Radiative efficiencies and global warming potentials of agricultural fumigants

A rounded assessment of the environmental impacts of fumigants used within the agricultural sector must consider the potential climate impacts of their release into the atmosphere. Within policy settings, the 100-year Global Warming Potential (GWP100) is the most commonly used metric. While GWP100 values are available for the widely used fumigant sulfuryl fluoride, no estimates are available for 4 alternative fumigants: ethyl formate, cyanogen, hydrogen cyanide and phosphine. Existing laboratory measurements of the infrared spectra and reaction rate coefficients of these gases are used to produce new estimates of their radiative efficiencies and atmospheric lifetimes, and the first estimates of their GWP100 and other climate emission metrics. Although uncertainties are considerable, their GWP100 values are estimated to be no more than 2% of the GWP100 value of sulfuryl fluoride. These new estimates will enable informed estimates of the climate impact of the use of these fumigants, which must account for the differing usage and release rates to achieve the same fumigant efficacy.


Introduction
Chemical fumigants are used as pesticides in the agricultural industry. Methyl bromide (CH 3 Br) was traditionally widely used but it is being phased out under the terms of the Montreal Protocol on substances that deplete the ozone layer. Atmospheric concentrations of one alternate for methyl bromide, sulfuryl fluoride (SO 2 F 2 ), are rapidly increasing (Gressent et al 2021) despite concerns overs its high (more than 4500) 100-year global warming potential (GWP 100 ) (Papadimitriou et al 2008).
Several alternative fumigants have been proposed but estimates of their global warming potential are often not available. These would, together with other safety and other environmental considerations, help assess the desirability of their use.
In this paper, first estimates are provided for 4 such alternatives: ethyl formate (C 3 H 6 O 2 ), cyanogen (C 2 N 2 ), hydrogen cyanide (HCN) and phosphine (PH 3 ). Two essential inputs to GWP calculations are: (i) the radiative efficiency (RE), which is normally reported as the radiative forcing for a 1 ppbincrease in the mole fraction of the gas, and requires information on the infrared absorption of the gas; and (ii) the atmospheric lifetime, which is needed for calculating the persistence of a pulse emission of a gas (as is assumed in the GWP framework); atmospheric lifetime also influences RE because it impacts the degree to which a gas is well mixed in the atmosphere after it has been emitted. The paper uses existing measurements of infrared absorption and reaction rate coefficients to provide new calculations of lifetimes, radiative efficiencies and global warming potentials (and other climate emission metrics).

Spectroscopic data
Radiative efficiency calculations (see section 3) require laboratory-measured or simulated absorption crosssections at appropriate infrared wavelengths (wavelengths greater than 3.3 μm or wavenumbers from 0-3000 cm −1 ). The prime source used here is the HITRAN2020 spectroscopic database (Gordon et al 2022 and https://hitran.org/) which is predominantly laboratory-based. HITRAN provides spectral data in two formats. One is via catalogues of individual spectral lines, henceforth referred to as 'line-by-line', and absorption crosssections (Kochanov et al 2019), where individual vibrational transitions are not resolved. Most of the absorption cross-section data used here are measured cross-sections from the Pacific Northwest National Laboratory (PNNL) (Sharpe et al 2004;Johnson et al 2010).
In addition to the four gases of interest, SO 2 F 2 is reconsidered to ensure consistency between the methodology used here and older results (e.g., Papadimitriou et al 2008).
In most cases, data is available at a range of temperatures. Generally, the integrated absorption cross-sections are relatively insensitive to temperature (e.g., Hodnebrog et al 2013Hodnebrog et al , 2020, although there is some variation in the shape of spectral features with temperature. Given other uncertainties in calculating radiative efficiencies and GWPs, absorption cross-sections close to room temperature (296 to 298 K) are used here.
Absorption cross-sections, where available, are extracted or derived in the wavenumber range 0-3000 cm −1 covering the thermal infrared spectral region; this is consistent with most previous studies, and with listings in the Intergovernmental Panel on Climate Change Sixth Assessment Report , Smith et al 2021. Any influence of these gases on the absorption of solar radiation (mostly at wavenumbers greater than 3000 cm −1 ) would require a much more detailed study but is estimated to alter values by no more than 5%-10%; this estimate is based on the additional 7% forcing from absorption of solar radiation found by Byrom and Shine (2022) for the case of methane.
To calculate radiative efficiency (see section 4), cross-section data (which is typically measured at about 0.1 cm −1 spectral resolution) is averaged to a resolution of 1 cm −1 ; it has units of cm 2 molecule −1 . The 0-3000 cm −1 integrated absorption cross-section is given in cm −1 (molecule cm −2 ) −1 . The absorption crosssection data for all the molecules studied here are presented in the bottom 5 frames of figure 1 and are also provided in the supplementary information at 1 cm −1 spectral resolution.

2.2.
Ethyl formate HITRAN2020 provides measured absorption cross-sections of C 3 H 6 O 2 from PNNL at wavenumbers 500-6500 cm −1 at 0.112 cm −1 resolution which were previously used in RE calculations (assuming the molecule to be well-mixed) by Hodnebrog et al (2020) (see table S6 of their supporting information). Measurements are made in the presence of N 2 at a pressure of 1 standard atmosphere. The 298.15 K spectrum is used, yielding a 0-3000 cm −1 integrated absorption cross-section of 1.468 × 10 −16 cm −1 (molecule cm −2 ) −1 .

Cyanogen
HITRAN2020 does not include an absorption cross-section file for C 2 N 2 . However, a PNNL spectrum was sourced from an author of the Sharpe et al (2004) study (Timothy J Johnson, PNNL, personal communication, 21 March 2022). This provides data at wavenumbers 575-6500 cm −1 at 0.112 cm −1 resolution at 298.15 K in the presence of N 2 at a pressure of 1 standard atmosphere. These data were provided in log 10 'absorbance' units; to derive absorption cross sections, these are first after converted to log e and the resulting optical depth is then used to derive the absorption cross section using the stated path length of 2.142 × 10 −6 grams/litre-metre (or equivalently 1 ppm-metre), which yields 2.48 × 10 15 molecule cm −2 . The integrated cross-section at wavenumbers up to 3000 cm −1 is 1.684 × 10 −18 cm −1 (molecule cm −2 ) −1 .
Cyanogen also has a very strong absorption band centred near 250 cm −1 (figure 1) which is not included in the PNNL data. Although this wavenumber region contributes relatively little to the radiative efficiency (see section 4), it was deemed important enough to include. This band is included in the HITRAN2020 line-by-line data. To generate cross-section data, line intensities at 296 K (in cm −1 (molecule cm −2 ) −1 ) are summed over 1 cm −1 spectral intervals and then divided by the spectral interval to generate the required cross-sections in cm 2 molecule −1 . The integrated cross-section of this band is 6.140 × 10 −18 cm −1 (molecule cm −2 ) −1 . Combining the PNNL and HITRAN data sources gives a total integrated cross-section of 7.824 × 10 −18 cm −1 (molecule cm −2 ) −1 .

Hydrogen cyanide
HITRAN2020 does not include an absorption cross-section file for HCN. Instead, as for cyanogen, this molecule is included in the HITRAN2020 line-by-line data, and a similar procedure is used to generate cross-sections. The integrated cross-section at 296 K is 2.318 × 10 −17 cm −1 (molecule cm −2 ) −1 . Hodnebrog et al (2020) report the integrated PNNL cross-section between 550 and 3000 cm −1 to be 1.4 × 10 −17 cm −1 (molecule cm −2 ) −1 , which is about 10% higher than that derived from the HITRAN2020 line-by-line data for the same spectral interval (1.23 × 10 −17 cm −1 (molecule cm −2 ) −1 ).

Phosphine
Phosphine is also available in the HITRAN2020 line-by-line data and absorption cross-sections are generated in the same way as for cyanogen. The integrated cross-section at 296 K is 2.588 × 10 −17 cm −1 (molecule cm −2 ) −1 .

Atmospheric lifetimes
We take the SO 2 F 2 lifetime of 36 years from Gressent et al (2021) which is mainly due to ocean surface hydrolysis and reaction with OH. The tropospheric sink of HCN mainly results from a chemical reaction with OH, and its atmospheric lifetime is taken to be 0.5 years (e.g., Li et al 2009).
There do not appear to be recent assessments of the lifetimes of the other gases considered here. It is assumed that the dominant loss process is a reaction with OH, and lifetimes are estimated using the simple method (e.g., Orkin et al 2020 and references therein) which calibrates against the lifetime of methyl chloroform (MCF), where the lifetime of a molecule x, t x OH is given by Figure 1. Top plot: Radiative efficiency of a weak absorber as a function of wavenumber (from Shine and Myhre 2020). The next 5 rows show the absorption cross-sections (at 296 K) at 1 cm −1 resolution, derived from observations as described in section 2, for SO 2 F 2 , C 3 H 6 O 2 , C 2 N 2 , HCN and PH 3 . Note the different vertical axes for the cross-section data.  Calvé et al (1997) based on an assumed typical tropospheric OH concentration of 10 6 molecule cm −3 . Balaganesh et al (2014) report measurements of the reaction of ethyl formate with chlorine atoms, which yields a lifetime of 3.5 years using global-average chlorine concentrations. Reaction with OH proceeds much faster than this and so the role of reaction with chlorine is not considered further here.
For cyanogen, less recent information seems available. Atkinson (1989) reports (on page 191) values of rate constant of <3 × 10 −14 cm 3 molecule −1 s −1 which would imply a minimum lifetime of 1.22 years, close to that implied (without reference) by Purohit and Kumar (2021). Atkinson (1989) also reports measurements by Phillips (1979) in the temperature range of 300-550 K which gives a rate constant of 3.11 × 10 −13 exp (−1448/ T) cm 3 molecule −1 s −1 (where T is temperature in K) with an estimated error of 15%. Extrapolating to 272 K yields ( ) k K 272 CY = 1.5 × 10 −15 cm 3 molecule −1 s −1 which gives a lifetime t EF OH of 24 years. Given the differences in these values, and the assumption that reaction with OH is the dominant atmospheric loss process, we use both 1.2 and 24 years in GWP 100 calculations.

Radiative efficiencies
RE calculations use the Pinnock-curve methodology updated by Shine and Myhre (2020), where the RE of a weak absorber absorbing at all wavenumbers from 0 to 3000 cm −1 is calculated at 1 cm −1 resolution, in an atmosphere containing contemporary values of water vapour, carbon dioxide, ozone, nitrous oxide, methane and clouds. This spectrally-resolved RE is shown in the top frame of figure 1, which indicates the wavenumber regions where additional weak absorber could contribute most effectively to RE. It is assumed that background concentrations of the gases studied here are zero, or at least low enough that the RE is linear in concentration change. Multiplying this curve by the actual absorption cross-section of a given gas (as in the lower frames of figure 1) at the same spectral resolution, and summing over all wavenumbers, yields its RE in W m −2 ppb −1 . The updated method includes the effect of stratospheric temperature adjustment. The Hodnebrog et al (2013) simple method for accounting for gas lifetime is applied, which impacts on the horizontal and vertical distribution of an emitted gas. For gases removed through reaction with tropospheric OH, the RE is found by multiplying the constant mole-fraction RE by where a = 2.962, b = 0.9312, c = 2.994, d = 0.9302; it is applicable for 10 −4 < τ < 10 4 years. Hodnebrog et al (2013Hodnebrog et al ( , 2020 note that this correction depends on an assumed distribution of emissions; the RE and GWP are dependent on the distribution of emissions, especially for the short-lived gases considered here, and so the correction should be treated as approximate for such gases. Table 1 shows both the constant mole-fraction and lifetime-corrected RE values, which follow expectations based on both the strength of the infrared absorption and the wavenumbers at which that absorption occurs. Sulfuryl fluoride and ethyl formate have by far the highest constant mole-fraction RE, with the other gases at least an order of magnitude smaller. However, the short lifetime of ethyl formate considerably reduces its RE when the lifetime correction is applied. The constant mole-fraction RE for SO 2 F 2 agrees well with the value of 0.222 W m −2 ppb −1 from Papadimitriou et al (2008) and the constant and lifetime-corrected values of 0.215 and 0.211 W m −2 ppb −1 (Hodnebrog et al 2020 -table S6), given the different choices of underlying spectral data. The constant molefraction RE for ethyl formate (0.13 W m −2 ppb −1 ) agrees with Hodnebrog et al (2020 -table S15), as it should, given the commonality of the method and spectral data. The constant mole-fraction RE for hydrogen cyanide is slightly lower than the Hodnebrog et al (2020 -table S20) value (0.011 versus 0.012 W m −2 ppb −1 ); this difference is within the uncertainties of the underlying spectroscopic data (see section 2). The constant molefraction value for cyanogen is considerably higher than Hodnebrog et al (2020 -table S17) value (0.0034 versus 0.001 W m −2 ppb −1 ) because of our inclusion of the strong absorption band centred near 250 cm −1 (figure 1). Apart from SO 2 F 2 , we know of no previous assessments of the lifetime-corrected RE.

Global warming potentials and other emission metrics
The standard method for calculating GWP 100 is adopted here (see section 8.SM.11.1 of Myhre et al 2013, which includes the method to convert RE from per molecule to per kg), with the absolute GWP 100 for CO 2 Table 1. Atmospheric lifetimes, radiative efficiencies (for both constant mole fraction and lifetime-corrected mole fraction) and 100-year global warming potentials (GWP 100 ), relative to an equal mass emission of carbon dioxide. See section 3 for a discussion of the different values of cyanogen lifetime used here.  (2021) is regarded as somewhat coincidental, although similar methods were used in their derivation. Table 1 shows that the GWP 100 of the four alternative fumigant gases to SO 2 F 2 have much lower values. The highest of these (about 100) is for cyanogen, when its higher (24-year) lifetime is used; it is still only 2% of the value for SO 2 F 2 . For reference, the GWP 100 of the fumigant methyl bromide is 2.4 (Smith et al 2021).
Whilst GWP 100 is the most widely-used metric to produce CO 2 -equivalent emissions for non-CO 2 gases, it is not the only such metric available. As discussed in Forster et al (2021) (see especially their Box 7.3), the Intergovernmental Panel on Climate Change refrains from recommending a particular emission metric 'because the appropriateness depends on the purposes for which gases and forcing agents are being compared'. We follow Forster et al (2021) in presenting metric values for two further time horizons of the GWP, GWP 20 and GWP 500 , using their absolute GWP values for CO 2 of 2.43 × 10 −15 and 3.14 × 10 −14 W m −2 yr kg −1 respectively. They present Global Temperature change Potentials (GTP) for two time horizons, GTP 50 and GTP 100 using absolute GTP values for CO 2 of 4.28 × 10 −16 and 3.95 × 10 −16 K kg −1 respectively. For gases with lifetimes less than 20 years, they also present a combined GTP (CGTP) which is the ratio of the absolute global temperature potential for a sustained step change in emissions of short-lived species divided by the absolute GTP for CO 2 ; as explained in Forster et al (2021) this is because of the similarity in the temperature response of a change in sustained emissions of a short-lived gas to a pulse emission of (the much longer lived) CO 2 . CGTP, which has the units of years, uses the same absolute GTP values for CO 2 as given above. The Forster et al (2021) GTP and CGTP calculations use a two-term impulse-response function (IRF(t)) for temperature given by where t is the time in years, c 1 = 0.444 K (W m −2 ) −1 , c 2 = 0.314 K (W m −2 ) −1 , d 1 = 3.424 years and d 2 = 285.004 years. Table 2 presents the values of these additional metrics, again without the small carbon cycle correction. The table emphasises the considerable impact, on the apparent CO 2 -equivalence, that the choice of metric has.

Uncertainties
The many possible sources of uncertainty in RE calculations are discussed in detail by Hodnebrog et al (2013 and and by Forster et al (2021) and Smith et al (2021); this includes uncertainties of typically 5% each in the experimental absorption cross-sections, in radiative transfer calculations and in the specification of the atmospheric profile. The dominant uncertainty (around 20%) originates from assumptions about the vertical profile for gases with lifetimes of less than 5 years, which impacts 4 of the 5 gases presented here. The calculation of GWP 100 and other emission metrics is also affected by lifetime uncertainties and uncertainties in the absolute metric values of CO 2 .  Smith et al (2021) assess the uncertainty (expressed as the 5%-95% confidence interval) of the GWP 100 of the relatively short-lived halocarbon HFC-32 (lifetime 5.4 years) to be 38%. It will certainly be higher for the shorter-lived gases discussed here, and a 50% uncertainty is tentatively assigned.
As noted in section 4, the GWPs, and other emission metrics, for short-lived species will be dependent on where (and even when) they are emitted. This impacts both the lifetime-correction to the RE and the lifetime used within the GWP calculation. Hodnebrog et al (2013) show that the RE lifetime correction for short-lived gases (0.2 years) emitted mostly in tropical regions is considerably smaller than the correction when they are emitted from mid-latitudes. This would, for example, increase the lifetime-corrected RE of hydrogen cyanide of 0.0065 W m −2 ppb −1 by around 30%.

Conclusions
A rounded assessment of the impact of using new fumigants in place of established ones requires consideration of their climate impact. This is most commonly achieved using the GWP 100 ; while GWP 100 values are available for sulfuryl fluoride, no values were available for 4 other fumigants (cyanogen, hydrogen cyanide, ethyl formate and phosphine). This letter has provided the first values for these, by exploiting available measurements of their infrared spectra, and deriving lifetimes from the literature, or from literature assessments of their reaction rate coefficients with the principal atmospheric oxidant OH.
While recognising the many uncertainties in these new values, they demonstrate that on a per kg emission basis, these alternate fumigants have GWP 100 values which are, at most, only around 2% of those of sulfuryl fluoride. These new estimates will enable informed assessments of the climate implications of the use of these fumigants, which would need to consider the equivalent release rates (for the same fumigant efficacy) of each gas, and the extent to which it is, in practice, mixed with other gases.
The principal uncertainty identified here is the atmospheric lifetime of the fumigant gases, particularly cyanogen. Further work could reduce these uncertainties, examine atmospheric removal paths other than reaction with OH, and explore the impact of the sensitivity of the GWP 100 to where and when the gases are emitted.