Deepak K. RaypersName, James S. GerberpersName, Graham K. MacDonaldpersName, Paul C. WestpersName (2015date). “Climate variation explains a third of global crop yield variability..” Nature Communicationstitle·j.
Object of study — the share of year-to-year maizeterm·key, riceterm·key, wheatterm·key and soybeanterm·key yield variabilityterm·dom explained by climate variabilityterm·dom
Research question — how much of the year-to-year variability in crop yieldsterm·key is associated with climate variations
Contribution — global maps at ~13,500 political units of how much and which climate variabilityterm·dom explains yield variabilityterm·dom
phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | climate variability explaining about a third of global crop yield variability — “Globally, climate variability accounts for roughly a third (~32–39%) of the observed yield variability.” | |
| claim-type | existence — “Globally, climate variability accounts for roughly a third (~32–39%) of the observed yield variability.” | |
| method — evidence | — “To examine how observed variations in yields were related to climate variations, we used the Climate Research Unit’s (CRU) 18 gridded monthly data, and then re-mapped the data to the ~13,500 political units where yield was measured.” | |
| object of study — evidence | — “We use detailed crop statistics time series for ~13,500 political units to examine how recent climate variability led to variations in maize, rice, wheat and soybean crop yields worldwide.” | |
| research question — evidence | — “In this study, we ask how much of the year-to-year variability in observed crop yields is associated with variations in climate across global croplands?” | |
| contribution — evidence | — “We use detailed crop statistics time series for ~13,500 political units to examine how recent climate variability led to variations in maize, rice, wheat and soybean crop yields worldwide.” | |
| mechanism | irrigation shifts sensitivity to temperature Where rice is irrigated, as in Japan, temperature variability matters more than precipitation variability. — “In Japan almost all the paddy rice crop is irrigated 22 , 26 and hence temperature variability was more important compared with precipitation variability.” | mechanisms[0] |
| mechanism | farmer adaptation Farmers adapted to climate change are also more adapted to variability, lowering explained variance. — “This was because farmers are already adapted, or adapting, to climate change 47 , which has made them also more adapted to variability.” | mechanisms[1] |
| sense | normal vs extreme climate variation - linear terms model normal variation, squared terms extreme variation — “Here, linear and squared terms represent normal and extreme variation, respectively, for example 1 , 5 , 16 .” | senses[0] |
| sense | coefficient of variation - yield s.d. divided by mean yield per political unit — “In general the coefficient of variation, or yield variability normalized by mean yields ( Fig. 1 ), has been lower in the top crop production regions of the world on account of their higher yields ( Supplementary Fig. 1 ) and conversely higher in the areas of lower yields and of less consequence to global crop production but exceptions such as the Australian wheat belt exist.” | senses[1] |
| relation | CRU —same-as→ Climate Research Unit — ( ) — “To examine how observed variations in yields were related to climate variations, we used the Climate Research Unit’s (CRU) 18 gridded monthly data, and then re-mapped the data to the ~13,500 political units where yield was measured.” — “the Climate Research Unit’s (CRU) 18 gridded monthly data” | concept_edges[0] |
| weight | CRU —same-as→ Climate Research Unit — 0.95 — “To examine how observed variations in yields were related to climate variations, we used the Climate Research Unit’s (CRU) 18 gridded monthly data, and then re-mapped the data to the ~13,500 political units where yield was measured.” | concept_edges[0] |
| relation | AIC —same-as→ Akaike Information Criterion — ( ) — “We first identified which functional form of Y c = f ( T c , P c ) from the set of 27 equations at each political unit fit the data best using the Akaike Information Criterion (AIC), which penalizes equations with more terms.” — “the Akaike Information Criterion (AIC)” | concept_edges[1] |
| weight | AIC —same-as→ Akaike Information Criterion — 0.95 — “We first identified which functional form of Y c = f ( T c , P c ) from the set of 27 equations at each political unit fit the data best using the Akaike Information Criterion (AIC), which penalizes equations with more terms.” | concept_edges[1] |
| relation | low-yield variability —causes→ stable farmer incomes — leads to — “In particular, low-yield variability leads to stable farmer incomes 8 , 9 , 10 and food supply 1 , 11 , and prevents price spikes that have disproportionate adverse impacts on the globally food-insecure who are mostly farmers 12 , 13 .” — “low-yield variability leads to stable farmer incomes” | concept_edges[2] |
| weight | low-yield variability —causes→ stable farmer incomes — 0.75 — “In particular, low-yield variability leads to stable farmer incomes 8 , 9 , 10 and food supply 1 , 11 , and prevents price spikes that have disproportionate adverse impacts on the globally food-insecure who are mostly farmers 12 , 13 .” | concept_edges[2] |
| effect direction | continental climate —causes→ temperature variability — increases — “This is because of the continental climate of Eastern Europe, which causes a greater amplitude of temperature variability 44 .” — “causes a greater amplitude of temperature variability” | concept_edges[3] |
| relation | continental climate —causes→ temperature variability — causes — “This is because of the continental climate of Eastern Europe, which causes a greater amplitude of temperature variability 44 .” — “the continental climate of Eastern Europe, which causes a greater amplitude of temperature variability” | concept_edges[3] |
| weight | continental climate —causes→ temperature variability — 0.75 — “This is because of the continental climate of Eastern Europe, which causes a greater amplitude of temperature variability 44 .” | concept_edges[3] |
| relation | extreme temperature variability —contrasted-with→ extreme precipitation variability — whereas — “In the upper and eastern Midwest of the United States and Canada extreme temperature variability was more important, whereas in the central and western parts of Midwestern U.S. extreme precipitation variability explained maize yield variability in more counties ( Fig. 3a );” — “extreme temperature variability was more important, whereas in the central and western parts of Midwestern U.S. extreme precipitation variability” | concept_edges[4] |
| weight | extreme temperature variability —contrasted-with→ extreme precipitation variability — 0.75 — “In the upper and eastern Midwest of the United States and Canada extreme temperature variability was more important, whereas in the central and western parts of Midwestern U.S. extreme precipitation variability explained maize yield variability in more counties ( Fig. 3a );” | concept_edges[4] |
| replication | original | |
| no type for this | climate variability → yield variability — climate variability statistically accounts for about a third of yield variability - an explained-variance relation, not an intervention — “Globally, climate variability accounts for roughly a third (~32–39%) of the observed yield variability.” | unhoused_relations[0] |
| limitation | Political-unit resolution may underestimate climate impacts at specific locations. — “For example, our estimation of crop yield variability due to climate variability may underestimate the importance of climate variability impacts at specific locations within political units.” | limitations[0] |
| limitation | Cloud cover, wind, ozone, timing of heat stress and soil moisture are not considered. — “Our study does not consider factors such as changing cloud cover (and solar radiation), wind speed, surface ozone exposure 56 , or decomposed the basic climate variables of temperature and precipitation further into the timing of heat stress 57 , the timing of dry and wet spells 58 , or soil moisture 59 .” | limitations[1] |
| limitation | The static crop calendar cannot capture changed harvest frequency. — “Climate change may also have influenced how frequently crops are harvested 62 , 63 , for example, now allowing double cropping in hitherto colder single cropped regions, but we were unable to include such precision as the only globally available crop calendar 64 was static, even though we updated it using the most recent information available (see Supplementary Fig. 6 ).” | limitations[2] |
| limitation | Climate variability is not the only controlling factor of yield variability. — “While climate variability is a significant factor and responsible for 32–39% of global crop yield variability, it is certainly not the only controlling factor 55 .” | limitations[3] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | Climate variability accounts for roughly a third of global yield variability. — “Globally, climate variability accounts for roughly a third (~32–39%) of the observed yield variability.” | content_tags.findings[0] |
| finding | In substantial breadbasket areas climate explains over 60% of yield variability. — “While some areas show no significant influence of climate variability, in substantial areas of the global breadbaskets, >60% of the yield variability can be explained by climate variability.” | content_tags.findings[1] |
| finding | Most harvesting regions show a climate influence on yields. — “However, the vast majority of crop harvesting regions did experience the influence of climate variability on crop yields: ~70% of maize harvesting regions, ~53% of rice harvesting regions, ~79% of wheat harvesting regions and ~67% of soybean harvesting regions.” | content_tags.findings[2] |
| finding | Climate explains ~41% of maize yield variability in the major grain belts. — “In these major maize grain belts, ~41% of the total year-to-year yield variability (0.8 tons/ha/year) was explained by inter-annual climate variability.” | content_tags.findings[3] |
| finding | Climate explains ~32% of rice yield variability globally. — “Year-to-year climate variability explains ~32% of rice yield variability globally ( Fig. 2b ) with precipitation variability explaining more of the variability in South Asia and temperature variability more of the variability in Southeast and East Asia ( Fig. 3b and Supplementary Figs 2 and 3 ).” | content_tags.findings[4] |
| finding | Climate explains ~35% of wheat yield variability globally. — “Averaged globally, climate variability explained ~35% of the wheat yield variability.” | content_tags.findings[5] |
| finding | Climate-driven maize variability equals about 22 million tons of annual global production. — “For example, ~39% of the maize yield variability of 0.6 tons/ha/year explained by climate variability over 94 million ha translates into an annual fluctuation of ~22 million tons in global maize production over the study period.” | content_tags.findings[6] |
| finding | Gridded and station-based analyses correlate significantly. — “We found statistically significant correlation ( r =0.54; P =0.001) between analyses conducted by the two different data sets.” | content_tags.findings[7] |
| quantity | ~32–39% — — “Globally, climate variability accounts for roughly a third (~32–39%) of the observed yield variability.” | content_tags.quantities[0] |
| quantity | ~13,500 — — “We use detailed crop statistics time series for ~13,500 political units to examine how recent climate variability led to variations in maize, rice, wheat and soybean crop yields worldwide.” | content_tags.quantities[1] |
| quantity | ~0.9 tons/ha/year (~22%) — — “Over the last three decades, maize yields had a global average variability of ~0.9 tons/ha/year (s.d.), which corresponds to ~22% of the global average yields of ~4 tons/ha/year ( Supplementary Fig. 1 ).” | content_tags.quantities[2] |
| quantity | ~22 million tons — — “For example, ~39% of the maize yield variability of 0.6 tons/ha/year explained by climate variability over 94 million ha translates into an annual fluctuation of ~22 million tons in global maize production over the study period.” | content_tags.quantities[3] |
| quantity | r =0.54; P =0.001 — — “We found statistically significant correlation ( r =0.54; P =0.001) between analyses conducted by the two different data sets.” | content_tags.quantities[4] |
| quantity | 27 — — “To avoid over-fitting we limited our analysis to a total of 27 combinations of climate variables, resulting in 27 regression equations, to capture the relationships between climate variability and crop yield variability at each political unit and of the basic form:” | content_tags.quantities[5] |
| variable | yield variability — “Globally, climate variability accounts for roughly a third (~32–39%) of the observed yield variability.” | content_tags.variables[0] |
| variable | climate variability — “Globally, climate variability accounts for roughly a third (~32–39%) of the observed yield variability.” | content_tags.variables[1] |
| definition | coefficient of variation — “In general the coefficient of variation, or yield variability normalized by mean yields ( Fig. 1 ), has been lower in the top crop production regions of the world on account of their higher yields ( Supplementary Fig. 1 ) and conversely higher in the areas of lower yields and of less consequence to global crop production but exceptions such as the Australian wheat belt exist.” | content_tags.definitions[0] |
| key-terms | climate variability, crop yields, maize, rice, wheat, soybean, food security, breadbaskets, precipitation, detrended |
| concept | climate variability — not defined in this paper's own words; year-to-year variation in growing-season and annual temperature and precipitation — “Globally, climate variability accounts for roughly a third (~32–39%) of the observed yield variability.” | concepts[0] |
| concept | yield variability — not defined in this paper's own words; year-to-year variation in detrended crop yields — “Globally, climate variability accounts for roughly a third (~32–39%) of the observed yield variability.” | concepts[1] |
| concept | coefficient of variation — yield variability normalized by mean yields — “In general the coefficient of variation, or yield variability normalized by mean yields ( Fig. 1 ), has been lower in the top crop production regions of the world on account of their higher yields ( Supplementary Fig. 1 ) and conversely higher in the areas of lower yields and of less consequence to global crop production but exceptions such as the Australian wheat belt exist.” | concepts[2] |
| concept | CRU — Climate Research Unit — “To examine how observed variations in yields were related to climate variations, we used the Climate Research Unit’s (CRU) 18 gridded monthly data, and then re-mapped the data to the ~13,500 political units where yield was measured.” | concepts[3] |
| concept | Climate Research Unit — not defined in this paper's own words; the source of the gridded monthly climate data — “To examine how observed variations in yields were related to climate variations, we used the Climate Research Unit’s (CRU) 18 gridded monthly data, and then re-mapped the data to the ~13,500 political units where yield was measured.” | concepts[4] |
| concept | AIC — Akaike Information Criterion — “We first identified which functional form of Y c = f ( T c , P c ) from the set of 27 equations at each political unit fit the data best using the Akaike Information Criterion (AIC), which penalizes equations with more terms.” | concepts[5] |
| concept | Akaike Information Criterion — penalizes equations with more terms — “We first identified which functional form of Y c = f ( T c , P c ) from the set of 27 equations at each political unit fit the data best using the Akaike Information Criterion (AIC), which penalizes equations with more terms.” | concepts[6] |
| concept | low-yield variability — not defined in this paper's own words; stable year-to-year yields — “In particular, low-yield variability leads to stable farmer incomes 8 , 9 , 10 and food supply 1 , 11 , and prevents price spikes that have disproportionate adverse impacts on the globally food-insecure who are mostly farmers 12 , 13 .” | concepts[7] |
| concept | stable farmer incomes — not defined in this paper's own words; farm income that does not swing year to year — “In particular, low-yield variability leads to stable farmer incomes 8 , 9 , 10 and food supply 1 , 11 , and prevents price spikes that have disproportionate adverse impacts on the globally food-insecure who are mostly farmers 12 , 13 .” | concepts[8] |
| concept | continental climate — not defined in this paper's own words; the climate type of Eastern Europe — “This is because of the continental climate of Eastern Europe, which causes a greater amplitude of temperature variability 44 .” | concepts[9] |
| concept | temperature variability — not defined in this paper's own words; year-to-year variation in temperature — “This is because of the continental climate of Eastern Europe, which causes a greater amplitude of temperature variability 44 .” | concepts[10] |
| concept | extreme temperature variability — not defined in this paper's own words; variation captured by squared temperature terms — “In the upper and eastern Midwest of the United States and Canada extreme temperature variability was more important, whereas in the central and western parts of Midwestern U.S. extreme precipitation variability explained maize yield variability in more counties ( Fig. 3a );” | concepts[11] |
| concept | extreme precipitation variability — not defined in this paper's own words; variation captured by squared precipitation terms — “In the upper and eastern Midwest of the United States and Canada extreme temperature variability was more important, whereas in the central and western parts of Midwestern U.S. extreme precipitation variability explained maize yield variability in more counties ( Fig. 3a );” | concepts[12] |
| F-test F | as written: F -tests — “Next we selected the ‘best-fit’ model, and then conducted F -tests to determine the goodness-of-fit of the selected model against the null model that assumes random climate variability.” | content_tags.statistics[0] |
| Akaike information criterion AIC | as written: Akaike Information Criterion (AIC) — “We first identified which functional form of Y c = f ( T c , P c ) from the set of 27 equations at each political unit fit the data best using the Akaike Information Criterion (AIC), which penalizes equations with more terms.” | content_tags.statistics[1] |
Full text — tagged
Climate variation explains a third of global crop yieldterm·key variability.
Abstract Many studies have examined the role of mean climate change in agriculture, but an understanding of the influence of inter-annual climate variations on crop yieldsterm·key in different regions remains elusive. We use detailed crop statistics time series for ~13,500 political units to examine how recent climate variabilityterm·dom led to variations in maizeterm·key, riceterm·key, wheatterm·key and soybeanterm·key crop yieldsterm·key worldwide. While some areas show no significant influence of climate variabilityterm·dom, in substantial areas of the global breadbasketsterm·key, >60% of the yield variabilityterm·dom can be explained by climate variabilityterm·dom. Globally, climate variabilityterm·dom accounts for roughly a third (~32–39%) of the observed yield variabilityterm·dom. Our study uniquely illustrates spatial patterns in the relationship between climate variabilityterm·dom and crop yieldterm·key variability, highlighting where variations in temperature, precipitationterm·key or their interaction explain yield variabilityterm·dom. We discuss key drivers for the observed variations to target further research and policy interventions geared towards buffering future crop production from climate variabilityterm·dom.
How mean historical and future climate change affects crop yieldsterm·key has received a great deal of attention 1 , 2 , 3 , 4 , 5 . However, how variations in climate impact crop yieldterm·key, and how they vary over time, has received less attention 6 , 7 . This is important both to help us understand how climate and crop yieldsterm·key are linked over time and also for ensuring future food securityterm·key. In particular, low-yield variabilityterm·dom leads to stable farmer incomesterm·dom 8 , 9 , 10 and food supply 1 , 11 , and prevents price spikes that have disproportionate adverse impacts on the globally food-insecure who are mostly farmers 12 , 13 . In this study, we ask how much of the year-to-year variability in observed crop yieldsterm·key is associated with variations in climate across global croplands? Further, we investigate which climatic variables—those related to warmth and growing season length, or those related to rainfall and moisture availability—best explain variations in yield across the world?
Previous analyses that have examined how crop yieldsterm·key and climate were related 3 , 14 , 15 , 16 , 17 have typically used national and regional data. For example, global studies are typically at the country scale 1 , and provide little insight on the spatial patterns of the within-country impacts. In contrast, analysis at the subnational 16 , sub-subnational 2 or local sites is available for specific countries only, and thus, provide little insight on global patterns. Our study uses newly available temporal geospatial data on crop harvested area and yields of four major crops (maizeterm·key, riceterm·key, wheatterm·key and soybeanterm·key) across 13,500 different political units of the world 12 , 13 —a major (>50x) increase in the level of spatial detail from previous analyses that examined how crop yieldsterm·key and climate were related 3 , 14 , 15 , 16 , 17 . Similar to other studies 1 , 2 , we examine the recent historical period (1979–2008) but across these 13,500 different political units of the world 12 , 13 . The increased spatial resolution helps to identify where, and how strongly, climate variabilityterm·dom is correlated with variations in crop yieldterm·key in each of these political units. Given multiple breadbasketsterm·key across the globe and globally traded commodities, our study provides a consistent investigation of the differences both within and across regions.
To examine how observed variations in yields were related to climate variations, we used the Climate Research Unitterm’s (CRUterm) 18 gridded monthly data, and then re-mapped the data to the ~13,500 political units where yield was measured. We explored a range of statistical models relating observed de-trended variations in temperature and precipitationterm·key during a crop’s growing season and annual conditions to the observed de-trended variations in yields at each political unit. Next we selected the ‘best-fit’ model, and then conducted F -teststerm·stat to determine the goodness-of-fit of the selected model against the null model that assumes random climate variabilityterm·dom. We conducted this analysis at each of the tracked 13,500 political units to draw conclusions on how much of the crop yieldterm·key variability was explained by climate variabilityterm·dom.
Different aspects of climate variabilityterm·dom—temperature, precipitationterm·key, and the interaction of the two—may affect crop growth and resultant productivity disproportionately. We classified how yield variabilityterm·dom was related to either normal or extreme fluctuations in temperature or precipitationterm·key variability—or their interactions. Here, linear and squared terms represent normal and extreme variation, respectively, for example 1 , 5 , 16 . The ‘best-fit’ model at each political unit was classified into one of seven broad categories and then mapped globally: models where the yield variabilityterm·dom was explained by (i) normal temperature or (ii) normal precipitationterm·key variations, but not both; models where the yield variabilityterm·dom was explained by (iii) normal and extreme temperature or (iv) normal and extreme precipitationterm·key variations, but not both; (v) where yield variabilityterm·dom was explained by extreme temperature or (vi) extreme precipitationterm·key variations, but not both; and (vii) temperature and precipitationterm·key terms and their combinations due to interactions between temperature and precipitationterm·key. We further developed reduced models of temperature and precipitationterm·key and mapped them at each political unit. The resulting global maps, which identify where and to what degree normal and extreme climate variabilityterm·dom explains yield variabilityterm·dom, and quantifies them, can be used to target research into causal relations between yield and climate variabilityterm·dom, and eventually policy interventions to stabilize farmer incomes and food supply.
Averaged globally over areas with significant relationships, we find that 32–39% of the maizeterm·key, riceterm·key, wheatterm·key and soybeanterm·key year-to-year yield variabilityterm·dom was explained by climate variabilityterm·dom. This translates into climate explained annual production fluctuations of ~22 million tons, ~3 million tons, ~9 million tons and ~2 million tons for maizeterm·key, riceterm·key, wheatterm·key and soybeanterm·key, respectively. Our spatially detailed assessment of the relationship between climate variabilityterm·dom and yield variabilityterm·dom shows distinct spatial patterns in the relative effects of temperature, precipitationterm·key and their interaction within and across regions.
Results Yield variabilityterm·dom We first establish where and by how much crop yieldsterm·key varied within countries and then identify how much of the year-to-year variation in crop yieldsterm·key was explained by year-to-year variations in climate.
In general the coefficient of variationterm·mth, or yield variabilityterm·dom normalized by mean yields ( Fig. 1 ), has been lower in the top crop production regions of the world on account of their higher yields ( Supplementary Fig. 1 ) and conversely higher in the areas of lower yields and of less consequence to global crop production but exceptions such as the Australian wheatterm·key belt exist. Over the last three decades, maizeterm·key yields had a global average variability of ~0.9 tons/ha/year (s.d.), which corresponds to ~22% of the global average yields of ~4 tons/ha/year ( Supplementary Fig. 1 ). The highest coefficient of variationterm·mth—which indicates greatest relative variability—in maizeterm·key yields was in areas outside the core maizeterm·key grain belts, including northeastern Brazil and in parts of Africa, India, northeast Mexico and the southeast United States ( Fig. 1 ). The global average riceterm·key yield variabilityterm·dom (standard deviation) was ~0.5 tons/ha/year (or ~13% of average riceterm·key yields). The coefficient of variationterm·mth in riceterm·key yields was similarly higher in more marginal rice-producing regions such as northeastern Brazil and central India. In contrast, some wheatterm·key regions with high coefficient of variationterm·mth in yields such as in Australia and the Great Plains states of the United States (U.S.) are key global wheatterm·key breadbasketsterm·key ( Fig. 1 ). The global average wheatterm·key yield variabilityterm·dom (s.d.) was 0.4 tons/ha/year (~17% of average yields over the study period). In the top soybeanterm·key production areas of the world such as in the Midwestern U.S. and Latin American countries, the coefficient of variationterm·mth was low.
Coefficient of variationterm·mth of crop yieldsterm·key over the entire study period. The ratio of the s.d. of yield over the 30-year period to the average yield over the same period. ( a ) maizeterm·key, ( b ) riceterm·key, ( c ) wheatterm·key, ( d ) soybeanterm·key (sample size of ~13,500 political units × 30 years per crop). White areas indicate where the crop is not harvested or analysed. Details on crop yieldsterm·key are given in reference 13 .
Climate explained yield variabilityterm·dom Not all crop growing regions showed statistically significant influence of year-to-year variations in climate on crop yieldterm·key variability as determined from conducting F -teststerm·stat (using a threshold of P =0.1; ~13,500 political units × 30 years sample size, Fig. 2 ). However, the vast majority of crop harvesting regions did experience the influence of climate variabilityterm·dom on crop yieldsterm·key: ~70% of maizeterm·key harvesting regions, ~53% of riceterm·key harvesting regions, ~79% of wheatterm·key harvesting regions and ~67% of soybeanterm·key harvesting regions. The percentage of global total average production harvested over these regions and thus influenced by climate variabilityterm·dom was ~78% of maizeterm·key, ~52% of riceterm·key, ~75% of wheatterm·key and ~67% of soybeanterm·key. In specific locations, within the top global crop production regions, climate variabilityterm·dom accounted for >60% of the variability in a crop’s yield, though there were also political units where climate impacts have been statistically insignificant ( Fig. 2 ). Where and how much of a crop’s yield varied on account of climate has been highly location- and crop–specific, and we describe this in greater detail in the subsequent sections.
Total crop yieldterm·key variability explained due to climate variabilityterm·dom over the last three decades. A value of 1.0 implies that the entire variability in observed yields was explained by climate variabilityterm·dom (coefficient of determination metric; sample size of ~13,500 political units × 30 years per crop). Similarly a value of 0.30–0.45 implies 30–45% of the variability in yields was explained by climate variabilityterm·dom. We cutoff the range at 0.75 (or 75%) and above to a single categorical colour. No effect implies that at the P =0.10 level, there was no statistical difference between the best fit model and the null model in the political unit. White areas indicate where the crop is not harvested or analysed. ( a ) maizeterm·key, ( b ) riceterm·key, ( c ) wheatterm·key, ( d ) soybeanterm·key.
Averaged globally over areas with significant relationships, we find that 32–39% of the maizeterm·key, riceterm·key, wheatterm·key and soybeanterm·key year-to-year yield variabilityterm·dom was explained by climate variabilityterm·dom ( Supplementary Data ). Climate variabilityterm·dom in general explains riceterm·key yield variabilityterm·dom the least.
Regional variations in maizeterm·key Approximately 75% of the global maizeterm·key production is concentrated in ~57% of the harvested areas comprising the American Midwestern region, central Mexico, southern Brazil, the maizeterm·key belts of Argentina and China, parts of Western Europe and South Africa, and some areas of India and Indonesia. In these major maizeterm·key grain belts, ~41% of the total year-to-year yield variabilityterm·dom (0.8 tons/ha/year) was explained by inter-annual climate variabilityterm·dom. Approximately 50% of global maizeterm·key production is concentrated in a proportionally even smaller ~31% of high yielding maizeterm·key belt comprising primarily two regions—the American Midwest and the Chinese Corn Belt—and in these two regions ~42% of the corresponding yield variabilityterm·dom (0.9 tons/ha/year) was explained by climate variabilityterm·dom.
In some specific political units within these maizeterm·key breadbasketsterm·key, more than 60% of the yield variabilityterm·dom has historically been related to climate variabilityterm·dom including numerous counties of the U.S. Midwestern states, and in Shanxi, Hebei and Shandong provinces of China ( Fig. 2a ); political units with >75% of the yield variabilityterm·dom explained by climate are also present, for example, many counties of Midwestern U.S.
When averaged over all the statistically significant maizeterm·key harvested areas with climate variabilityterm·dom impacts globally 39% of the yield variabilityterm·dom was explained and in the top ten global maizeterm·key producing nations we find the following ( Supplementary Data ): in the United States, France and Italy 41–49% of the observed maizeterm·key yield variabilityterm·dom can be explained by climate variabilityterm·dom, whereas in South Africa it was ~50%, and in Argentina and China it was 32 and 44%, respectively ( Fig. 2a and see Supplementary Data ).
In the upper and eastern Midwest of the United States and Canada extreme temperature variabilityterm·dom was more important, whereas in the central and western parts of Midwestern U.S. extreme precipitation variabilityterm·dom explained maizeterm·key yield variabilityterm·dom in more counties ( Fig. 3a ); overall temperature variabilityterm·dom was more important for explaining maizeterm·key yields in the upper and eastern Midwest of the United States and precipitationterm·key variability was more important in the central and western Midwest ( Supplementary Figs 2 and 3 ). Temperature variabilityterm·dom influenced maizeterm·key yield variabilityterm·dom more in some colder countries such as in Canada, but also in some warmer countries such as Spain and Italy with within-country variations.
Selected models explaining crop yieldterm·key variability classified into seven categories of temperature and precipitationterm·key variations. White areas indicate where the crop is not harvested or analysed. ( a ) maizeterm·key, ( b ) riceterm·key, ( c ) wheatterm·key, ( d ) soybeanterm·key. Regions where models with only normal temperature (T) terms are selected are shown in yellow colour; regions where models with normal and extreme temperature (T 2 ) terms are selected are shown in tan colour; regions where models with only extreme temperature terms are selected are shown in red colours. Similarly, regions where models with normal, normal and extreme, and only extreme precipitationterm·key (P) terms are selected are shown in the maps with different shades of blue. Regions where models with both temperature, precipitationterm·key and their interactions terms were selected are shown in purple colour.
Regional variations in riceterm·key Approximately 75% of global riceterm·key production was from China, India and Indonesia. Averaged over all rice-harvesting areas with statistically significant climate influence (around 52% of global riceterm·key harvested areas), we estimate that yields have varied by ~0.1 tons/ha/year. Year-to-year climate variabilityterm·dom explains ~32% of riceterm·key yield variabilityterm·dom globally ( Fig. 2b ) with precipitationterm·key variability explaining more of the variability in South Asia and temperature variabilityterm·dom more of the variability in Southeast and East Asia ( Fig. 3b and Supplementary Figs 2 and 3 ). In some key riceterm·key producing nations, however, climate variabilityterm·dom was more important: in 80% of the riceterm·key harvested areas in Japan climate variabilityterm·dom was statistically significant. Averaged over these areas we find that ~79% of the riceterm·key yield variabilityterm·dom (~0.2 tons/ha/year) was explained, whereas, in South Korea, ~47% of the yield variabilityterm·dom was explained by climate variabilityterm·dom ( Fig. 2b ). In both countries temperature variabilityterm·dom was more important ( Supplementary Figs 2 and 3 ). In India, China, Indonesia, Thailand, Brazil, Cambodia, Peru and Spain, 25–38% of the yield variabilityterm·dom was explained by climate variabilityterm·dom ( Supplementary Data ). As with maizeterm·key, there are specific regions where >60% of yield variabilityterm·dom was explained by climate variabilityterm·dom such as in the central Indian states of Madhya Pradesh, Chhattisgarh and Karnataka ( Fig. 2b ).
Regional variations in wheatterm·key Approximately 75% of global wheatterm·key production came from ~66% of the harvested lands in the United States, Canada, Argentina, Europe, North Africa, India, China and Australia. In these highly productive wheatterm·key belts, ~36% of the year-to-year yield variabilityterm·dom was explained by climate variabilityterm·dom ( Fig. 2c ). Approximately 34–45% of the wheatterm·key yield variabilityterm·dom in the United States, Canada, United Kingdom, Turkey, Australia and Argentina was explained by climate variabilityterm·dom. To give an indication of the magnitude of this effect, the climate driven variability in the United States wheatterm·key yields equates to, on average, more than half the entire annual production of wheatterm·key in Mexico.
In the more productive regions of some countries the variability explained by climate was even higher. In the most productive Australian wheatterm·key belt (among the top 50% of global wheatterm·key producers) climate variabilityterm·dom explained ~43% of the total yield variabilityterm·dom and in parts of Western Australia it was > 60%. In Western Europe in the United Kingdom, France, Germany, Spain and Italy, climate variabilityterm·dom explained ~31–51% of the wheatterm·key yield variabilityterm·dom. In Eastern Europe and the former Soviet Republics such as the Russian Federation, Ukraine, Kazakhstan and in Hungary, 23–66% of the wheatterm·key yield variabilityterm·dom was explained by climate variabilityterm·dom and normal and extremes of temperature variabilityterm·dom was important ( Fig. 3c ). Although temperature variabilityterm·dom in Western Europe was in general more important, precipitationterm·key variability also explained part of the wheatterm·key yield variabilityterm·dom with the exception of Spain where precipitationterm·key variability was the dominant factor ( Fig. 3c and Supplementary Figs 2 and 3 ). In India and China, the top two global wheatterm·key producers, we detected statistically significant relationships in 71 and 62% of their wheatterm·key harvested lands and on average 32 and 31% of yield variabilityterm·dom, respectively, was explained by climate variabilityterm·dom. In China precipitationterm·key variability explained most of the variability; in India temperature and precipitationterm·key variability were equally important ( Fig. 3c ). Averaged globally, climate variabilityterm·dom explained ~35% of the wheatterm·key yield variabilityterm·dom.
Regional variations in Soybeanterm·key Approximately 50% of the world’s total soybeanterm·key production was harvested from ~42% of the land concentrated in only three countries: the United States, Brazil and Argentina. Adding soybeanterm·key lands in India and China made up 75% of the top soybeanterm·key production global areas. In general, the variability in soybeanterm·key yield related to climate variabilityterm·dom was higher in Argentina (~43% of yield variabilityterm·dom of 0.5 tons/ha/year averaged over all areas with statistically significant climate influence, but ~47% when averaged over the most productive areas), followed by ~36% of the yield variabilityterm·dom explained over all the statistically significant U.S. soybeanterm·key areas. Approximately 26–34% of the yield variabilityterm·dom in Brazilian, Indian and Chinese soybeanterm·key yields was explained by climate variabilityterm·dom with locations of substantially higher variability explained present in all countries ( Fig. 2d ).
Discussion We show how much of the year-to-year variability in crop yieldsterm·key was associated with climate variabilityterm·dom within and across regions. As the demand for crops increases globally 19 and productivity gains fail to keep pace with projected demands 12 , ensuring the stability of national food supplies and farmer livelihoods to variable production will be even more important. Low global food stocks in conjunction with fluctuation in agricultural production can, in particular, contribute to food price spikes 20 , 21 . Regions with high crop yieldterm·key variability would disproportionately contribute to this effect especially if they are also the major breadbasketsterm·key of the world 20 , 21 . Even in regions with comparatively lower yields, fluctuations in crop production may impact the local food securityterm·key. Our study is unique in giving a global spatially detailed account of where and by how much crop yieldsterm·key have varied and how much of this was driven by climate variabilityterm·dom.
We found that there were numerous regions where climate variabilityterm·dom explained more than 60% of the yield variabilityterm·dom in maizeterm·key, riceterm·key, wheatterm·key and soybeanterm·key ( Fig. 2 ). Many of these regions were in the most productive global areas such as Midwestern U.S. and the Chinese Corn Belt for maizeterm·key, and Western Europe and Australia for wheatterm·key.
Our study identifies unique spatial patterns in the effects of temperature and/or precipitationterm·key variability on yields—for example, riceterm·key and wheatterm·key in India ( Fig. 3b,c ) as well as maizeterm·key and soybeanterm·key in the United States ( Fig. 3a,d ). Our simple classification of the prevailing relationships between climate and crop yieldsterm·key enables digging deeper into trends for particular regions. While relatively high resolution compared with past research our results are constrained by the resolution of the data, which is at the political unit and monthly climate data. Within political units, at specific field/subnational locations, the climate variabilityterm·dom impact could be higher or lower.
The 32–39% of the yield variabilityterm·dom explained by climate variabilityterm·dom translates into large fluctuations in global crop production. For example, ~39% of the maizeterm·key yield variabilityterm·dom of 0.6 tons/ha/year explained by climate variabilityterm·dom over 94 million ha translates into an annual fluctuation of ~22 million tons in global maizeterm·key production over the study period. Similar climate variabilityterm·dom driven average annual riceterm·key, wheatterm·key and soybeanterm·key production variability is ~3, 9 and 2 million tons, respectively. These average fluctuations are similar to the total maizeterm·key production of many Latin American and African countries or the total riceterm·key production of some Asian countries or total wheatterm·key production of some Eastern European countries. In some cases the impact of climate variabilityterm·dom is higher in poorer regions such as in northeastern Brazil for maizeterm·key, and Central India for riceterm·key. However, even in the most productive global areas such as wheatterm·key in Western Europe and maizeterm·key in the United States Midwest the influence of climate variabilityterm·dom on yield variabilityterm·dom is very high and in specific political units >75%. The following section discusses our regional and continental findings in the context of previous smaller-scale research, which we use to help validate/corroborate our results and explore possible drivers.
In the North China Plains (provinces of Hebei, Henan, Shandong, Beijing, Tianjin and Shanxi) though crops are irrigated 22 , water availability is a major problem 23 . Maizeterm·key is a summer crop in this region and monsoonal rainfall supplements river and groundwater irrigation. High growing season temperature is common. Hence, both the temperature and precipitationterm·key variability controls maizeterm·key yield variabilityterm·dom in the North China plains. To the westpersName of the North China Plains, in the more arid Loess Plateau region, adaptation strategies to the arid climate and the coincidence of rainfall during the later stages of crop growth 24 lead to normal and extreme temperature variabilityterm·dom being a better explanation of maizeterm·key yield variabilityterm·dom in some areas of Gansu and Ningxia and all of Shaanxi. Although it may appear counter-intuitive that temperature variabilityterm·dom would dominate for rainfed maizeterm·key, it is consistent with findings for rainfed maizeterm·key areas in the United States 25 where extreme temperature was found to be a better predictor of maizeterm·key grain yield due to its control on soil water demand and transpiration rates. In contrast, wheatterm·key is a winter crop and is highly dependent on irrigation in the North China Plains. What our analysis shows is more dependence on precipitationterm·key variability for wheatterm·key yields, which may be due to the direct controlling influence on surface irrigation water availability. In northeastern China (provinces of Heilongjiang, Jilin, Liolin) maizeterm·key and soybeanterm·key are not widely irrigated so precipitationterm·key variability was important, but riceterm·key is irrigated so temperature variabilityterm·dom became more important.
In Japan almost all the paddy riceterm·key crop is irrigated 22 , 26 and hence temperature variabilityterm·dom was more important compared with precipitationterm·key variability. South Korean harvested riceterm·key is similarly mostly irrigated and thus temperature variabilityterm·dom was more important for explaining riceterm·key yield variabilityterm·dom. In Indonesia the variability in riceterm·key yield explained by climate variabilityterm·dom is often low (in the 0 to 15% range only) and the explanation is on account of temperature variabilityterm·dom 27 except in some parts such as Central Java where precipitationterm·key variability is also important 28 . This is because riceterm·key is widely irrigated in Indonesia 22 , 29 .
In South Asia, especially northwest India, temperature variabilityterm·dom influences wheatterm·key yield variabilityterm·dom widely, similar to other findings 30 but further south in central and south India precipitationterm·key variability in general is more important as between half and three-fourths of wheatterm·key is rainfed winter wheatterm·key compared with only a few percent in the northwest. Riceterm·key yield variabilityterm·dom is more influenced by precipitationterm·key variability in India indicating the rainfed paddy growing conditions. In the more irrigated parts 22 as in northwest India precipitationterm·key and temperature variabilityterm·dom or only temperature variabilityterm·dom was important. In the extreme southwestern parts of India similarly precipitationterm·key and/or temperature variabilityterm·dom was important as this region receives very high rainfall. Temperature variabilityterm·dom was the important factor for riceterm·key yield variabilityterm·dom in Bangladesh due to high availability of water and intense irrigation controlling the influence of precipitationterm·key variability. In some of the highly irrigated riceterm·key areas in India such as areas of WestpersName Bengal state, and the Mahanadi system in northern Orissa, climate variabilityterm·dom was not even statistically significant ( Figs 2b and 3b ).
In Australia wheatterm·key yield variabilityterm·dom is largely explained by precipitationterm·key variability as the wheatterm·key is grown under rainfed conditions 22 and in agreement with previous findings 31 , 32 ; controlling for precipitationterm·key variability, however, temperature variabilityterm·dom was also an important factor in explaining wheatterm·key yield variabilityterm·dom 33 especially in parts of Western Australia, South Australia and Queensland.
We found that maizeterm·key yield variabilityterm·dom is explained best by normal and extreme precipitation variabilityterm·dom related to ENSO in many countries of Africa similar to previous findings as in Zimbabwe 34 , which in turn is related to sea surface temperature 35 . In South Africa maizeterm·key is grown primarily in the Highveld region with drier conditions in the westpersName and wetter conditions in the east 36 . Our analysis reflects these conditions with precipitationterm·key variability being more important in the drier westpersName and temperature variabilityterm·dom more important moving towards the wetter eastern provinces of South Africa’s Highveld. Moreover, high maizeterm·key yield variabilityterm·dom in South Africa has been a concern 36 ; indeed, we found that climate variabilityterm·dom explained >60% of maizeterm·key yield variabilityterm·dom in the Highveld region especially in the drier western parts of the Highveld of South Africa.
Elsewhere, as in Kenya, we found that maizeterm·key yield variabilityterm·dom was explained only by a complex relationship between both precipitationterm·key and temperature variabilityterm·dom consistent with previous studies 37 . In Cameroon in WestpersName Africa and in northeastern Nigeria precipitationterm·key variability alone does not explain maizeterm·key yield variabilityterm·dom agreeing with previous findings 38 , 39 because, while rain is beneficial for stable maizeterm·key production, it also triggers nitrogen leaching from nutrient poor soils, leading to a negative feedback. In many of the other WestpersName African countries rainfall variability explains maizeterm·key yield variabilityterm·dom but analyses show that this was not the case everywhere and neither does climate variabilityterm·dom explain maizeterm·key yield variabilityterm·dom in all countries here as farmers adopt various management strategies to overcome the high rainfall variability 40 . However, other than Nigeria, our analysis in WestpersName Africa was only at the country level and within-country explanatory skill was lost on account of the scale of the available yield statistics. Overall, precipitationterm·key variability is more important in sub-Saharan Africa, pointing to the predominantly rainfed system of maizeterm·key cultivation 41 .
In most of the Eastern Europe and many regions of Western European countries, the effect of temperature variabilityterm·dom in explaining wheatterm·key yield variabilityterm·dom was more important as also found in previous regional and global studies (refs 42 , 43 , Fig. 3c ). This is because of the continental climateterm·dom of Eastern Europe, which causes a greater amplitude of temperature variabilityterm·dom 44 . Our study shows that normal, both normal and extreme, and extreme temperature variabilityterm·dom was important in explaining wheatterm·key yield variabilityterm·dom. In Southern Europe and in the Mediterranean regions in addition to heat stress the water limiting conditions that are common 44 , 45 , 46 resulted in precipitationterm·key variability also being important for wheatterm·key yield variabilityterm·dom. The influence of climate variabilityterm·dom on wheatterm·key yield variabilityterm·dom was not statistically significant everywhere. Neither was the explained variability in statistically significant areas high everywhere. This was because farmers are already adapted, or adapting, to climate change 47 , which has made them also more adapted to variability. In the United Kingdom either precipitationterm·key variability or both temperature and precipitationterm·key variability explained ~45% of wheatterm·key yield variabilityterm·dom; the precipitationterm·key variability is in turn related with the North Atlantic Oscillation 48 .
Maizeterm·key is partly irrigated in France, but irrigation does not fully mitigate dry conditions 49 ; hence precipitationterm·key variability is important and also because irrigated maizeterm·key areas have only recently increased in area and thus historically precipitationterm·key variability could not be compensated as effectively as more recently. The net result is that in many maizeterm·key areas of France historically both temperature and precipitationterm·key variability are important 50 .
In the United States climate variabilityterm·dom was important especially in the Midwestern U.S. for maizeterm·key yields. While in the upper Midwest temperature variabilityterm·dom was more important, in the central Midwest precipitationterm·key variability was more important. In Nebraska, a U.S. Great Plains state with a prevalence of irrigated maizeterm·key in its western part, temperature variabilityterm·dom was more important than in the eastern parts where precipitationterm·key variability was more important. Many of the counties of the Great Plains states with dryland maizeterm·key meet their crop water demands partly from irrigation 51 and we identify large number of counties where both precipitationterm·key and temperature variabilityterm·dom was important. In other rainfed maize-producing countries normal and extreme temperature conditions explained maizeterm·key yield variabilityterm·dom due to increased soil water demand that raised transpiration rates and vapor pressure deficits 25 , 52 . Overall only temperature variabilityterm·dom explained maizeterm·key and soybeanterm·key yield variabilityterm·dom in more harvested regions (~37 and 38%, respectively) compared with precipitationterm·key only explained regions (~31 and 36%, respectively); climate variabilityterm·dom explained part of the yield variabilityterm·dom in ~91% of the U.S. maizeterm·key harvested areas and 82% of soybeanterm·key harvested areas. Less adaptation of farmers to increasingly warmer temperatures may explain why in larger areas temperature variabilityterm·dom was important 53 .
Only ~46% of the maizeterm·key harvested regions of Mexico have crop yieldterm·key variability influenced by climate variabilityterm·dom (~27% of the yield variabilityterm·dom was explained). Precipitationterm·key variability was more important overall, but pockets of regions where temperature variabilityterm·dom was more important exists such as in Sinaloa where irrigated maizeterm·key is important, and in Guerrero. Temperature variabilityterm·dom explained maizeterm·key yield variabilityterm·dom also in most Central American countries. Further south in Brazil, precipitationterm·key variability was more important overall; in specific regions temperature variabilityterm·dom is overall more important such as Mato Grosso state due to its wetter climate, although in ~23% of Brazil’s maizeterm·key harvested areas both temperature and precipitationterm·key variabilities were important in explaining part of the maizeterm·key crop yieldterm·key variability. In Argentina both temperature and precipitationterm·key variabilities were equally important overall, though in specific locations temperature variabilityterm·dom was more important presumably due to irrigated maizeterm·key.
Although this is the most spatially detailed global assessment of the links between historical climate variabilityterm·dom and yield done to date, our study has some limitations. For example, our estimation of crop yieldterm·key variability due to climate variabilityterm·dom may underestimate the importance of climate variabilityterm·dom impacts at specific locations within political units. Future studies should investigate this problem at an even finer resolution globally, but this is challenging given historical yield data availability.
In some countries both crop yieldterm·key and weather data may have quality issues 13 , 18 . Our study is based on yield data at the county/district/municipal/department or larger political unit level, so we used crop harvested area weighted gridded weather data for the political units. However, weather data from individual stations could give a distinct climate-yield response signal due to its very localized scale. To test this latter issue, we carried out a separate analysis using daily station data from ~100 U.S. counties 54 that contributed to ~25% of total U.S. maizeterm·key production. We found statistically significant correlation ( r =0.54; P =0.001) between analyses conducted by the two different data sets. A stronger relationship is likely not present with station data analysis due to the sheer size of some political units and lack of complete coverage, which is present in gridded data ( Supplementary Fig. 4 ). As our yield was measured at the political unit, the use of the harvested area weighted gridded weather data 18 for each political unit is appropriate, similar to previous upscaling usage 1 , and the likely reason that we typically found a stronger statistical relationship with yields over time ( Supplementary Fig. 5 ). In contrast, the use of station data would be appropriate if crop yieldsterm·key were measured at same sites or locally, and the direct use of gridded data then less appropriate without downscaling.
While climate variabilityterm·dom is a significant factor and responsible for 32–39% of global crop yieldterm·key variability, it is certainly not the only controlling factor 55 . Our study only considered broad precipitationterm·key and temperature effects though in an unprecedented spatial detail; however, there are myriad other factors that could influence climate-yield relationships, as informed by more local scale research. Our study does not consider factors such as changing cloud cover (and solar radiation), wind speed, surface ozone exposure 56 , or decomposed the basic climate variables of temperature and precipitationterm·key further into the timing of heat stress 57 , the timing of dry and wet spells 58 , or soil moisture 59 . We have also not considered the amplification or dampening of climate variabilityterm·dom impacts via other agronomic challenges such as pest and pathogen infestation 60 and irrigation 61 . Climate change may also have influenced how frequently crops are harvested 62 , 63 , for example, now allowing double cropping in hitherto colder single cropped regions, but we were unable to include such precision as the only globally available crop calendar 64 was static, even though we updated it using the most recent information available (see Supplementary Fig. 6 ). Other factors to consider in future studies are altitudinal effects 65 and the quality of crop yieldsterm·key 48 . What we have investigated is the influence of the variability of temperature and precipitationterm·key on crop yieldterm·key variability. The unexplained yield variabilityterm·dom includes the numerous agronomic challenges and decisions that farmers make each year such as the availability and use of agronomic inputs 57 , pest and pathogen infestations 60 , 66 , soil management 66 , 67 , irrigation 61 , distribution of varied crop maturity types 68 , socio-economic conditions 55 , 63 , 69 and political or social strife 13 .
Our study therefore is an initial assessment to identify locations worldwide where historically climate variabilityterm·dom has been relatively important in explaining crop yieldterm·key variability. From the perspective of stabilizing farmer incomes and national food supply and security, this new high-resolution information at the global scale should help direct further research and policy more effectively to those regions where climate variabilityterm·dom poses the greatest risk and provide leverage points 70 in the most critical regions. If climate variabilityterm·dom is predicted to increase in the same regions where climate variabilityterm·dom historically explained most of the crop yieldterm·key variability, strategies to stabilize crop production should be prioritized to ensure stable future crop production and prevention of future food price spikes. The high-resolution models that we have built may be used to evaluate future climate-related yield variabilityterm·dom research, provide cross-comparison against the results of crop simulation models and address alternate factors contributing to the spatial heterogeneity in climate-yield response.
Methods Modelling set-up Further details regarding the data used are given in Supplementary Methods 1 . To determine how much of the variability in crop yieldsterm·key was explained by climate variabilityterm·dom, we first detrendedterm·key the crop yieldterm·key and climate variables—temperature and precipitationterm·key—following 1 (see the example in Supplementary Fig. 7 ) over the period 1979–2008. Note that we use two forms of temperature and precipitationterm·key—the seasonal or growing season average value and the average conditions 12 months before harvest or the annual value to account for antecedent conditions. This resulted in four different combinations of detrendedterm·key climate variables, and as we used both the linear and squared forms of seasonal and annual temperature and precipitationterm·key there was a total of eight forms of climate variables. We used these detrendedterm·key variables in different combinations to linearly regress with the detrendedterm·key crop yieldsterm·key at each of the 13,500 political units. To avoid over-fitting we limited our analysis to a total of 27 combinations of climate variables, resulting in 27 regression equations, to capture the relationships between climate variabilityterm·dom and crop yieldterm·key variability at each political unit and of the basic form: where Y c is the observed set of detrendedterm·key crop yieldsterm·key for crop ‘c’ in units of tons/ha/year at each political unit; In equation 1 , T c can represent for crop ‘c’ at a given political unit the temperature associated with the main growing season 64 or the temperature for 1 year before the crop’s harvest to capture antecedent conditions. P c similarly is the precipitationterm·key for the main growing season for the crop ‘c’ for the political unit and for 1 year before the crop’s harvest. The function f is limited to linear and quadratic forms of these two detrendedterm·key meteorological parameters, as is common practice in studies correlating climate and agricultural production 1 , 5 , 16 . The terms included in each of the 27 regression equations and their classification are provided in the Supplementary Table and further details are given in Supplementary Methods 2 .
Statistical tests The generated regression equations at each political unit, for example, ~13,500 sets of 27 equations per crop, were statistically tested next. We first identified which functional form of Y c = f ( T c , P c ) from the set of 27 equations at each political unit fit the data best using the Akaike Information Criterion (AIC)term·stat, which penalizes equations with more terms. However, because the model that best fits the data may be no better than a random climate (null model), we conducted F teststerm·stat at the P =0.10 level to determine whether the chosen model was significantly better than the null model. In 21–47% of the global crop-harvested areas, we found that the chosen model was no better than the null model at the P =0.10 significance level. Thus, in the remainder 53–79% of global crop harvested areas yield variabilityterm·dom is significantly influenced by climate variabilityterm·dom over the study period and our reported numbers are averages over these areas.
Using the statistically significant model with the best functional representation, we next determined the coefficient of determination ( r 2 ) or explanatory power of the complete model, and the reduced models containing only temperature and only precipitationterm·key terms. The residual is the unexplained yield variations.
The 30-year study period average harvested area and yield information at each subnational location was used together with the observed coefficient of determination for computing national and global harvested areas weighted averages. Global and country-specific numbers are averaged only over those 53–79% of global crop harvested areas where the statistical models were significant.
Model bias and sensitivity As a simple assessment of model bias, we performed a bootstrapping exercise to assess the influence of including specific combinations of years (80% of the years selected at each iteration) in our data on the overall yield predictions (using a test set of 20% of the years) for each political unit, which we standardized as the ratio of the average bias from the 99 repetitions to the average of the crop yieldsterm·key for the study period in each political unit ( Supplementary Fig. 8 ). This is analogous to a leave-group-out cross validation approach used to examine uncertainty in model selection. Locations of models with more restrictive P cutoff values ( F -teststerm·stat) at P =0.01 and P =0.05 are shown in Supplementary Fig. 9 . In general, even though we used a less-restrictive P value of 0.1, the models selected generally were significant at P =0.05 or less.
Author contributions D.K.R. led the effort to design, conduct, analyze and write this report. J.S.G., G.K.M., P.C.W. contributed to statistical designing and writing. All authors analyzed and commented on the results.
Additional information How to cite this article : RaypersName, D. K. et al . Climate variation explains a third of global crop yieldterm·key variability. Nat. Commun. 6:5989 doi: 10.1038/ncomms6989 (2015).
Supplementary Material Supplementary Figures 1-9, Supplementary Table 1, Supplementary Methods and Supplementary References Coefficient of determination (R 2 ) per crop-country combination averaged over significant areas Acknowledgments We thank George Allez, Peder Engstrom, Maryan Abdi, Lewei He and Madison Rogers for help in collecting and digitizing a portion of the data. We thank Peder Engstrom for help with plotting Supplementary Fig. 4 . This work greatly benefitted from discussions with Jonathan Foley. We also benefitted from the comments of Kimberly Carlson, Lijun Zuo and other colleagues. Research support was primarily provided by the Gordon and Betty Moore Foundation and the Institute on Environment. Additional research support was from the McKnight Foundation,the Grantham Foundation for the Protection of the Environment, the World Wildlife Fund, The Nature Conservancy, Stanford University, the National Science Foundation (NSF), the Department of Energy (DOE) and the National Aeronautics and Space Administration’s (NASA) Interdisciplinary Earth Science program. Contributions by General Mills, Mosaic, Cargill, Pentair, Google.org, Kellogg’s, Mars and PepsiCo supported stakeholder outreach and public engagement. G.K.M. was also supported by the Natural Sciences and Engineering Research Council of Canada.
References Associated Data Supplementary Materials Supplementary Figures 1-9, Supplementary Table 1, Supplementary Methods and Supplementary References Coefficient of determination (R 2 ) per crop-country combination averaged over significant areas