I therefore perform such an attribution. This study utilizes prior studies' results for yield responses to temperature, precipitation, CO 2 concentration, and surface ozone [ Van Dingenen et al ., 2009 ; Avnery et al ., 2011 ; Shindell et al ., 2012 ; Challinor et al ., 2014 ], combined with modeling of the time‐dependent impacts of emissions of all major drivers of climate change on these four parameters (see Section 2). This relatively simple process‐based analysis provides only global scale averages, but it incorporates results from detailed modeling and its simplicity allows rigorous quantification of uncertainties related to these processes. The goals of this study are thus to attribute crop yield changes at the global scale to emissions of individual pollutants based on prior process‐level results, consistently including climate and atmospheric composition changes, and discuss pathways for further advancement of knowledge in this area.

The Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report (AR5) concluded that climate change has substantially decreased crop yields, with addition losses likely over the 21st century ( Porter et al. , 2014 ). Assessments have analyzed a large body of research examining the effect of historical emissions and future scenarios, providing a wealth of information on regional and crop‐specific yield responses [e.g., Parry et al. , 2004 ; Porter et al. , 2014 ; Rosenzweig et al. , 2014 ]. These studies have often separated out the role of particular processes, such as temperature or CO 2 concentration changes, but attribution of responses to individual pollutants such as CO 2 , methane, or black carbon (BC) has been overlooked. This is important as policy makers have leverage over pollutant emissions, not individual processes, and the pollutants affect various processes differently. For example, CO 2 emissions lead to warming and increased CO 2 concentrations whereas methane emissions lead to warming and increased ozone concentrations. Hence, the roles of individual climate‐altering pollutants cannot be readily discerned from analyses of the response to historical or future climate change driven by many agents.

These relationships are combined into an analytic model to calculate the full chain from emissions through climate and composition impacts to crop yield response (Figure 1 ). The uncertainty analysis is carried out using 20,000 member Monte Carlo calculations. These incorporate uncertainties in crop yield response to each physical change, in the transient climate sensitivity, composition responses, in the RF attributable to each pollutant, and in the precipitation changes associated with forcing and temperature change as detailed above. This allows proper accounting for uncertainties that are systematic across the various pollutants in the net yield change calculations and those that are systematic across time for individual pollutants. Some individual components of uncertainty are asymmetric, but as the uncertainties presented here are a function of multiple components these asymmetries become small in the totals and hence, only the mean of positive and negative uncertainty is presented.

The crop yield response to these temperature, precipitation, and CO 2 changes and their uncertainties are taken from a large, recent meta‐analysis of detailed site and ecosystem models that isolated those responses based primarily on studies of wheat, rice, and maize [ Challinor et al ., 2014 ]. Yield changes in response to ozone are included using the assessment of the impact of ozone changes on wheat, rice, maize, and soybeans and their uncertainties produced in response to individual pollutant changes in the Goddard Institute for Space Studies (GISS) composition‐climate model [ Shindell et al ., 2005 ; Van Dingenen et al ., 2009 ; Shindell et al ., 2012 ].

Temperature response to forcing is then modeled using the time dependence of the impulse‐response function from the Hadley Centre climate model [ Boucher et al ., 2009 ], a widely used response function [e.g., Collins et al. , 2013b ]. The magnitude is set to yield an equilibrium climate sensitivity of 3.2 C for doubled CO 2 , consistent with the AR5, and the relative uncertainty of that AR5 estimate is also used [ Collins et al. , 2013a ]. Observations indicate that the land‐area averaged warming is approximately 1.6 times the global mean response [ Vose et al ., 2012 ], which is incorporated here as crop yields are obviously affected by land temperatures. Precipitation changes take place through a fast response that is part of the rapid adjustment to RF and a slow response that follows surface temperature changes [ Myhre et al ., 2013 ]. Both fast and slow land‐area precipitation changes for each pollutant (based on it's RF or induced temperature change) and uncertainties are taken from simulations with a suite of state‐of‐the‐art climate models [ Samset et al. , 2016 ].

Global mean temperature changes are driven by the global mean radiative forcing (RF) because of each emitted compound, and so the time‐dependent forcing is then calculated from the time‐dependent composition for long‐lived gases. RF for most short‐lived compounds is taken from the IPCC AR5 [ Myhre et al ., 2013 ]. RF attributable to individual aerosol precursors including indirect cloud effects was not provided in AR5, and hence to incorporate this important component for SO 2 , BC, and organic carbon (OC), I use a combination of modeling and literature analysis [ United Nations Environment Programme and World Meteorological Organization , 2011 ; Shindell et al. , 2012 ] as in prior work [ Shindell , 2015 ]. The relative uncertainties in RF presented in the AR5 [ Myhre et al ., 2013 ] are used for all emissions. The RF uncertainties, and all others used here, are 5–95% confidence intervals. Forcings include indirect chemical responses, for example, stratospheric ozone depletion because of halocarbons, tropospheric ozone increases because of methane, and NO x emissions affecting ozone, methane, and nitrate aerosols. For the contribution of historical emissions, the halocarbon forcing is calculated by scaling results for HFC‐134a by the preindustrial‐to‐present RF for all halocarbons relative to that for that single example gas.

The analysis includes agricultural yield changes in response to changes in surface CO 2 and ozone concentrations, temperature, and precipitation. Modeling of composition and temperature changes follows that developed in previous work [ Shindell , 2015 ] and relies largely on the conclusions of broad scientific assessments. In brief, starting with long‐lived greenhouse gases, changes in CO 2 are calculated using the four exponential decay timescales given in the IPCC AR4 [ Forster et al ., 2007 ]. Evolution of methane uses the observationally constrained perturbation timescale of 12.4 yr [ Prather et al ., 2012 ] and the equilibrium response per unit methane emissions change calculated with the GISS‐PUCCINI model [ Shindell et al ., 2009 ]. Lifetimes for N 2 O and HFC‐134a and radiative efficiencies for N 2 O, HFC‐134a, and CO 2 are taken from the IPCC AR5 [ Myhre et al. , 2013 ].

To examine how society's actions can affect future yields, I compare high and low emission scenarios. These results largely utilize the high and low Representative Concentration Pathways (RCPs) used in the IPCC AR5 [ Meinshausen et al ., 2011 ] for CO 2 , CH 4 , and N 2 O. Ozone and aerosol precursors were similar across the RCPs, so their impacts are nearly identical in the scenarios (other than methane). Many halocarbons have been controlled, but hydrofluorocarbon (HFC) emissions are growing rapidly. Emissions across RCPs differ for HFCs, as for long‐lived greenhouse gases, but the range is not consistent with other studies. In particular, the high emission RCP8.5 case is markedly less than in other studies. Hence, although I use RCP2.6 HFCs for the low emission scenario, I use the RCP8.5 emissions plus half the difference between the emissions in a higher reference scenario [ Xu et al. , 2013 ] and the RCP8.5 for the higher case (along with an uncertainty of half that difference so that the range spans the RCP8.5 up to the higher reference scenario).

Combining individual attributions allows evaluation of realistic pollutant mixtures. Present‐day climate and composition have decreased agricultural yields 9.5 ± 3.0% relative to the preindustrial (Figure 5 ). Examining processes, climate change had the largest effect, with smaller, nearly offsetting, impacts from CO 2 fertilization and surface ozone. CO 2 fertilization is almost wholly attributable to CO 2 emissions, however, whereas surface ozone‐induced yield losses are attributable primarily to NO x (3.1%) and methane (1.7%). Though crop yield models often neglect ozone impacts, the emissions that drive ozone changes also cause climate change, particularly methane, and hence this separation is unrealistic as well as inconsistent with the inclusion of the impacts of CO 2 concentration changes. Examining pollutants, ∼93% of the losses stem from non‐CO 2 drivers, especially methane. Aerosols also played a substantial role, with a net impact of increasing yields. Neglecting surface ozone, non‐CO 2 impacts are still approximately nine times larger than CO 2 impacts. Historical emissions will continue to affect future yields, with a net “committed” impact over the next 100 years of −2.4 ± 1.2% attributable mostly to CO 2 (−1.8 ± 0.9%) and to a lesser extent to N 2 O (−0.4 ± 0.1%).

Pollutants are often compared using their integrated impact over a particular time horizon [ Myhre et al ., 2013 ], e.g., under the Kyoto Protocol. These results indicate that RF‐based comparisons cannot capture relative agricultural impacts. For example, the ratio of integrated agricultural losses per ton of methane relative to a ton of CO 2 is −1170 over 20 years, whereas over 50 or 100 years it is 620 and 220, respectively. For a ton of N 2 O, the ratios for these three time horizons are −2030, 2040, and 1240. As the sign varies with the time horizon, clearly these ratios differ greatly from forcing‐based metrics, which are always positive for these agents. These results highlight the flaws in assuming that non‐CO 2 drivers of climate change can be readily represented by a “CO 2 ‐equivalent”.

As emissions magnitudes vary widely across pollutants, I also evaluated yield changes attributable to 1% of current anthropogenic and biomass burning emissions [ Lamarque et al ., 2010 ] (Figure 4 ). Increases stem largely from OC and SO 2 emissions, and in the near‐term from CO 2 . Yield losses are larger, with the greatest contributions from NO x and BC initially, from methane for years 6–37, and from CO 2 for years 38–100. Although BC and OC have particularly large impacts, they are typically emitted as products of incomplete combustion (PIC = BC + OC + CO). The net PIC impact is also yield losses, but substantially less than those attributable to BC alone.

CO 2 impacts also change sign over time (Figure 2 ). Yields are initially increased by fertilization (Figure 3 ). CO 2 ‐induced warming suppresses yields, but this effect grows slowly owing to the lag in climate response combined with CO 2 's long residence time, thus outweighing fertilization only after 10 years. The impact of precipitation changes is small, consistent with previous results for large spatial scales [ Lobell and Field , 2007 ; Li et al. , 2010 ]. In contrast, the effects of methane through temperature and composition are both damaging, with ozone impacts dominant initially and warming impacts greater after 3 years (Figure 3 ). Changes in CO 2 produced from methane oxidation play only a small role.

The impacts of different pollutants vary greatly in magnitude (and even sign) and temporal evolution (Figure 2 ). The greatest agricultural damages per ton are initially from short‐lived BC, then from longer‐lived HFC‐134a, and finally from N 2 O. Short‐lasting gains are produced by OC, SO 2 , and NH 3 because of their near‐term cooling effects. NO x is highly damaging for the first year because of its contribution to ozone formation, remains damaging (but much smaller) during the first decade because of warming from that ozone, but thereafter transitions to increasing yield owing to cooling because of reduced methane.

4 Discussion and Conclusions

The pollutant attribution results may be surprising, but the process attribution results are in reasonable agreement with studies using detailed site or ecosystem models. This is partially to be expected given that the process‐level responses utilized here come from meta‐analysis of the detailed models, but also indicates that this framework realistically captures the global scale behavior in the more complex models over time, even when multiple processes are at work. The resulting agricultural yield responses indicate that although CO 2 has been the largest driver of climate change, it does not drive the bulk of crop yield responses to emissions of climate‐altering pollutants.

No other results for the total historical changes including both climate and composition are available for comparison, as indeed no prior results have included both climate and composition changes consistently (i.e., including both CO 2 and ozone). My results can be compared with prior results for a subset of processes, however. Historical yield responses to climate change and CO 2 (but not ozone) are presented in the IPCC AR5, summarizing estimates from various models and observation‐based estimates, and including all available spatial scales and time periods. They find that the most common results are yield reductions from 0 to 7.5% over the past three decades, the median length in the underlying studies [Porter et al., 2014]. As roughly half the observed surface warming and CO 2 increase has taken place during the past three decades, the full preindustrial to present‐day results calculated here are compared with twice the shorter‐term AR5 values. For climate and CO 2 impacts, the net during the industrial‐era was thus most commonly 0–15% yield reductions in the IPCC AR5 [Porter et al., 2014], similar to my ∼2–8% reductions. For 2100 relative to 2000 under all scenarios, the AR5 most common result was decreases of 10–25% [Porter et al., 2014], whereas I find −7 to −29% (without surface ozone). Separating these processes, detailed models indicate that the fraction of projected climate change‐induced losses offset by CO 2 fertilization is ∼66–90% [Parry et al., 2004] or ∼30–175% [Rosenzweig et al., 2014], whereas I find an offset of ∼30–80%. As CO 2 drives roughly half to two‐thirds of the climate changes under the high emission scenario, it appears that in most of the detailed crop models the net effect of CO 2 emissions is only weakly negative or positive (consistent with my uncertainty range, which is substantially greater for CO 2 than for other pollutants owing to the variations in fertilization in the detailed models and opposing near‐term and long‐term impacts; Figure 5). We can therefore infer that the overall yield losses in the detailed models likely stem largely or entirely from non‐CO 2 emissions. Finally, researchers have also found comparable or slightly larger global values for the present‐day impact of ozone [Van Dingenen et al., 2009; Avnery et al., 2011].

The meta‐analysis of crop yield response upon which much of this study is based provided linear responses to mean changes. This appears to be a reasonable approximation at the global mean level, although local responses will be nonlinear. Even at the global level, responses may become nonlinear as changes in CO 2 or climate increase, although this is partially included in the uncertainty associated with the linear responses as this study examines similar ranges to those in the studies upon which the meta‐analysis is based. Changes in the distribution of climate and climate extremes will also impact crop yields [Tubiello et al., 2007; Porter et al., 2014], but both the yield responses and the change in climate extremes and distributions themselves are more difficult to quantify [Collins et al., 2013a]. In particular, changes in precipitation are quite inhomogeneous and thus, regional responses can differ markedly from the land‐area average response [Collins et al., 2013a], although at least at the global scale the influence of precipitation is comparatively small (Figure 3).

Additional factors influenced by climate change or emissions that were not included in the meta‐analyses, such as wind speed, sunlight, or cloud cover, and nitrogen availability, are incorporated into more detailed crop models [Rosenzweig et al., 2014] and could modify these global aggregate results, as could agricultural adaptation [Challinor et al., 2014; Porter et al., 2014]. It would also be useful to explore differences between regions and between various crop types. For example, C 3 plants tend to be more sensitive to CO 2 fertilization than C 4 plants [Leakey, 2009], and wheat and soy are more sensitive to ozone than rice or maize [Van Dingenen et al., 2009; Avnery et al., 2011]. It would also be valuable to examine the behavior of other crops as their process‐level responses become better characterized as these four crops represent approximately 75% of the total calories that humans consume directly or indirectly [Cassman, 1999]. Further studies could attempt to include the effects of weeds, pests, and diseases as well [e.g., Tubiello et al., 2007; Gregory et al., 2009; Luck et al., 2011], and those of aerosols [e.g., Greenwald et al., 2006]. In addition, metrics other than total crop tonnage could be explored, as, for example, observations suggest that C 3 crops have lower content of some nutrients when grown under elevated CO 2 [Myers et al., 2014]. Finally, this analysis extends only to 2100, and further work could explore the longer‐term commitment resulting from emissions of gases with very long lifetimes such as CO 2 and N 2 O more fully.

Human choices related to agricultural practices, such as fertilizer application, irrigation, planting time, and cultivar choice, which were not included in this study, of course have a large impact on crop yields and have clearly dominated historical trends. Nonetheless, it is useful to understand the underlying influence of global change upon which the impact of local choices are imposed given that the former cannot be readily addressed by the actions of local farmers or authorities. Although this work builds closely upon prior studies, and knowledgeable experts could infer some of the qualitative conclusions, quantifying the impacts of the various drivers of climate change requires detailed modeling of the time‐dependent evolution of each compound, its RF, and the climate response. Furthermore, it is unrealistic to expect policy makers to infer the relative impacts of CO 2 and methane based on a set of complex studies examining the role of various physical processes. Many climate change mitigation measures target‐specific pollutants, for example, shifting from coal‐fired power to renewables to reduce CO 2 emissions, reducing methane leakage and venting in the fossil fuel industry, reducing over‐application of fertilizer to reduce N 2 O emissions, shifting to low‐warming HFCs, and controlling emissions from diesel vehicles to reduce BC and co‐emissions [e.g., Millar et al., 2010; Delucchi and Jacobson, 2011; Shindell et al., 2012; Fang et al., 2016; Shindell et al., 2016]. An emissions‐based view facilitates analysis of the potential agricultural benefits of such strategies. Presenting the crop yield impacts in an emissions‐based view instead of a process‐based view thus provides much clearer information to decision makers, and follows the perspective adopted in recent IPCC Assessments of moving from concentration‐based to emission‐based attribution of climate forcing.