2.1 Crop yield simulations

We use projections from five different GGCMs (GEPIC, LPJ-GUESS, LPJmL, PEGASUS, and pDSSAT) that participated in the first phase of ISIMIP (Rosenzweig et al., 2014; Warszawski et al., 2014) in order to test for a dependence of projected yield changes on the GMT pathway (see Sect. 1 for their basic characteristics). Each crop model was forced by climate projections from five different GCMs (HadGEM2-ES, IPSL-CM5A-LR, MIROC-ESM-CHEM, GFDL-ESM2M, NorESM1-M) generated for four RCPs (RCP2.6, RCP4.5, RCP6.0, RCP8.5) in the context of the Coupled Model Intercomparison Project, phase 5 (Taylor et al., 2012). CMIP5 was an effort by the climate modelling community to provide a new suite of climate simulations in time for the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report (AR5). The RCPs cover the range from climate mitigation (RCP2.6, RCP4.5) to business-as-usual (RCP6.0) and high-emissions scenarios (RCP8.5). Climate projections have been bias corrected to better match observed historical averages of the considered climate variables. For the future, the bias-correction preserves absolute changes in monthly temperature and relative changes in monthly values of the other variables simulated by the GCMs while also correcting the daily variability about the monthly mean (Hempel et al., 2013). Separate simulations are available for each of the four major crops, wheat, maize, rice, and soy, on a global 0.5 ^∘ × 0.5^∘ grid, covering the time period from 1971 to 2099. The considered crop is assumed to grow everywhere on the global land area, only restricted by soil characteristics and climate but independent of present or future land use patterns (“pure crop” simulations). Each model has provided a pair of simulations (“runs”) for each climate change scenario: (1) a rain-fed run and (2) a full-irrigation run assuming no water constraints. This design provides full flexibility with regard to the application of future land use and irrigation patterns. While the crop yield ($Y_{{\mathrm{varCO}}_{\mathrm{2}}}$) in “default” simulations accounts for the fertilization effects due to the increasing levels of pCO₂, the ISIMIP setting also includes a sensitivity experiment in which the crop models were forced by the same climate change projections but pCO₂ was kept fixed at a “present-day” reference level that differs from GGCM to GGCM (see Table 1). We will refer to this run as the “fixed-CO₂” run and indicate the associated crop yields by $Y_{{\mathrm{fixedCO}}_{\mathrm{2}}}$. As a special case, the default simulations for pDSSAT do not use annual pCO₂ changes. Instead, pCO₂ was changed every 30 years using the average pCO₂ of the respective 30-year time slice.

2.2 Effect of temperature change

We analyse the dependence of yield changes on ΔGMT separately for rain-fed and full-irrigation simulations, and for each crop. While yields in a given grid cell of course depend on the local temperature, long-term changes in local temperature are in turn a manifestation of global greenhouse-gas related warming (Frieler et al., 2012). The aim here is testing to what extent local long-term changes in yields can be described in terms of a single global measure of warming, ΔGMT. Since the time of attaining a given ΔGMT differs between GCMs and scenarios, we group all available data into ΔGMT intervals (bins) separated by 0.5 ^∘C steps with 0.5 ^∘C width (±0.25 ^∘C around the central temperature), where ΔGMT is calculated relative to the present-day (1980–2010 average) reference level. For all annual data falling into a given interval and at each grid point we apply a separate one-way analysis of variance (ANOVA fixed-effects model) to individually calculate the yield variance explained by (1) different GGCMs, (2) the GCMs, and (3) the RCPs. The quantification of the RCP dependence of the relationship between global warming and yield change is limited to warming levels of up to 2 to 3 ^∘C above present depending on the GCM because only one RCP (RCP8.5) reaches temperatures above this threshold. However, we also provide the patterns of yield change for the higher concentration scenario. In the main text, all figures except Figs. 9 and 10 refer to a ΔGMT level of 2.5 ^∘C, and all figures except Figs. 3, 4, and 11 refer to crop model simulations driven by HadGEM2-ES climate. See Fig. 1 for the years associated with ΔGMT = 2.5 ^∘C in HadGEM2-ES. The Supplement (Ostberg et al., 2018) contains analogous figures for other GMT levels and GCMs.

Figure 1GMT projections from HadGEM2-ES for the four RCPs. The horizontal line and shading indicate the 2.5 ^∘C bin. The original annual GMT values (thin lines) are smoothed (thick lines) in order to obtain a contiguous time interval for each ΔGMT bin. The smoothing is based on a singular spectrum analysis with a time window of 20 years (Golyandina and Korobeynikov, 2014; Golyandina et al., 2015; Korobeynikov, 2010). Years where the thick line falls within the shaded area are associated with ΔGMT = 2.5 ^∘C, and the corresponding time interval is delineated by the dashed vertical lines.

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We do not impose a specific functional relationship between GMT change and change in crop yields. Yield change for any GMT level between the central levels of the considered bins could be derived by a simple linear interpolation among the patterns of neighbouring bins but without assuming a linear relationship between global mean warming and yield change across the full range of warming.

2.3 Effect of pCO₂ change

The direct effect of CO₂ fertilization on crop yields is expected to introduce some scenario dependence into the relationship between GMT change and yield change. We test to what degree the scenario dependence of the relationship can be explained by introducing pCO₂ as an additional predictor for within-bin fluctuation of yields. To this end, we evaluate two different approaches to estimate the direct CO₂ effect on crop yields within the different GMT bins, described in detail below. The two approaches differ in terms of the crop model simulations that they require: approach (a) only requires the default crop yield simulations with increasing pCO₂ whereas approach (b) requires a pair of simulations with increasing pCO₂ and with fixed pCO₂ at the present-day reference level.

2.4 Emulator of temperature and CO₂ effects

Based on the spatial patterns of purely climate-induced yield change ΔY_clim(i) and added CO₂ fertilization effect a₁(i), which are derived separately for each rain-fed and irrigated crop and specific to each crop model and GCM, we propose the following two-step interpolation method to compute crop yield changes for any given pair of ΔGMT and pCO₂, using either the coefficients from approach (a) or (b):

1. linear interpolation of ΔY_clim(i) between the two neighbouring ΔGMT bins to the desired ΔGMT value;

2. addition of the CO₂ pattern described by a₁(i) ⋅ (pCO₂ − 370 ppm), where a₁(i) is also interpolated linearly between the respective coefficients from the neighbouring ΔGMT bins.

The application of these two steps using coefficients from method (a) above will be called emulator approach (a); their application using coefficients from regression method (b) will be called emulator approach (b). In addition, we propose a third, very basic emulator approach (c) in which the yield change for any given ΔGMT is derived from a simple linear interpolation of the average yield change in the neighbouring warming bins of the default simulations $\mathrm{\Delta }{Y}_{{\mathrm{varCO}}_{\mathrm{2}}}\left(i\right)$ with respect to the historical reference period, without using the associated pCO₂ as an additional predictor.

The linear interpolation of any of the previous coefficients between two neighbouring warming bins is illustrated for a ΔGMT of 2.3 ^∘C as follows:

where coef can be ΔY_clim(i), a₁(i), or $\mathrm{\Delta }{Y}_{{\mathrm{varCO}}_{\mathrm{2}}}\left(i\right)$.

Using GGCM projections for the HadGEM2-ES climate input to train the emulators, we test which of the emulator approaches, (a), (b), or (c), provides the best reproducibility for yield changes simulated under the four RCPs (Sect. 4). While approach (b) requires a pair of crop model simulations – one with time-varying pCO₂ and one with fixed present-day pCO₂ – approaches (a) and (c) only require the default simulations with time-varying pCO₂. Thus, a comparison of the three approaches could provide some important guidance regarding future crop model experiments required to allow for the proposed highly efficient emulation of crop model simulations. Since simulated crop yields are subject to considerable inter-annual variability, we also test what effect the number of available training data has on the reliability of the derived regression coefficients. For that purpose, we train the emulators using either all available simulation data from the four RCPs or only simulation data from RCP8.5 and compare the fraction of the land surface for which derived fits are statistically significant as well as the difference between simulated and emulated yield changes. Due to the 30-year time slices of constant pCO₂ used by pDSSAT in the default run, approach (a) cannot be applied to this model using only RCP8.5 data. Since only RCP8.5 reaches ΔGMT > 3.5 ^∘C, this limits the temperature range of emulator approach (a) for pDSSAT even when using all available training data.

We evaluate and compare the performance of the three emulator approaches at the grid scale as well as the scale of large regions. Grid point yields (in tons per hectare) are multiplied by the fixed year-2000 crop-specific growing area from the MIRCA2000 dataset (Portmann et al., 2010) to derive regional total crop production (in tons). MIRCA2000 provides gridded growing areas for a total of 26 rain-fed and irrigated crops based on a combination of census, remote sensing, and other geographic data sources.

3.1 Patterns of relative changes at different levels of global warming and main sources of variance

Figure 2Average wheat yield change at ΔGMT = 2.5 ^∘C as a percentage of the mean historical yield (1980–2010 average) under rain-fed conditions for each crop model forced by HadGEM2-ES. The average is calculated across all RCPs which reach the global mean warming interval from 2.25 to 2.75 ^∘C, namely RCP4.5, RCP6.0, and RCP8.5. Note that pDSSAT is run over a limited domain excluding areas north of 60^∘ N. Regions with marginal historical yields (defined as lying below the 2.5 % quantile of historical yields on year-2000 cropland) are masked to avoid exaggerated relative yield increases. Analogous figures for different crops, for irrigated conditions, and for absolute yield change (in tons per hectare) are available in the Supplement.

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In general, increasing GMTs correspond to an expansion of arable land to higher latitudes with concurrent yield reductions in equatorial regions. The highest positive changes in projected yields under rain-fed conditions at 2.5 ^∘C ΔGMT are typically in the northern high latitudes and mountainous regions for all crops (Fig. 2 for wheat; figures for other crops in the Supplement). These locations were previously inhibited by a short growing season, which extends with increasing air temperature (Ramankutty et al., 2002). Yield gains also occur over previously moisture-limited regions, such as the northwestern US and northeastern China, in agreement with the findings of Ramankutty et al. (2002). In contrast, near the Equator most crop yields decrease, especially maize and wheat. Since most cultivated land currently lies in low and middle latitudes, potential yield changes in those regions contribute a higher relative importance for today's food production system than changes in high latitudes.

While variations exist in the magnitude of projected yield changes, there is a high degree of consistency in the direction of yield change across ensemble members, especially over the high latitudes, where most of the largest projected yield changes occur, but where yields are in general smaller (Fig. 3). Utilizing output from all available combinations of GCM, GGCM, and RCP scenarios, more than three-quarters of the ensemble members indicate increasing crop yields over the upper mid-latitudes in the Northern Hemisphere for all crops at 2.5 ^∘C.

Figure 3Percentage of crop model simulations (combination of a single GCM, GGCM, and RCP scenario) indicating an increase (blue) or decrease (red) in yield of greater than 5 % at each grid point at 2.5 ± 0.25 ^∘C ΔGMT as compared to the historical period for maize, rice, soybeans, and wheat under rain-fed conditions. White indicates either a change of less than 5 % or disagreement among the models in the direction of yield change. Note that only four out of five GGCMs provided results for rice. An analogous figure for irrigated conditions is available in the Supplement.

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The simulated yield values at each grid point and within each GMT bin are subject to variation due to the selection of impact model, GCM forcing, and emissions scenario. When considering all of these factors, the variance attributable to the impact model selection is much greater than that associated with the GCM or scenario choice in most regions (Fig. 4). This holds for rain-fed as well as irrigated simulations. The predominance of the impact model component in total variance is particularly evident in the middle to high latitudes for all four considered crops, where impact model variance accounts for up to 90 % of the grid point variance at 2.5 ^∘C.

Figure 4Fraction of total yield variance attributable to the impact models (GGCMs, a), climate models (GCMs, b), and scenarios (RCPs, c) for each crop. Figure shown for rain-fed runs at ΔGMT = 2.5 ± 0.25 ^∘C warming; an analogous figure for irrigated runs is provided in the Supplement.

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Figure 5Difference in global mean yield change (sum of rain-fed and irrigated, and weighted by year-2000 growing areas) between the default ($Y_{{\mathrm{varCO}}_{\mathrm{2}}}$) and fixed-CO₂ simulations ($Y_{{\mathrm{fixedCO}}_{\mathrm{2}}}$), for each crop over the range of pCO₂ associated with the ΔGMT = 2.5 ^∘C bin. Results are as simulated by LPJmL forced with output from HadGEM2-ES. Each colour represents an emissions scenario. Points mark individual years while dotted lines and shaded areas indicate the linear best fit and its 95 % confidence interval for each scenario. The black dotted line indicates the linear best fit through all available scenarios. Analogous figures for other GGCMs and warming bins are available in the Supplement.

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3.2 Direct impacts of increasing pCO₂

In addition to air temperature warming, pCO₂ has a direct influence on crop yields. As it varies within the different ΔGMT bins, it is expected to induce part of the fluctuations of the yield changes at given GMT levels. We find that this CO₂ effect shows little scenario dependence (see Fig. 5 for the global average effect within the LPJmL simulations at ΔGMT = 2.5 ^∘C), consistent with a short response time of plants to pCO₂ changes. As expected, the CO₂-induced yield differences increase with heightened atmospheric CO₂ level under all emissions scenarios, implying a stronger CO₂ fertilization impact with increased pCO₂.

Figure 6Climate-change-induced yield changes at ΔGMT = 2.5 ^∘C of global warming and the year-2000 pCO₂ level (370 ppm). Left column panels: patterns of ΔY_clim(i) derived at each grid point i using approach (a) (see Eq. 1). Right column panels: corresponding patterns of ΔY_clim(i), derived using approach (b) (see Eq. 3). Both types of patterns are derived from LPJmL simulations forced by HadGEM2-ES assuming rain-fed conditions and expressed as absolute differences compared to the historical period (1980–2010). Rows: different crop types. Analogous figures for irrigated conditions, for different GGCMs, and using relative instead of absolute yield changes are available in the Supplement.

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Figure 7CO₂-induced yield changes at 2.5 ^∘C of global warming for LPJmL forced by HadGEM2-ES assuming rain-fed conditions. Analogous to Fig. 6, but showing the scaling coefficients a₁(i) from approach (a) (left column panels) and approach (b) (right column panels), multiplied by the average pCO₂ change compared to the year 2000 (370 ppm) across all years falling into the GMT bin. Rows: different crop types. Analogous figures for irrigated conditions, for different GGCMs, and using relative instead of absolute yield changes are available in the Supplement.

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At the grid point level, two approaches have been used to separate purely climate-change-induced from CO₂-induced yield change (following Eqs. 1 to 3). Figure 6 shows the climate-change-induced yield change at ΔGMT = 2.5 ^∘C for LPJmL under rain-fed conditions, using all available runs that fall into the warming bin to estimate ΔY_clim(i). Figures for irrigated conditions and the other GGCMs are available in the Supplement. The two methods result in broadly similar patterns, with yield increases in the upper middle and high latitudes, mixed regions with decreases and increases in the lower mid-latitudes, and mostly decreases in the tropics. However, the magnitude of change differs between the two approaches: approach (a) generally estimates larger changes outside the tropics while yield decreases in the tropics are larger in approach (b). There are also some regions where both approaches disagree regarding the direction of change, such as the high latitudes of both western North America and eastern Russia for wheat and parts of Southeast and South Asia for all crops. Patterns of climate-induced yield change match better between both approaches under irrigated conditions (see Supplement).

In GEPIC, both approaches disagree on the direction of change for maize yields over large parts of Europe. In LPJ-GUESS, both approaches disagree on the direction of change in most of the tropics for all crops. While tropical yield change is predominantly negative in approach (b) mirroring results of the other crop models, approach (a) estimates mostly positive climate effects on tropical crops. In pDSSAT, approach (a) generally produces larger areas with negative yield change than approach (b). At the same time, positive yield effects in approach (a) have a larger magnitude than those in approach (b) in many regions. In PEGASUS, both approaches disagree on the direction of change over large parts of the US for maize and soybeans, and large parts of China for wheat.

The estimates of CO₂-induced yield change also differ between the two approaches (Fig. 7 for LPJmL results under rain-fed conditions). We expect CO₂ fertilization to have a positive or at least neutral effect on yields, and this is confirmed by approach (b) for all GGCMs and crops. Only GEPIC simulations show negative CO₂ effects on soybean and wheat yields in a few regions for approach (b). This can be explained by nutrient interactions in the model: CO₂ fertilization leads to yield increases first but also increases nutrient depletion in the soil compared to the fixed-CO₂ run. If fertilizer application is insufficient to replenish nutrient stocks this can lead to lower yields despite the beneficial effect of higher pCO₂. With approach (a), however, areas of negative estimated CO₂ effects are widespread in all GGCMs and all crops. Generally, the magnitudes of the estimated CO₂ effect are also much larger, often surpassing those of approach (b) even in regions where the direction of change matches.

Given that approach (a) contradicts our expectation of how CO₂ fertilization should affect yields in many regions, we conclude that approach (a) is not reliable in separating the effects of climate change on yield from those of pCO₂ change. By design, climate-induced and CO₂-induced yield changes add up to the full yield change (see Eq. 1), which is why the difference among the patterns of estimated CO₂ effects explains why climate change patterns from Fig. 6 also differ substantially between both approaches in some regions. Approach (a) has a structural disadvantage to approach (b) in that it estimates both the climate-induced and CO₂-induced effect on yields from the same linear regression model (Eq. 1). In addition to changes in pCO₂ annual yields in each warming bin are subject to substantial inter-annual climate variability, which means that individual years with a higher pCO₂ do not necessarily have a higher yield. In contrast, approach (b) only estimates the CO₂-induced yield change from the regression model (Eq. 2) while both the default and the fixed-CO₂ runs are subject to identical climate variability. There is inter-annual variability in the CO₂-induced yield change as well (see Fig. 5 for the global average effect); however, it is much smaller than the total yield variability.

While approaches (a) and (b) should provide similar estimates of the CO₂-induced yield change given a large sample, our sample size is limited by the number of years falling into each ΔGMT bin (Table 2). This number varies between 7 years in the 4.5 and 5.0 ^∘C bin and up to 66 years in the 1.0^∘C bin when yield data from all RCPs are used to train the emulator. The number of years varies between 7 and 13 years if only data from RCP8.5 are used. Given the limited sample size and possibly large variability, the derived fits are often not statistically significant. For approach (a) we found that derived fits were rarely significant on more than 25 % of the crop-specific growing area (Portmann et al., 2010) using a p value of 0.05 (figure available in the Supplement). Values were even lower if only RCP8.5 was used for the regression. In contrast, fits derived using approach (b) were mostly statistically significant (p < 0.05) on more than 70 % of the growing area, often on more than 90 % of the area. We also found only a small negative effect in terms of statistical significance if only RCP8.5 was used in approach (b).

Table 2Number of years of yield data available in each ΔGMT bin for HadGEM2-ES. Only RCP8.5 reaches warming levels above 3 ^∘C.

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Figure 8Validation of the three emulator approaches. Maps show the difference (emulated minus simulated) among the simulated LPJmL yields forced by HadGEM2-ES climate for RCP4.5 under rain-fed conditions, averaged over all years falling into the ΔGMT bin of 2.5 ^∘C (2066–2094), and the emulated yields for the same years based on approach (a) (left column panels), approach (b) (middle column panels), and approach (c) (right column panels). Rows: different crops. MAD: mean absolute difference, regardless of sign, averaged across all grid points. Analogous figures for irrigated conditions and for different GGCMs are available in the Supplement.

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