculations, the changes340

in tropospheric flux divergence are smaller in magnitude than 12 Wm−2. From equation 2341

it follows that the expected perturbations to |Q| are less than approximately 0.1 K/day.342



For comparison, the global mean shortwave convergence of roughly 67 Wm−2 corresponds343

to a column-integrated heating of 0.56 K/day, and the global mean longwave divergence344

of 169 Wm−2 corresponds to a cooling of −1.4 K/day [Kiehl and Trenberth, 1997].345

The perturbations to the heating rates for selected forcing cases are shown in Fig-346

ure 10 through Figure 13. The cases are doubling CO2 from concentrations in 1860 Figure 10

Figure 11

Figure 12

Figure 13

347

(case 2b−1a); increasing CH4 and N2O from 0 to values in 1860 (case 3a−1a); increasing348

the WMGHGs from concentrations in 1860 to 2000 (case 3b−3a); and increasing H2O349

by 20% (case 4a−2b). The addition of WMGHGs generally increases the absorption of350

upwelling longwave and downwelling solar radiation and therefore increases the corre-351

sponding heating rates (Figures 10 through 12). The addition of H2O, however, increases352

the atmospheric emission to the surface by an amount sufficient to cause the atmosphere353

to cool further (Figure 13a).354

There are three significant features in the comparison of AOGCM and LBL heating355

rates. First, it is evident from inspection of the figures that the differences among the356

AOGCM calculations are frequently as large as the mean perturbation to the heating rates357

obtained from the LBL codes. Second, the omission of CH4 and N2O from the AOGCM358

shortwave parameterizations is reflected in the zero mean perturbation to AOGCM short-359

wave heating rates plotted in Figure 11b. Third, some of the longwave parameterizations360

in AOGCMs show evidence of poor numerical formulation or implementation. Some of361

the AOGCMs produce oscillations in the vertical profile of longwave heating-rate pertur-362

bations which are absent from the corresponding LBL calculations. These oscillations363

are particularly evident for the cases of doubling CO2 and increasing WMGHGs from364

concentrations in 1860 to 2000 shown in Figures 10a and 12a, respectively. As equation 1365



shows, the calculation of heating rates requires numerical differentiation of vertical radia-366

tive flux profiles. The existence of these oscillations suggests that some of the AOGCM367

parameterizations yield flux profiles which are insufficiently continuous with respect to368

differentiation by the vertical coordinate.369

4. Discussion and conclusions

This paper discusses the findings from the Radiative Transfer Model Intercomparison370

Project (RTMIP). The basic goal of RTMIP is to compare the radiative forcings computed371

with AOGCMs in the IPCC AR4 against calculations with LBL models. The radiatively372

active species included in RTMIP are the primary well-mixed greenhouse gases CO2, CH4,373

N2O, CFC-11, and CFC-12. In the current generation of AOGCMs, the forcings by these374

species are combined with forcings by a wide variety of other agents including tropospheric375

and stratospheric ozone, direct and indirect effects of aerosols, solar variability, land-use376

change, and urbanization [IPCC , 2001]. The participants in RTMIP have focused on377

WMGHGs since these collectively represent the most important positive forcing on climate378

[Boucher and Haywood , 2001] and there are minimal uncertainties in the benchmark LBL379

calculations. Intercomparisons of forcing by other radiatively active species, for example380

aerosols, are complicated by significant uncertainties in the representations of aerosol381

chemical composition and microphysical properties. In some sense, a minimum criterion382

for the realism of simulations of climate change with an AOGCM is the fidelity of its383

calculation of radiative forcing by WMGHGs.384

One other aspect of radiative parameterizations which is omitted from RTMIP is the385

accuracy of the absolute fluxes. The range of clear-sky shortwave fluxes and divergences386

from the participating AOGCMs is considerably larger than the range of shortwave forc-387



ings obtained in this study. The range of clear-sky divergence has a direct effect on the388

thermal evolution and the mean atmospheric states simulated with the AOGCMs included389

in RTMIP. For example, the range of clear-sky divergence is approximately 8 Wm−2,390

which is approximately 12% of mean divergence averaged across all models and calcula-391

tions. The magnitude of the divergence is governed primarily by Beer’s law and by the392

column-integrated masses of absorptive species. Since the masses of the WMGHGs, O3,393

and H2O are identical across the models, the range of divergence is caused by the diverse394

formulations of shortwave radiative transfer in the AOGCMs.395

Perhaps the most basic finding of RTMIP is that there are no sign errors in the mean396

forcings averaged across the AOGCM ensemble. In the set of 228 forcings calculated with397

individual AOGCMs in RTMIP, there is only one value with an erroneous sign. The mean398

longwave forcings from the increase in WMGHGs from 1860 to 2000 calculated with the399

AOGCM and LBL codes differ by less than 0.12 Wm−2 at the top of model, surface, and400

pseudo-tropopause at 200mb. The errors in the corresponding mean shortwave forcings are401

larger, increasing from 0.06 Wm−2 at TOM to 0.37 Wm−2 at the surface (a 43% relative402

error). The biases in shortwave forcings are caused primarily by the omission of CH4 and403

N2O from the shortwave parameterizations in all of the participating AOGCMs. While404

the AOGCMs tend to slightly underestimate the longwave forcings by CO2, the mean405

shortwave forcings are in good agreement with the LBL estimates. The mean AOGCM406

forcings from increased H2O do not differ significantly from the LBL calculations with the407

exception of the surface shortwave forcing.408

The biases in the AOGCM forcings are generally largest at the surface level. For five out409

of seven surface shortwave forcings and four out of seven surface longwave forcings, the410



probability that the mean AOGCM and LBL values agree is less than 0.01. In addition,411

the largest biases in the shortwave and longwave forcings from all seven experiments412

occur at the surface layer. The reasonable accuracy of AOGCM forcings at TOM and the413

significant biases at the surface together imply that the effects of increased WMGHGs on414

the radiative convergence of the atmosphere are not accurately simulated.415

These results suggest several directions for future development of the radiative param-416

eterizations in AOGCMs. First, tests of the accuracy of radiative parameterizations must417

address the accuracy of forcings as well as the absolute fluxes. The accuracy of shortwave418

and longwave forcings at the surface should be given special attention. Second, the short-419

wave parameterizations in all the AOGCMs should be enhanced to include the effects of420

CH4 and optionally N2O on near-infrared radiation. Third, AOGCMs should evaluate421

the radiative convergence of shortwave radiation in the atmosphere using benchmark cal-422

culations. This is a particularly clean test of the radiation physics since it is governed423

to first order by just Beer’s law, and the current models exhibit an improbably large424

spread of the convergence. Efforts to address these issues would have several benefits for425

the climate-modeling community and for groups using their models in scientific and so-426

cietal applications. Better agreement of the AOGCMs with LBL calculations would lead427

to greater confidence in simulations of past and future climate. It would also facilitate428

the analysis of forcing-response relationships from the complex and heterogeneous multi-429

model ensembles that have become a standard component of international climate-change430

assessments.431



Acknowledgments. We acknowledge the international modeling groups for provid-432

ing their data for analysis, the Program for Climate Model Diagnosis and Intercompar-433

ison (PCMDI) for collecting and archiving the model data, the JSC/CLIVAR Work-434

ing Group on Coupled Modelling (WGCM) and their Coupled Model Intercomparison435

Project (CMIP) and Climate Simulation Panel for organizing the model data analysis436

activity, and the IPCC WG1 TSU for technical support. The IPCC Data Archive at437

Lawrence Livermore National Laboratory is supported by the Office of Science in the438

U.S. Department of Energy. We would also like to thank the IPCC Technical Support439

Unit for WG1 for their assistance in contacting the AOGCM groups participating in440

the IPCC AR4. Seung-Ki Min (MIUB) and Asgeir Sorteberg (BCCR) kindly provided441

special access to their model results. Jeffrey Yin (NCAR) provided critical support by442

downloading large volumes of model output from the IPCC Data Archive.443

We would like to thank Petri Raisanen for his comments on the paper and Lawrence444

Buja (NCAR), Marco Giorgetta (MPI), Andy Lacis (GISS), Seung-Ki Min (MIUB), Erich445

Roeckner (MPI), Asgeir Sorteberg (BCCR), Bin Wang (LASG), and Joerg Wegner (MPI)446

for discussions of their AOGCMs. David Edwards (NCAR) and Gene Francis (NCAR)447

provided very useful assistance and advice regarding their GENLN LBL code. The efforts448

of John Yio (LLNL) and Matthew Macduff (PNL) to build the web-based archive for449

the RTMIP results have been instrumental in distributing and collecting the data for the450

intercomparison.451

NCAR is supported by the National Science Foundation.452



Notes

1. line 189: Need references for AOGCMs.453

2. line 199: Add ref to Fu/Ramaswamy paper to methods section once the reference is ready

3. line 201: Need SW resolution for GFDL; need SW solver used by ICSTM and the number of streams when they used

the solver

4. line 217: Insert minor N2O bands into LW forcing figure in window.

5. line 317: Add ref to Ramaswamy paper et al paper on methane to results section once the reference is ready

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Table 1. Atmospheric constituents for the radiative calculations

Calculation CO2 CH4 N2O CFC-11 CFC-12 H2Oa

(ppmv) (ppbv) (ppbv) (pptv) (pptv)

1a 287 0 0 0 0 1

2a 369 0 0 0 0 1

2b 574 0 0 0 0 1

3a 287 806 275 0 0 1

3b 369 1760 316 267 535 1

3c 369 1760 275 0 0 1

3d 369 806 316 0 0 1

4a 574 0 0 0 0 1.2

a Multiplier applied to the H2O mixing ratios in the AFGL MLS profile.



Table 2. Changes in atmospheric constituents for forcing calculations

Casea CO2 CH4 N2O CFC-11 CFC-12 H2Ob

(ppmv) (ppbv) (ppbv) (pptv) (pptv)

2a − 1a 287 → 369 – – – – –

2b − 1a 287 → 574 – – – – –

3a − 1a – 0 → 806 0 → 275 – – –

3b − 3a 287 → 369 806 → 1760 275 → 316 0 → 267 0 → 535 –

3b − 3c – – 275 → 316 0 → 267 0 → 535 –

3b − 3d – 806 → 1760 – 0 → 267 0 → 535 –

4a − 2b – – – – – 1 → 1.2

a Differences between calculations in Table 1.

b Change in multiplier applied to the H2O mixing ratios in the AFGL MLS profile.

Table 3. Sensitivity of TOM and surface forcings to features of the calculationsa

Band Feature 〈δFTOM(Band)〉〈δFSRF (Band)〉

LW Vertical resolution −0.011±0.017 −0.004±0.009

LW Temperature interpolation 0.011±0.020 0.016±0.013

SW O2 absorption 0.000±0.001 0.001±0.003

a 〈δFTOM(Band)〉 and 〈δFSRF (Band)〉 are the mean changes in TOM and surface forcing

when features of the forcing calculation are changed. The changes are averaged across the

seven calculations listed in Table 2.



Table 4. AOGCMs in the intercomparison

Originating groupa Country Model

BCCR Norway BCCR-BCM2.0

CCCma Canada CGCM3.1(T47/T63)

CCSR/NIES/FRCGC Japan MIROC3.2(medres/hires)

CNRM France CNRM-CM3

GFDL USA GFDL-CM2.0/2.1

GISS USA GISS-EH/ER

INM Russia INM-CM3.0

IPSL France IPSL-CM4

LASG/IAP China FGOALS-g1.0

MIUB/METRI/KMA Germany/Korea ECHO-G

MPIfM Germany ECHAM5/MPI-OM

MRI Japan MRI-CGCM2.3.2

NCAR USA CCSM3

NCAR USA PCM

UKMO UK UKMO-HadCM3

UKMO UK UKMO-HadGEM1

a The acronyms for the groups are given in Table 5.



Table 5. Acronyms for modeling groups

Acronym Originating group

BCCR Bjerknes Centre for Climate Research

CCCma Canadian Centre for Climate Modelling and Analysis

CCSR Center for Climate System Research (The University of Tokyo),

CNRM Centre National de Recherches Meteorologiques (Meteo-France)

FRCGC Frontier Research Center for Global Change

GFDL Geophysical Fluid Dynamics Laboratory (NOAA)

GISS Goddard Institute for Space Studies (NASA)

IAP Institute of Atmospheric Physics

ICSTM Imperial College of Science, Technology, and Medicine

INM Institute for Numerical Mathematics

IPSL Institut Pierre Simon Laplace

LaRC Langley Research Center

LASG Laboratory of Numerical Modeling for Atmospheric Sciences and

Geophysical Fluid Dynamics

MPIfM Max Planck Institute for Meteorology

MRI Meteorological Research Institute

MIUB Meteorological Institute of the University of Bonn

METRI/KMA Meteorological Research Institute / Korean Meteorological Administration

NCAR National Center for Atmospheric Research

NIES National Institute for Environmental Studies

UKMO UK Met Office / Hadley Centre for Climate Prediction and Research



Table 6. LBL radiation codes in the intercomparison

Group No. Originating groupa Country Model Reference

1 GFDL USA GFDL LBL Schwarzkopf and Fels [1985]

2 GISS USA LBL3 –

3 ICSTM UK GENLN2 Edwards [1992]; Zhong et al. [2001]

4 NASA LaRC USA MRTA Kratz and Rose [1999]

5 U. Reading UK RFM Dudhia [1997]; Stamnes et al. [1988]

a The acronyms for the groups are given in Table 5.



Table 7. Characteristics of the LBL radiation calculationsa

Group Line Line H2O CO2 SW SW SW LW LW

No. data patches Cont. Cont. Res. Solver Stream Res. Solver

(cm−1) (cm−1)

1 H2K H2001 CKD2.4 None – A/D 32 0.0001/ Gauss.

0.1

2 H2K None Tipping/ None 0.01/ A/D 1 0.000125/ Gauss.

Ma 0.1 0.0025

3 H2K Voigt CKD2.2 GENLN 0.01 – 2 0.002 5-pt. Gauss.

4 H2K None MT-CKD1.0 MT-CKD1.0 – – – 0.005 8-pt. Gauss.

5 H2K H2001 CKD2.4.1 RFM 0.005 DISORT 4 0.0025 Gauss.

a Abbreviations and references: H2K and H2001 are the Hitran 2000 database and its

updates in 2001 [Rothman et al., 2003]; Voigt is a compilation of ozone absorption cross-

sections [Voigt et al., 2001]; CKD is the Clough-Kneizys-Davies continuum [Clough et al.,

1989]; MT-CKD is the Mlawer-Tobin update to CKD [Clough et al., 2005]; Tipping/Ma

refers to their continuum [Tipping and Ma, 1995]; GENLN is the General Line-by-Line

Atmospheric Transmittance and Radiance Model [Edwards, 1992]; RFM is the Reference

Forward Model based upon GENLN [Dudhia, 1997]; A/D is the adding-doubling method

[Liou, 1992]; DISORT is the Discrete Ordinate Radiative Transfer package [Stamnes et al.,

1988]; and Gauss. is Gaussian quadrature [Liou, 1992].



Table 8. LW Forcing

Forcing Cases (Table 2)

Level Fielda 2a−1a 2b−1a 3a−1a 3b−3a 3b−3c 3b−3d 4a−2b

TOM 〈Fgcm〉 0.88 2.45 3.61 2.19 0.59 1.10 3.57

σ(Fgcm) 0.13 0.35 0.82 0.30 0.23 0.26 0.46

〈Flbl〉 1.01 2.80 3.63 2.09 0.48 0.93 3.78

σ(Flbl) 0.02 0.06 0.05 0.13 0.14 0.14 0.09

〈Fgcm〉 − 〈Flbl〉 −0.13 −0.35 −0.02 0.10 0.10 0.17 −0.20

pt(Fgcm, Flbl) 0.001 0.001 0.938 0.305 0.254 0.077 0.116

200mb 〈Fgcm〉 1.82 5.07 3.37 2.95 0.47 0.95 4.45

σ(Fgcm) 0.17 0.43 0.73 0.32 0.15 0.30 0.39

〈Flbl〉 1.95 5.48 3.47 3.00 0.41 0.89 4.57

σ(Flbl) 0.02 0.07 0.03 0.10 0.11 0.12 0.14

〈Fgcm〉 − 〈Flbl〉 −0.13 −0.42 −0.10 −0.06 0.06 0.06 −0.11

pt(Fgcm, Flbl) 0.008 0.002 0.595 0.544 0.393 0.486 0.334

Surface 〈Fgcm〉 0.38 1.12 1.80 1.21 0.43 0.74 11.95

σ(Fgcm) 0.13 0.39 0.87 0.38 0.18 0.28 0.75

〈Flbl〉 0.57 1.64 1.14 1.08 0.28 0.46 11.52

σ(Flbl) 0.02 0.04 0.05 0.12 0.11 0.11 0.40

〈Fgcm〉 − 〈Flbl〉 −0.19 −0.52 0.67 0.12 0.15 0.28 0.43

pt(Fgcm, Flbl) 0.000 0.000 0.008 0.285 0.044 0.005 0.121

a 〈F 〉 and σ(F ) are the mean and standard deviation of a distributions of forcings F .

pt(F1, F2) is the Student t-test probability that distributions F1 and F2 have the same

mean. Fgcm and Flbl are the distributions of forcings from the AOGCMs and LBL models.



Table 9. SW Forcing

Forcing Cases (Table 2)

Level Fielda 2a−1a 2b−1a 3a−1a 3b−3a 3b−3c 3b−3d 4a−2b

TOM 〈Fgcm〉 0.07 0.21 0.00 0.07 0.00 0.00 0.63

σ(Fgcm) 0.07 0.21 0.00 0.07 0.00 0.00 0.21

〈Flbl〉 0.04 0.12 0.15 0.13 0.00 0.09 0.75

σ(Flbl) 0.00 0.01 0.01 0.00 0.00 0.00 0.01

〈Fgcm〉 − 〈Flbl〉 0.03 0.08 −0.15 −0.06 −0.00 −0.09 −0.12

pt(Fgcm, Flbl) 0.138 0.141 0.000 0.004 0.235 0.000 0.039

200mb 〈Fgcm〉 −0.27 −0.79 0.00 −0.27 0.00 0.00 0.37

σ(Fgcm) 0.09 0.28 0.00 0.09 0.00 0.00 0.23

〈Flbl〉 −0.27 −0.77 −0.35 −0.41 −0.02 −0.13 0.51

σ(Flbl) 0.01 0.02 0.01 0.01 0.01 0.00 0.01

〈Fgcm〉 − 〈Flbl〉 0.00 −0.02 0.35 0.14 0.02 0.13 −0.13

pt(Fgcm, Flbl) 0.959 0.768 0.000 0.000 0.008 0.000 0.036

Surface 〈Fgcm〉 −0.49 −1.47 0.00 −0.49 0.00 0.00 −4.89

σ(Fgcm) 0.46 1.40 0.00 0.46 0.00 0.00 0.98

〈Flbl〉 −0.32 −0.96 −0.95 −0.86 −0.02 −0.53 −5.87

σ(Flbl) 0.01 0.02 0.04 0.02 0.00 0.02 0.31

〈Fgcm〉 − 〈Flbl〉 −0.18 −0.50 0.95 0.37 0.02 0.53 0.98

pt(Fgcm, Flbl) 0.144 0.170 0.000 0.006 0.002 0.000 0.004

a 〈F 〉 and σ(F ) are the mean and standard deviation of a distributions of forcings F .

pt(F1, F2) is the Student t-test probability that distributions F1 and F2 have the same

mean. Fgcm and Flbl are the distributions of forcings from the AOGCMs and LBL models.



A.

B.

Figure 1. Panel A: Net upward longwave flux at 200 hPa for year 2000 WMGHGs

(calculation 3b, table 1) divided by the surface Planck function versus wavelength. Blue,

green, red, and yellow arrows indicate the principal infrared absorption bands of CO2,

N2O, CH4, and H2O, respectively. Panel B: Longwave radiative forcing F200(LW ) at

200 mb by CO2 (case 2b−1a, table 2), N2O and CFCs (case 3b−3c), CH4 and CFCs

(case 3b−3d), and H2O (case 4a−2b).D R A F T July 7, 2005, 4:01pm D R A F T


A.

B.

Figure 2. Panel A: Net downward surface shortwave flux for year 2000 WMGHGs

(calculation 3b, table 1) divided by TOM incident solar flux versus wavelength. Blue,

green, red, and yellow arrows indicate the principal near-infrared absorption bands of

CO2, N2O, CH4, and H2O, respectively. Panel B: Shortwave radiative forcing FSRF (SW )

at the surface by CO2 (case 2b−1a, table 2), N2O (case 3b−3c), CH4 (case 3b−3d), and

H2O (case 4a−2b).D R A F T July 7, 2005, 4:01pm D R A F T


A.

B.

Figure 3. Panel A: Longwave forcings at TOM, 200 hPa, and the surface for increasing

CO2 from 287 to 369 ppmv (case 2a−1a, table 2). AOGCM forcings are shown as box-

and-whisker diagrams with percentiles given in the legend. The minimum-to-maximum

range and median are plotted for the LBL codes. Panel B: Corresponding shortwave

forcings.D R A F T July 7, 2005, 4:01pm D R A F T


A.

B.


CO2 from 287 to 574 ppmv (case 2b−1a, table 2; same symbols as Figure 3). Panel B:

Corresponding shortwave forcings.



A.

B.


CH4 from 0 to 806 ppbv and N2O from 0 to 275 ppbv (case 3a−1a, table 2; same symbols

as Figure 3). Panel B: Corresponding shortwave forcings.



A.

B.


WMGHGs from year 1860 to year 2000 concentrations (case 3b−3a, table 2; same symbols

as Figure 3). Panel B: Corresponding shortwave forcings.



A.

B.


N2O from 275 to 316 ppbv and CFCs from 0 to year 2000 concentrations (case 3b−3c,

table 2; same symbols as Figure 3). Panel B: Corresponding shortwave forcings.



A.

B.


CH4 from 806 to 1760 ppbv and CFCs from 0 to year 2000 concentrations (case 3b−3d,

table 2; same symbols as Figure 3). Panel B: Corresponding shortwave forcings.



A.

B.


H2O mixing ratios by 20% through the column (case 4a−2b, table 2; same symbols as

Figure 3). Panel B: Corresponding shortwave forcings.



A.

B.

Figure 10. Panel A: Longwave heating rate perturbations for increasing CO2 from

287 to 574 ppmv (case 2b−1a, table 2). Panel B: Corresponding shortwave heating rate

perturbations.



A.

B.

Figure 11. Panel A: Longwave heating rate perturbations for increasing CH4 from 0

to 806 ppbv and N2O from 0 to 275 ppbv (case 3a−1a, table 2). Panel B: Corresponding

shortwave heating rate perturbations.



A.

B.

Figure 12. Panel A: Longwave heating rate perturbations for increasing WMGHGs

from year 1860 to year 2000 concentrations (case 3b−3a, table 2). Panel B: Corresponding




A.

B.

Figure 13. Panel A: Longwave heating rate perturbations for increasing H2O mix-

ing ratios by 20% through the column (case 4a−2b, table 2). Panel B: Corresponding



radiative forcing by well-mixed greenhouse...

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