A study of the radiative forcing and global warming potentials of hydrofluorocarbons

Journal of Quantitative Spectroscopy & Radiative Transfer 112 (2011) 220–229

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A study of the radiative forcing and global warming potentials of hydrofluorocarbons Hua Zhang a,, Jinxiu Wu b, Peng Lu c,a a b c

Laboratory for Climate Studies, National Climate Center, China Meteorological Administration, Beijing 100081, China Shanghai Meteorological Media Center, Shanghai 200030, China Chinese Academy of Meteorological Sciences, Beijing 100081, China

a r t i c l e i n f o

Keywords: HFCs Correlated k-distribution Radiative forcing Global warming potential (GWPs) Global temperature potential (GTPs)

abstract We developed a new radiation parameterization of hydrofluorocarbons (HFCs), using the correlated k-distribution method and the high-resolution transmission molecular absorption (HITRAN) 2004 database. We examined the instantaneous and stratospheric adjusted radiative efficiencies of HFCs for clear-sky and all-sky conditions. We also calculated the radiative forcing of HFCs from preindustrial times to the present and for future scenarios given by the Intergovernmental Panel on Climate Change Special Report on Emission Scenarios (SRES, in short). Global warming potential and global temperature potential were then examined and compared on the basis of the calculated radiative efficiencies. Finally, we discuss surface temperature changes due to various HFC emissions. & 2010 Elsevier Ltd. All rights reserved.

1. Introduction Hydrofluorocarbons (HFCs) have been widely used in industry since 1990 as part of efforts to replace ozonedepleting substances (ODSs) such as chlorofluorocarbons (CFCs), and emissions of HFCs have increased greatly in recent years. However, HFCs are potent greenhouse gases associated with global warming and are included in the Kyoto Protocol of the United Nations’ Framework Convention on Climate Change (http://www.unfccc.int). Two main properties of HFCs make them potent greenhouse gases: they have relatively long lifetimes, and their absorption region is located in the 8–12 mm atmospheric window. HFCs of industrial importance have lifetimes ranging from 1.4 to 270 years [1] and can remain in the atmosphere long after being emitted. Hence, HFCs have accumulated in the atmosphere, and increasing

 Corresponding author. Tel.: + 86 10 6840 0070; fax: + 86 10 6840 8508. E-mail address: [email protected] (H. Zhang).

0022-4073/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jqsrt.2010.05.012

concentrations may significantly alter the climate. The observed mixing ratios of HFCs can be explained by anthropogenic emissions, such as those associated with refrigerants and detergents [2]. Observational data show that HFC concentrations have increased rapidly since preindustrial times, with especially rapid rates of increase since the 1990 s [1–3]. The atmospheric abundances of HFC-134a and HFC-152a increased from 0.015 and 0.09 pptv in the 1990s to 35 and 3.9 pptv in 2005, respectively. Similarly, observed concentrations of HFC-32, HFC-125, and HFC-143a were 3 pptv in 2005, 3.7 pptv in 2005, and 3.3 pptv in 2003 [1]. The atmospheric window is not only in a transparent region for the major greenhouse gases (e.g., CO2, H2O, and O3) but also in the large Earth’s terrestrial emission region. Absorption of terrestrial radiation by HFCs located in the window can change the atmospheric properties of this spectral region and significantly affect the ‘‘cooling to space’’ of the earth-atmosphere system [2]. The absorptive efficiency of a single HFC molecule is many thousands of times greater than that of carbon dioxide (CO2). Therefore, even very small amounts of these gases emitted to the atmosphere

H. Zhang et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 112 (2011) 220–229

can make large contributions to the total radiative forcing of the climate system and thus produce long-lasting effects on the radiative energy balance of the earth-atmosphere and global climate change [2]. Radiative forcing has been used to denote an externally imposed perturbation in the radiative energy budget of the Earth’s climate system, while the global warming potential (GWP) is one type of simplified index based on the climate system in a relative sense. Both have been employed in the Kyoto Protocol as metrics for quantitative comparison. To investigate the effects of increasing contributions of human-made long-lived greenhouse gases on global warming, many researchers have studied the radiative forcing of HFCs and other replacements for ODSs [4–11]. Recent studies have used various databases of absorption cross-sections, including the spectroscopy and warming potentials of atmospheric greenhouse gases (SWAGG) [7–9], high-resolution transmission molecular absorption (HITRAN) [8–10], and Ford Motor Company [9–11] databases. The radiation models employed have included the broadband model [8] and narrowband model [5–7,10,11]. However, because previous studies have used different absorption cross-section datasets and radiation models, large uncertainties exist in the final results of the calculated radiative forcing. For HFC-134a, which has the highest atmospheric abundance of HFCs, calculated radiative forcing has differed by as much as 37% [4,8], whereas HFC-152a, HFC-125, HFC-143a, HFC-32, and HFC-134 results have shown differences of 47%, 49%, 49%, 72%, and 17%, respectively [7–11]. The spectral absorption cross-sections of HFCs have been updated in HITRAN 2004 [12]. This study builds on those new parameterizations with a correlated k-distribution method according to a high-accuracy band-dividing method (998-band) [13,14], with the aim of reducing the uncertainties noted above. Section 2 provides a brief description of the dataset and radiative transfer model; in Section 3, the global mean radiative efficiencies of HFCs for all-sky conditions are calculated with the 998-band method. Finally, the radiative forcings due to concentration changes of HFCs since preindustrial to present times and for the future 100 years are calculated. Section 4 discusses the GWPs and global temperature potentials (GTPs) of HFCs and analyzes surface temperature changes due to pulse and sustained HFC emissions. Conclusions are summarized in Section 5.

2. Introduction to the dataset and radiative transfer model The molecular absorption database HITRAN is generally accepted by the international scientific community and is widely used to provide inputs to radiative transfer models. The database is updated approximately every 4 years, and has developed from the previous HITRAN 1986, HITRAN 1992, HITRAN 1996, and HITRAN 2000 versions to the present HITRAN 2004 version. The infrared absorption cross-sections of HFCs from HITRAN 2004 used in this paper were measured under different

221

combinations of temperatures and pressures. First, we analyzed the dependence of the absorption cross-sections on different temperatures and pressures; the absorption cross-sections under 22 pressures and three temperatures were then obtained by linearly interpolating the crosssections at known temperatures and pressures. The following 22 pressures were obtained from the interpolation of mid-latitude atmospheric profiles provided by the US Air Force Geophysics Laboratory: 0.01, 0.0158, 0.0215, 0.0251, 0.0464, 0.1, 0.158, 0.215, 0.398, 0.464, 1.0, 2.15, 4.64, 10.0, 21.5, 46.4, 100.0, 220.0, 340.0, 460.0, 700.0, and 1013.25 hPa. The three temperatures were 160, 260, and 300 K. These values were intended to cover the range of the Earth’s atmosphere. For example, for the pressure, the absorption coefficients to be obtained at the aboveprescribed pressures were calculated by linearly interpolating the two absorption coefficients at the two known neighboring pressures under the same temperature. The effects of different temperatures and pressures on absorption cross-sections can be better considered by this method than by using integrated absorption crosssections of HFCs obtained under one given temperature and pressure condition, as has been widely used in previous studies [7,9,11]. In the future, we will be able to more accurately calculate absorption cross-sections of halocarbons under more temperatures and pressures as the HITRAN database is further improved and more temperature and pressure conditions are provided. To show how different input data affect the modeled radiative transfer results, Table 1 lists integrated absorption cross-sections of HFCs obtained using the HITRAN 2004 data and corresponding values from the Intergovernmental Panel on Climate Change [1]. Using HITRAN 2004, the reference temperature was 296 K and wavenumber regions of each of HFC were all obtained from HITRAN 2004. For the IPCC [1] dataset, HFC-32, HFC-134, HFC-134a, and HFC-152a were measured at 296 K and were from the Ford Motor Company dataset; wavenumber regions were 200–2000 cm  1 for HFC-32 and HFC-134a, 450–2000 cm  1 for HFC-134, and 700–2000 cm  1 for HFC-152a. Further, HFC-125 and HFC-143a were measured at 253 K and were obtained from SWAGG; their wavenumber regions were 0–3000 cm  1. As shown in Table 1, the integrated absorption cross-sections of HFC-32, HFC-125, and HFC-134a in HITRAN 2004 were

Table 1 Comparison between integrated absorption cross-sections of this work and IPCC (2007). Gases

HFC-32 HFC-125 HFC-134 HFC-134a HFC-143a HFC-152a

Integrated cross-section (10  17 cm2 molecule  1 cm  1) This work

Adopted in IPCC (2007)

5.24 16.12 11.37 12.38 14.0 6.89

5.77 16.73 10.57 13.07 12.01 6.87

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smaller than those of the IPCC [1], whereas the HFC-134, HFC-143a, and HFC-152a values were larger than those given by the IPCC [1]. Additionally, comparing this work and previous studies, the differences in the integrated absorption cross-sections of HFCs among past studies have generally been within 10% except for HFC-143a. For HFC-134a, the integrated absorption cross-sections in this work were 2%, 9%, and 5% less than those reported by Pinnock et al. [5], Highwood and Shine [7], and Gohar et al. [11], respectively. For HFC-143a, the values used here were 14% and 17% higher than those of Pinnock et al. [5] and Highwood and Shine [7], respectively. The 998-band method was designed as an algorithm for atmospheric remote sensing (see http://www.ccsr. u-tokyo.ac.jp/  clastr/index.html, Open-CLASTR) and has been discussed in detail by Zhang et al. [14]. By this method, bands are divided as follows. The longwave region of 10–2680 cm  1 is divided into 534 narrow bands regularly spaced with an average interval of 5 cm  1, and the k-intervals in each band are optimized with a minimum of 2 and a maximum of 16. According to Goody and Yung [15] and Peixoto and Oort [16], each narrow band contains almost all observed absorptive gases, as much as possible so as to include the weakest band in the 998-band method [14]. In this study, we first calculated the effective absorption coefficients of HFCs at all k-intervals in the 998-band division by the correlated k-distribution method [17,18] at 22 pressures and three temperatures; these values were then used as inputs in our radiation model. Radiative flux and heating rate were calculated under six model atmospheres: tropical (TRO), mid-latitude summer (MLS), mid-latitude winter (MLW), subarctic summer (SAS), subarctic winter (SAW), and US Standard (USS) atmospheres. Each atmosphere was divided into 100 layers with a vertical resolution of 1 km, the surface at 0 km, and the top of the atmosphere (TOA) at 100 km. The thermal radiation transfer was solved using a two-stream algorithm developed by

Nakajima et al. [19]. The global mean radiative efficiency was obtained by averaging the results of the six model atmospheres arithmetically. To calculate the stratospheric adjusted radiative forcings of HFCs, the 998-band method was improved in this work using an iterative method. Fig. 1 provides a schematic illustration of the iterative method, where x is convergence value, and Dt is the time-step iteration with a unit of days (here, we used 1 day). If the convergence condition is satisfied, then the new radiative equilibrium in the stratosphere is assumed to be reached after the adjustment. Perturbation of HFCs from 0 to 0.1 ppbv is used to maintain their weak limit and then to obtain their radiative forcing due to 1 ppbv perturbation [20], i.e., the radiative efficiency by linear scaling. This method is suited for calculating radiative forcing due to trace gases having concentrations significantly less than 1 ppbv [9].

3. Radiative forcing due to HFCs The World Meteorological Organization (WMO [21]) has defined instantaneous radiative forcing as the change of net radiative flux at the tropopause due to a variation in the concentration of greenhouse gases or other factors. Adjusted radiative forcing has been defined by the IPCC [22] as the change of net radiative flux at the tropopause after allowing stratospheric temperatures to readjust to radiative equilibrium, but with surface and tropospheric temperatures held fixed. According to the definition of radiative forcing, positive radiative forcing makes the troposphere and surface system warmer, leading to an increase in the surface temperature; in contrast, negative radiative forcing makes the troposphere-surface system cooler, leading to a decrease in the surface temperature. Therefore, the radiative forcing of HFCs can be used to estimate their effects on the global climate system due to their concentration changes.

Fig. 1. Schematic for stratospheric adjusted radiative forcing.

H. Zhang et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 112 (2011) 220–229

radiative efficiencies for clear sky and cloudy sky, respectively (with cloud type i). Next, we calculated the area-averaged stratospheric adjusted radiative efficiencies [7] due to HFCs for the all-sky condition, using the formula ! pffiffiffi pffiffiffi! 1 3 1 3 REmean ¼  REtro þ   REmid þ 1  REsub 2 2 2 2

In model atmospheres, HFCs are assumed to be well mixed; however, in reality, their concentrations could vary with height due to their varying lifetimes of 1.4–270 years in the atmosphere [1]. Sihra et al. [9] noted that the vertical distributions of HFCs concentrations have some effects on their radiative forcing and proposed an empirical coefficient called the lifetime correction factor for lifetimes greater than 0.25 years to include such effects: 10.241  t  0.358, where t is lifetime (in years). Although there are still some errors in the radiative forcing calculation after such corrections, the errors after these corrections should become smaller than before [9]. Thus, we conducted lifetime corrections of HFCs after calculating the stratospheric adjusted radiative efficiencies. Clouds can have a great effect on the radiative forcing due to gases. We used annually varying monthly mean cloud fields constructed from the International Satellite Cloud Climatology Project (ISCCP) D2 dataset [23], which contains cloud fractions and cloud water content for 15 cloud types according to cloud phase states, cloud top pressures, and cloud optical depths with a spatial resolution of 2.51  2.51 from July 1983 to June 2007. The cloud fractions and cloud water content for tropical, mid-latitude, and subarctic atmospheres are zonal mean values between 01N and 301N, 301N and 601N, and 601N and 901N, respectively, as listed in Table 2. The mean effective radius is assumed to be 30 mm for ice clouds, but 10 mm for liquid clouds [24]. We added these cloud parameters into our radiation transfer model to consider cloud effects. The thermal surface emissivity was set to 1.0 in our radiative transfer calculations. For the above three atmospheres, we derived the stratospheric adjusted radiative efficiency in all-sky conditions; our formula was similar to that given by Yang et al. [24] but instead of the radiative heating rate, RE ¼

15 X

Ci REi þð1CÞREclear

223

ð2Þ where REmean is the global mean radiative efficiency, and REtro, REmid, and REsub are the radiative efficiencies for tropical, mid-latitude, and subarctic atmosphere, respectively. Table 3 lists the global mean instantaneous radiative efficiencies for clear sky, the stratospheric adjusted radiative efficiencies for clear-sky and all-sky conditions, and the lifetime adjusted radiative efficiencies of HFCs for all sky, where the values for clear sky are averaged from the results of six model atmospheres and the values for all sky are area-averaged as above. The IPCC [1] values are also included in Table 3 for comparison; and the HFC lifetimes are from the IPCC [1]. As indicated in Table 3, the calculated stratospheric adjusted radiative forcing of HFCs are up to 8% larger than the corresponding instantaneous radiative forcing for the same 0.1 ppbv perturbation in clear sky. The effect of stratospheric adjustment on radiative forcing depends on whether the adjustment induces a heating or a cooling of the lower stratosphere, which can produce an increase or a decrease in thermal infrared emissions from the lower stratosphere to the troposphere, respectively [8]. Taking HFC-134a as an example, the integrated heating rates for the whole longwave region caused by 0.1 ppbv perturbations for six model atmospheres are shown in Fig. 2. The heating rates vary with different model atmospheres, but their magnitudes are almost the same and their vertical distributions are similar for the six atmospheres. The calculated heating rate profile of HFC-134a for USS was near the middle of the results for other atmospheres, and we thus chose the USS results as an example in the

ð1Þ

i¼1

P where Ci is the cloud amount for each cloud type, C= Ci is the total cloud amount, and REclear and REi are the Table 2 Cloud conditions derived from ISCCP D2 dataset. Types

Tropical atmosphere Cloud Water or ice amount (%) content (g/m3)

Cu(water) 11.43 Sc(water) 9.38 St(water) 0.75 Cu(ice) 0.00 Sc(ice) 0.00 St(ice) 0.00 Ac(water) 5.55 As(water) 4.43 Ns(water) 1.14 Ac(ice) 0.95 As(ice) 0.18 Ns(ice) 0.06 Ci(ice) 15.36 Cs(ice) 5.25 Dc(ice) 2.49

0.03 0.07 2.47 0.01 0.20 5.90 0.05 0.09 0.07 0.06 0.14 0.11 0.01 0.06 0.27

Mid-latitude atmosphere

Subarctic atmosphere

Effective radius (mm)

Cloud Water or ice amount (%) content (g/m3)

Effective radius (mm)

Cloud Water or ice amount (%) content (g/m3)

Effective radius (mm)

10 10 10 30 30 30 10 10 10 30 30 30 30 30 30

9.50 10.48 2.26 2.03 1.12 0.30 2.55 3.67 1.66 9.02 6.43 2.20 13.27 6.89 3.54

10 10 10 30 30 30 10 10 10 30 30 30 30 30 30

2.43 5.36 5.17 3.42 5.76 2.85 0.38 0.82 1.03 9.48 12.99 4.93 6.49 1.59 0.64

10 10 10 30 30 30 10 10 10 30 30 30 30 30 30

0.03 0.09 2.79 0.03 0.17 4.26 0.05 0.10 0.08 0.09 0.18 0.11 0.01 0.08 0.25

0.03 0.11 4.11 0.04 0.22 3.76 0.06 0.13 0.10 0.10 0.22 0.10 0.01 0.09 0.24

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Table 3 A comparison of instantaneous radiative efficiency, stratospheric adjusted radiative efficiency, lifetime adjusted radiative efficiency, and the radiative efficiency in IPCC (2007) for HFCs. Gases

Instantaneous radiative efficiency for clear sky/ W m  2 ppbv  1

Stratospheric adjusted radiative efficiency for clear sky/W m  2 ppbv  1

Stratospheric adjusted radiative efficiency for all-sky/ W m  2 ppbv  1

Lifetime adjusted radiative efficiency for all-sky/ W m  2 pbv  1

Radiative efficiency in IPCC (2007)/ W m  2 ppbv  1

HFC-32 HFC-125 HFC-134 HFC-134a HFC-143a HFC-152a

0.189 0.401 0.329 0.294 0.291 0.214

0.195 0.421 0.356 0.307 0.304 0.223

0.147 0.318 0.304 0.232 0.231 0.168

0.127 0.295 0.272 0.210 0.217 0.132

0.11 0.23 0.45 0.16 0.13 0.09

0.1

Pressure / hpa

1

10

100

TRO MLS MLW SAS SAW USS

1000 -6E-004 -4E-004 -2E-004

0E+000

2E-004

4E-004

6E-004

Heating rate / K Day -1 Fig. 2. Heating rates of 0.1 ppbv perturbation of HFC-134a for six model atmospheres.

following analysis. As shown in Fig. 2, the heating rates of HFC-134a for USS are positive from the surface to the lower stratosphere at a height of approximately 3 hPa, which could cause a warming effect on these levels. Therefore, the down-radiative flux from the lower stratosphere to the troposphere would be increased when the stratospheric temperatures reach a new equilibrium, resulting in an increase in the radiative forcing. Therefore, the stratospheric adjusted radiative forcing of HFC-134a due to 0.1 ppbv perturbation is 4% larger than its instantaneous forcing (see Table 3). For the same reason, the stratospheric adjusted radiative forcings of other HFCs in Table 3 are all larger than their corresponding instantaneous forcings. The area-averaged stratospheric adjusted radiative efficiencies of HFCs for the all-sky condition in Table 3 show that clouds could reduce the adjusted clear-sky radiative forcing for the same perturbation by as much as 25%. HFCs absorb in the weak line limit [20]; therefore, their optical depths are small, and the impact of clouds on

their radiative forcing is large due to smaller upward irradiance during all-sky conditions, in agreement with the results of Jain et al. [8]. Table 3 also gives the final global mean radiative efficiencies of HFCs after lifetime corrections on the basis of the stratospheric adjusted radiative efficiencies for the all-sky case. The differences in the radiative efficiencies brought about by the lifetime correction are closely related to the lifetime; that is, the shorter the lifetime, the larger the difference becomes. Thus, HFC-152a with the shortest lifetime shows the largest difference ( 21%), whereas HFC-143a with the longest lifetime has the smallest difference (approximately  5%). This result indicates that lifetime corrections should be considered in HFC radiative forcing calculations. We know that the lifetimes of most HFCs are less than 52 years, with the exception of HFC-23. Therefore, the effect of lifetime on the forcing of HFCs cannot be ignored, especially for very short-lived HFCs. The differences between our input data and IPCC [1] values are less than 10%, except

H. Zhang et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 112 (2011) 220–229

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HFCs. In Fig. 3(a), the concentration of HFCs from 2010 to 2100 increases significantly. The largest abundance and highest rate of increase are shown for HFC-134a, which is projected to reach approximately 900 pptv by 2100. Fig. 3(b) indicates that the corresponding radiative forcings of HFCs will increase rapidly in the next 90 years due to increases in their concentrations. The total radiative forcing will increase by approximately 1500%, from about 0.015 W m  2 in 2010 to about 0.23 W m  2 in 2100. The greatest contribution (  80%) to total radiative forcing will be from HFC-134a.

for HFC-143a, as shown in Table 1. Cloud effects could produce a maximum difference in radiative forcing due to HFCs of –25%. The differences in the radiative efficiencies of HFCs between the final results in this work and those of the IPCC [1] range from  40% to approximately + 67%. These differences likely arose from differences in the spectral input data for HFCs, cloud effects, lifetime corrections, etc. For comparison, Table 4 presents the radiative forcing from preindustrial times to 2005 as calculated in this work and as given by IPCC [1], and from preindustrial times to 2000 as given by IPCC/TEAP [2]. Present-day concentrations of HFCs [1] are also listed in Table 4 for reference. It should be noted that the concentration of HFC-143a in 2005 was based on observational data of about 3.3 pptv with an increasing rate of 0.5 pptv yr  1 in 2003 [2]. As shown in Table 4, the total radiative forcing due to the five kinds of HFCs considered in this work from preindustrial times to 2005 was about 0.0103 W m  2, which is 37% larger than the value of 0.0075 W m  2 given by the IPCC [1] and 232% larger than the value of 0.0031 W m  2 from preindustrial times to 2000 reported by the IPCC/TEAP [2]. The SRES has given ten scenarios for changes in HFC concentrations. We used the average value of these ten scenarios to calculate HFC radiative forcings in the future 90 years. Fig. 3 shows the calculated average value of the concentration and corresponding radiative forcings of

4. GWPs and GTPs of HFCs On the basis of the updated radiation efficiencies given above, we developed GWP and GTP models for HFCs. We then used these models to calculate the GWPs and GTPs of HFCs in the future 20, 100, and 500 years. According to GWP’s definition, its formula is given as [1] R TH R TH RFx ðtÞdt ax ½xðtÞdt GWPx ¼ R0TH ¼ R0TH ð3Þ 0 RFr ðtÞdt 0 ar ½xðtÞdt xðtÞ ¼ et=t

ð4Þ

  X t ai exp  rðtÞ ¼ a0 þ

ð5Þ

ai

i

Table 4 Radiative forcing of HFCs since 1750. Gases

Abundance IPCC (2007)/pptv

Radiative forcing in this work (1750–2005)/W m  2

Radiative forcing in IPCC (2007) (1750–2005)/W m  2

Radiative forcing in IPCC/TEAP (1750–2000)/W m  2

HFC-32 HFC-125 HFC-134a HFC-143a HFC-152a

3 3.7 35 4.3 3.9

0.0004 0.0011 0.0074 0.0009 0.0005

0.0003 0.0009 0.0055 0.0004 0.0004

0.0000 0.0003 0.0024 0.0002 0.0002

1000

0.5

HFC32 HFC125 HFC134a HFC143a HFC152a sum

0.1

Radiative forcing/ W m-2

Abundance/ pptv

HFC32 HFC125 HFC134a HFC143a HFC152a

100

10

0.01

1E-3

1 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100

Time/ year

2010

2020

2030

2040

2050

2060

2070

Time/ year

Fig. 3. Changes in HFCs abundances (a) and corresponding radiative forcings (b) from 2010 to 2100.

2080

2090

2100

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H. Zhang et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 112 (2011) 220–229

where TH is the considered time horizon (i.e., 20, 100, and 500 years in this study), and t is the time. The terms RFx and RFr are the radiative forcings due to agent x and CO2, respectively. The terms ax and ar are the radiative efficiencies due to an one-unit increase in the atmospheric concentration of gas x and CO2, respectively. x(t) and r(t) are the respective time-decaying functions of pulses of the injected gas x and CO2, where t is the lifetime of gas x in formula (4). The CO2 time-decaying function, as used in formula (5), was adopted from the IPCC [1]; in the function, a0, ai, and ai are parameters for the calculation (detailed values have been reported by the IPCC [1]). Researchers (e.g., [25,26]) have widely debated the concept of GWP since its introduction in the first IPCC Assessment Report [27]. First, GWP values cannot be easily developed for all substances that have an impact on climate; there are also serious limitations in using global mean GWPs to assess the possible climate impacts of short-lived species and in comparing those impacts to those of the long-lived greenhouse gases; further, the effects of the different lifetimes of gases cannot be distinguished [1]. Second, GWPs only express equivalence, in terms of the integrated radiative forcing over a chosen time horizon, of pulse emissions of different gases; GWPs do not give the contribution of different gases to increasing temperatures [26]. This implies that GWPs are not necessarily equivalent in terms of the temporal evolution of temperature change [25,26,28,29]. The concept of GTP was proposed by Shine et al. [30] and adopted by the IPCC [1]. Following the convention of the IPCC to quote GWP relative to CO2, GTP is defined as the ratio of the global temperature changes over the time horizon of a gas x and the reference gas CO2 for a pulse emission (1 kg at t= 0) and sustained emission (1 kg yr  1). The GTP from a pulse emission and sustained emission are expressed here as GTPP and GTPS, respectively. GTP was given by Shine et al. [30] as GTPxTH ¼

DTxTH DTrTH

ð6Þ

where TH is the considered time horizon (here, 20, 100, and 500 years), and DTx and DTr are the global mean surface temperature changes caused by gas x and CO2, respectively, which can be obtained from the following formula, as a simple relationship between the global mean surface temperature change, DT, and the global mean radiative forcing DF, as follows [30]: C

dDTðtÞ DTðtÞ ¼ DFðtÞ dt l

ð7Þ

In the above equation, t is time, C is the heat capacity of the system, and l is a climate sensitivity parameter, which indicates the change in equilibrium surface temperature per unit radiative forcing. The absolute global temperature potentials for pulse and sustained emissions are expressed as AGTPP and AGTPS, respectively, indicating the temperature changes at time t due to 1 kg emission at t =0 with units K kg  1 and constant 1 kg yr  1 increase in emissions between t = 0 and t in units of K (kg yr  1)  1, respectively. The GTPs for pulse and sustained emissions can also be expressed by the following equations, respectively [30]: GTP P ¼

AGTPXP AGTPCP

ð8Þ

GTP S ¼

AGTPXS AGTPCS

ð9Þ

The parameters required for calculating GWP and GTP are radiative efficiencies and time-decaying functions of HFCs and CO2. Here, we used our calculated radiative efficiencies of HFCs; the time-decaying function of HFCs and CO2 and the radiative efficiency of CO2 data were obtained from the IPCC [1]. The heat capacity of the system and climate sensitivity parameter required for the calculation of GTP were the same as those used by Shine et al. [30]. Table 5 lists the GWPs, GTPPs for pulse emissions, and GTPSs for sustained emissions of HFCs with time horizons of 20, 100, and 500 years, respectively; GWPs given by the IPCC [1] are also listed for comparison. The GWPs of HFCs given in Table 5 indicate that their contributions to climate change are hundreds to thousands of times larger than that of the same emission of CO2. Further, in general, for the same time horizon, longer lifetimes of HFCs correspond to greater GWPs. Note that by the GWP metric, the HFCs shown in Table 5 seem to still have effects on the climate system beyond their lifetime scopes. For example, the GWP value for HFC-143a with a lifetime of 52 years is 2850 for the 500-year horizon, indicating that the GWP metric may largely overestimate the long-term effects of HFCs on climate change. In contrast, the new metric of GTP has been significantly improved in this aspect. The GWP values of HFCs found in this study and those of the IPCC [1] over the 100-year time horizon differ in the range + 21 to 75%. Here, special attention should be given to the fact that the IPCC [1] listed the values of radiative efficiencies and GWPs of HFCs from IPCC/TEAP [2], but renewed the radiative

Table 5 Comparisons between GWPs, GTPPs, and GTPSs of HFCs in this work and the GWPs of HFCs in IPCC (2007) with time horizons of 20, 100, and 500 years, respectively. Here, the lifetime in the calculation is given for reference. Gases

Lifetime/yr

GWP 20/100/500 (yr)

GWP in IPCC (2007) 20/100/500 (yr)

GTPP 20/100/500 (yr)

GTPS 20/100/500 (yr)

HFC-32 HFC-125 HFC-134 HFC-134a HFC-143a HFC-152a

4.9 29 10 14 52 1.4

2727/817/254 8235/4713/1513 5345/1820/566 5080/1966/612 9940/7829/2850 649/191/59

2330/675/205 6350/3500/1100 3200/1100/330 3830/1430/435 5890/4470/1590 437/124/38

1670/2/0 8004/1113/0 4007/10/0 4406/55/0 10124/4288/3 273/0/0

3469/885/257 8362/5008/1532 6098/1791/573 5538/2125/619 9764/8107/2885 914/207/60

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efficiencies of CO2 at the same time. Thus, our calculations used the radiative efficiencies of CO2 with the updated background concentration listed in the IPCC [1]. We used a different time-decaying function of CO2 from that listed in the IPCC [1] (i.e., [2]) but adopted its renewed function [1] and the same time-decaying functions of HFCs as before (i.e., [2]). Therefore, the radiative efficiencies for both HFCs and CO2 and the time-decaying function of CO2 together are the main causes for the difference in GWP calculations. The background concentration of CO2 increased from 365 ppmv in 1998 to 378 ppmv in 2005, leading to a difference of 9% in the radiative efficiency of CO2. With the improvement of the time-decaying function of CO2 from IPCC/TEAP [2] to IPCC [1], the differences of GWPs over time horizons of 20, 100, and 500 years between the old and new time-decaying function of CO2 are 0%, 1%, and 1%, respectively. The differences of the radiative efficiencies of HFCs between this work and the IPCC [1] are in the range  40% to approximately +67%. Therefore, we can conclude from the above analyses that the GWP differences are mainly attributable to the computation of radiative efficiencies of HFCs. The physical meaning of GTPP is almost the same as that of GWP; the most significant difference between them is that GWP is the ratio of the integrated radiative forcing caused by 1 kg HFCs to that caused by 1 kg CO2 over a given time horizon, whereas GTPP is the ratio of the surface temperature change caused by 1 kg HFCs to that caused by 1 kg CO2 over a given time horizon, which directly reflects the surface temperature change caused by HFCs relative to CO2 over the same time horizon. In Table 5, for the 20-year time horizon, the GTPPs of HFCs are all less than their corresponding GWPs except for HFC-143a, which has a relatively long lifetime; the shorter the lifetime of a gas is, the greater is the difference between its GTPP and GWP. For the 100-year and 500-year time horizons, the GTPPs of all HFCs are much less than their corresponding GWPs, and all of the 500-year GTPPs are nearly zero. This result matches that found by Shine et al. [30] and implies that the GTP metric is a good measure for short-lived species, whereas GWP usually significantly overestimates the effect of pulse-emitted short-lived species on long-term climate change. The 100-year GTPP of HFCs in Table 5 indicates that the emitted substances will have been broken down in the atmosphere beyond their lifetimes during the integrated time horizon, which will reduce their accumulated concentration and thus decrease their effects on the surface temperature changes. Therefore, the GTPPs for the 100-year time horizon are much smaller than those for the 20-year time horizon. Taking HFC-152a, which has a short lifetime of 1.4 years, as an example, its 100-year GTPP is approximately zero, showing that the surface temperature change caused by the pulse emission of 1 kg HFC-152a at the initial time is zero, i.e., it has no effect on surface temperature over the 100-year period. For the same reason, because 500 years is much longer than the atmospheric lifetime of all HFCs, all 500-year GTPPs of HFCs are nearly zero. Therefore, GTPP not only directly reflects the surface temperature change due to pulse emission of a substance, but also expresses more clearly

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the effect of atmospheric lifetime on the surface temperature change. HFCs are widely used in industrial production, and emissions of HFCs have increased nearly constantly in recent years. GTPS considers the effect of the sustained emission of gases on the surface temperature change; thus, GTPS could provide a good metric for assessing regulatory policies for some special industries and agricultural activities that produce sustained emissions of these gases. Table 5 also gives the GTPS values calculated in this study. Shine et al. [30] experimentally verified that GTPSs calculated from formula (7) are more accurate than GTPPs from the same formula. Although GTPS and GWP are based on quite different concepts, as can be seen in Table 5, the differences between GWP and GTPS values are less than those between GWPs and GTPPs for the same gas over the same time horizon, and the difference between GTPS and GWP decreases as the time horizon increases. The difference between the 500-year GTPS and GWP of HFCs is only about 1%. Shine et al. [30] explained that GTPS and GWP have a similar mathematical expression if the time horizon is long enough, so that their results are similar to each other. Because GTPs measure surface temperature change more directly than do GWPs, the sustained emission condition is more suitable to the actual situation. Further, because it is convenient to obtain GTPS with almost the same parameters (e.g., radiative efficiency, lifetime) as GWP, GTPS is a much better metric for evaluating the effect of gas emissions on climate change compared to GWP and GTPP. We calculated the 500-year AGTPP and AGTPS of HFCs by formula (7) to estimate the surface temperature change caused by pulse and sustained emissions of HFCs during the future 500 years. Fig. 4 shows the results. Fig. 4(a) illustrates that the surface temperature change caused by pulse emission of HFCs reaches a peak value rapidly at the initial stage of emission and then recovers to zero over time. The recovery rate is related to the atmospheric lifetime of HFCs; for example, HFC-152a with the shortest lifetime recovers most rapidly, whereas HFC-143a with the longest lifetime has the slowest recovery rate. Fig. 4(b) shows that the surface temperature change caused by sustained emission of HFCs increases over the whole emission process, but increases greatly at the initial stage of emission; the large initial increasing rate is then followed by slow and smooth increase. Additionally, Fig. 4(b) indicates that the time required from the initial time of emission to a nearly zero rate of surface temperature change is also related to atmospheric lifetime. The required time increases with the increase of lifetime. This means that sustained emission of HFCs can cause a rapid increase in their concentrations in the atmosphere at the initial stage. Then, because the emitting and breakdown of HFCs occurs simultaneously beyond their lifetimes, their production and decomposition rates tend to balance each other, making their accumulated atmospheric concentration stable. Thus the induced surface temperature change will eventually arrive at a new stable level.

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6

HFC-32 HFC-125 HFC-134 HFC-134a HFC-143a HFC-152a

60

Temperature change / 10-10 K

Temperature change / 10-13 K

80

40

20

0

0

100

200

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HFC-32 HFC-125 HFC-134 HFC-134a HFC-143a HFC-152a

4

2

0

0

Time / Years

100

200

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Time / Years

Fig. 4. Temperature changes due to a pulse emission of 1 kg of HFCs (a) and sustain emission of 1 kg yr  1 of HFCs (b).

5. Conclusions The effective absorptive coefficients of HFCs were calculated with HITRAN 2004 using the correlated k-distribution method and the 998-band division method. The total radiative forcing due to HFCs (except HFC-134) calculated by the 998-band method was approximately 0.0103 W m  2 from preindustrial time to 2005 and will become 0.23 W m  2 by 2100. This result indicates that HFCs will affect climate change significantly in the future. The global mean stratospheric adjusted radiative efficiencies of HFCs for all-sky conditions were calculated based on their radiative forcing after lifetime corrections; values ranged from 0.127–0.295 W m  2 ppbv-1. The GWPs and GTPs of HFCs for 20-, 100-, and 500-year time horizons were then each calculated on the basis of the updated radiative efficiencies calculated in this study. Next, we conducted detailed comparisons among the GWPs and GTPPs of pulse emissions, and the GTPSs of sustained emissions, of HFCs. The surface temperature changes were calculated with AGTPs caused by pulse and sustained emissions of HFCs during the future 500 years. The results show that the contributions of HFCs to future climate change are hundreds to thousands of times greater than the contributions of the same emission of CO2; thus HFCs will have a long-term impact on global warming. Finally, this paper also shows that GTPS is an optimal metric for assessing the long-term effects of HFC emissions on global climate change.

Acknowledgements The authors would like to thank Prof. Qiang Fu, Department of Atmospheric Science, University of Washington for his suggestion to the stratospheric adjusted radiative forcing scheme used in this work and

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