Global crop yield response to extreme heat stress under multiple climate change futures

Anthropogenic climate change challenges current and future global food production due to the direct effects of changes in mean climatic conditions, increasing risks from extreme weather events, increased atmospheric CO₂ concentration and increasing pest damage [1, 2]. The Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC) reports moderate increase in global crop yield for global mean temperature increase up to 3 °C—mostly due to beneficial CO₂ fertilization effects on photosynthesis rate and transpiration demand—but general decrease above this threshold [3]. The report further concludes projected changes in the frequency and severity of extreme climatic events will have more serious consequences for food production and food insecurity, than changes in mean climate alone [3].

Yet global climate impact assessments to date fail to address adequately effects of changes in climate extremes on crops [1, 2, 4–7], especially the negative impact of heat waves during the reproductive stage, identified as a major threat to yield in many parts of the world. Previous analyses modelling the effect of extreme heat stress on crops have been limited to single regions [8–12] or do not quantify impacts on yield [13, 14]. Moreover, most previous studies present only a partial estimate of uncertainty related to the range of climate change projections by considering at most four global climate models (GCMs) using the older SRES emissions scenarios [3, 4, 6, 7]. Finally, anticipated benefits from CO₂ fertilization effects remain a large source of uncertainty [15].

Here we use a new version of the global crop yield model PEGASUS [5] that takes into consideration heat stress sensitivity around crop anthesis (HSA) [10, 16] and CO₂ fertilization effects for maize, spring wheat and soybean. We use an ensemble of 72 climate change projections spanning the 21st century together with the CRU TS 2.10 observed climate dataset [17] for the years 1971–2000 to drive PEGASUS and produce a robust estimate of uncertainties related to future climate change. Our approach takes into account impacts of change in mean climate conditions, extreme temperatures and elevated atmospheric CO₂ concentration. We explore PEGASUS' sensitivity to HSA and CO₂ fertilization effects and show impacts on global crop yield and production on present-day harvested areas. We present results from different Representative Concentration Pathways (RCPs) [18] to evaluate potential benefits of mitigation policy. Although we make use of one single global gridded crop model and do not evaluate across-model uncertainty, PEGASUS enables a first assessment of the effect of HSA on global crop productivity, currently missing in other comparable state-of-the-art global gridded crop models [19]. Key sources of uncertainty resulting from the use of a single crop model (i.e., consisting primarily of uncertainty in the magnitude of CO₂ fertilization effects, temperature thresholds for HSA, and model representation of water, temperature and nitrogen stresses), the use of static harvested areas, and assumptions about farmers' adaptation responses (i.e., decision of planting dates and choice of crop cultivars) are addressed in the discussion section.

2.1. Crop modelling

2.2. Climate modelling

2.3. Global average yield and production estimates

2.4. Representative concentration pathways and climate change futures

We find global average yield decreases for all maize simulations (ΔY ranges from − 2.9 ± 2.6% under RCP 2.6 to − 12.8 ± 6.7% under RCP 8.5 by the 2080s for CC) whereas corresponding yields of spring wheat and soybean, when CO₂ fertilization effects are included, increase throughout the 21st century owing to large positive responses in C₃ crops (ΔY ranges from 9.9 ± 3.6% under RCP 2.6 to 34.3 ± 13.5% under RCP 8.5 for spring wheat and from 7.1 ± 7.0% under RCP 2.6 to 15.3 ± 26.5% under RCP 8.5 for soybean by the 2080s for CC) (figure 1 and table 1). HSA strongly influences maize and spring wheat yields, contributing to nearly half of expected losses for maize by the 2080s under RCP 8.5 (ΔY = −12.8 ± 6.7% for CC compared to ΔY = −7.0 ± 5.3% for CC_w/o HSA) and substantial reductions in expected yield gains for spring wheat (ΔY = 34.3 ± 13.5% for CC compared to ΔY = 72.0 ± 10.9% for CC_w/o HSA). In contrast, HSA moderately affects soybean global yield trajectories due to its higher critical temperature threshold to HSA (see Methods and appendix A) (ΔY = 15.3 ± 26.5% for CC compared to ΔY = 20.4 ± 22.1% for CC_w/o HSA). Soybean exhibits a larger range of results spanning both positive and negative outcomes globally whereas maize results are mostly negative and wheat results mostly positive with CO₂ fertilization effects. Differences between crop responses and the larger range of results for soybean reflect differences in specific temperature tolerance to HSA (e.g. soybean has higher critical temperature tolerance but lower limit temperature tolerance in comparison to maize—see appendix A) as well as differences in GCM precipitation and temperature patterns and in spatial patterns of production specific to each crop. Figure S2 in the SI (available at stacks.iop.org/ERL/9/034011/mmedia) illustrates level of agreement in GCM simulations for each crop. In the case of soybean, there are as many areas showing a net decrease in yield as there are showing a net increase. However, in some important soybean production areas such as the USA and Brazil, there is no agreement on whether the sign of the projected yield changes is positive or negative (see also section Spatial patterns).

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When CO₂ fertilization effects are excluded from simulations (dashed lines in figure 1), spring wheat and soybean yields follow maize's negative trend, soybean being the most affected crop: ΔY = −26 ± 17.3% for soybean, ΔY = −22.0 ± 5.7% for maize, and ΔY = −24.1 ± 7.1% for spring wheat respectively for RCP 8.5 by the 2080s (see table 1). Soybean also shows the widest range of simulated yields when including HSA with and without CO₂ effects.

Maize is by far the most negatively affected crop and our results suggest a climate change future following RCP 2.6 could avoid fairly significant losses otherwise expected with higher RCPs, due to their larger heat and water stress conditions—since CO₂ fertilization effects are minimal for maize, a C₄ crop. On the contrary, spring wheat and soybean, both C₃ crops, could benefit greatly from higher CO₂ concentration in the atmosphere arising from RCP 8.5 or RCP 6.0 as, in these cases, beneficial CO₂ fertilization effects outweigh negative effects of mean climate change and extremes. However, crop response to elevated CO₂ remains the largest source of uncertainty as little is known about their actual response in the field throughout the world, especially under tropical climatic conditions and varied soil nutrient availability (all experiments to date have been conducted either in chambers or in fields located in the United States and in Europe, i.e., under temperate climatic conditions—see Discussion).

Finally, maize, spring wheat and soybean have different tolerance thresholds to extreme temperatures (see appendix A), leading to substantial differences in yield response. Spring wheat is the most affected by extreme temperatures and soybean is the least affected. By the 2080s for RCP 8.5, HSA accounts for 45% of total negative impacts on maize, offsets 25% of positive impacts on soybean and 52% of positive impacts on spring wheat when averaged at the global scale (table 1).

We confirm previous findings of regional disparities in crop yield impacts, with yield increases in high latitudes and large yield reductions in mid and low latitudes (figure 2). Maize, with the largest cultivated area, shows a uniform decrease in yield over mid and low latitudes by the 2080s (figure 2(a)). In contrast, spring wheat and soybean present disparate results owing to contradictory effects resulting from beneficial CO₂ fertilization and detrimental extreme heat stress, the latter playing a critical role in some regions (figures 2(d) and (g) respectively). The number of simulations agreeing in the sign of change in yield is also higher for maize than for the other crops (see figure S1 in the SI (available at stacks.iop.org/ERL/9/034011/mmedia), which presents corresponding maps of ensemble simulations and their agreement).

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Comparison between maps from top (CC) and middle (CC_w/o HSA) rows in figure 2, indicates crop harvested areas at risk of HSA. In the case of maize (figures 2(a) and (b)), greater HSA sensitivity occurs in the American corn-belt, the Middle-East, west and south Asia, and northeast China. Within the top-five producing countries (figure 3), Brazil, Mexico and Argentina experience large decreases in national production, exacerbated by HSA (blue and yellow bars). The United States also faces a notable decrease in all simulations. China's small gain owing to CO₂ fertilization effects is cancelled out by HSA. These losses among the top-five producing countries (i.e., accounting for 80% of global maize production) could play a major role in future world supply of maize, with consequences for stability of international crop markets and higher risks of future food insecurity as already experienced during the 2008 global food crisis [31, 32].

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In the case of spring wheat (figures 2(d) and (e)), all current cultivated areas experience heat stress damage: the most severely impacted regions are again the mid and low latitudes, including the northern part of the United States, the Near-East and eastern part of Australia. In fact, all top-five producing countries exhibit drastic reductions in anticipated production increases due to HSA (figure 3). Note country ranking is estimated according to PEGASUS spring wheat harvested area [30], which does not include winter wheat and hence differs from country rankings that include both winter and spring wheat (see Methods).

Finally, in the case of soybean (figures 2(g) and (h)), the United States, Brazil and India (accounting for more than 60% of global soybean production) are the most affected among the top-five producing countries (figure 3). In contrast, Argentina, the third largest soybean producing country, shows a large increase in its production, which could increase its ranking to second in terms of world production, before Brazil. China also displays large gains in production but only when CO₂ fertilization effects are included and little change under CC_w/o CO2 . Finally, the main region of production, the central part of the United States, faces the most critical HSA effects.

When CO₂ fertilization effects are not taken into account (figures 2(c), (f) and (i)), yields of all three crops decrease uniformly in mid and low latitudes whereas changes in yields in high latitudes remain positive. In addition, we find a net decrease in yields for the top-five producing countries of each crop, including even Canada, a high latitude country, in the case of spring wheat (red bars in figure 3).

Impacts by the 2080s follow a regular gradient among income levels of nations (as defined by the World Bank [28]—see Methods) for maize and partly for spring wheat, whereas impacts are mixed in the case of soybean (figure 4). For maize, we find high income (HI) economies face the least damage while low income (LI) ones suffer the most. As seen in the global average trends (figure 1), maize yields decrease under nearly all simulations.

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For spring wheat, yields increase from HI to medium low income (MLI) countries when CO₂ fertilization effects are included. LI countries are less positively affected. Under CC_w/o CO2, yields decrease the most for LI and HI groups. Spring wheat displays the strongest response to CO₂ fertilization effects and greater HSA compared to the other crops.

In the case of soybean, medium high income (MHI) countries experience large increases in yield when including CO₂ effects and small decreases under CC_w/o CO2. LI economies also experience a small increase in yield when including CO₂ effects and a decrease without it. HI and MLI economies are the most impacted regions experiencing a large decrease in yield under CC_w/o CO2, which is cancelled out with positive CO₂ fertilization effects. Spread in the results is similar within all groups, whereas HI economies exhibit larger uncertainties in impacts, which is also the case for maize.

Apart from maize, which shows greater impacts with decreasing income level, we find relative differences in results due to HSA or CO₂ fertilization effects do not show systematic patterns by income levels and repeat global trends illustrated in figures 1 and 2.

PEGASUS is more responsive to CO₂ effects and HSA than different pathways of radiative forcing. Yet CO₂ effects on C₃ and C₄ crops vary greatly, resulting in quite different outcomes depending on crop–RCP combination. When all factors are taken into account, global average maize yield by the 2080s displays much greater reduction under RCP 8.5 (ΔY = −12.8 ± 6.7%) than under RCP 2.6 (ΔY = −2.9 ± 2.6%), and moderate losses under RCP 4.5 (ΔY = −6.8 ± 4.2%) and 6.0 (ΔY = −8.3 ± 5.2%) (figure 1). In contrast, yields of spring wheat and soybean increase the most under RCP 8.5 (up to 34.3 ± 13.5%), followed by RCP 6.0 (up to 23.0 ± 6.8%), RCP 4.5 (up to 16.7 ± 5.3%) and RCP 2.6 (up to 9.9 ± 3.6%). By the 2050s, maize yield may be a little higher under RPC 4.5 than under RCP 6.0. Similarly, soybean yield could be slightly higher under RCP 6.0 than RCP 8.5. These differences highlight the complexity of crop–climate–CO₂ interactions.

Relative changes in production (figure S3 in the SI available at stacks.iop.org/ERL/9/034011/mmedia for top-five countries) and yield (figure S4 in the SI available at stacks.iop.org/ERL/9/034011/mmedia for income-level groups) under RCP 2.6 are much smaller than under RCP 8.5 (figures 3 and 4 respectively). However, the range of uncertainties is greatly reduced. A strong mitigation scenario resulting in a low stabilized radiative forcing (i.e., RCP 2.6) could therefore contribute to reduced uncertainties in projections of overall impacts and thus facilitate adaptation planning. In contrast, a business as usual future such as RCP 8.5 is associated with large uncertainties in projected impacts, and designing adaptation strategies for such an uncertain future is much more challenging.

Finally, when assuming CO₂ fertilization to be negligible (i.e., CC_w/o CO2 ), we find dramatic yield losses for all three crops by the 2080s under RCP 8.5; whereas corresponding yield losses are reduced by more than 80% under RCP 2.6 (see two last rows in table 1). In this case, our findings present major differences between RCP trajectories and further emphasize the importance of better quantifying the role of elevated atmospheric CO₂ on crops (see discussion, section 7).

Our paper fills an important gap in previous assessments of climate change impact on global crop yield by simulating, for the first time at the global scale, effects of extreme heat stress during the crop reproduction phase and an extensive range of future climate scenarios (72) encompassing differences in GHG emissions and GCMs. Table 2 compares key results presented here against other global scale impact assessments. We identified studies using different crop simulation approaches, including the LPJmL model [4], the DSSAT suite of crop models [6, 7] and version 1.0 of PEGASUS [5] under climate change only (referred to in the table as CC_{w/o HSA, CO2}) and CC_w/o HSA scenarios. Table 2 also includes results from a statistical model using historical observed data [33]. PEGASUS 1.1 differs from 1.0 by including an improved interpolation algorithm of monthly climate data to daily values using a weather generator and being sensitive to specific extreme heat stress (see Method section and appendix A). Some studies reported results for each individual crop and some reported multi-crop averages. Effects of HSA in PEGASUS 1.1 lead to more pessimistic outcomes. Importantly, PEGASUS 1.1 produces a wider range of estimated ΔY than any previous study. For instance, impacts on soybean yields may be largely positive or negative even when CO₂ fertilization effects are taken into account. Previous studies listed in table 2 considered only two to four GCMs to drive their crop models, whereas our study, using PEGASUS 1.1, takes into account an ensemble of eighteen GCMs, which increases the range of uncertainties, due to climate model scenarios.

Our results include some important scientific uncertainties and assumptions. First, we use global values of temperature thresholds for HSA for each crop whereas in reality temperature thresholds vary not only among crop types but also among crop cultivars. Second, this analysis omits winter wheat and therefore gives only a partial assessment on total global wheat yield (spring wheat as simulated in PEGASUS accounts for 35% of total wheat harvested area). Third, PEGASUS does not include negative impacts related to crop pest and disease factors, which have yet to be explicitly examined in crop models [1], or crop interactions with pollutants such as ozone, and nutrient–CO₂ interactions. Fourth, our study assumes no adaptation in fertilizer application rates, which does not represent realistic scenarios of future fertilizer application rates. In fact, we constrain our analysis to focus on biophysical aspects of climate impacts without speculating on future developments in the world economy and trade and gain in yield due to improvements in agro-technologies. Adaptation scenarios taking into account future fertilizer application rates would require additional information on economy and trade, which is beyond the scope of this study. Similarly, irrigation scenarios here do not rely on actual water resources available, assuming water is available in irrigated cropland. A more realistic assessment would require linkage to a global water model, which could lead to reductions in irrigated crop yield due to water scarcity. Fifth, CO₂ fertilization effects on crops, which are included here, remain controversial [34–36]. Atmospheric CO₂ concentrations continue to rise rapidly, having recently surpassed 400 parts per million. The potential for CO₂ fertilization effects to alleviate the largely negative impacts of climate change on crops, and ultimately food security, is unclear. Little is known about actual crop response to elevated CO₂ effects in many parts of the world. Current Free-Air CO₂ Enrichment (FACE) experiments [37] have been conducted in temperate climates, principally in the United States and a few in Europe. CO₂ effects in tropical climates could be very different and possibly more sensitive to soil nutrient availability. Differences in the impacts found here with and without CO₂ fertilization highlight the urgency for further study of CO₂ effects on crops across agroecosystems [38]. In addition, elevated CO₂ is expected to reduce C–N ratios in crops, hence reducing the quality of grains by reducing the overall protein content [39]. Although this last point is paramount for global food security, CO₂ effects on grain protein content are omitted from current global crop models. Sixth, monthly temperature series generated within CIAS do not take into account changes in the frequency of extreme temperatures, which would increase risk of HSA. As a result, our simulation results are probably conservative and may underestimate the yield impact of extreme temperatures. Finally, our study uses only one crop model and therefore omits a key source of uncertainty in crop response to changing climate inputs. The need for research into uncertainties associated with different impact models is increasingly recognized [19, 40].

To conclude, our results quantify the importance of extreme weather events on crop yield and confirm regional disparities in climate change impacts. By the 2080s under RCP 8.5, we find strong HSA effects for maize (responsible for up to 45% of global average yield losses under RCP 8.5 by the 2080s relative to the 1980s) and spring wheat (responsible for up to 52% reduction of global average yield gains) and smaller consequences for soybean (responsible for up to 25% reduction of global average yield gains). Future GHG emission pathways are shown here to play an important role in determining future crop production. These results highlight the importance of climate mitigation to avoid important yield impacts. Strong radiative forcing, leading to a large increase in global mean temperature and hence higher extreme temperatures, will impact crops negatively in some of the regions contributing most to global production and across different income countries. The potential effects on global food prices and crop yield reduction in currently food insecure areas represent significant consequences for global food security. The wide range of impacts across regions underscores the need for carefully targeted adaptation responses including breeding and technology programmes for greater crop heat tolerance.

We are particularly grateful to Sudipta Goswami for his technical assistance in generating the climate data and to Tim Osborn and Craig Wallace for providing the latest version of the ClimGen software (http://www.cru.uea.ac.uk/∼timo/climgen/) used in generating the climate change scenario data. Funding was provided by the European Commission Collaborative Project FP7-ENV-2010.4.2.1-1, ERMITAGE, for the provision of the climate data from CIAS, a Tyndall Centre for Climate Change Research doctorate stipend to DD, a Natural Sciences and Engineering Research Council (NSERC) of Canada Discovery Grant to NR, and a Natural Environment Research Council of the United Kingdom fellowship to RW, along with financial support through the ERMITAGE project to JP and RW.

PEGASUS is a light-use efficiency (LUE) type global crop model that integrates, in addition to climate, the effect of planting date decision and cultivar choice, irrigation, and fertilizer application on crop yield for maize, spring wheat and soybean [5]. PEGASUS 1.1 used in this study includes several improvements since version 1.0 to reflect multiple climate change impacts on crop yields. These include the effects of elevated atmospheric CO₂ concentration on photosynthesis rate and transpiration demand, specific heat stress at anthesis and a stochastic weather generator to create daily data from monthly climate inputs.

A.1. CO₂ effect on LUE coefficient

PEGASUS operates at a daily time-step. The LUE model assumes photosynthesis in unstressed conditions is proportional to incoming solar radiation. Additionally, temperature, soil moisture availability, and nutrient availability can limit daily net biomass production ($\mathcal {P}$). $\mathcal {P}$ is expressed in mol C m⁻² s⁻¹ as:

$$\begin{equation}\label {eq.NPP} \mathcal {P} = \varepsilon {\rm APAR} f_T f_{W} f_N \end{equation} \tag{ A.1 }$$

where ε  (mol C mol quanta⁻¹) is the LUE coefficient, APAR (mol quanta m⁻²s⁻¹) represents the daily average absorbed photosynthetically active radiation. f_T, f_W, and f_N are three limiting factors varying between 0 (high stress) and 1 (no stress) of daily mean temperature, daily soil moisture, and soil nutrient status, respectively. ε increases with CO₂ so that:

$$\begin{equation}\label {eq.LUE} \varepsilon = \frac {100 {\rm CO}_2}{{\rm CO}_2 + {\rm e} ^{r1 - r2\cdot {\rm CO}_2}} \end{equation} \tag{ A.2 }$$

where CO₂ is the concentration of carbon dioxide in the atmosphere (ppm), and r1 and r2 are shape coefficients. The shape coefficients are calculated by solving equation (A.2) using two known points (ε_amb, CO_2amb) and (ε_hi, CO_2hi). ε_amb is tuned to simulate present-day global crop yield data at CO_2amb = 380 ppm as in Deryng et al, (2011) [5]. At CO_2hi = 550 ppm, parameters are ε_hi = 1.06 × ε_amb for maize, ε_hi = 1.13 × ε_amb for wheat, and ε_hi = 1.19 × ε_amb for soybean according to free-air CO₂ enrichment (FACE) results [36]:

$$\begin{eqnarray}&&\label {eq.r1} r1 = \ln \Bigg [\frac {{\rm CO}_{2_{\rm amb}}}{0.01\cdot \varepsilon _{\rm amb}} - {\rm CO}_{2_{\rm amb}}\Bigg ] + r2\cdot {\rm CO}_{2_{\rm amb}}\end{eqnarray} \tag{ A.3 }$$

$$\begin{eqnarray} &&\label {eq.r2} r2 = \frac {\ln [\frac {{\rm CO}_{2_{\rm amb}}}{0.01\cdot \varepsilon _{\rm amb}} - {\rm CO}_{2_{\rm amb}}] - \ln [\frac {{\rm CO}_{2_{hi}}}{0.01\cdot \varepsilon _{hi}} - {\rm CO}_{2_{hi}}]}{{\rm CO}_{2_{hi}} - {\rm CO}_{2_{\rm amb}}} \end{eqnarray} \tag{ A.4 }$$

A.2. CO₂ effect on transpiration

The water stress factor f_W [5] depends on daily potential evapotranspiration demand (PET), which is reduced by CO₂ concentration following a similar and simplified approach to Easterling et al [41], also used in the SWAT and EPIC models [42, 43], so that:

$$\begin{equation}\label {eq.PET} {\rm PET} = {\rm PET}_{\rm amb} \times \Bigg (1.5 -0.5 \ \frac {{\rm CO}_2}{{\rm CO}_{2_{\rm amb}}}\Bigg ) \end{equation} \tag{ A.5 }$$

where PET_amb corresponds to PET estimated under CO_2amb. While CO₂ effect on LUE coefficient is crop specific, CO₂ influence on PET is identical for all crops.

A.3. Heat stress at anthesis

Crops are sensitive to extreme temperatures, particularly around the reproductive stage, called anthesis. Following the methodology developed by Challinor et al [16] and used in several other studies [10, 14], PEGASUS' account of extreme temperature stress on crop yield follows three steps:

• (i)  
  estimation of the crop thermal sensitivity period (TSP);
• (ii)  
  identification of an extreme temperature event according to crop specific temperature tolerance threshold;
• (iii)  
  application of a heat stress factor f_HSA on storage organ production, which depends on duration and intensity of the high temperature event.

Crop TSP includes a couple of days before and after anthesis and is estimated as a function of crop growing period length (GPL), which depends on growing degree days accumulation [5] and varies with crop cultivars. Anthesis is scheduled when the number of days since emergence reaches half of crop GPL (calculated between emergence and maturity), i.e., 0.5 GPL; TSP starts a few days before anthesis at 0.45 GPL and ends after anthesis at 0.7 GPL. A high temperature event occurs when daily effective temperature (T_eff) exceeds a critical temperature (T_cr) threshold. Above this threshold, the daily heat stress factor f_HSAd during the TSP is calculated according to:

$$\begin{eqnarray} \label {eq.fHSAd} f_{\rm HSAd} = \left \{ \begin{array}{@{}ll} \displaystyle 1 &\quad\qquad \mbox {if } T_{\rm eff} < T_{\rm cr}\\ \displaystyle 1 - \frac {T_{\rm eff} - T_{\rm cr}} {T_{\rm lim} - T_{\rm cr}} &\quad\qquad \mbox {if }T_{\rm cr} \le T_{\rm eff} < T_{\rm lim}\\ \displaystyle 0 &\quad\qquad \mbox {if }T_{\rm eff}\ge T_{\rm lim} \end{array} \right . \end{eqnarray} \tag{ A.6 }$$

T_eff is defined as (T_mean + T_max)/2, where T_mean is the daily mean temperature and T_max is the daily maximum temperature [44], T_lim is the limit temperature above which f_HSAd is maximal. Crop specific T_cr and T_lim come from a synthesis of values found in the literature [10, 11, 14, 33, 45–49] (table A.1). Temperature tolerance differs for each crop. Here, HSA critical temperature thresholds are 25 °C for spring wheat, 32 °C for maize and 35 °C for soybean. Hence, as temperatures increase spring wheat yield is impacted first, followed by maize and finally soybean. However, HSA impact functions differ among crop type as temperature thresholds at zero pod-set are 35 °C for spring wheat, 45 °C for maize and 40 °C for soybean.

The daily heat stress factor is accumulated and averaged over the TSP so that f_HSA is expressed as:

$$\begin{equation} \label {eq.fHSA} f_{\rm HSA} = \frac {1}{{\rm TSP}} \sum _1^{\rm TSP} f_{\rm HSAd} \end{equation} \tag{ A.7 }$$

Finally, crop yield (Y in t Ha⁻¹) affected by HSA is expressed as:

$$\begin{equation} \label {eq.Y} Y = \frac {{\rm EF}}{{0.45\ {\rm DF}}} C_{so} \times f_{\rm HSA} \end{equation} \tag{ A.8 }$$

where C_so represents the amount of dry carbon accumulated in the storage organs at harvesting date, EF is the economic fraction of the storage organs, DF is the dry fraction of the economic yield to convert weight of dry matter to weight of fresh matter, and 0.45 is the mass of carbon contained in one unit of dry matter [5].

Table A.1.  Temperature critic (T_cr) and limit (T_lim) (in °C) for maize, wheat and soybean used in this study (PEGASUS 1.1) and corresponding values found in the literature.

	Maize		Wheat		Soybean
Reference	Tcr (°C)	Tlim (°C)	Tcr (°C)	Tlim (°C)	Tcr (°C)	Tlim (°C)
PEGASUS 1.1	32	45	25	35	35	40
Lobell et al (2013) [8]	30
Moriondo et al (2011) [10]	31	40
Semenov and Shewry (2011) [11]			27
Teixeira et al (2011) [14]	35	45	27	40	35	40
Thuzar et al (2010) [45]					34
Modhej et al (2008) [46]			22
Spiertz et al (2006) [47]			25
Porter and Gawith (1999) [48]			24	31
Ferris et al (1998) [49]			25	35

B.1. CIAS

B.2. RCPs

B.3. MAGICC

B.4. ClimGEN

B.5. Weather generator