The guiding scientific rationale of GGCMI Phase 2 is to provide a comprehensive, systematic evaluation of the response of process-based crop models to critical interacting factors, including CO2, temperature, water, and applied nitrogen under two contrasting assumptions on growing season adaptation (CTWN-A). The dataset is designed to allow researchers to

enhance understanding of models sensitivity to climate and nitrogen drivers;

The GGCMI Phase 1 intercomparison was a relatively limited computational exercise, requiring yield simulations for 19 crops across a total of 310 model years of historical scenarios, and had the participation of 14 modeling groups. The GGCMI Phase 2 protocol is substantially larger, involving over 1400 individual 30-year global scenarios, or over 42 000 model years; 12 modeling groups nevertheless participated. To reduce the computational load, the GGCMI Phase 2 protocol reduces the number crops to five (maize, rice, soybean, spring wheat, and winter wheat). The reduced set of crops includes the three major global cereals and the major legume and accounts for over 50 % of human calories in 2016: nearly 3.5 billion tons or 32 % of total global crop production by weight . This set of major crops has the advantage of historical yield data globally available at subnational scale , and has been frequently used in subsequent analyses e.g.,.

The Phase 2 protocol involves a suite of uniform perturbations from a historical climate time series. The baseline climate scenario for GGCMI Phase 2 is one of the weather products used in Phase 1, daily climate inputs for 1980–2010 from the 0.5∘ NASA AgMERRA (“agricultural”-modified Modern Era Retrospective analysis for Research and Applications) gridded reanalysis product. AgMERRA is specifically designed for agricultural modeling, with satellite-corrected precipitation . The experimental protocol consists of 9 levels for water supply perturbations, 7 for temperature, 4 for CO2, and 3 for applied nitrogen, for a total of 756 simulations (Table ), 672 for rainfed agriculture and an additional 84 for irrigated (W∞). Values of climate variable perturbations are selected to represent reasonable ranges for changes over the medium term (to 2100) under business-as-usual emissions. Values for nitrogen application levels are intended to cover a wide range of potentials. The resulting GGCMI Phase 2 dataset captures the distribution of crop model responses over a wide range of potential future climate and management conditions.

The protocol samples over all possible permutations of individual perturbations; i.e., all values are applied across all crops and regions, so that the protocol includes many combinations that are not realistic. For example, we simulate high N application to soybeans, which are N fixers and need little fertilizer. This choice also means that CO2 changes are applied independently of changes in climate variables, so that higher CO2 is not associated with higher temperatures or other particular climate changes. The purpose of the experiment is not to produce individual scenarios that represent realistic future states but to sample over a wide range of parameter space to enable understanding the factors that drive agricultural changes.

While all CTWN perturbations are applied uniformly across the historical time series, they are applied in different ways. CO2 and nitrogen levels are specified as discrete values applied uniformly over all grid cells. Temperature perturbations are applied as absolute offsets from the daily mean, minimum, and maximum temperature time series for each grid cell, and water perturbations are applied as fractional changes to daily precipitation. The irrigated scenario (W∞) is a particular case of water supply levels, in which crops are assumed to have no water constraints. That is, all crop water requirements are fulfilled regardless of local water supply limitations. To facilitate comparison, irrigated simulations use the same growing seasons as all other simulations, even though in reality irrigated growing seasons may be different , and both irrigated and rainfed cases are simulated with near-global coverage.

The uniform perturbations of the GGCMI Phase 2 protocol require some care in interpretation. Temperature and precipitation perturbations should be considered as differences from historical climatology within the growing season only. That is, a T+1 simulation represents a 1 ∘C warmer growing season, not a 1 ∘C warmer annual mean temperature. (The distinction is important because in climate projections, winters generally warm more than summers; e.g.,.) In the GGCMI Phase 2 protocol, temperature and precipitation perturbations are applied uniformly in space, but future changes in temperature and precipitation will not be spatially or temporally uniform. In a realistic climate projection, higher latitudes generally warm more strongly than lower latitudes e.g.,, and the northern high latitudes warm more quickly than the southern ones. A GGCMI Phase 2 simulation therefore represents a possible future state that could occur in each grid cell but not one that would in reality occur simultaneously in all grid cells across the globe. The GGCMI Phase 2 simulations are intended to be used for climate impact assessment not directly but instead as a “training set” for statistical emulation of each crop model. Once an emulator is constructed from the outputs described here, it can be driven with growing-season climate anomalies from any climate model projection. The GGCMI Phase 2 protocol does not involve any simulated changes in climate variability, but demonstrate that these effects are relatively minor and that GGCMI Phase 2 emulators can effectively reproduce crop model yields under realistic future climate scenarios.

The area simulated in the GGCMI Phase 2 protocol extends considerably outside currently cultivated areas, because cultivation may shift under climate change. Figure  shows both the present-day cultivated area of rainfed crops (left) and model coverage (right). (Figs. S1–S2 for currently cultivated area for irrigated crops; model coverage is the same.) Each model covers all currently cultivated areas and much of the uncultivated land area, run at 0.5∘ spatial resolution. To reduce the computational burden, the protocol requires simulation over only 80 % of Earth land surface area, omitting areas assumed to remain non-arable even under an extreme climate change, including Greenland, far-northern Canada, Siberia, Antarctica, the Gobi and Sahara deserts, and Central Australia. The protocol also allows omitting regions judged unsuitable for cropland for non-climatic reasons. Selection criterion involve a combination of soil suitability indices at 10 arcmin resolution and excludes those 0.5∘ grid cells in which at least 90 % of the area is masked as unsuitable according to any single index, and which do not contain any currently cultivated cropland. Currently cultivated areas are provided by the MIRCA2000 (Monthly Irrigated and Rainfed Crop Areas around the year 2000) data product . Soil suitability indices measure excess salt, oxygen availability, rooting conditions, toxicities, and workability, and are provided by the IIASA (International Institute for Applied Systems Analysis) Global Agro-Ecological Zone model GAEZ;. The procedure follows that proposed by . All modeling groups simulate the minimum required coverage, but some provide simulations that extend into masked zones, including, e.g., the Sahara and central Australia (Fig. , right).

The 12 models included in GGCMI Phase 2 are all process-based crop models that are widely used in impacts assessments (Table ). Although some models share a common base (e.g., the LPJ or EPIC families of models), they have subsequently developed independently. Wherever possible, the GGCMI Phase 2 protocol harmonizes inputs, but differences in model structure mean that several key factors cannot be fully standardized across the experiment. These include soil treatment (which affects soil organic matter and carryover effects of soil moisture across growing years) and baseline climate inputs.

While 10 of the 12 models participating in GGCMI Phase 2 use the AgMERRA historical daily climate data product, two models require subdaily input data and thus use different baseline climate inputs: Processes of Radiation, Mass and Energy Transfer (PROMET) uses ERA-Interim reanalysis , and the Joint UK Land Environment Simulator (JULES) uses a bias-corrected version of ERA-Interim, the 3 h WFDEI (WATCH Forcing Data ERA-Interim) , specifically the WFDEI version with precipitation bias-corrected against the Climate Research Unit (CRU) TS3.101/TS3.21 precipitation totals . The data products show some differences (Figs. S3–S4, which compare data products over currently cultivated areas for each crop). For example, for maize-growing areas, ERA-Interim daily precipitation is biased high from that in AgMERRA by 7 % (<1σ), while mean daily precipitation in WFDEI is only 3 % higher. Precipitation differences are largest in wheat areas, where ERA-Interim is substantially wetter (+60 mm yr-1 or 10 %). Temperature differences are largest for rice, with ERA-Interim 1 ∘C cooler than AgMERRA, and smaller for other crops, e.g., maize with ERA-Interim 0.45 ∘C cooler and WFDEI 0.1 ∘C warmer. These differences are relatively small compared to the perturbations tested in the protocol.

Planting dates and growing season lengths are standardized across models, following the procedure described in for the “fullharm” setting. (The exception is that Phase 2, unlike Phase 1, uses identical growing seasons for rainfed and irrigated cases, to allow for direct comparison of simulations along the W dimension.) This harmonization is important because the parametrization of growing seasons can have strong effects on simulated yields . In all the GGCMI Phase 2 crop models, sowing dates are prescribed directly, but the length of the growing season is a product of crop phenology, which is driven mostly by phenological parameters and temperature. Modelers were therefore asked to adjust their phenological parameters so that the average growing season length of the baseline scenario (C=360, T=0, W=0) matched the harmonization target. (The one exception to this harmonization protocol involves CARbon Assimilation In the Biosphere (CARAIB), whose team kept their own growing season specifications rather than tuning to standard lengths.) Two aspects of the procedure should be noted. First, the target growing seasons used in GGCMI Phase 2 are crop and location specific. For example, present-day maize is sown in March in Spain, in July in Indonesia, and in December in Namibia . Second, because temperature varies between years in the 30-year baseline climatology, realized growing season length will still vary in individual years even after harmonization.

The dependence of harvest dates on climate parameters means that growing seasons will alter under climate change in a model with phenological parameters tuned to match target growing seasons in the baseline climate. In general, warmer future scenarios produce shorter growing seasons. We denote simulations that allow these future changes as “A0” experiments, where 0 denotes “no adaptation”. The GGCMI Phase 2 protocol includes a second set of experiments, “A1”, that assume that future cultivars are modified to adjust to changes along the T dimension in the CTWN experiment. For these simulations, modelers adjust phenological parameters for each temperature scenario to hold growing season length approximately constant. (CARAIB simulations follow the same principle, fixing growing season length at their baseline levels.) That is, the A1 simulations require running a model with seven different choices of cultivar parameters, one per warming level. Parameter settings for T=0 are identical in both A0 and A1. The A1 simulations roughly capture the case in which adaptive crop cultivar choice ensures that crops reach maturity at roughly the same time as in the current temperature regime. This assumption is simplistic, and does not reflect realistic opportunities and limitations to adaptation but provides some insight into how crop modifications could alter projected impacts on yields and is sufficiently easy to implement in a large model intercomparison project as GGCMI.

Growing seasons for maize, rice, and soybean are taken from the SAGE (Center for Sustainability and the Global Environment, University of Wisconsin) crop calendar , gap filled with the MIRCA2000 crop calendar and, if no SAGE or MIRCA2000 data are available, with simulated Lund–Potsdam–Jena managed Land (LPJmL) growing seasons and are identical to those used in GGCMI Phase 1 . In GGCMI Phase 2, we separately treat spring and winter wheat and so must define different growing seasons for each. As for the other crops, we use the SAGE crop calendar, which separately specifies spring and winter wheat, as the primary source for 69 % of grid cells. In the remaining areas where no SAGE information is available, we turn to, in order of preference, the MIRCA2000 crop calendar and to simulated LPJmL growing seasons . These datasets each provide several options for wheat growing season for each grid cell but do not label them as spring or winter wheat. We assign a growing season to each wheat type for each location based on its baseline climate conditions. A growing season is assigned to winter wheat if all of the following hold, and to spring wheat otherwise:

The monthly mean temperature is below freezing point (<0 ∘C) at most for 5 months per year (i.e., winter is not too long).

Nitrogen (N) application is standardized in timing across models. N fertilizer is applied in two doses, as is often the norm in actual practice, to reduce losses to the environment. In the GGCMI Phase 2 protocol, half of the total fertilizer input is applied at sowing and the other half on day 40 after sowing, for all crops except for winter wheat. For winter wheat, in practice the application date for the second N fertilizer application varies according to local temperature, because the length of winter dormancy can vary strongly. In the GGCMI Phase 2 protocol, the second fertilization date for winter wheat must lie at least 40 d after planting and – if not contradicting the distance to planting – no later than 50 d before maturity. If those limits permit, the second fertilization is set to the middle day of the first month after sowing that has average temperatures above 8 ∘C.

All stresses in models are disabled other than those related to nitrogen, temperature, and water. For example, model responses to alkalinity, salinity, and non-nitrogen nutrients are all disabled. No other external N inputs are permitted – that is, there is no atmospheric deposition of nitrogen – but some models allow additional release of plant-available nitrogen through mineralization in soils. In LPJmL, the Lund–Potsdam–Jena General Ecosystem Simulator (LPJ-GUESS), and Agricultural Production Systems sIMulator (APSIM), soil mineralization is a part of model treatments of soil organic matter and cannot be disabled. Some additional differences in model structure mean that several key factors are not standardized across the experiment. For example, carryover effects across growing years including residue management and soil moisture are treated differently across models.

All models in GGCMI Phase 2 provide 30-year time series of annual crop yields for each scenario, 0.5∘ grid cell and crop, in units of t ha-1 yr-1. They also provide all available variables of the following six: total aboveground biomass yield; the dates of planting, anthesis and maturity; applied irrigation water in irrigated scenarios; and total evapotranspiration. We term these seven variables the “mandatory” outputs, but note that some models do not compute all of them; e.g., CARAIB does not compute the anthesis date. Besides these seven “mandatory” data products (Table , bold), the protocol requests any or all of 18 “optional” additional output variables (Table , plain text). Participating modeling groups provided between 3 (PEPIC) and 18 (APSIM-UGOE) of these optional variables.

All output data are supplied as NetCDF version 4 files, each containing values for one variable in a 30-year time series associated with a single scenario, for all grid cells. Filenames follow the naming conventions of GGCMI Phase 1 , which themselves are derived from those of ISIMIP . Filenames are specified as [model]_[climate]_hist_fullharm_[variable]_[crop] _global_annual_[start-year]_[end-year]_[C]]_[T]_[W]_[N]_[A].nc4 Here, [model] is the crop model name; [climate] is the original climate input dataset (typically AgMERRA); [variable] is the output variable (of those in Table ); [crop] is the crop abbreviation (“mai” for maize, “ric” for rice, “soy” for soybean, “swh” for spring wheat, and “wwh” for winter wheat); and [start-year] and [end-year] specify the first and last years recorded on file. [C], [T], [W], [N], and [A] indicate the CTWN-A settings, each represented with the respective uppercase letter and the number indicating the level (e.g., “C360_T0_W0_N200”; see Table ). Except for the CTWN-A letters, the entire filename needs to be in small caps. All filenames include the identifiers global and annual to distinguish them as global, annual model output, following the updated ISIMIP file naming convention .

Output data are provided on a regular geographic grid, identical for all models. Grid cell centers span latitudes from -89.75 to 89.75∘ and longitudes from -179.75 to 179.75∘. Missing values where no crop growth has been simulated are distinguished from crop failures: a crop failure is reported as zero yield but non-simulated areas (including ocean grid cells) have yields reported as “missing values” (defined as 1×1020 in the NetCDF files). Following NetCDF standards, latitude, longitude, and time are included as separate variables in ascending order, with units “degrees north”, “degrees east”, and “growing seasons since 1 January 1980 00:00:00”.

Following GGCMI Phase 1 standards, the first entry in each file describes the first complete cropping cycle simulated from the given climate input time series. In the AgMERRA time series used for GGCMI Phase 2, the first year provided is 1980 but the date of the first entry can vary by crop and location. In the Northern Hemisphere, for summer crops like maize (sown in spring 1980 and harvested in fall 1980), the first harvest record would be of 1980, but for winter wheat (sown in fall 1980 and harvested in spring 1981) the first harvest record would be of 1981. Output files report the sequence of growing periods rather than calendar years. While there is generally one sowing event per calendar year (since simulations with harmonized growing seasons do not permit double cropping), in some cases harvest events may skip or repeat within a calendar year. For example, because soybeans in North Carolina are typically harvested well into December, some calendar years may include no harvest (if it is not completed until after 31 December) or two harvests (one in January and one 11 months later in the following December).

All models participating in GGCMI Phase 2 have be evaluated against historical yields and site-specific experimental data. Most models (9 of 12, all but CARAIB, JULES, and PROMET) have been evaluated in their global setup in the GGCMI Phase 1 evaluation exercise , and many have used the GGCMI Phase 1 online tool to similarly evaluate subsequent model versions e.g.,. Evaluating the performance of crop models in the GGCMI Phase 2 archive is complicated by the artificial nature of the protocol: the settings in the CTWN-A experiment design do not reflect actual conditions in the real world. The protocol includes one scenario of near-historical climate inputs (T0, W0, C360), but the prescribed uniform nitrogen application levels do not reflect real-world fertilizer practices. Models also omit detailed calibrations to reflect the performance of historical cultivars.

We provide a partial evaluation of the models' skill in reproducing crop yield characteristics using the methodology of , developed for GGCMI Phase 1. evaluate how well model crop yield responses in a historical run capture real-world yield variations driven by year-to-year temperature and precipitation variations. Following this approach, we compare yields in the GGCMI Phase 2 baseline simulations with detrended historical yields from the Food and Agriculture Organization of the United Nations by calculating the Pearson product moment correlation coefficient over 26 years of yield. The procedure is sensitive to the detrending method and the area mask used to aggregate yields; we use a 5-year running mean removal and the MIRCA2000 cultivation area mask for aggregation. In some cases, the model time series are shifted by 1 year to account for discrepancies in FAO or model year reporting. Because the GGCMI Phase 2 protocol imposes fixed, uniform nitrogen application levels that are not realistic for individual countries, we evaluate control runs for each model at multiple N levels whenever possible. Overall, nine of the GGCMI Phase 2 models (Table 3) provide historical runs for all three nitrogen levels (10, 60, and 200 kg ha-1 yr-1).

As expected due to the unrealistic features described above, correlation coefficients for the GGCMI Phase 2 simulations are slightly lower than those found in the Phase 1 evaluation, but models show reasonable fidelity at capturing year-to-year variation (Fig. ). For example, global correlation coefficients in Phase 1 and Phase 2, respectively, are 0.89 and 0.74 for maize, 0.67 and 0.64 for wheat, and 0.64 and 0.59 for soybeans. (Phase 1 values are from Figs. 1–4 and 6 in .) Differences in fidelity between regions and crops exceed differences between models; that is, Fig. c–f show more color similarity in horizontal than vertical bars. For example, maize in the United States is consistently well simulated, while maize in Indonesia is problematic (mean Pearson correlation coefficients of 0.68 and 0.18, respectively). Note that in this methodology, simulations of crops with low year-to-year variability such as irrigated rice and wheat will tend to score more poorly than those with higher variability. In some cases, especially in the developing world, low correlation coefficients may point to reporting problems in the FAO statistics and to real-world variability caused by variations in management rather than weather . No single model consistently exhibits greater fidelity than others. Instead, each model shows near best-in-class performance for at least one location–crop combination. For example, pDSSAT is the best model for maize in the US, LPJmL and GEPIC are best in Germany, PROMET is best in Argentina, and PEPIC and LPJ-GUESS are best in France.

Crop models in the GGCMI Phase 2 ensemble show broadly consistent responses to climate and management perturbations in most regions, with a strong negative impact of increased temperature in all but the coldest regions. Mapping the distribution of baseline yields and yield changes shows the geographic dependencies that underlie these results. Absolute yield potentials show strong spatial variation, with much of the Earth's surface area unsuitable for any of these crops (Fig. , left). Crop yield changes under climate perturbations also show distinct geographic patterns (Fig. , right, which shows fractional yield differences between the baseline and T+4 A0 scenarios). In general, models agree most on yield response in regions where yield potentials are currently high and therefore where crops are currently grown. In A0 simulations, models show robust decreases in yields at low latitudes, and highly uncertain ensemble mean increases at most high latitudes. Low-latitude yield reductions are due in part to shortening of the growing season under warming and in part to the direct effects of higher temperature. In A1 simulations, where growing seasons length does not change, temperature-related reductions in yield are more muted (see Fig. S14). In both A0 and A1 simulations, models show some increases in high mountain regions that are currently cold limited.

Projections of strong yield growth at higher latitudes should be treated with caution, since the effects evident in Fig.  are due in part to inaccuracies in model representations of present-day crop yields. For example, at latitudes north of 45∘, the GGCMI Phase 2 models collectively suggest strong (but uncertain) growth in soybean yields under warmer conditions (Fig. g). However, model differences are greater in the baseline than future simulations and greatest in currently cultivated areas (Fig. ). Both the mean projected growth and the inter-model spread are driven by three models that show almost zero present-day potential soybean yields across the entire high-latitude region, even in locations where soybeans are currently grown (Fig. , left). PROMET, for example, involves a stronger response to cold than other models (e.g., LPJmL) with frost below -8 ∘C irreversibly killing non-winter crops and prolonged periods of below-optimum temperatures also leading to complete crop failure. Over the high-latitude regions simulated by both models, 52 % of grid cells in PROMET report 0 yield in the present climate vs. 11 % of cells in the T+4 scenario, leading to a strong yield gain in warmer future climates. In LPJmL outputs, the same high-latitude area is deemed suitable for cultivation even in baseline climate, with crop failure rates of 4 % and 5 % in present and T+4 cases, so that projected yield changes are modest (Fig. ). These spurious low baseline yields result in very large fractional changes in the T+4 warming scenario, when all models agree that conditions become favorable for soybeans. Those models that most accurately reproduce present-day high-latitude soybean yields of 1–2 t ha-1 in fact show a slight decrease in yield under a warming scenario (Fig. a). Apparent future yield increases in the multi-model mean are driven by the least realistic simulations.

The GGCMI Phase 2 exercise offers the opportunity to examine and characterize not just crop response to a single temperature change but nonlinearities in responses and interactions between factors. We illustrate a few of these relationships in Figs. – using A0 simulations to capture maximum climate effects. We choose crops and factors whose effects are reasonably well understood and show that these are reproduced in models. It is expected, for instance, that increases in precipitation should buffer the effects of warmer temperatures and that CO2 increases should reduce damage to crops in scenarios where water is limited. Models generally confirm expected behavior but also provide insight into unforeseen interactions. To show geographic effects, we divide model responses in Figs. – by the primary Köppen–Geiger climate regions , showing the yield changes across all simulated grid cells in each region. In each panel, we examine relationships between two factors, showing yield response against one for several scenarios of the other, in box plots that show the inter-model spread. The responses highlighted here are qualitatively similar across all crops included in this study (Figs. S5–S9 for all simulated area and S10–S13 for cultivated area only).

For all crops, warming scenarios with precipitation held constant produce yield decreases in most regions. These impacts are robust for even moderate climate perturbations. For rainfed maize, even a 1 ∘C temperature increase with other factors held constant produces a median regional decline in potential yield that exceeds the variance across models, in all but the “cold-continental” regions (Fig. a). The remaining areas (“warm temperate”, “equatorial”, and “arid”) account for nearly three-quarters of global maize production. In the high-latitude “cold-continental” region, potential yield changes are positive but highly uncertain, for the reasons discussed previously; uncertainties are larger even for maize than for soybeans. (Compare Fig. a and b.) Temperature effects are somewhat nonlinear, with the largest impacts for maize in the warm “tropical” region (for soybeans, temperature effects are more complex; see Fig. S5). Precipitation effects on rainfed crops are more strongly nonlinear. The curvature of the precipitation response can be seen by eye in Fig. b: soybean yields are strongly negatively impacted by reduced rainfall, peak under increased precipitation of 20 %, and actually decline at higher precipitation levels.

As expected, precipitation and temperature effects interact, with increases in precipitation buffering yield responses to temperature. Increased rainfall mitigates the negative impacts of warmer temperatures caused by increased evapotranspiration e.g.,. For maize, the effect is relatively modest outside the “arid” regions (Fig. a). Globally, a 4 ∘C temperature rise with no change in precipitation results in median loss of ∼13 % of rainfed maize, with all models showing a negative response. With a 20 % increase in precipitation, the median yield loss is ∼8 %. For soybeans, the equivalent values are ∼11 % and 1 %, respectively. Decreased rainfall, on the other hand, amplifies yield losses and also increases inter-model variance. That is, models agree that the response to decreased water availability is negative in sign but disagree on its magnitude. Outside of arid regions, the interaction effect itself shows little nonlinearity (i.e., response slopes in Fig. a and b are roughly parallel). As expected, irrigated crops are more resilient to temperature increases in all regions, especially so where water is already limiting (other than winter wheat; Fig. S9).

Increased CO2 boosts yields overall through the well-known CO2 fertilization effect (Fig. ). The effect is strongest for the C3 crops (wheat, soybeans, and rice), while maize, a C4 grass, has a comparatively muted response. We show irrigated rice and rainfed soy in Fig.  as representative C3 crops. The effect of CO2 on yields is nonlinear, as expected, with significant benefit from small increases but with effects plateauing at higher concentrations (Fig. ). CO2 and temperature effects show minimal interaction. This effect is seen in Fig. a, which shows nearly parallel response slopes at different CO2 levels. That is, CO2 fertilization does little to change the nature of the temperature response. On the other hand, CO2 and precipitation effects interact strongly, as expected since higher CO2 levels allow reduced stomatal conductance and evapotranspiration losses, mitigating the effect of reduced rainfall e.g.,. This interaction is seen in Fig. b as smaller yield losses from reduced rainfall when CO2 levels are higher. For example, for soy, raising CO2 to 510 ppm actually outweighs the multi-model median damages caused by a 20 % precipitation reduction in all climate regions. All crops show similar behavior, but note that model uncertainties for wheat are substantially higher than those for other crops. (Compare Fig. a for soy and Fig. S7 for wheat.)

We show some additional cases in the Supplement. As noted previously, the A1 adaptation simulations involve significantly moderated temperature impacts relative to the A0 simulations shown here (Fig. S14). Figures S15 and S16 show the response in the nitrogen dimension and an irrigation water demand response example.