1 Introduction

Methane (CH4) is a greenhouse gas (GHG) that directly drives warming, which leads to physical and economic impacts on many sectors, including agriculture, energy, human health, and biodiversity, associated with climate change (Harmsen et al. 2019; Smith et al. 2020). Methane also causes additional damages through driving the process of formation of tropospheric ozone (O3), including impacts to human health (Malley et al. 2017; Turner et al. 2016), climate (IPCC 2013), biodiversity (Unger et al. 2020), and crops and vegetation (Ainsworth 2017; Emberson 2020; Emberson et al. 2018). The 12-year lifetime of CH4 makes it a relatively short-lived GHG. However, it is longer-lived than most other O3 precursors (nitrogen oxides, non-methane volatile organic compounds, and carbon monoxide), whose atmospheric lifetimes are measured in weeks to months (IPCC 2013). In general, reductions in nitrogen oxides and CH4 are the most effective actions to reduce O3 concentrations (West et al. 2007). In addition, due to the long equilibration time, O3 variations driven by changes in CH4 emissions are unconstrained by the location of those emissions (Aakre et al. 2018; Van Dingenen et al. 2018a; Wild et al. 2004). Therefore, CH4 emission changes in a certain region (e.g. USA) would (with a response time of 12 years) affect O3 concentration levels all over the world, which has direct implications for this study. Prior literature has used this relatively uniform response to quantify the O3 benefits of CH4 emissions reduction anywhere in the world, as in the Social Cost of Methane (SC-CH4) (Colbert et al. 2020; Marten et al. 2015; Marten and Newbold 2012; Shindell et al. 2017; Waldhoff et al. 2011) and the marginal health benefits of CH4 mitigation (Sarofim et al. 2017). These marginal benefits can be used to conduct cost–benefit analyses, comparing the marginal climate and health benefits of mitigating a tonne of CH4 to the cost of that mitigation activity. U.S. Government rulemakings on Oil and Gas (EPA 2020, 2016a) and Landfills (EPA 2016b) have included CH4 from the SC-CH4 and acknowledged the additional value to reduced mortality. The work presented here adds to this literature by estimating the marginal benefit of CH4 mitigation on agricultural systems.

While climate-related factors such as temperature, precipitation, growing season calendars, or carbon dioxide (CO2) concentrations have more ambiguous impacts on agricultural yields, depending on the crop and geographic location (Asseng et al. 2015; Calvin and Fisher-Vanden 2017; Snyder et al. 2020), O3-related damages are systematically negative for crop growth and productivity (Ainsworth et al. 2012; Fiscus et al. 2005; Fuhrer and Booker 2003; Monks et al. 2015; Shindell et al. 2019). O3 has significantly increased since pre-industrial levels (Lamarque et al. 2005; Tarasick et al. 2019), though the location of these increases varies across the globe. In the last 30 years, the shift on precursor emissions from developed economies to developing regions has reduced O3 levels in North America and Europe (Cooper et al. 2014; Fleming et al. 2018; Logan et al. 2012), while those levels have substantially increased in East Asia (Chang et al. 2017; Xu et al. 2020; Zhang et al. 2020). These increases result in significant economic losses on agriculture and food security related threats, which will be increasingly important in the coming decades given the challenge of sustainably feeding an increasing global population (Searchinger et al. 2014).

Prior work has quantified yield losses and/or economic damages associated to O3 concentration for current and future periods using different methodologies. Exposure-response-function models (ERFs), which calculate the productivity losses for different crops given the O3 concentration level, have been an extensively applied method to estimate both relative yield losses and the subsequent economic damages at global and regional levels for current and/or future periods (Avnery et al. 2011a, 2011b; Chuwah et al. 2015; Feng et al. 2019; McGrath et al. 2015; Sampedro et al. 2020; Sharma et al. 2019; Tang et al. 2013; Van Dingenen et al. 2009; Wang and Mauzerall 2004). While the ERF models are a well-accepted methodology to estimate yield impacts, recent studies conclude the amount of O3 absorbed by the plant is a more accurate indicator than the exposure in order to estimate relative yield losses (Ronan et al. 2020). Several studies make use of these dose–response or flux-based models, which consider the O3 uptake by plants, to estimate yield productivity losses (Grünhage et al. 2012; Mills et al. 2011, 2018a, 2018b; Peng et al. 2019; Pleijel et al. 2019). However, these flux-based models require ancillary data available at high time and spatial resolution, limiting their application in global studies. Even though the methods, parameters and assumptions are substantially different across the type of models and studies, they all find that high O3 levels generate significant relative yield and economic losses.

Recent literature has analyzed the O3-related yield losses attributable to CH4 and other precursor emissions, and conclude that, while the effects of decreasing NOx or CO are more ambiguous and depend on the geographical location, CH4 reductions would significantly improve crop productivity in all regions (Avnery et al. 2013; Shindell et al. 2019; Shindell 2016). However, there are no studies that estimate the marginal impact of a tonne of CH4 on agricultural systems. Our study fills that gap in literature and estimates the O3-related damages to crop revenues associated with CH4 emissions at a global scale. Applying an innovative methodology based on the use of both an atmospheric chemistry and an integrated assessment model, we analyze the marginal damages attributable to different CH4 pulses in USA under multiple assumptions (e.g. year of the pulse) in order to provide a robust range of marginal damages at both global and regional levels. Our results suggest that the global marginal damages to crop production range from ~ 423 to 556 $2010/t-CH4 (hereinafter $/t-CH4). These marginal damages complement a previous study (Sarofim et al. 2017), where the authors estimate O3-related marginal damages to human health associated to CH4 emissions.

2 Study design

In this work we estimate O3-driven marginal damages to crop revenues for a central scenario, by implementing a shock in CH4 emissions in USA. Because the damages will be affected by a range of assumptions, such as the underlying socioeconomic development pathway, the size and the year of the CH4 pulse, or the discount rate used, we estimate the impact under multiple sensitivities in order to test the robustness of our results to these variables (Sect. 2.1). The methodology (Sect. 2.2) is based on an integrated modelling framework that connects two different models, namely the Global Change Analysis Model (GCAM) and TM5-Fast Scenario Screening Tool (TM5-FASST). The details of these models can be found in Appendix I. By combining and processing the outputs of these models, we calculate the O3-driven marginal damages to crop revenues for each region and crop.

2.1 Scenarios

The marginal damages of a tonne of CH4 on crop yields are directly affected by several variables. We test the sensitivity of our results to the size of the pulse (PulseSize), the year in which the pulse is implemented (PulseYear), the future socioeconomic and technological change pathway (Storyline), and the discount rate (DR) that is used for discounting future damages to current values.

For the Storyline, we make use of the Shared Socioeconomic Pathways (SSPs) (O’Neill et al. 2014), which present five different narratives with different demographic and economic assumptions (Dellink et al. 2017; Samir and Lutz 2017); energy-system assumptions on electricity technologies, fuel preferences, or building energy demands; future agricultural yield improvement rates; and food demands. In terms of emissions, each SSP includes sector, fuel, region, and period specific emission factors for air pollutans (non-GHG), as described in Rao et al., (2017). We estimate the damages for three different PulseSizes: 5%, 10%, and 15% of the GCAM projected USA CH4 emissions in 2020 of ~ 28 Tg, or 1.42 2.84 and 4.25 Tg, respectively. PulseYear also has a direct impact on the marginal damages, since each period has different crop production and emissions, so we have considered 4 different time periods where the pulse is implemented, namely 2020, 2030, 2040, and 2050. We also explore the sensitivity of the results to different rates for discounting the future damages, an uncertain parameter that has been extensively discussed in existing literature (Nordhaus 1994; Stern 2006). We use a range of moderate static values (2%, 3%, and 5%) and three additional dynamic discounting rates, based on the GDP per capita growth of each region, so that the discounting changes over time and by region. For calculating these dynamic rates, we apply the Ramsey formula (Ramsey 1928):

$$ Dr_{r,t} = \rho + \eta *g_{r,t} $$
(1)

where Dr is the discount rate in region r and period t, ρ is the pure time preference, η is the coefficient of relative risk aversion, and g is the growth rate. We test three different time preference parameters (ρ = 0.1%, ρ = 1%, and ρ = 3%) with the relative risk aversion equal for all the regions and periods (η = 1).

Our main results are calculated for a central scenario generated by combining the SSP2 storyline (“Middle of the Road”), a pulse of 2.84 Tg (10%) in 2020 and using a rate of 3% for discounting future damages (see Discussion). All the other PulseSize-Storyline-PulseYear-DR combinations have also been calculated and shown for sensitivity analysis. This is summarized in Table 1. We note that the pulse is based on a share of USA CH4 emissions in 2020. A given pulse size is used consistently over each time period to isolate the effects of the alternative sensitivity dimensions, rather than linking the pulse to the corresponding SSP narrative, which would confound the impact of the pulse size and underlying emissions.

Table 1 Summary of the scenarios and assumptions

2.2 Methodology

The methodology consists of a sequential connection of two different models (Fig. 1), namely the Global Change Analysis Model (GCAM v5.2), and the TM5-Fast Scenario Screening Tool (TM5-FASST) (Appendix I). We use GCAM to estimate future GHG and air pollutant emissions and agricultural production and prices by region, period, and crop. We note that GCAM projects the agricultural production for all FAO crop commodities classified into twelve aggregate crop categories, as described in online documentation.Footnote 1 The mapping between GCAM crop categories and the FAO commodities is included in Appendix II.

Fig. 1
figure 1

Overview of the methodology

We then translate those GHG and air pollutant emissions to TM5-FASST in order to obtain the O3 concentration levels. Given that the half-life of CH4 is 12 years (IPCC 2013), the O3 formation in a certain year would not only be affected by those year emissions, but also by the CH4 emissions from the previous 30 years. Therefore, a CH4 shock in a certain period has direct implications in O3 formation in subsequent years. In order to capture that dynamic, which is relevant for this study, we transform the O3 concentration values obtained from TM5-FASST (“steady-state” concentration) so they follow the actual timeline of formation after a pulse on CH4 emission (“transient” approach). This transformation, which improves the calculations with a more realistic emissions-concentration relation (CH4–O3), is explained in detail in Appendix I.

Using these adapted O3 concentration values, we estimate relative yield losses (hereinafter RYLs) using the Weibull exposure–response functions from Wang and Mauzerall (2004). These RYLs are estimated for four different crops (maize, rice, soybeans and wheat) and for the 56 countries/regions in TM5-FASST. Therefore, these damages need to be re-scaled to GCAM regions and expanded to the rest of the crop categories. The RYLs from the 56 TM5-FASST regions are downscaled to country level and re-aggregated to GCAM regions (see Appendix III) based on 2010 data on harvested area from Geophysical Fluid Dynamics Laboratory.Footnote 2 RYLs calculated for four crops have been extended to the rest of the GCAM categories based on their carbon fixation pathway. Significant differences between C3 and C4 plant species in terms of stomatal conductance or transpiration rates will directly affect their sensitivity to damages attributable to O3 exposure (Knapp 1993; Leisner and Ainsworth 2012). Therefore, maize RYL coefficients are applied to C4 crop types, while a weighted average of wheat and rice (or wheat, rice and soybeans, in some casesFootnote 3) RYL coefficients are applied to C3 categorized commodities. This procedure ensures that the damages calculated in this study cover all the agricultural production.

We have also estimated RYLs for two symmetric scenarios within each SSP narrative for all different pulses, one that includes the CH4 pulse (PulseScen), and other that does not incorporate it (noPulseScen). So, by difference we are able to estimate the additional RYLs directly attributable to a determined pulse for each scenario (n), period (t), region (i) and crop (j) with the following equation:

$$ Pulse.RYL_{n,t,i,j} = \Delta RYL_{n,t,i,j} = RYL_{n,t,i,j} \left( {PulseScen} \right) - RYL_{n,t,i,j} \left( {noPulseScen} \right) $$
(2)

Once having estimated the crop damage coefficients directly driven by the CH4 shock, economic damages to crop revenues for a determined scenario (n), period (t), region (i) and crop (j) are calculated as:

$$ Damage_{n,t,i,j} = Prod_{n,t,i,j} *Price_{n,t,i,j} * Pulse.RYL_{n,t,i,j} $$
(3)

These economic damages are linearly interpolated in order to have year-by-year results. Then, they are aggregated to cumulative values using different discount rates. Note that for cumulative results we consider 50 years after the Pulseyear, which is the maximum allowed by GCAM.Footnote 4 Cumulative damages using a determined discount rate (r), can be defined as:

$$ Damage_{n,i,j} = \mathop \sum \limits_{t = PulseYear}^{t + 50} \frac{{Damage_{n,t,i,j} }}{{r^{{\left( {t - PulseYear} \right)}} }} $$
(4)

The final step is to transform cumulative damages into marginal damages, by dividing the damage by the CH4 pulse. Therefore, the total marginal damages for all crops (j), in region (i), under the socioeconomic narrative (n) would be defined as:

$$ MD_{n,i} = \mathop \sum \limits_{j} \frac{{\mathop \sum \nolimits_{t = PulseYear}^{t + 50} \frac{{Damage_{n,t,i,j} }}{{r^{{\left( {t - PulseYear} \right)}} }}}}{Pulse} $$
(5)

3 Results

We focus our discussion of the results on the central scenario, which is defined by a 10% pulse (2.84 Tg) of 2020 CH4 emissions in USA in 2020 (PulseYear), under the SSP2 socioeconomic storyline (“Middle of the Road”), with a 3% discount rate. The following figures show the projected CH4 emissions and the effects of the CH4 shock in the central scenario in 2020 in terms of O3 concentration, measured by the seasonal 7-h mean daytime O3 concentrationFootnote 5 (M7) and RYLs for four different crops.

Future CH4 emissions would be substantially different across SSP narratives, as shown in Fig. 2. The differences in CH4 emissions driven by SSP storylines are large both at USA and global levels. Globally, SSP1 limits the lower bound while SSP3 limits the upper bound of the CH4 emissions trajectory. In the SSP3 narrative, there is a large increase in meat consumption by the end of the century (+ 80%), driven by demand in developing economies, so there is a subsequent increment in the CH4 emissions associated with beef, dairy and sheep production. In addition, in the SSP3 narrative there is a large increase on CH4 emissions associated to wastewater treatment (Daelman et al. 2012), and the largest increase on CH4 emissions from the energy system across the narratives. In the SSP1, the increment on meat demand and the reliance on fossil fuels (associated with energy-system emissions) are the smallest across the narratives, so it projects the lowest CH4 levels. Globally, in 2030, compared to SSP2, emissions diverge from − 12% to + 16%. This range increases to (− 20%, + 32%) in 2050, and to (− 38%, + 193%) in 2100. In USA, lower and upper bounds are defined by SSP1 and SSP5, respectively, which have the smallest and largest increments in meat demand, respectively. Taking SSP2 as the point of comparison, uncertainty ranges in USA account for (− 10%, + 26%) in 2030, (− 23%, + 42%) in 2050 and (− 33%, + 125%) in 2100.

Fig. 2
figure 2

Methane (CH4) emissions per period for USA and the rest of the world (RoW) (Tg). The line represents emissions for the SSP2 storyline (Shared Socioeconomic Pathway), while shaded areas represent the ranges determined by all SSP storylines

Figure 3 shows that the CH4 pulse would increase O3 concentration levels, measured by the 3-month mean of 7-h daytime O3 during crop season, up to 0.12 ppbv around the world. Two essential factors for O3 formation are emissions of precursor gases and their reaction with solar radiation. Figure 4 indicates that the largest variations in O3 levels are located in regions closer to the equator belt, with the highest solar irradiance. We note there are some seasonal differences in O3 concentrations, largely associated with NOx emissions. In some regions such as Europe or North America, the large NOx levels could reduce O3 concentration through titration at night and during wintertime (Jhun et al. 2015), while this negative relationship plays a minor role during daytime and summertime. Given that, in this study, the O3 exposure is calculated to analyze the RYLs, Fig. 3 shows the changes in O3 for summertime (July), as it is a representative month for the growing season in those areas with largest crop production (Northern HemisphereFootnote 6). The RYLs associated to these variations on the growing-season mean of 7-h daytime O3 are shown in following figure.

Fig. 3
figure 3

Seasonal 3-monthly mean of 7-h daytime ozone (M7) attributable to the methane (CH4) pulse in the central scenario in 2020 (ppbv). We use July as the representative month for this metric. The pulse in the central scenario represents a 10% increase of projected 2020 USA CH4 emissions in 2020 under the SSP2 (Shared Socioeconomic Pathway) storyline

Figure 4 shows that larger RYLs would occur in those regions that suffer larger O3 increments, accounting for up to 0.1% in some countries for some crops in 2020. Additionally, the figure demonstrates that there are significant divergences between the crops analyzed, driven by the maximum stomatal conductance which a species can reach. Globally, variations on rice and maize yield damages account for less than 0.02%, while RYL coefficients of soybeans and, to a lesser extent, wheat would increase up to 0.08–0.1% in several regions, such as the Mediterranean area, Middle East, or the West Coast of USA.

Fig. 4
figure 4

Differences in relative yield losses (RYLs) attributable to the methane (CH4) pulse in the central scenario in 2020 for maize, rice, soybeans and wheat (%). The pulse in the central scenario represents a 10% increase of projected 2020 USA CH4 emissions in 2020 under the SSP2 (Shared Socioeconomic Pathway) storyline

Focusing on USA, the additional RYLs driven by the CH4 pulse in 2020 for the central scenario could represent up to 0.038%, depending on the period and the commodity, with additional impacts in the subsequent periods (see Appendix V). In order to compare the additional RYLs attributable to the central methane pulse with the total RYLs associated to O3 exposure in USA, Fig. 5 shows that total RYLs account for 5.3–8.1%, 1.4–2.6%, 17.6–23.0%, and 4.0–6.3% for maize, rice, soybeans, and wheat, respectively during the time horizon analyzed.

Fig. 5
figure 5

Timetrends of total relative yield losses (RYLs, %) in USA for maize, rice, soybeans and wheat, following the SSP2 (Shared Socioeconomic Pathway) socioeconomic narrative

Once having estimated the additional RYLs driven by shocks in CH4 emissions in USA for four representative crops, these are re-scaled to GCAM regions and extended to the rest of the commodities to ensure that the analysis covers all the agricultural production (see Sect. 2.2). Then, multiplying these RYLs by the agricultural production and price of each crop, in each region and period and for each narrative, we can obtain the O3-related economic damages to crop revenues driven by CH4 pulses (see Methodology). Agricultural production levels and prices in each year are obtained from GCAM and presented in Figs. 6 and 7.

Fig. 6
figure 6

Agricultural production of different commodities per period and region (USA and RoW) (Mt). Lines represent the projections under the SSP2 storyline (Shared Socioeconomic Pathway). Shaded areas represent ranges determined by SSP storylines

Fig. 7
figure 7

Regional prices of different commodities per period and region (USA and RoW) ($2010/kg). Lines represent the projections under the SSP2 storyline (Shared Socioeconomic Pathway). Shaded areas represent uncertainty ranges determined by SSP storylines. Note that FodderHerb is not regionally traded in the model, so there is a single global price

Figure 6 shows that future agricultural production levels vary with the socioeconomic narrative, indicated by the shaded area in the graphs, as population growth rates and food demand parameters are some of the most relevant drivers for crop production. In the SSP2 storyline, agricultural production increases at a decreasing rate up to 2060, where it stabilizes or decreases for some commodities (e.g. MiscCrops). This trend is similar to the global population projection under the SSP2 socioeconomic storyline.Footnote 7 However, some specific crops such as corn, sugar, and oilcrop (the category that includes soybeans) present a continuously increasing production that does not stabilize with population peak. This is largely driven by the non-food (bioenergy) demand for these commodities at a global level. The increases in production in 2100, compared to 2020 values, are 53.4% (40.8–60.5%), 73.4% (59.7–87.5%), and 55.1% (19.7–60.4%) for corn, oilcrop, and sugar, respectively. USA presents similar patterns in terms of future agricultural production levels. In 2020, it is the largest producer of corn and oilcrop, representing 34.2% and 21.2% of global production, respectively. The increasing demand for these two commodities for bioenergy purposes entails a continuous increase of production, which does not stabilize with population peak, similar to the global trend. Therefore, regional production in 2100, compared to 2020, for corn and oilcrop would increase around 35.8% (30.2–57.8%) and 91.0% (81.6–143.9%). In terms of price trajectories, they are also directly related to the socioeconomic narratives. In the SSP2 storyline, price variations are relatively small, as demonstrated in Fig. 7. At a global level, the largest increments in prices in 2100, compared to 2020 levels, are represented by FodderGrass, which increases around 21% followed by FodderHerb (6%). On the other hand, oilcrop (− 15%), palmfruit (− 13%) and wheat (− 11%) represent the largest relative reductions. In USA, FodderGrass (9%) and FodderHerb (6%) also present the largest price increases, closely followed by rice (5%). On the contrary, oilcrop (− 18%) and wheat (− 11%) show the main price relative reductions.

Given that economic damages to crop revenues driven by CH4 pulses are calculated by multiplying additional RYLs attributable to the shocks by the agricultural production and price of each crop, marginal damages are calculated by aggregating and discounting those damages and dividing them by the emission shocks, as described in the Methodology section. However, other analyzed variables such as the pulse size (PulseSize), the PulseYear, the socioeconomic narrative (SSP), or the discount rate have direct impacts on the results. Therefore, we have developed a sensitivity analysis, in order to examine which variables would most impact to marginal damages.

Figure 8 shows that, in the central scenario, total marginal damage accounts for 493 $/t-CH4, of which 98 $/t-CH4 are attributable to damages in USA and 395 $/t-CH4 in the rest of the world. The figure shows that the damages wil be affected by different factors such as the socioeconomic narrative (SSP) or the discount rate. PulseSizes and PulseYears also have a direct impact on O3-related marginal damages to crop revenues and they are analyzed in the following figures.

Fig. 8
figure 8

Ozone-related marginal damages to crop revenues driven by a methane (CH4) pulse by region, discount rate and SSP storyline (Shared Socioeconomic Pathway) for the central pulse ($2010/t-CH4). This pulse represents 10% increase of projected 2020 USA methane emissions in 2020. Damages are calculated, accumulated and discounted for 50 years (PulseYear + 50)

Figure 9 shows global marginal damage to crop revenues attributable to variations in CH4 emissions, broken down for different regions around the world. The most affected regions are USA, China, India, EU-15 and Brazil which are the main crop producersFootnote 8 and, except for the latter, also generate the larger O3 precursor emissions during the time horizon analyzed. The Appendix VI includes a table with the marginal damages for each region in the central scenario. Figure 9 also shows that marginal damages do not always increase with increments in PulseSizes or time periods (PulseYears), due to different factors such as the non-linearity of the exposure–response functions or the implicit threshold in the estimation of the seasonal mean daytime O3 concentration (see Methodology). The evolution of some air pollutants, such as NOx, will impact these trends: in those regions where these pollutants increase more and the reduction is delayed (e.g. developing Asia), marginal damages tend to increase along with the pulse implementation year. This trend is not observed in those regions where the projected reduction in air pollutants starts in the nearer term (e.g. USA). When the pulse is 5% (1.42 Tg), marginal damages in USA increase until 2040 and they drop in 2050. However, the increases in marginal damages in other regions such as Central Asia or India are the drivers of increasing global values during the analyzed time horizon. Likewise, if the pulse is 15% of the emissions (4.25 Tg), the global marginal damages increase over time. Moreover, in this case USA also presents larger marginal damages in all the periods (including from 2040 to 2050), as the size of the pulse entails additional RYLs increases in every time step. However, the figure shows a different pattern for the 10% pulse (2.84 Tg). At a global level, marginal damages increase up to 2040, when they peak. In 2050, additional RYLs driven by the pulse decrease compared to previous period in some regions that bear most of the marginal damages, namely USA, China or India.

Fig. 9
figure 9

Ozone-related marginal damages to crop revenues driven by a methane (CH4) pulse by region, PulseSize and PulseYear under the SSP2 storyline (Shared Socioeconomic Pathway) and using a discount rate of 3% ($2010/t-CH4). Damages are calculated, accumulated and discounted for 50 years (PulseYear + 50). The definition of the GCAM regions is detailed in Appendix III

Finally, Fig. 10 shows the O3 related marginal damages to crop revenues for the central scenario and how they vary by modifying each variable individually with respect to central assumptions. In the central scenario marginal damages account for 493 $/t-CH4, distributed as 98$/t-CH4 in USA and 395 $/t-CH4 in the rest of the world. Regarding the uncertainty range, using a higher discount rate would determine the lower bound of the total marginal damages (423 $/t-CH4) while setting the PulseYear to 2040 would determine the upper bound of the damages (556 $/t-CH4). Focusing on USA, the lower PulseSize (5%) and setting the pulse to 2040 would indicate the lower and upper bounds of the uncertainty range of the marginal damages, which account for 76 $/t-CH4 and 113 $/t-CH4, respectively.

Fig. 10
figure 10

Sensitivity analysis of the ozone-related marginal damages to crop revenues. The central scenario represents a 10% increase of projected 2020 USA methane emissions in 2020 under the SSP2 storyline (Shared Socioeconomic Pathway) and using a discount rate of 3%. The solid line indicates the marginal damages in the central scenario. The dashed lines show the lower and upper bounds, respectively

4 Discussion and conclusion

The release of methane (CH4) due to human activities leads to physical impacts and related economic damages in many sectors, including agriculture, energy, human health, vegetation, and biodiversity. The physical impacts arise through two key routes, climate change -through driving warming- and air pollution, as methane is a precursor for the formation of ozoneFootnote 9 (O3). Improving the understanding of these physical impacts and economic damages is important for policymaking. Cost–Benefit Analysis (CBA) is a prominent tool that is used to assist policymaking in considering damages and the benefits of mitigation to reduce these. CBA requires monetisation of damages, including both the climate and ozone-related impacts of methane releases. To assist the process of monetising methane damages, for consideration in CBA studies, this study focusses on the air pollution damages related to ozone formation, specifically in the form of the economic costs that are produced for agriculture due to crop-yield losses. We estimate that total global crop damages to crop revenues per tonne of methane account for $493 2010$/t-CH4 in our central scenario. In order to check the sensitivity of our results to different variables, we re-calculate these marginal damages modifying key parameters, namely socioeconomic narratives, discount rates, pulse sizes, and years when the pulse is implemented. We find that the effect of altering each of these variables is relatively small, ranging from about − 14% to + 13% of our central estimate (about $423 per t-CH4 to about $556). Implementing a larger pulse size has only a very modest increase in damages, while a smaller pulse decreases damages by about $44 per tonne. As for the socioeconomic narrative, we find that the SSPs with higher reference yield improvement rates (e.g. SSP1) have smaller damages. The temporal pathway is not completely smooth, as the damages depend on the underlying O3 concentrations (which vary across regions over time), where the production is, how much is produced, and what the prices are. Results also show that applying a higher discount rate would have a significant impact as it determines the lower bound of the total marginal damages, demonstrating that the valuation of near-term versus distant damages plays a significant role on the presented results. In terms of regional distribution of these damages, about 19% of the damages occur in USA, with the EU-15 region, China, and India being the next most heavily impacted because they are the largest crop producers and the largest emitters of O3 precursors.

The results obtained in this work can complement other estimates of damages from methane. At a global level, the calculated marginal damages to crop revenues under central scenario assumptions are equal to about 39–59% of the climate damages, as estimated by the Social Cost of Methane in different studies (Colbert et al. 2020; Marten et al. 2015; Marten and Newbold 2012; Shindell et al. 2017; Waldhoff et al. 2011). Moreover, the damages estimated in this study would represent 28–64% of the damages associated to increased premature mortality reported in Sarofim et al., (2017). While that study found only about 11% of the global mortality damages are in USA, we find that a large share of the agricultural damages occur in this region (~ 19%), due to its role as a major agricultural producer. Appendix VII includes a comparison between these climate and non-climate (ozone-related) damages.

The study has some caveats and limitations. Damages have been calculated in absence of climate change related impacts. Future changes on temperature and precipitation pathways will also have an impact for crop yields, as reflected in different studies (Lobell et al. 2014; Rosenzweig et al. 2014; Snyder et al. 2021, 2020; Waldhoff et al. 2020). The damages associated with climate change cannot be linearly added up with the ozone-related damages calculated in this study (Da et al. 2021). The aggregation of these different impacts and the effects on global and regional agricultural systems is therefore a complex undertaking that is planned to be explored in future work.

Furthermore, we also acknowledge the uncertainty associated with the rate used to discount future damages to present values. In the central case of the analysis, we apply a discount rate of 3%, because it has been the central value used historically by the U.S. federal Government for rulemaking, following the guidelines of the Interagency Working Group on the SCC (IWG) (IWG 2010; Stock and Greenstone 2021). However, we recognize that the real interest rate on the 10-year Treasury note, which has been used to calibrate the social rate of time preference, has been substantially below 3% for the last couple of decades (Carleton and Greenstone 2021; Council of Economic Advisers 2017). In this line, recent reviews show that lower discount rates (or even declining rates, see Arrow et al. 2013) are now being applied in different regions, including USA (OECD 2018; O’Mahony 2021). In our analysis, we use additional lower and higher, static and dynamic, and region-specific discount rates to capture this uncertainty (see Sect. 2.1), considering its direct implications for the estimation of the monetized damages and relevance for non-substitutable capital. The alternative discount rates we apply in our sensitivity analysis range from 1.5 to ~ 5%, in order to represent the discount rates recommended by the National Academies SCC assessment (National Academies of Sciences 2017), and the most recent scientific literature. For example, a recent report focused on the estimation the social cost of carbon (Rennert et al. 2022) proposed four alternative discount rates of 1.5%, 2%, 2.5%, and 3%. Similarly, Drupp et al. 2018, based on a survey of over 200 experts, recommend to use a median discount rate of 2.3%. All these values have been incorporated to our sensitivity analysis, while declining discount rates will be explored in future research.

In addition, the model used to estimate the O3 concentrations and the subsequent yield losses (TM5-FASST) adds the individual O3 responses from each precursor as an approximation to obtain the response to combined changes in precursors. While this is clearer for some precursors (e.g. NMVOC), the relation between NOx and O3 is more complex with more non-linearities (Wu et al. 2009). However, the O3 exposure metrics used in this study, namely the growing-season mean of 7-h (or 12-h) daytime O3, is constrained to the daytime and to summer season when the effect of the NOx titration is reduced in most parts of the world. In addition, we use this exposure metric because it has been proven to be more robust than other threshold-based measures (e.g. AOT40). The TM5-FASST documentation paper (Van Dingenen et al. 2018b) includes a detailed validation section where the authors discuss the model performance and the tradeoffs between accuracy and applicability. In addition, a previous study discusses some limitations of the combined used of the models applied in this study, while showing the advantages and disadvantages of using the global exposure–response functions, in contrast to using regional or national data, or using the more detailed “flux-based” models (Sampedro et al. 2020). We also acknowledge that in this study we only calculate the damages to agricultural crops, and we do not include the damages to forest products, pasture, or other ecosystems, which have been proven to be significant in several studies (Emberson 2020; Fuhrer et al. 2016, 1994; Grulke and Heath 2020; Unger et al. 2020; Wittig et al. 2009).