The expected concentrations of trifluoroacetic acid (TFA) from the degradation of HFO-1234yf (CF
We conclude that, with the current knowledge of the effects of TFA on humans and ecosystems, the projected emissions through 2040 would not be detrimental.
We carried out various tests and conclude that the model results are robust.
The major uncertainty in the knowledge of the TFA concentrations and their spatial distributions is due to uncertainties in the future projected emissions.
The use of olefinic hydrofluorocarbons (HFCs) as substitutes for HFC-134a
(1,1,1,2-tetrafluoroethane; CF
Previous studies have focused on TFA formation from emissions of either
HFC-134a at the current or previous levels (Kanakidou et al.,
1995; Kotamarthi et al., 1998) or HFO-1234yf substituted for current levels
of HFC-134a usage (Luecken et al., 2010); then, they have mostly scaled it for scenarios of HFO-1234yf emissions in the future over the continental USA and Europe (Henne et al., 2012; Papasavva et al., 2009). Some works have distinguished between uses of HFC-134a in MAC versus total usage, while others have evaluated maximum use scenarios. These studies suggest that toxic levels of TFA in water bodies are not produced over Europe, North America, or China if HFO-1234yf replaces all the current use of HFC-134a (Henne
et al., 2012; Kazil et al., 2014; Luecken et al., 2010; Wang et al., 2018).
Russell et al. (2012) conducted a model study to determine TFA concentration in terminal water bodies in the contiguous USA, with TFA deposition rates from Luecken et al. (2010). They found that, after 50 years of continuous emissions, aquatic concentrations of 1 to 15
Kazil et al. (2014) investigated, using the WRF-Chem model, the atmospheric turnover time of HFO-1234yf, the dry and wet deposition of TFA, and the TFA rainwater concentration over the contiguous USA between May and September 2006. They also examined where TFA deposited emissions of three specific regions in the USA. They concluded that the average TFA rainwater concentration was 0.89
The above-noted studies focused on the USA and Europe and, most recently, China. The emissions of the sum of HFC-134a and HFO-1234yf in the USA and Europe are expected to increase only in proportion to the population in the future since the per capita number of MAC, stationary AC, and other cooling units are unlikely to increase rapidly. India, China, and the Middle East are the regions with expected large increases in HFO-1234yf use. In these regions, the number of units and associated usage will increase rapidly as the economies grow. Perhaps Latin America and parts of Africa will also see similar increases. The above-noted studies from the USA and Europe do not allow us to draw firm conclusions about TFA's formation from realistic future emissions from Asia (i.e., China and the Indian subcontinent), where the markets are not saturated, and meteorology is very different from North America and Europe. The rate of degradation of parent compounds and precipitation will differ in the warmer tropical and subtropical regions from those seen for the USA and Europe; the seasonality will also be different. The precipitation across Asia is associated with the Asian monsoon, which is stronger in comparison to the monsoon in the southwestern USA. It is also essential to look at the Middle East emissions, since the studies of Kazil et al. (2014) and Russell et al. (2012) have shown that TFA rainwater concentrations are larger over drier areas of the USA, and there can be more accumulation in arid regions.
In 2019, the Kigali Amendment to the Montreal Protocol went into force. According to the amendment, the production and use of HFCs has to be phased down in the coming decades. This should reduce the emissions of HFCs, such as HFC-134a, but will likely increase emissions of HFO-1234yf.
A description of the models used (GEOS-Chem and WRF-Chem), HFO-1234yf emission scenarios, and the chemical scheme are given in Sect. 2. In Sect. 3, we compare the precipitation in GEOS-Chem and WRF-Chem with observations. We evaluate the GEOS-Chem model's ability to reproduce wet deposition by comparing sulfate rainwater concentrations with observations. We performed simulations using both the models for the three domains individually to calculate the TFA's dry and wet deposition and rainwater concentrations over India, China, and the Middle East. We performed 2-year runs in GEOS-Chem to check for interannual variability. We compare our simulation results with other studies for the USA, Europe, and China. The HFO-1234yf emissions from all the regions together were also simulated to assess the interregional effects. Major findings from this study are summarized in Sect. 4.
We used the GEOS-Chem (v12.0.3;
The global anthropogenic emissions were from the Emissions Database for Global Atmospheric Research (version 4.3). The global emissions are superseded by regional emission inventories for India (Speciated Multi-pOllutants Generator, SMOG, and MIX; Li et al., 2017; Pandey et al., 2014; Sadavarte and Venkataraman, 2014), China (MIX), Europe (EMEP), USA (NEI2011), Canada (CAC), and Mexico (BRAVO; Kuhns et al., 2005). We used the biomass burning from Global Fire Emissions Database (GFED) version 4 (Giglio et al., 2013). The biogenic volatile organic carbon (VOC) emissions were from the Model of Emissions of Gases and Aerosols from Nature (MEGAN) version 2.1 inventory of Guenther et al. (2012). The details on other emissions are described in David et al. (2018, 2019).
The Weather Research and Forecast with Chemistry (WRF-Chem) model (Fast
et al., 2006; Grell et al., 2005), version 4.1.3, was used to simulate
meteorology and chemistry over India, China, and the Middle East
individually. The WRF-Chem simulations were integrated for 14 months,
beginning on 1 November 2014 and ending on 31 December 2015, with the first 2 months of the simulation used to spin up the model chemistry. The three model domains, shown in Fig. 1, have a horizontal grid spacing of 30 km and 40 vertical levels reaching a model top of 50 hPa. The vertical levels stretch in size, with a fine resolution near the surface and a coarser
resolution in the upper troposphere. The model meteorology was initialized
with the Global Forecast System (GFS) archived at 0.5
The model domains for India, China, and the Middle East used in the present study. The land regions for the emissions are shown in color.
The wet removal scheme in WRF-Chem for MOZART chemistry, based on Neu and Prather (2012), was used to compute the dissolution of soluble trace gases into precipitation and their release into the gas phase upon evaporation of hydrometeors. Neu and Prather (2012) estimate trace gas removal by multiplying the effective Henry's law equilibrium aqueous concentration by the net precipitation formation (conversion of cloud water to precipitation minus the evaporation of precipitation). Dry deposition of trace gases was described with the Wesely (1989) parameterization. Diagnostic information on the wet and dry deposition of TFA was determined at every time step, and accumulated values were included in the output files.
HFO-1234yf is just now entering the market driven by regional (e.g., the European Union's MAC Directive 2006/40/EC), national (e.g., Japan and USA) F-gas regulations, and the Kigali Amendment to the Montreal Protocol. HFC-134a is currently the primary working fluid of MAC and other applications (refrigerants, insulating foams, and aerosol propellants). Therefore, we have to estimate the future emission levels from the three regions of interest. Unlike the developed countries, India, China, and the Middle East are growing rapidly, and the use of air conditioning and refrigeration (and other uses of HFCs and HFOs) is expected to increase rapidly. Therefore, one has to consider the likely economic growth and other factors in estimating emissions levels. Here, we explore a few different potential scenarios for emissions of HFO-1234yf.
TFA production from HFO-1234yf increases linearly with the rise in
HFO-1234yf emissions, i.e., there is no feedback on this process since the
primary drivers for the degradation of this chemical, the OH radical, will
not be altered by their relatively small emissions. In addition, the changes
in the abundance of OH in the troposphere in the next few decades are
unlikely to be different (e.g.,
We used the following four future HFO-1234yf emissions scenarios for the 2020 to 2040 period: (1) the estimate of the upper range scenario HFO-1234yf emissions based on Velders et al. (2015) estimate, (2) the lower range scenario of HFO-1234yf based on Velders et al. (2015) estimate, (3) the Greenhouse Gas Air Pollution Interactions and Synergies (GAINS) model (Amann et al., 2011) with maximum technically feasible reduction (MTFR) estimates of HFO-1234yf, and (4) the GAINS maximum HFO (max HFO) scenario. Given the relatively short lifetime of HFO-1234yf, the TFA production per year is dependent only on the emissions in that year. Figure 2 shows the HFO-1234yf emission projection from India, China, and the Middle East for the four scenarios between 2020 and 2040. The scenario based on S. Kumar et al. (2018) is similar to the fourth scenario we considered. Therefore, we have not specifically included this possibility.
The projected HFO-1234yf emissions scenarios between 2020 and 2040
from Velders et al. (2015).
The emission estimates of HFO-1234yf in the GAINS model depend on when
countries will comply with the Kigali Amendment, current and future
emissions based on country-level activity data, uncontrolled emission
factors, the removal efficiency of emission control measures, and the extent
to which such measures are applied (Purohit and Höglund-Isaksson, 2017). The GAINS model uses the fuel input for the transport sector that is provided by the exogenous projections (e.g., IEA, 2017). First, using the annual mileage per vehicle (veh-km) and specific fuel consumption (SFC), GAINS estimates the number of vehicles (by type and fuel). Second, using the penetration rate of a MAC, the number of vehicles with MAC is calculated. Next, using the specific refrigerant charge (different for MAC used in vehicle types), the HFO-1234yf consumption in mobile air conditioners is calculated. Note that the HFO-1234yf is assumed to be substituted for
HFC-134a, one to one, in all vehicles. For HFO-1234yf use in MAC, HFO-1234yf
emissions are estimated separately for banked emissions, i.e., leakage
from equipment in use, and for scrapping emissions, i.e., emissions
released at the end of life of the equipment. The leakage rate in the GAINS
model assumes a percentage of the charge per year. For example, if the
refrigerant charge in MAC is 0.5 kg, then the emissions from the bank will be 0.05 kg (
To minimize numerical errors (in using small emissions) and compare them
with previous studies, we used HFO-1234yf emissions of
The chemical degradation of HFO-1234yf and the production of TFA were added
to both the GEOS-Chem NO
Wet deposition is one of the primary removal processes for TFA. This deposition depends on precipitation amounts and how well our model captures the wet deposition process, making it crucial to evaluate the models used here to capture these two factors.
First, we compared the annual total precipitation amounts calculated by
GEOS-Chem and WRF-Chem with the observed daily total accumulated
precipitation from the Tropical Rainfall Monitoring Mission
(TRMM_3B42_daily product) in the three regions (Fig. S3a). The TRMM product is at a 0.25
To evaluate the accuracy of the TFA wet deposition, it is useful to compare
sulfate wet deposition amounts produced by the oxidation of SO
Scatterplot of simulated and observed sulfate rainwater concentration in
The slope, correlation coefficient (
Before presenting the results of the calculations for India, China, and the
Middle East from the present study, we note that our models agree with the
previous studies over the USA (Kazil et al., 2014; Luecken et al., 2010), China (Wang et al., 2018), and Europe (Henne et al., 2012). Figure 4 shows the comparison of annual mean (a) TFA deposition (dry and wet combined) and (b) TFA rainwater concentration over the USA, China, and Europe. We have normalized the emissions to match those of the previous studies for meaningful comparisons. (The emissions used to compare TFA from the USA, China, and Europe are 24.5, 42.7, and 19.2 Gg yr
Comparison of the present study with other studies over the USA,
China, and Europe for
Figure 5 shows the annual mean mixing ratios of HFO-1234yf over India,
China, and the Middle East as simulated by GEOS-Chem and WRF-Chem. We
present here only results with emissions in GEOS-Chem (WRF-Chem) of
41.3 (41.9), 40.6 (39.9), and 37.8 (38.1) Gg yr
Annual mean surface mixing ratios of HFO-1234yf simulated in
GEOS-Chem simulated mean total deposition rates (dry and wet deposition
combined) to be 0.874, 0.501, and 0.477 kg km
GEOS-Chem and WRF-Chem simulated annual total deposition rates of
TFA (kilograms per square kilometer per year; hereafter kg km
Figure 7 shows the percentage contribution of dry and wet deposition to
total TFA deposition between GEOS-Chem and WRF-Chem in the three domains. It
should be noted that the sum of the two (dry and wet) percent contributions
do not add up to exactly 100 % because of transport in and/or out of the
domains. For the total amount of HFO-1234yf emissions mentioned in Fig. S1 and discussed in Sect. 2.2, the total TFA deposition (dry and wet combined) in India, China, and the Middle East domains from GEOS-Chem were 23.4, 20.5, and 18.7 Gg yr
Percentage contribution of
Figure 8 shows the total TFA deposition (dry and wet combined) for the four emission scenarios (Fig. 2) calculated from GEOS-Chem and WRF-Chem. Our results show that the differences in the calculated extent of TFA formed and deposited are about a factor of 2 between the models. In all cases, the computed TFA dry and wet deposition varies linearly with the emissions. Therefore, we can calculate the amounts of TFA formed and deposited for any envisioned emission of HFO-1234yf.
Total TFA deposited (dry and wet combined) in four emission scenarios for 2020 to 2040 within India, China, and the Middle East domains calculated using GEOS-Chem (solid lines) and WRF-Chem (dashed lines). The values from the two models are reasonably close for India and the Middle East, while they differ by almost a factor of 2 for China.
Figure 9 shows the monthly variation in mean TFA rainwater concentration in
the three domains calculated from GEOS-Chem and WRF-Chem. The TFA rainwater
concentration also varies linearly with the emissions. Figure 9 shows the
following: (a) higher concentrations are to be expected when there is little
rain/precipitation (Fig. S10) to remove TFA. This point has been noted in previous studies (Kazil et al., 2014; Russell et al., 2012; Wang et al., 2018). So, if all the TFA were concentrated into a small amount of rain, the concentrations have to be larger. Such events are infrequent. They are, relative to the rainier regions, more frequent in the Middle East. The large rainwater concentration does not mean that the amount of deposited TFA is larger. (b) The rainwater concentrations varied inversely with the precipitation amount, as seen by comparing the rainwater TFA levels with the total precipitation (Fig. S10). A clear signal for the rainfall variation
was seen over India, where the monsoon season (June, July, August, and a
part of September) brings large and almost constant precipitation. This large
precipitation makes the TFA rainwater concentrations extremely small. In
other words, this is simply a dilution effect. (c) When the rainfall is
small, there are considerable variations, as one would expect. Lesser total
precipitation arises because of fewer showers and often in spatially and
temporally sporadic events. So, the concentrations can vary a great deal.
This was also evident over China during dry seasons. (d) The calculated
TFA rainwater concentrations were comparable to previous calculations for
China (scaled to emissions; Fig. 4b). The variation in rainfall amounts
and their geographical distribution as climate changes are uncertain, but
there are some estimates. For example, Terink et al. (2013) suggest that
there could be a
Box and whisker plot of TFA rainwater concentration calculated from GEOS-Chem and WRF-Chem in the three domains. In the box plot, the inside line and square are the median and mean, respectively. Box boundaries are the 25th and 75th percentiles, and whiskers indicate the 5th and 95th percentiles. The dashed horizontal line is the no observable effect concentration (NOEC) level. It is important to note that these values, including the 95th percentile values, are at least 100 times lower than the NOEC for harming aquatic bodies, even when normalized for higher projected emissions in 2040.
It is important to know the regions of high TFA rainwater concentrations.
Therefore, we plotted the spatial pattern of annual mean TFA rainwater
concentration in the three domains from both models (Fig. S11). It is noticeable that most of the regions in all
three domains did not have high TFA rainwater concentrations. There were
some grids with TFA rainwater concentrations that exceeded 50
The primary reason for carrying out these calculations was to estimate the
potential impact of HFO-1234yf usage in the three regions of the study for
the current and future emissions. The effects of interest here are TFA
formation from HFO-1234yf and its consequences to human and ecosystem
health. Figure 10 shows the mean TFA rainwater concentration for the four
emission scenarios calculated from GEOS-Chem and WRF-Chem. In all the
scenarios, the annual mean TFA rainwater concentration was well below the no
observed effect concentration (NOEC) for aquatic species, which is
Mean TFA rainwater concentration in four scenarios for 2020 to 2040 for India, China, and the Middle East domains calculated using GEOS-Chem (solid lines) and WRF-Chem (dashed lines). The NOEC is denoted above, and it is 2 orders of magnitude larger than calculated TFA concentrations for any of the scenarios.
Neale et al. (2021) have summarized the impact of TFA on human and ecosystem health. Their conclusion suggests that the NOEC on aquatic systems is
TFA quantities deposited via dry deposition to land and vegetation would be much smaller than those noted in Neale et al. (2021) to have any significant detrimental health effect. Indeed, they note that there are other sources of TFA that are much higher than those expected from HFO-1234yf degradation. Neale et al. (2021) also point out that the TFA deposited to snow in the Arctic would not significantly contribute to marine water bodies even if it all melted down, since the volume of the melt would be much smaller than those of the receiving water bodies.
Lastly, since TFA can accumulate over land and water bodies, we can estimate
the influence of accumulation on the potential future impacts. The total TFA
amount in rainfall would not change. However, the amounts in water bodies
could increase. For the 20 years modeled here, the total TFA in water bodies
would be larger than those observed for 2020 if TFA merely accumulates. It
is hard to calculate precisely where the water bodies would accumulate TFA
without a hydrological model. However, these values would still be orders of
magnitude smaller than the NOEC of
Based on these observations, and assuming that the NOEC concentration holds, it appears that the TFA from the expected emissions of HFO-1234yf in these three regions would not constitute a health threat to plants or humans (even if we assume that there is no water treatment to remove TFA in drinking water).
The model results discussed in the previous sections are for 1 year, namely 2015. To assess the influence of interannual variability in meteorology, we simulated the TFA deposition and rainwater concentration for 2016 with the GEOS-Chem model for the total HFO-1234yf emissions described in Sect. 2.2. Figure 11 shows the fraction of TFA in the three domains for 2015 and 2016 that is (a) dry deposited and (b) wet deposited, as well as (c) the annual mean TFA rainwater concentrations. The total precipitation in both years was comparable (shown in Fig. S12). The results of our 2-year simulations lead us to conclude that the interannual differences are small. Therefore, we suggest that the results of 2015 are applicable going forward to 2040.
Annual percentage of total TFA
It is important to note that most TFA is deposited outside of the domains,
even though the estimated lifetime of HFO-1234yf is about 10 d.
Therefore, TFA is dispersed significantly from the source region. Figure 12a
shows that roughly 25 %–50 % of the HFO-1234yf emitted from a given region was converted and deposited (via dry and wet deposition) as TFA within the domain (see Fig. 1 for domain boundaries). Figure 12b shows the percentage of TFA deposition (dry and wet combined) calculated from GEOS-Chem and WRF-Chem within the three domains over land. The remaining TFA was
transported outside the domain. It is difficult to quantify the exact
locations of these depositions outside the domain since the concentrations
become very small, even though in the aggregate that accounts for somewhere
between 30 % and 45 %. The fraction that was deposited within the region of emission was even smaller and ranged between 7 % and 27 %. Therefore, it can be concluded that a significant fraction ended up in the oceans. This is especially true for India and the Middle East emissions. Interestingly, a substantial amount of the TFA from the Middle East emissions is deposited in the Arabian Sea. Therefore, we conclude that even though HFO-1234yf is short lived, it is still sufficiently long lived to travel thousands of kilometers. Such an expectation is in accord with the calculated distances traveled by an air mass for even about 2 m s
Annual percentage of total TFA deposition (dry and wet combined)
calculated from GEOS-Chem and WRF-Chem within the three
Annual percentage of total TFA deposition (dry and wet combined) in India, China, and the Middle East from global and regional (individual regions) emissions.
Percentage decrease in TFA deposition (dry and wet combined) by
adding Criegee intermediate chemistry to HFO-1234yf emissions over domains in
The deposition outside of the region and domains also means that the emitting regions are not the only areas affected by their emission of HFO-1234yf. This is in spite of the relatively short turnover time of HFO-1234yf. (Note that we call this the turnover time because of the way we calculate it in the model.) Since the three countries/regions studied here are adjacent to each other and their domains overlap (Fig. 1), it is possible to estimate the impact of the neighbors' emissions on each other. We consider the emissions over the rest of the world (excluding India, China, the Middle East, the USA, and Europe) from Fortems-Cheiney et al. (2015), assuming HFC-134a is substituted with HFO-1234yf on a mole-per-mole basis (the maximum likely emissions scenario). Figure S13 shows the annual spatial distribution of HFO-1234yf emissions from all the regions as simulated in GEOS-Chem. The percentage deposition of TFA (dry and wet combined) from global and regional (individual regions) emissions of HFO-1234yf is shown in Fig. 13. The TFA deposition increased by 7 %–18 % in the three domains because of the emissions from its neighbors. Figure 13 suggests that, if the entire world switches to HFO-1234yf, the impact of TFA from the near and far neighbors would be noticeable but still be at most a factor of 2 or 3 larger. Figure S14 shows the spatial pattern of the annual total TFA via (a) dry and (b) wet deposition rates from global emissions of HFO-1234yf. The dominant TFA deposition regions were most parts of India, southeastern China, parts of Iran, and the southern Arabian Sea. We discussed, in Sect. 3.5, the potential impacts of such a global switch.
We examined the influence of the Criegee intermediates (CIs) potential reactions with TFA on its
tropospheric levels. We used the CI concentrations in the boundary layer
(0–2 km) from Chhantyal-Pun et al. (2017) in GEOS-Chem and simulated the model for 7 months (January to July) using 2015 meteorology. Figure S15
shows the mean surface CI concentration for those 7 months calculated at
2
We have investigated TFA formation from emissions of HFO-1234yf, its dry and
wet deposition, and its rainwater concentration over India, China, and the
Middle East with GEOS-Chem and WRF-Chem models. We estimated the TFA
deposition and rainwater concentrations between 2020 and 2040 for four
HFO-1234yf emission scenarios. The models were simulated for a year (2015),
with additional 2016 simulations to understand the interannual variability.
We also simulated the model using global emissions to assess interregional
effects on TFA deposition. The main results of the study are summarized
below:
Using two models at different spatial resolutions helped us assess the variation in model transport, precipitation, and cloud treatment. These variations yield slightly different calculated TFA levels from the emission of HFO-1234yf. Even though there are discernable differences, the overall conclusions are the same and point to this study's robustness. The accuracy of the GEOS-Chem model's ability to calculate wet deposition over the regions of interest was tested by comparing calculated sulfate rainwater concentration with observations. The model reproduces well the multiyear sulfate rainwater concentration ( Our calculated TFA amounts over the USA, Europe, and China were comparable to those previously reported when normalized to the same emissions. The controlling factor for the amount of TFA from HFO-1234yf is its emissions. The uncertainties in the models and chemistry are secondary to the extent of emissions. The TFA deposition was largest over eastern India, southeastern China, northern Iran, and the southern Arabian Sea. The TFA wet deposition was comparable between the two models. There are large variations in TFA rainwater concentrations associated with rainfall extent. The mean TFA rainwater concentration calculated for the four emission scenarios from GEOS-Chem and WRF-Chem was below the no observable effect concentration (NOEC), suggesting the ecological and human health impacts to be not significant. With a chemical turnover time of HFO-1234yf of 10 d, its impact is not local and extends well beyond the region of emissions. This study highlights the enhanced TFA formation by the simultaneous use of HFO-1234yf by neighboring regions. If all the Northern Hemisphere countries were to use HFO-1234yf, the impact would be higher by a factor of 2 or 3. However, these amounts are still much lower than the NOEC noted above. We estimate that continued use of HFO-1234yf in India, China, and the Middle East are unlikely to lead to detrimental human health effects, based on the current understanding of the effects of TFA in water bodies, as summarized by Neale et al. (2021). (Note that we do not assume the water is treated specifically to remove TFA before consumption.) We note that a hydrology model of the water flow and TFA concentrations in them would be beneficial to quantify the extent of TFA accumulation in pools and flow out to large water bodies.
The GEOS-Chem code is available from
The data that support the findings of this study are available at
The supplement related to this article is available online at:
ARR designed the study. LMD carried out the GEOS-Chem simulations, and LMD and MB performed the WRF-Chem simulations. LHI, PP, and GJMV provided the emissions data. LMD, MB, and ARR carried out the data analysis. SG extracted information from publications and assembled the data on sulfate deposition. LMD and ARR prepared the paper, with input from all the coauthors. All the authors contributed to the editing of the paper.
The authors declare that they have no conflict of interest.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
We are grateful to Jan Kazil (NOAA/CSL) and Rajesh Kumar (NCAR), for their help with the WRF-Chem. We are thankful to Jared Brewer and Viral Shah, for helping with TFA chemistry in GEOS-Chem. We are thankful to Kirpa Ram, for providing the sulfate rainwater concentration data over India. We are grateful to Anwar Khan, Rabi Chhantyal Pun, Dudley Shallcross, and Andrew Orr-Ewing, for providing their calculated Criegee intermediate concentrations.
This research has been supported by the Global Forum for Advanced Climate Technologies. NCAR is supported by the National Science Foundation (USA). Pallav Purohit and Lena Höglund-Isaksson received funding from IIASA and the National Member Organizations that support the institute.
This paper was edited by Maria Kanakidou and reviewed by two anonymous referees.