resolutionoftheuncertaintiesintheradiativeforcingof hfc...

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Journal of Quantitative Spectroscopy &

Radiative Transfer 93 (2005) 447–460

0022-4073/$ -

doi:10.1016/j.

�CorresponReading, RG

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Resolution of the uncertainties in the radiative forcing ofHFC-134a

Piers M. de F. Forstera,b,�, J.B. Burkholderb, C. Clerbauxc,d, P.F. Coheurd,M. Duttae, L.K. Gohara, M.D. Hurleyf, G. Myhreg, R.W. Portmannb,

K.P. Shinea, T.J. Wallingtonf, D. Wuebblese

aDepartment of Meteorology, The University of Reading, P.O. Box 243, Earley Gate, Reading, RG6 6BB, UKbNOAA Aeronomy Laboratory, 325 Broadway, Boulder, CO 80305-3328, USA

cService d’Aeronomie/CNRS, Institut Pierre-Simon Laplace, Paris, FrancedService de Chimie Quantique et Photophysique, Universite Libre de Bruxelles, Bruxelles, Belgium

eUniversity of Illinois, Urbana, IL, USAfFord Motor Company, Dearborn, MI, USA

gUniversity of Oslo, Oslo, Norway

Received 30 January 2004; received in revised form 25 August 2004; accepted 25 August 2004

Abstract

HFC-134a (CF3CH2F) is the most rapidly growing hydrofluorocarbon in terms of atmosphericabundance. It is currently used in a large number of household refrigerators and air-conditioning systemsand its concentration in the atmosphere is forecast to increase substantially over the next 50–100 years.Previous estimates of its radiative forcing per unit concentration have differed significantly �25%. Thispaper uses a two-step approach to resolve this discrepancy. In the first step six independent absorptioncross section datasets are analysed. We find that, for the integrated cross section in the spectral bands thatcontribute most to the radiative forcing, the differences between the various datasets are typically smallerthan 5% and that the dependence on pressure and temperature is not significant. A ‘‘recommended’’ HFC-134a infrared absorption spectrum was obtained based on the average band intensities of the strongestbands. In the second step, the ‘‘recommended’’ HFC-134a spectrum was used in six different radiativetransfer models to calculate the HFC-134a radiative forcing efficiency. The clear-sky instantaneous

see front matter r 2004 Elsevier Ltd. All rights reserved.

jqsrt.2004.08.038

ding author. Department of Meteorology, The University of Reading, P.O. Box 243, Earley Gate,

6 6BB, UK. Tel.: +44 118 378 6020; fax: +44 118 378 8905.

ress: [email protected] (P.M. de F. Forster).

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P.M. de F. Forster et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 93 (2005) 447–460448

radiative forcing, using a single global and annual mean profile, differed by 8%, between the 6 models, andthe latitudinally-resolved adjusted cloudy sky radiative forcing estimates differed by a similar amount. Wecalculate that the radiative forcing efficiency of HFC-134a is 0:16� 0:02Wm�2 ppbv�1:r 2004 Elsevier Ltd. All rights reserved.

Keywords: HFC-134a; Radiative forcing; Uncertainties; Global warming potential

1. Introduction

As a result of the success of the implementation of the Montreal Protocol and its amendments,many replacements to chlorofluorocarbons (CFCs) have been introduced or are being considered.A popular replacement has proven to be the hydrofluorocarbons (HFCs). Unlike the CFCs andthe interim hydrochlorofluorocarbons (HCFCs), the HFCs do not destroy stratospheric ozone[1,2]; however, many of them are potent greenhouse gases and they are included in the gases forwhich emissions can be controlled under the Kyoto Protocol. HFC-134a is widely used inrefrigerators and air conditioning systems and it is currently emitted far more than any otherHFC. The potential potency of a greenhouse gas emissions is normally classified by its globalwarming potential (GWP) which takes into account the radiative forcing that would arise from apulse in emission of 1 kg of the gas in the atmosphere and the lifetime of the gas [3]. Unfortunatelythe two most recent studies that have attempted to quantify the radiative forcing of HFC-134adiffer by more than 20%: 0:200Wm�2 ppbv�1 [4] and 0:159Wm�2 ppbv�1 [5]. In light of thewidespread industrial use of HFC-134a it is important to reduce the uncertainty associated withestimates of its contribution to radiative forcing of climate change. Recently a two-modelcomparison [6] found agreement to within 7% for the HFC-134a radiative forcing; their values arealso reported here. Their reported values are 25% below that reported by Jain et al. [4] andreasons for this remain unclear.In this work we bring together 6 measurements of the absorption cross section of HFC-134a

and 5 radiative transfer modelling groups, including the three groups involved in the earlierstudies, to try to evaluate reasons for previous differences and provide an accurate estimate of theradiative forcing of HFC-134a and its uncertainty. We employ a two-step approach. First, theabsorption cross-section data are reviewed and a recommended spectrum is derived. Second, therecommended spectrum is given to the 5 modelling groups to calculate the radiative forcing.

2. Cross section analysis

The infrared absorption spectrum of HFC-134a has been the subject of numerousinvestigations [7–14]. For this paper JBB performed another measurement of the absorptioncross section using a high resolution Fourier transform spectrometer at the NOAA AeronomyLaboratory (NOAA) and we critically evaluated it alongside the other 5 studies that had availablespectral data [9–14]. The source and experimental conditions of the HFC-134a spectra consideredin this evaluation are summarized in Table 1. The cross section data were downloaded from public

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Table 1

HFC-134a infrared absorption spectrum measurements considered in this evaluation

Spectra T (K) Pressure

(diluent gas)

(Torr)

Spectral

range

(cm�1)

Spectral

resolution

(cm�1)

URL

Clerbaux [9] 253–287 0 700–1500 0.03 http://cfa-www.harvard.edu/

HITRAN/

http://ara.lmd.polytechnique.fr/

Ford [10] 296 700 (air) 200–2000 0.50 [email protected]

RAL [11] 203–296 0–750 (air) 600–1600 0.03 http://www.msf.rl.ac.uk/

NIST [12] 295 0 495–1596 0.20 http://www.nist.gov/kinetics/spectra/

NOAA 296 630 ðN2Þ 620–1325 0.004 [email protected]

Stony-Brook

[13]

190–296 20–750 830–1430 0.01 http://cfa-www.harvard.edu/

HITRAN/

All spectra were recording using Fourier transform spectroscopy under the specified conditions. See text for comparison

and evaluation.

P.M. de F. Forster et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 93 (2005) 447–460 449

websites, the spectra were compared and the integrated band intensities were calculated usingcommon integration limits.Spectra have been recorded over a range of temperature (190–296K), diluent pressure

(0–750Torr, air or N2), and resolution (0.004–0.50 cm�1). The infrared spectrum of HFC-134aconsists of several strong bands in the region 800–1400 cm�1; which are important for radiativeforcing calculations [15,16]: 843 cm�1 (CF3 sym. stretch), 972 cm�1 (CH2 rock), 1096 cm�1 (CF3

stretch), 1189 cm�1 (CF3 sym. stretch), 1296 cm�1 (CH2 wag). The absorption bands are diffusewith superimposed weak fine structure (e.g., see feature at 1203 cm�1 in Fig. 1).A summary of the band intensity results near room temperature from these studies is given in

Table 2. As shown in Table 2, the available spectra do not all cover the same spectral regions.However, all spectra do include the three most intense spectral bands in the 1000–1400 cm�1

region that account for approximately 80–85% of the total integrated band intensity. Absorptionspectra recorded in the various laboratories at resolutions between 0.03 and 0:50 cm�1

demonstrate that the diffuse band shapes and integrated intensities are independent of resolution,to within 5%. Only the weak fine structure showed any resolution dependence, however, this didnot influence the integrated band intensity. The laboratory spectra also demonstrate that theintegrated band intensities have no discernable dependence (o5%) on the presence of diluent gas(0–740Torr; air or N2). Finally, RAL [11] and Stony-Brook [13] have reported absorption spectrarecorded at reduced temperature, down to 190K. At reduced temperatures, there is a slightdecrease in the absorption bandwidths; however, there is no discernable (o5%) change in theintegrated band intensities. Therefore, the infrared absorption spectrum of HFC-134a recorded atroom temperature, 296K, and atmospheric pressure (N2 or air diluent) is appropriate for input inradiative forcing calculations in the troposphere and stratosphere regions.In the evaluation of the absolute band intensities, each spectrum was divided into eight bands.

The integration limits used in this analysis were 500–600, 620–700, 800–900, 940–1010, 1030–1130,1140–1240, 1240–1325 and 1350–1490 cm�1: The integrated band intensities accounting formissing bands are given in Table 2; it reveals that there is generally excellent agreement between

http://cfa-www.harvard.edu/HITRAN/


http://ara.lmd.polytechnique.fr/

http://[email protected]

http://www.msf.rl.ac.uk/

http://www.nist.gov/kinetics/spectra/

http://[email protected]



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Wavenumber (cm-1)

1120 1140 1160 1180 1200 1220 1240 1260 1280

Abs

orpt

ion

Cro

ss S

ectio

n (1

0-18

cm2

mol

ecul

e-1)

0.0

0.5

1.0

1.5

2.0

2.5

Ford

NIST

NOAA

RAL

Clerbaux

Stony Brook

1180 1185 1190 11951.0

1.5

2.0

2.5

Fig. 1. IR absorption cross-section spectra of HFC-134a (CF3CH2F) compared in this study. The spectra are

designated as: Clerbaux [9], Ford [10], NIST [12], RAL [11], NOAA, and Stony-Brook [13]. The most important

absorption band for the radiative forcing is also shown (band 6 of Table 2), with a blow up of the 1180–1195 cm�1

region.


the spectra. As seen from the bottom six rows of Table 2, for the three most intense bands (bands5, 6, and 7) the integrated band intensities of each of the six spectra are generally within a fewpercent of the average of all the spectra. For the less intense bands, the integrated cross sections ofthe six spectra generally agree to within approximately 10%. The larger uncertainty of the weakerbands reflects the influence of factors such as baseline uncertainty and the fact that measurementconditions were typically optimized for the strongest bands, therefore leading to poorer signal tonoise in the weaker bands. Fig. 1 shows a comparison of the most intense band at1140–1240 cm�1; the agreement between the six spectra is excellent. The total integrated crosssections given in the right hand column of Table 2 can also be compared with values of 1:33�10�16 cm2 mol�1 cm�1 (440–1535 cm�1) reported by Fisher et al. [7] and 1:32�10�16 cm2 mol�1 cm�1 (610–1490 cm�1) reported by Cappellani and Restelli [8]. Where the samebands are included, the consistency of the total integrated cross sections is remarkably good. Thefact that the integrated cross sections of the three strongest bands, determined independently bysix laboratories, [9–13] span a range whose extremes are within 7% of the average indicates thatthe infrared absorption spectrum of HFC-134a is well determined.

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Table 2

Comparison of integrated band intensities calculated using cross section spectra downloaded from the URLs given in Table 1

Spectrum

source

Band #1

500–600 cm�1

Band #2

620–700 cm�1

Band #3

800–900 cm�1

Band #4

940–1010 cm�1

Band #5

1030–1130 cm�1

Band #6

1140–1240 cm�1

Band #7

1240–1325 cm�1

Band #8

1350–1490 cm�1

Total

integrated

cross section

Ford [10] 1.40�10�18 5.06�10�18 2.48�10�18 8.40�10�18 1.46�10�17 5.29�10�17 3.99�10�17 5.20�10�18 1.30�10�16

NIST [12] 1.25�10�18 4.90�10�18 2.38�10�18 8.41�10�18 1.48�10�17 5.44�10�17 4.15�10�17 5.70�10�18 1.33�10�16

RAL[11] 5.26�10�18 2.04�10�18 7.91�10�18 1.37�10�17 5.13�10�17 3.83�10�17 4.38�10�18 1.24�10�16

NOAA 5.90�10�18 2.61�10�18 8.73�10�18 1.54�10�17 5.70�10�17 4.29�10�17 1.39�10�16

Clerbaux [9] 2.51�10�18 8.06�10�18 1.42�10�17 5.53�10�17 4.16�10�17 4.48�10�18 1.32�10�16

Stony-Brook [13] 1.57�10�17 5.59�10�17 4.19�10�17 1.34�10�16

Fisher [7] 1.32�10�16

Cappellani [8] 1.33�10�16

Average (AVG) 1.33�10�18 5.28�10�18 2.40�10�18 8.30�10�18 1.47�10�17 5.45�10�17 4.10�10�17 4.94�10�18 1.27�10�16

Std Dev 1.06�10�19 4.39�10�19 2.19�10�19 3.22�10�19 7.39�10�19 2.10�10�18 1.62�10�18 6.25�10�19

Std Dev/Avg 0.080 0.083 0.091 0.039 0.050 0.039 0.039 0.126

Ford/AVG 1.057 0.958 1.032 1.012 0.990 0.971 0.973 1.053

NIST/AVG 0.943 0.928 0.990 1.013 1.006 0.999 1.012 1.154

NOAA/AVG 1.117 1.086 1.051 1.046 1.047 1.045 0.887

RAL/AVG 0.996 0.849 0.953 0.930 0.942 0.935

Clerbaux/AVG 1.044 0.971 0.964 1.015 1.015 0.907

St-Bk/AVG 1.065 1.027 1.020

(units: cm2 mol�1 cm�1). The total integrated cross-sections from the last column include the group averages for missing bands.

P.M

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.F

orster

eta

l./

Jo

urn

al

of

Qu

an

titative

Sp

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py

&R

ad

iative

Tra

nsfer

93

(2

00

5)

44

7–

46

0451

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Wavenumber (cm-1)

400 600 800 1000 1200 1400 1600 1800 2000

Abs

orpt

ion

cros

s se

ctio

n (1

0-18 c

m2 m

olec

ule-1

)

0.0

0.5

1.0

1.5

2.0

2.5

Fig. 2. Recommended HFC-134a infrared absorption spectrum used in the radiative forcing model evaluation. See text

the evaluation and determination of the recommended spectrum.


The HFC-134a spectrum used in the radiative forcing calculations presented in this paper isshown in Fig. 2 and was obtained by normalizing the Ford [7] spectrum to the average of the sixspectra as given in Table 2 (scaling factor of 1.03). The normalization of a single spectrum, thatcovers the entire wavenumber range of interest, was chosen to minimize any small systematicerrors that might be present in comparing individual bands. The absolute band intensity of therecommended HFC-134a spectrum is estimated to be accurate to 5% at the 95% confidence level.The radiative forcing from each band depends on the overlap of a band with Planck function atatmospheric temperatures and the absorption bands of other gases. However, the most intenseHFC-134a band occurs in the atmospheric window and contributes most to the radiative forcing.A digitized copy of HFC-134a infrared spectrum can be obtained from the journal archive or theauthors.

3. Radiative forcing calculations

Five groups, employing six different radiative transfer codes, were asked to use therecommended IR cross section to calculate three radiative forcings for HFC-134a. Firstly, an

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instantaneous radiative forcing at the tropopause was calculated using the group’s own clear skyglobal and annual mean profile. While differences may still arise through inter-group variations intropopause height and background profile (see Section 4), this forcing would hopefully compare theradiative transfer models relatively directly. The second radiative forcing requested was a cloudy-sky instantaneous radiative forcing, using a single global mean profile. This was designed toinvestigate the role of clouds. The third radiative forcing asked for their ‘‘best-estimate’’ of theglobal and annual mean forcing, taking all factors into account. This gave groups considerablelatitude and differences in this ‘‘best-estimate’’ forcing would likely be representative of the totaluncertainty in the HFC-134a radiative forcing calculation. For all forcings we used a perturbationof 0.1 ppbv from a background of zero, and scaled the answers by a factor of 10 to estimate theforcing efficiency in Wm�2 ppbv�1: This preserved the weak limit approximation for the gas. Forthe instantaneous clear sky forcing HFC-134a was kept constant throughout the atmosphere andfor the ‘‘best-estimate’’ forcing its concentration varied with height as each group saw fit. Inpractice only the ILLINOIS group applied this correction, the other groups simply reduced theirbest-estimate radiative forcing by 5% to account for this effect to be consistent with the valuederived by ILLINOIS. Details of the radiative transfer schemes and methodologies of the fiveparticipating groups are outlined next. The models used the HITRAN 2000 [17] line database,except for OSLO and ILLINOIS, which used an earlier (1992) version of the HITRAN database.The models all included atmospheric absorption by H2O; CO2; CH4; N2O;CFC-11 and CFC-12.READING (RFM). The reference forward model (RFM) [18] version 4.21 was used. It is a

line-by-line radiative transfer model developed at Oxford University, and is based on theGENLN2 model [19]. It has been compared with other line-by-line models and validated againstobservations [5]. The water vapour continuum used is CKD 2.41 [20]. Only an instantaneousclear-sky forcing was computed with this model.READING (NBM). This is a 10 cm�1 narrow band model (NBM) [21]. It uses the CKD 2.41

water vapour continuum [20]. The best-estimate forcing was calculated using 3 profilesrepresenting the tropics and extra tropics and included the effects of clouds and stratosphericadjustment. For the best-estimate radiative forcing (READING in Table 4), the cloudy-adjustedradiative forcing is scaled by the ratio of the instantaneous clear-sky radiative forcing between theREADING (RFM) and READING (NBM).OSLO. The GENLN2 line-by-line model [22] has been used to calculate the optical depths and

includes the 1989 water vapour continuum of Clough et al. [23]. The DISORT model [24] is usedin the calculations of radiative fluxes [25]. Two background vertical profiles are adopted in theradiative transfer calculations, one tropical and one extra tropical; clouds and stratospherictemperature adjustment are included in the ‘‘best estimate’’ radiative forcing.NOAA. This is a line-by-line model developed at NOAA [26] that uses the MT-CKD 1.0

continuum [27] . The ‘‘best-estimate’’ radiative forcing was calculated using randomly overlappingclouds and stratospheric adjustment; it also employed a 10� zonally seasonal averaged climatologyof trace gas and clouds fields, using CTM 2-D fields for CH4 and N2O:ILLINOIS. This is a 10 cm�1 NBM used in conjunction with a chemical transport model [4].

This radiative transfer model is also integral to the integrative assesment model used in climatestudies at Illinois. The latitudinal resolution employed for the ‘‘best estimate’’ radiative forcingwas 5 degrees and included the effects of clouds, stratospheric adjustment and vertical profilechanges of HFC-134a. The vertical profile was from the final year of a 10-year run of the 2-D

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chemical transport model, with a fixed 0.1 ppbv lower boundary. In contrast to the othermethodologies the model-derived trace gas and temperature climatology was used in the radiativetransfer scheme.CNRS. The line-by-line radiative transfer model LBLRTM [28] was used. Radiance fluxes

calculations were compared with other model results and were validated using remote sensedmeasurements [29]. The water vapour (CKD 2.4) and CO2 continua [20] were included. Only aclear-sky instantaneous calculation was performed.Table 3 presents the clear and cloudy-sky instantaneous radiative forcings calculated with a

single global and annually averaged profile calculated by the 6 models; Table 4 presents the bestestimate radiative forcing. For READING the line-by-line and NBM model employed the samebackground profile. The tables also give some supplementary information to elucidate differencesin the radiative forcing calculations. We use the next section to discuss the results in the twotables.

Table 4

Using a latitudinally resolved background profile this table gives the global mean best-estimate radiative forcing for

10� 0:1ppbv of HFC-134a provided by the 4 modelling groups

Rad. F. Cloudy-sky Cloud forcing SFC Temp Trop-T Trop-P

(Wm�2) OLR (Wm�2) (Wm�2) (K) (K) (hPa)

READING 0.166 236.6 19.3 287.3 210.3 140.6

OSLO 0.156 234.3 18.9 287.5 207.5 150.0

NOAA 0.155 231.8 31.9 287.2 208.8 164.5

ILLINOIS 0.156 237.8 31.8 288.2 208.1 160.1

NCEP-reanal 236.2 31.6 287.6 207.0 167.0

Supplementary data and data from the NCEP reanalysis project is also shown. The tropopause height and temperature

are global averages from the WMO lapse rate tropopause of the different profiles.

Table 3

Using a single background profile this table gives the global mean clear and cloudy sky instantaneous radiative forcing

for 10� 0:1ppbv of HFC-134a provided by the 5 modelling groups. Supplementary data and data from the NCEP

reanalysis project is also shown. For the READING, NOAA and CNRS model and the NCEP reanalysis the

tropopause height and temperature is calculated using the WMO lapse rate tropopause definition in the single global

mean temperature profile. For ILLINOIS and OSLO the tropopause height and temperature are global mean of

tropopause heights

Model Clear-Rad. F. Cloudy-Rad. F. Rad. F. Ratio Clear OLR LW Cloud SFC Temp Trop-T Trop-P

(Wm�2) (Wm�2) Cloudy/clear (Wm�2) forcing (Wm�2) (K) (K) (hPa)

READING (RFM) 0.205 259.5 287.2 210.0 128.6

READING (NBM) 0.200 0.154 0.77 254.0 19.7 As above

OSLO 0.200 0.150 0.75 253.2 18.9 287.5 207.5 150.0

NOAA 0.197 0.143 0.72 256.5 28.6 287.2 211.6 140.6

ILLINOIS 0.211 0.158 0.75 269.4 31.7 288.2 208.1 160.1

CNRS 0.212 258.1 287.1 207.0 100.5

NCEP-reanal 267.8 31.6 287.6 206.3 137.0

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4. Radiative forcing uncertainties

The calculation of radiative forcing as defined by IPCC [3] requires an estimate of the globally andannually averaged net downward irradiance change at the tropopause after allowing for stratospherictemperatures to adjust to radiative equilibrium. As well as the radiative transfer itself a number offactors influence the radiative forcing calculation. These are discussed below, in rough order ofimportance for HFC-134a. Table 5 summarizes the effects of the various factors on the clear skyinstantaneous radiative forcing and gives an overview of the uncertainties found from this section.

4.1. Tropopause height

Freckleton et al. [30] showed that for CFC-12 changing the tropopause from the top ofconvection (identified by a change in static stability) to the cold point could increase the radiativeforcing by up to 10%. A smaller influence was identified if a single global and annually averagedmean profile was used. A tropopause defined as the top of convection has been suggested as moreappropriate [31]. While the top of convection can easily be defined in a 1-D radiative convectivemodel it is not clear how to apply it in observed profiles. For this study all the groups choose atropopause using the WMO lapse rate definition. However, some groups (READING, NOAA,CNRS) calculated their tropopause height for the global and annual mean profile from the globaland annual mean temperature profile and others (OSLO and ILLINOIS) used a global andannual average of the tropopause heights themselves (Table 3). Mostly due to this there was a50mb (�3 km) variation in their globally averaged value between the different climatologies(Table 3). NOAA found an 8.0% increase in the radiative forcing in the instantaneous globalmean case when the tropopause is changed from the WMO definition to the temperatureminimum. In the best estimate case the change was 6.3%.

4.2. Clouds

They effectively raise the emitting surface, reducing the effective column of the gas. This surfaceis also at a cooler temperature, reducing the upwelling radiation. These two mechanisms combine

Table 5

A summary of the effects of the various factors on the clear sky instantaneous radiative forcing and gives an overview of

the uncertainties found from this section

Process Effect on clear-sky instantaneous

radiative forcing (%)

Contribution to total uncertainty in the

best-estimate of radiative-forcing (%)

Clouds 25% reduction �5%

Stratospheric adjustment 10% increase �4%

Vertical profile of HFC-134a 5% reduction Not assessed

Background profile N/A �4%

Tropopause height N/A �10%

Radiative transfer N/A �3%

Absorption cross section N/A �5%

The uncertainty from the absorption cross section found in the previous section is also given.

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and, for HFC-134a, including clouds has been shown to reduce the radiative forcing by �25–30%[4,10]. In this work the reduction due to clouds is similar (23–28%, Table 3). The extra uncertaintyin the radiative forcing introduced by clouds is approximately 5% (the uncertainty fromdifferences in the clear/cloudy radiative forcing ratio in Table 3). However, in our case, the rangeof clear sky radiative forcing is no larger than the range in instantaneous cloudy-sky radiativeforcing.

4.3. Stratospheric adjustment

For most HFCs their strongest IR absorption bands occur in the window region. In thestratosphere these bands absorb more upwelling radiation from a warmer troposphere than theyemit. Therefore addition of halocarbons generally leads to a warming of the lower stratosphere,which acts to increase the radiative forcing by approximately 9% from its clear sky value. This isin contrast to carbon dioxide increases, which cool the stratosphere, and lead to a reduction of theradiative forcing [10]. For the models used here this increase is 8% for the NOAA model, 9% forthe ILLINOIS model, 12% for the READING model and 10% for the OSLO model [see also 6](these numbers are not shown in the tables). Therefore the uncertainty in this factor contributes�4% to uncertainty in the radiative forcing.

4.4. Background temperature and other trace-gas concentrations

In this work several different background profiles were used in the radiative calculations.Sensitivity studies performed with the NOAA model found that a surface temperature uncertaintyof 0.2K would give approximately a 1% error in radiative forcing. The NOAA model also foundthat water vapour and pressure differences between two climatologies could also lead to radiativeforcing differences of �2%. Pinnock et al. [10] and Jain et al. [4] have previously assessed theeffects of absorption band overlap. In our study CNRS find that including present dayconcentrations of CFC-11 and CFC-12 in the background profile reduced the HFC-134a forcingby 1%. NOAA find a 15% increase in radiative forcing when excluding N2O and CH4 from thecalculation, this differs from the 5% increase found for each gas separately in the previous studies[4,10] and may partly explain why the NOAA model has the lowest radiative forcing.

4.5. Vertical profile of HFC-134a

Due to chemical destruction in the stratosphere and troposphere, compounds with a shortlifetime can exhibit a reduction of their mixing ratio with height. This leads to a reduction inradiative forcing by as much as 30% for gases with a lifetime of less than 2 years [32]. The averagetotal lifetime of HFC-134a is quoted as 14.0 years [33]. Its decay comes primarily from reactionwith OH in the troposphere and thus its inferred stratospheric lifetime is much larger. This leadsto only a small drop off in the HFC-134a mixing ratio in the stratosphere and only a �4.5–5.5%reduction in its radiative forcing [4,30,34]. The uncertainty in this effect cannot be assessed here asall models use the ILLINOIS model as a basis for quantifying this effect. For simplicity wereduced the constant vertical-profile forcing from the other models by 5%.

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4.6. Radiation scheme

The clear sky instantaneous forcing from the two READING models which use the samebackground profile differ by �2% (Table 3). These two models employ the same water vapourcontinuum and the same line strength databases. For HFC-134a changing these additionalfeatures had little effect on the radiative forcing. For example, in the Reading NBM, a changefrom the HITRAN 1992 to HITRAN 2000 line database reduced the clear-sky instantaneousradiative forcing by less than 1%; the NOAA and CNRS model found a similarly small influencewith two quite different versions of the water vapour continuum. It should be noted that allmodels explicitly integrate over zenith angle, use of a constant diffusivity parameter haspreviously been shown to be inappropriate [10]. Line by line models are expected to be moreaccurate than NBMs, as they can provide a better representation of overlap between gases.

4.7. Global averaging

As there can be significant nonlinearities in the radiative forcing calculation, a single calculationwith a global and annual mean profile will not necessarily give the same answer as averagingradiative calculations over latitudinally resolved profiles. Variations of clouds, tropopause height,temperature and the profile of the atmospheric gases can all contribute to this. Highwood andShine [32] find that there is significant absorption by HFC-134a below 800 cm�1; where it overlapswith water vapour. Therefore, it is important to perform radiative calculations using extra-tropical profiles of water vapour. The use of profiles, representative of the tropics and extratropics, is adequate for resolving these nonlinearities [30]. Accounting for the extra-tropicalprofiles of water vapour, increases the globally averaged forcing by a few percent.

5. Discussion

5.1. Choosing a good model

The uncertainties can appear large in Table 5; however, by comparing aspects of model to theavailable observational data the uncertainties can be minimized; in our case we have used theNCEP reanalysis data [35] as an illustrative comparison. For example, making sure a model hasan outgoing longwave radiation (OLR) close to 236Wm�2 and a clear sky OLR close to269Wm�2 to give a longwave cloud forcing of 30–35Wm�2 (the observed range quoted in IPCC[3]) would be worthwhile goals. Although the LW cloud forcing is more uncertain than othervariables, the table shows that the READING (NBM) and OSLO models have a smaller cloudLW forcing than NCEP data would suggest. However, there is no evidence that the differences incloud forcing have an impact on the derived forcing, and the effect may be small, as long as themodels are constrained to get the correct OLR. Tables 3 and 4 show that most modelsunderestimate of the clear-sky values of OLR, rather than overestimate the cloudy sky OLRvalues. However, it is especially the clear sky OLR rather than the cloudy sky OLR that isuncertain. Details such as the tropopause height and surface temperature used in the backgroundclimatology can also readily be compared to the various observational datasets. For example, the

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surface temperature of 288K in the ILLINOIS model’s climatology seems too high, whencompared to the NCEP reanalysis data.In our comparison none of the four best-estimate radiative forcings stand out as being generally

worse or better than the others. For example, ILLINOIS do not use a more accurate line-by linemodel for their radiative transfer calculation, yet they are the only group to calculate a verticalprofile for HFC-134a albeit with a 2-D model. In the future using a line-by line model with CTMfields will give an optimum approach; further, rigorously constraining the model to as manyrelevant observational truths is recommended. However, in the interim a multi-model averagemay provide a more accurate representation of the true forcing than a single model result. Usingthis methodology we obtain HFC-134a radiative forcing efficiency of 0:16Wm�2 ppbv�1:

5.2. Uncertainties

Despite the uncertainties discussed in Section 4 (see Table 5), the overall range of results fromthe models is relatively small. There is an 8% range for the 6 instantaneous clear sky calculations(Table 3); a 10% range for the 4 instantaneous cloudy sky calculations (Table 3); and only a 7%range for the 4 best-estimate calculations (Table 4). This level of agreement is probably fortuitous,as the best-estimate calculation would be expected to generally have the largest error. The resultsof our work indicate that when comparing two model results one may expect: (i) up to a 7%difference from using different cross section data and (ii) up to a �10% difference from thedifferent aspects of the radiative transfer calculation. It would be unlikely if all these differencescompounded. However, differences of around 14% (0:02Wm�2 ppbv�1) would be likely (addingRMS errors). Past differences of over 20% between the ILLINOIS and READING group appearto come down to the cross-sections used, although the quoted cross-sections employed in thesepast studies were not significantly different than that used in this study; other model differencespush the wrong way to explain the difference and are now much smaller (6%). Here READINGgives a larger forcing than the ILLINOIS group, whereas previously the ILLINOIS group gave a25% larger forcing than READING.

6. Conclusions

We have succeeded in both understanding and reducing many of the uncertainties involved inthe calculation of the radiative forcing for HFC-134a. We explored uncertainties in cross sectiondata and radiative transfer modelling. Our four-model average gives a radiative forcing efficiencyof 0:16� 0:02Wm�2 ppbv�1: This agrees well with the value of 0:15Wm�2 ppbv�1 quoted in thelatest IPCC report [3]. Most of our uncertainty arises from the radiative forcing calculation,rather than the absorption cross section. Our methodology illustrates the usefulness of comparingsupplementary material from models to help gauge an individual model’s performance and judgethe quality of its radiative forcing estimate. Multi-model comparisons are useful for under-standing uncertainties; in the absence of particular Models with clearly defined advantages overthe others, and, in a future where economic and political decisions may be made employingradiative efficiencies, it could be beneficial to obtain a multi-model consensus.

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Acknowledgements

CC and PFC are grateful to M. Iacono and T. Clough for providing the LBLRTM radiativetransfer code. PFC is Postdoctoral Researcher with the Fonds National de la RechercheScientifique (FNRS, Belgium). MDH and TJW thank Camilla Bacher and Ole John Nielsen(Copenhagen University) for help obtaining IR data at low frequencies (200–600 cm�1). TheUniversity of Reading acknowledge support from NERC Grant NER/L/S/2001/0066, theCRYOSTAT EC Project (EV2K-CT-2001-00116) and a NERC Advanced Research Fellowship(PMF). This work was a Stratospheric Processes and their Role in Climate (SPARC) initiative.

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