MEAN AND VARIANCE CHANGE IN CLIMATE SCENARIOS: METHODS, AGRICULTURAL APPLICATIONS, AND MEASURES OF UNCERTAINTY

Our central goal is to determine the importance of including both mean and variability changes in climate change scenarios in an agricultural context. By adapting and applying a stochastic weather generator, we first tested the sensitivity of the CERES-Wheat model to combinations of mean and variability changes of temperature and precipitation for two locations in Kansas. With a 2°C increase in temperature with daily (and interannual) variance doubled, yields were further reduced compared to the mean only change. In contrast, the negative effects of the mean temperature increase were greatly ameliorated by variance decreased by one-half. Changes for precipitation are more complex, since change in variability naturally attends change in mean, and constraining the stochastic generator to mean change only is highly artificial. The crop model is sensitive to precipitation variance increases with increased mean and variance decreases with decreased mean. With increased mean precipitation and a further increase in variability Topeka (where wheat cropping is not very moisture limited) experiences decrease in yield after an initial increase from the 'mean change only case. At Goodland Kansas, a moisture-limited site where summer fallowing is practiced, yields are decreased with decreased precipitation, but are further decreased when variability is further reduced. The range of mean and variability changes to which the crop model is sensitive are within the range of changes found in regional climate modeling (RegCM) experiments for a CO₂ doubling (compared to a control run experiment). We then formed two types of climate change scenarios based on the changes in climate found in the control and doubled CO₂ experiments over the conterminous U. S. of RegCM: (1) one using only mean monthly changes in temperature, precipitation, and solar radiation; and (2) another that included these mean changes plus changes in daily (and interannual) variability. The scenarios were then applied to the CERES-Wheat model at four locations (Goodland, Topeka, Des Moines, Spokane) in the United States. Contrasting model responses to the two scenarios were found at three of the four sites. At Goodland, and Des Moines mean climate change increased mean yields and decreased yield variability, but the mean plus variance climate change reduced yields to levels closer to their base (unchanged) condition. At Spokane mean climate change increased yields, which were somewhat further increased with climate variability change. Three key aspects that contribute to crop response are identified: the marginality of the current climate for crop growth, the relative size of the mean and variance changes, and timing of these changes. Indices for quantifying uncertainty in the impact assessment were developed based on the nature of the climate scenario formed, and the magnitude of difference between model and observed values of relevant climate variables.     

Impact of temperature and precipitation variability on crop model predictions

Future climate changes, as well as differences in climates from one location to another, may involve changes in climatic variability as well as changes in means. In this study, a synthetic weather generator is used to systematically change the within-year variability of temperature and precipitation (and therefore also the interannual variability), without altering long-term mean values. For precipitation, both the magnitude and the qualitative nature of the variability are manipulated. The synthetic daily weather series serve as input to four crop simulation models. Crop growth is simulated for two locations and three soil types. Results indicate that average predicted yield decreases with increasing temperature variability where growing-season temperatures are below the optimum specified in the crop model for photosynethsis or biomass accumulation. However, increasing within-year variability of temperature has little impact on year-to-year variability of yield. The influence of changed precipitation variability on yield was mediated by the nature of the soil. The response on a droughtier soil was greatest when precipitation amounts were altered while keeping occurrence patterns unchanged. When increasing variability of precipitation was achieved through fewer but larger rain events, average yield on a soil with a large plant-available water capacity was more affected. This second difference is attributed to the manner in which plant water uptake is simulated. Failure to account for within-season changes in temperature and precipitation variability may cause serious errors in predicting crop-yield responses to future climate change when air temperatures deviate from crop optima and when soil water is likely to be depleted at depth.     

Contributions of individual variation in temperature, solar radiation and precipitation to crop yield in the North China Plain, 1961–2003

An understanding of the relative impacts of the changes in climate variables on crop yield can help develop effective adaptation strategies to cope with climate change. This study was conducted to investigate the effects of the interannual variability and trends in temperature, solar radiation and precipitation during 1961–2003 on wheat and maize yields in a double cropping system at Beijing and Zhengzhou in the North China Plain (NCP), and to examine the relative contributions of each climate variable in isolation. 129 climate scenarios consisting of all the combinations of these climate variables were constructed. Each scenario contained 43 years of observed values of one variable, combined with values of the other two variables from each individual year repeated 43 times. The Agricultural Production Systems Simulator (APSIM) was used to simulate crop yields using the ensemble of generated climate scenarios. The results showed that the warming trend during the study period did not have significant impact on wheat yield potential at both sites, and only had significant negative impact on maize yield potential at Beijing. This is in contrast with previous results on effect of warming. The decreasing trend in solar radiation had a much greater impact on simulated yields of both wheat and maize crops, causing a significant reduction in potential yield of wheat and maize at Beijing. Although decreasing trends in rainfed yield of both simulated wheat and maize were found, the substantial interannual variability of precipitation made the trends less prominent.     

Yield Variability as Influenced by Climate: A Statistical Investigation

One of the issues with respect to climate change involves its influence on the distribution of future crop yields. Many studies have been done regarding the effect on the mean of such distributions but few have addressed the effect on variance. Furthermore, those that have been done generally report the variance from crop simulators, not from observations. This paper examines the potential effects of climate change on crop yield variance in the context of current observed yields and then extrapolates to the effects under projected climate change. In particular, maximum likelihood panel data estimates of the impacts of climate on year-to-year yield variability are constructed for the major U.S. agricultural crops. The panel data technique used embodies a variance estimate developed along the lines of the stochastic production function approach suggested by Just and Pope. The estimation results indicate that changes in climate modify crop yield levels and variances in a crop-specific fashion. For sorghum, rainfall and temperature increases are found to increase yield level and variability. On the other hand, precipitation and temperature are individually found to have opposite effects on corn yield levels and variability.     

Change in climate variability in the 21st century

As climate changes due to the increase of greenhouse gases, there is the potential for climate variability to change as well. The change in variability of temperature and precipitation in a transient climate simulation, where trace gases are allowed to increase gradually, and in the doubled CO₂ climate is investigated using the GISS general circulation model. The current climate control run is compared with observations and with the climate change simulations for variability on three time-scales: interannual variability, daily variability, and the amplitude of the diurnal cycle. The results show that the modeled variability is often larger than observed, especially in late summer, possibly due to the crude ground hydrology. In the warmer climates, temperature variability and the diurnal cycle amplitude usually decrease, in conjunction with a decrease in the latitudinal temperature gradient and the increased greenhouse inhibition of radiative cooling. Precipitation variability generally changes with the same sign as the mean precipitation itself, usually increasing in the warmer climate. Changes at a particular grid box are often not significant, with the prevailing tendency determined from a broader sampling. Little change is seen in daily persistence. The results are relevant to the continuing assessments of climate change impacts on society, though their use should be tempered by appreciation of the model deficiencies for the current climate.     

Projected temperature changes indicate significant increase in interannual variability of U.S. maize yields

Climate change has the potential to be a source of increased variability if crops are more frequently exposed to damaging weather conditions. Yield variability could respond to a shift in the frequency of extreme events to which crops are susceptible, or if weather becomes more variable. Here we focus on the United States, which produces about 40% of the world’s maize, much of it in areas that are expected to see increased interannual variability in temperature. We combine a statistical crop model based on historical climate and yield data for 1950–2005 with temperature and precipitation projections from 15 different global circulation models. Holding current growing area constant, aggregate yields are projected to decrease by an average of 18% by 2030–2050 relative to 1980–2000 while the coefficient of variation of yield increases by an average of 47%. Projections from 13 out of 15 climate models result in an aggregate increase in national yield coefficient of variation, indicating that maize yields are likely to become more volatile in this key growing region without effective adaptation responses. Rising CO₂ could partially dampen this increase in variability through improved water use efficiency in dry years, but we expect any interactions between CO₂ and temperature or precipitation to have little effect on mean yield changes.     

基于气象要素的逐日玉米产量气象影响指数

利用1981—2020年5—9月气象数据与玉米产量数据,通过改进逐日降水适宜度并构建逐日气候适宜度模型,建立基于相似年逐日气象要素的作物生育期气候适宜度序列,利用气象产量与气候适宜指数建立模型,设计逐日作物产量气象影响指数以表征气象条件对作物的影响程度,基于该指数构建东北地区玉米逐日产量预报模型并分析其逐日预报准确率,用以表明该指数的准确性。结果表明:利用3个相似年预报结果加权集成综合相似年逐日作物产量气象影响指数可提高逐日预报准确率,黑龙江年尺度逐日预报准确率年际间波动小于东北其他地区。综合相似年月尺度下,随着玉米发育期的推进和实时气象数据的引入,月尺度平均预报准确率逐渐提高。东北地区玉米产量8月31日的日尺度预报准确率普遍高于7月31日;辽宁日尺度预报差异较大,但随着玉米发育期推进逐日预报产量和实际产量接近,准确率也提高。基于气象要素构建的逐日作物产量影响指数和同期气象影响指数可以定量评估不同时段气象条件对作物产量的影响程度,在一定程度上可提高农业气象业务定量化评价水平。     

Interannual Climate Variability of the Past Millennium from Simulations

The interannual variability of global temperature and precipitation during the last millennium is analyzed using the results of ten coupled climate models participating in the Paleoclimate Modelling Intercomparison Project Phase 3. It is found that large temperature(precipitation) variability is most dominant at high latitudes(tropical monsoon regions), and the seasonal magnitudes are greater than the annual mean. Significant multi-decadal-scale changes exist throughout the whole period for the zonal mean of both temperature and precipitation variability, while their long-term trends are indistinctive. The volcanic forcings correlate well with the temperature variability at midlatitudes, indicating possible leading drivers for the interannual time scale climate change.     

Climate Variability-Observations, Reconstructions, and Model Simulations for the Atlantic-European and Alpine Region from 1500-2100 AD

A detailed analysis is undertaken of the Atlantic-European climate using data from 500-year-long proxy-based climate reconstructions, a long climate simulation with perpetual 1990 forcing, as well as two global and one regional climate change scenarios. The observed and simulated interannual variability and teleconnectivity are compared and interpreted in order to improve the understanding of natural climate variability on interannual to decadal time scales for the late Holocene. The focus is set on the Atlantic-European and Alpine regions during the winter and summer seasons, using temperature, precipitation, and 500 hPa geopotential height fields. The climate reconstruction shows pronounced interdecadal variations that appear to “lock” the atmospheric circulation in quasi-steady long-term patterns over multi-decadal periods controlling at least part of the temperature and precipitation variability. Different circulation patterns are persistent over several decades for the period 1500 to 1900. The 500-year-long simulation with perpetual 1990 forcing shows some substantial differences, with a more unsteady teleconnectivity behaviour. Two global scenario simulations indicate a transition towards more stable teleconnectivity for the next 100 years. Time series of reconstructed and simulated temperature and precipitation over the Alpine region show comparatively small changes in interannual variability within the time frame considered, with the exception of the summer season, where a substantial increase in interannual variability is simulated by regional climate models.     

Changes in Climate and Crop Production During the 20th Century in Argentina

This work was focused on the assessment of changes occurring in crop production and climate during the 20th century in Argentina. The study was carried out for nine sites located in the Pampas region that are representative of contrasting environments. We have considered the four main crops cultivated in this area (wheat, maize, sunflower and soybean). Historical climatic data and crop production related variables (yield, planted area, harvested area) were analyzed and, by means of crop simulation models, we quantified the impact of climate on crop yields. Changes occurring in climate during the three last decades of the 20th century were characterized by important increases in precipitation especially between October and March, decreases in maximum temperature and solar radiation in particular during spring and summer and increases in minimum temperature during almost all of the year. These changes contributed to increases in yields, especially in summer crops and in the semiarid zone, mostly due to increases in precipitation, although changes in temperature and radiation also affected crop yields but to a lesser extent. Comparing the period 1950–1970 with 1971–1999, yields increases attributable to changes in climate were 38% in soybean, 18% in maize, 13% in wheat, and 12% in sunflower while mean observed yield increases were 110% for maize, 56% for wheat and 102% for sunflower.     

土壤湿度年际异常对中国春、夏季气候模拟的影响

基于NCAR大气模式CAM3.1模式,设计了有、无土壤湿度年际异常两组试验对中国区域近40a(1961-2000年)气候进行了模拟。从气候态和年际变率的角度,通过分析两组试验的差值场来探讨土壤湿度年际异常对气候模拟的影响,并初步探讨了影响的可能机制。结果表明:模式模拟的温度和降水对土壤湿度的年际异常非常敏感,土壤湿度的年际变化对中国春夏季气候及其年际变率均有显著影响。当不考虑土壤湿度年际异常时,模式模拟的春夏季平均温度、最高温度、最低温度在我国大范围内降低,春夏季降水在东部大部分地区明显减少,西部增加。而模式模拟的春夏季温度、降水年际变率在中国大部分地区减弱。但当考虑土壤湿度的年际变化,则能在一定程度上提高模式对气候年际变率的模拟能力。在进一步分析表明土壤湿度年际异常时,主要通过改变地表能量通量和环流场,对温度、降水产生影响。当不考虑土壤湿度年际异常时,地表净辐射通量减少,地表温度降低,感热通量减少。感热通量差值场的空间变化和温度差值场的空间变化一致,感热通量对温度有一定影响。而潜热通量差值场的空间变化和降水的差值场的空间变化一致,可见降水受地表潜热通量的影响。土壤湿度年际异常引起的环流场的变化也是导致气候变化的原因之一,地表能量和环流场年际变率的改变对春夏季气候年际变率存在一定影响。     

中国东部区域土壤湿度的变化及其与气候变率的关系

利用中国100°E以东地区98站共11a的旬土壤湿度、降水和气温资料,对不同区域土壤温度、降水和气温的变化趋势、年际变率及它们之间的相互关系进行了详尽的分析。结果表明：土壤湿度、降水和气温有较明显的变化趋势;土壤中各厚度层土壤湿度和降水的关系呈正相关关系,与气温呈反相关关系,且可通过0．01的置信度检验。这也说明现有土壤湿度观测资料在研究气候变化中的有效性。     

A scenario of European climate change for the late twenty-first century: seasonal means and interannual variability

A scenario of European climate change for the late twenty-first century is described, using a high-resolution state-of-the-art model. A time-slice approach is used, whereby the atmospheric general circulation model, HadAM3P, was integrated for two periods, 1960–1990 and 2070–2100, using the SRES A2 scenario. For the first time an ensemble of such experiments was produced, along with appropriate statistical tests for assessing significance. The focus is on changes to the statistics of seasonal means, and includes analysis of both multi-year means and interannual variance. All four seasons are assessed, and anomalies are mapped for surface air temperature, precipitation and snow mass. Mechanisms are proposed where these are dominated by straightforward local processes. In winter, the largest warming occurs over eastern Europe, up to 7°C, mean snow mass is reduced by at least 80% except over Scandinavia, and precipitation increases over all but the southernmost parts of Europe. In summer, temperatures rise by 6–9°C south of about 50°N, and mean rainfall is substantially reduced over the same area. In spring and autumn, anomalies tend to be weaker, but often display patterns similar to the preceding season, reflecting the inertia of the land surface component of the climate system. Changes in interannual variance are substantial in the solsticial seasons for many regions (note that for precipitation, variance estimates are scaled by the square of the mean). In winter, interannual variability of near-surface air temperature is considerably reduced over much of Europe, and the relative variability of precipitation is reduced north of about 50°N. In summer, the (relative) interannual variance of both variables increases over much of the continent.     

Effects of temperature rise and increase in CO2 concentration on simulated wheat yields in Europe

A crop-growth-simulation model based on SUCROS87 was used to study effects of temperature rise and increase of atmospheric CO₂ concentration on wheat yields in several regions in Europe. The model simulated potential and water-limited crop production (growth with ample supply of nutrients and in the absence of damage by pests, diseases and weeds). Historic daily weather data from 13 sites in Western Europe were used as starting point.For potential production (optimal water) a 3 °C temperature rise led to a yield decline due to a shortening of the growing period on all locations. Doubling of the CO₂ concentration caused an increase in yield of 40% due to higher assimilation rates. It was found that effects of higher temperature and higher CO₂ concentration were nearly additive and the combination of both led to a yield increase of 1–2 ton ha^-1. A very small CO₂-temperature interaction was found: the effect of doubled CO₂ concentration on crop yield was larger at higher temperatures. The inter-annual yield variability was hardly affected.When water was limiting crop-production effects of temperature rise and higher CO₂ levels were different than for the potential production. Rise in temperature led to a smaller yield reduction, doubled CO₂ concentration to a larger yield increase and combination of both led to a large yield increase (3 ton ha^-1) in comparison with yields simulated for the present situation. Both rise in temperature and increase in the CO₂ concentration reduced water requirements of the crop. Water shortages became smaller, leading to a reduction in inter-annual variability. It is concluded that when no major changes in precipitation pattern occur a climate change will not affect wheat yields since negative effects of higher temperatures are compensated by positive effects of CO₂ enrichment.     

Projections of uncertainties in climate change scenarios into expected winter wheat yields

Summary The crop model CERES-Wheat in combination with the stochastic weather generator were used to quantify the effect of uncertainties in selected climate change scenarios on the yields of winter wheat, which is the most important European cereal crop. Seven experimental sites with the high quality experimental data were selected in order to evaluate the crop model and to carry out the climate change impact analysis. The analysis was based on the multi-year crop model simulations run with the daily weather series prepared by the stochastic weather generator. Seven global circulation models (GCMs) were used to derive the climate change scenarios. In addition, seven GCM-based scenarios were averaged in order to derive the average scenario (AVG). The scenarios were constructed for three time periods (2025, 2050 and 2100) and two SRES emission scenarios (A2 and B1). The simulated results showed that: (1) Wheat yields tend to increase (40 out of 42 applied scenarios) in most locations in the range of 7.5–25.3% in all three time periods. In case of the CCSR scenario that predicts the most severe increase of air temperature, the yields would be reduced by 9.6% in 2050 and by 25.8% in 2100 if the A2 emission scenario would become reality. Differences between individual scenarios are large and statistically significant. Particularly for the time periods 2050 and 2100 there are doubts about the trend of the yield shifts. (2) The site effect was caused by the site-specific soil and climatic conditions. Importance of the site influence increases with increasing severity of imposed climatic changes and culminates for the emission scenario A2 and the time period 2100. The sustained tendency benefiting two warmest sites has been found as well as more positive response to the changed climatic conditions of the sites with deeper soil profiles. (3) Temperature variability proved to be an important factor and influenced both mean and standard deviation of the yields. Change of temperature variability by more than 25% leads to statistically significant changes in yield distribution. The effect of temperature variability decreases with increased values of mean temperature. (4) The study proved that the application of the AVG scenarios – despite possible objections of physical inconsistency – might be justifiable and convenient in some cases. It might bring results comparable to those derived from averaging outputs based on number of scenarios and provide more robust estimate than the application of only one selected GCM scenario.     

Evaluation of the CORDEX regional climate models performance in simulating climate conditions of two catchments in Upper Blue Nile Basin

This study was targeted at evaluating the performance of six Regional Climate Models (RCMs) used in Coordinated Regional Climate Downscaling Experiment (CORDEX). The evaluation is on the bases of how well the RCMs simulate the seasonal mean climatology, interannual variability and annual cycles of rainfall, maximum and minimum temperature over two catchments in western Ethiopia during the period 1990–2008. Observed data obtained from the Ethiopian National Meteorological Agency was used for performance evaluation of the RCMs outputs. All Regional Climate Models (RCMs) have simulated seasonal mean annual cycles of precipitation with a significant bias shown on individual models; however, the ensemble mean exhibited better the magnitude and seasonal rainfall. Despite the highest biases of RCMs in the wet season, the annual cycle showed the prominent features of precipitation in the two catchments. In many aspects, CRCM5 and RACMO22 T simulate rainfall over most stations better than the other models. The highest biases are associated with the highest error in simulating maximum and minimum temperature with the highest biases in high elevation areas. The rainfall interannual variability is less evident in Finchaa with short rainy season experiencing a larger degree of interannual variability. The differences in performance of the Regional Climate Models in the two catchments show that all the available models are not equally good for particular locations and topographies. In this regard, the right regional climate models have to be used for any climate change impact study for local-scale climate projections.     

Mechanisms for projected future changes in south Asian monsoon precipitation

Results are first presented from an analysis of a global coupled climate model regarding changes in future mean and variability of south Asian monsoon precipitation due to increased atmospheric CO₂ for doubled (2 × CO₂) and quadrupled (4 × CO₂) present-day amounts. Results from the coupled model show that, in agreement with previous studies, mean area-averaged south Asian monsoon precipitation increases with greater CO₂ concentrations, as does the interannual variability. Mechanisms producing these changes are then examined in a series of AMIP2-style sensitivity experiments using the atmospheric model (taken from the coupled model) run with specified SSTs. Three sets of ensemble experiments are run with SST anomalies superimposed on the AMIP2 SSTs from 1979–97: (1) anomalously warm Indian Ocean SSTs, (2) anomalously warm Pacific Ocean SSTs, and (3) anomalously warm Indian and Pacific Ocean SSTs. Results from these experiments show that the greater mean monsoon precipitation is due to increased moisture source from the warmer Indian Ocean. Increased south Asian monsoon interannual variability is primarily due to warmer Pacific Ocean SSTs with enhanced evaporation variability, with the warmer Indian Ocean SSTs a contributing but secondary factor. That is, for a given interannual tropical Pacific SST fluctuation with warmer mean SSTs in the future climate, there is enhanced evaporation and precipitation variability that is communicated via the Walker Circulation in the atmosphere to the south Asian monsoon to increase interannual precipitation variability there. This enhanced monsoon variability occurs even with no change in interannual SST variability in the tropical Pacific.     

Evaluation of high-resolution simulations of daily-scale temperature and precipitation over the United States

Extreme climate events have been increasing over much of the world, and dynamical models predict further increases in response to enhanced greenhouse forcing. We examine the ability of a high-resolution nested climate model, RegCM3, to capture the statistics of daily-scale temperature and precipitation events over the conterminous United States, using observational and reanalysis data for comparison. Our analyses reveal that RegCM3 captures the pattern of mean, interannual variability, and trend in the tails of the daily temperature and precipitation distributions. However, consistent biases do exist, including wet biases in the topographically-complex regions of the western United States and hot biases in the southern and central United States. The biases in heavy precipitation in the western United States are associated with excessively strong surface and low-level winds. The biases in daily-scale temperature and precipitation in the southcentral United States are at least partially driven by biases in circulation and moisture fields. Further, the areas of agreement and disagreement with the observational data are not intuitive from analyzing the simulated mean seasonal temperature and precipitation fields alone. Our evaluation should enable more informed application and improvement of high-resolution climate models for the study of future changes in socially- and economically-relevant temperature and precipitation events.     

East African food security as influenced by future climate change and land use change at local to regional scales

Climate change impacts food production systems, particularly in locations with large, vulnerable populations. Elevated greenhouse gases (GHG), as well as land cover/land use change (LCLUC), can influence regional climate dynamics. Biophysical factors such as topography, soil type, and seasonal rainfall can strongly affect crop yields. We used a regional climate model derived from the Regional Atmospheric Modeling System (RAMS) to compare the effects of projected future GHG and future LCLUC on spatial variability of crop yields in East Africa. Crop yields were estimated with a process-based simulation model. The results suggest that: (1) GHG-influenced and LCLUC-influenced yield changes are highly heterogeneous across this region; (2) LCLUC effects are significant drivers of yield change; and (3) high spatial variability in yield is indicated for several key agricultural sub-regions of East Africa. Food production risk when considered at the household scale is largely dependent on the occurrence of extremes, so mean yield in some cases may be an incomplete predictor of risk. The broad range of projected crop yields reflects enormous variability in key parameters that underlie regional food security; hence, donor institutions’ strategies and investments might benefit from considering the spatial distribution around mean impacts for a given region. Ultimately, global assessments of food security risk would benefit from including regional and local assessments of climate impacts on food production. This may be less of a consideration in other regions. This study supports the concept that LCLUC is a first-order factor in assessing food production risk.     

Impacts of a nuclear war in South Asia on soybean and maize production in the Midwest United States

Crop production would decline in the Midwestern United States from climate change following a regional nuclear conflict between India and Pakistan. Using Agro-IBIS, a dynamic agroecosystem model, we simulated the response of maize and soybeans to cooler, drier, and darker conditions from war-related smoke. We combined observed climate conditions for the states of Iowa, Illinois, Indiana, and Missouri with output from a general circulation climate model simulation that injected 5 Tg of elemental carbon into the upper troposphere. Both maize and soybeans showed notable yield reductions for a decade after the event. Maize yields declined 10–40 % while soybean yields dropped 2–20 %. Temporal variation in magnitude of yield for both crops generally followed the variation in climatic anomalies, with the greatest decline in the 5 years following the 5 Tg event and then less, but still substantial yield decline, for the rest of the decade. Yield reduction for both crops was linked to changes in growing period duration and, less markedly, to reduced precipitation and altered maximum daily temperature during the growing season. The seasonal average of daily maximum temperature anomalies, combined with precipitation and radiation changes, had a quadratic relationship to yield differences; small (0 °C) and large (?3 °C) maximum temperature anomalies combined with other changes led to increased yield loss, but medium changes (?1 °C) had small to neutral effects on yield. The exact timing of the temperature changes during the various crop growth phases also had an important effect.