Thursday, June 9, 2011

Said AlSarmi & Richard Washington, J. Geophys. Res., 116 (2011), Recent observed climate change over the Arabian Peninsula

Recent observed climate change over the Arabian Peninsula
Key Points
  • Arabian Peninsula is warming significantly
  • Many Arabian Peninsula stations reported high warming rates
  • The warming in minimum temperature is the highest and most spatially coherent
Said AlSarmi and Richard Washington

Climatology Research Group, Oxford University Centre for the Environment, University of Oxford, Oxford, UK


We have examined trends in temperature and precipitation parameters for the Arabian Peninsula (AP) during the last 2 to 3 decades. The data set has been carefully quality controlled and checked for homogeneity. Although of low density (21 stations) and relatively short time period, a clear picture of climate change in the region has emerged. The general pattern of the AP mean annual temperature trend is one of warming, with 14 of 21 stations show statistically significant warming at 0.05 level and most at 0.001 level and only one (Seeb) showing statistically significant cooling. The highest statistically significant mean annual warming trends are found in Oman (Sur = 1.03 °C decade−1) and Emirates (Dubai = 0.81 °C decade−1). The season of maximum warming in mean temperature is March to April. The highest monthly mean temperature trend in the AP occurs in Sur in May (1.47 °C decade−1). There is a broad statistically significant increase in mean annual maximum temperature in AP in 12 out of 21 stations, with the highest trends in central and eastern/southeastern AP. Only SW AP and the Gulf of Oman do not show warming. The highest monthly maximum temperature trend in the AP occurs in Bahrain in March (2.27 °C decade−1). The second highest significant warming trends are reported in Doha in February (1.54 °C decade−1). For minimum temperature, 16 out of 21 stations show statistically significant warming trends, with the highest annual trends observed in the Emirates (Dubai = 1.24 °C decade−1), northwest Oman (Sohar = 1.17 °C decade−1) and Qatar (Doha = 1.13 °C decade−1). The highest monthly minimum temperature warming rate occurred in October. Both Dubai and Kuwait reported the highest significant rate of 2.00 °C decade−1. The general mean annual diurnal temperature range trend is negative in the AP, with six out of 21 stations show statistically significant negative trends while three stations show statistically significant positive trends. Trends in mean annual precipitation are significant at only two stations which show a decrease in precipitation.

Saturday, April 23, 2011

Elinor Breman, Lindsey Gillson & Kathy Willis, The Holocene, How fire and climate shaped grass-dominated vegetation and forest mosaics in northern South Africa during past millennia

The Holocene,

How fire and climate shaped grass-dominated vegetation and forest mosaics in northern South Africa during past millennia

  1. Elinor Breman
    1. Oxford University, UK
  1. Lindsey Gillson
    1. University of Cape Town, South Africa
  1. Kathy Willis
    1. University of Oxford, UK


Grassland and savanna are globally important ecosystems, both ecologically and economically. These grass-dominated systems are at risk from current and future climate change and increasing anthropogenic impact. Key questions for understanding the resilience and variability of grass-dominated ecosystems under current and future environmental conditions include: How have these systems responded to climate change and disturbance in the past? What are the principal driving agents responsible for their present-day composition and distribution? Do the palaeoecological data provide evidence for feedbacks between climate, fire and anthropogenic activities? In this study, the temporal dynamics of grassland, savanna and forest in the summer rainfall region of northern South Africa were reconstructed for the last ∼6500 years. Palaeoecological techniques used include analyses of fossil pollen, charcoal and stable isotopes. Data from two sites located at the present-day grassland-savanna ecotone in Mpumalanga province of South Africa are reported. Results indicate that a mosaic of grassland, savanna and Podocarpus forest occupied the landscape throughout the late Holocene, with grassland and forest dominating higher altitudes, and savanna and forest lower altitudes. Podocarpus forest retreated and grass-dominated vegetation expanded its range around 1800 cal. yr BP at the lower altitude site (Lowveld) and 600 cal. yr BP at the higher altitude site (Highveld), representing a change from a stable state forest savanna/grassland mosaic to an increasingly grass-dominated system. Climatic stress, changes in fire regime and anthropogenic impact led to the vegetation transitions recorded, and resulted in changes in water and nutrient cycles. In an increasingly warm world, with fluctuating water availability and heightened anthropogenic use of natural resources, the future of grass-dominated ecosystems appears far from stable.

Wednesday, March 23, 2011

Climatological determinants of woody cover in Africa, by S. P. Good & K. K. Caylor, PNAS, Vol. 108, No. 12

PNAS (March 22, 2011), Vol. 108, No. 12, pp. 4902-4907;  doi: 10.1073/pnas.1013100108

Climatological determinants of woody cover in Africa

  1. Stephen P. Good1 and 
  2. Kelly K. Caylor
  1. Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544
  1. Edited* by Ignacio Rodriguez-Iturbe, Princeton University, Princeton, NJ 08544, and approved January 28, 2011 (received for review September 3, 2010)


Determining the factors that influence the distribution of woody vegetation cover and resolving the sensitivity of woody vegetation cover to shifts in environmental forcing are critical steps necessary to predict continental-scale responses of dryland ecosystems to climate change. We use a 6-year satellite data record of fractional woody vegetation cover and an 11-year daily precipitation record to investigate the climatological controls on woody vegetation cover across the African continent. We find that—as opposed to a relationship with only mean annual rainfall—the upper limit of fractional woody vegetation cover is strongly influenced by both the quantity and intensity of rainfall events. Using a set of statistics derived from the seasonal distribution of rainfall, we show that areas with similar seasonal rainfall totals have higher fractional woody cover if the local rainfall climatology consists of frequent, less intense precipitation events. Based on these observations, we develop a generalized response surface between rainfall climatology and maximum woody vegetation cover across the African continent. The normalized local gradient of this response surface is used as an estimator of ecosystem vegetation sensitivity to climatological variation. A comparison between predicted climate sensitivity patterns and observed shifts in both rainfall and vegetation during 2009 reveals both the importance of rainfall climatology in governing how ecosystems respond to interannual fluctuations in climate and the utility of our framework as a means to forecast continental-scale patterns of vegetation shifts in response to future climate change.

Tuesday, March 15, 2011

M. Auffhammer, Nature Climate Change (March 15, 2011), Agriculture: Weather dilemma for African maize

Nature Climate Change (March 15, 2011)

Agriculture: Weather dilemma for African maize

Nature Climate Change
Published online
The impact of climate change on food production remains uncertain, particularly in the tropics. Research that exploits the results of historical crop trials indicates that Africa's maize crop could be at risk of significant yield losses.
Maize in a farmer's field in Kenya. Millions of people depend on maize for food and their livelihoods, so understanding the potential impacts of climate change on the crop is highly important. Using data from historical crop trials in Africa, Lobell and colleagues1 show that yields of tropical maize are sensitive to exposure to very hot days and that drought stress significantly increases their sensitivity to warming — results that could help farmers adapt to climate change on the continent and elsewhere.
The growing global demand for calories — caused by an expanding population and a rise in average wealth — is one reason for the current peak in food prices. Coupled to this have been decreases in food supply caused by extreme weather events, such as last year's Russian heatwave. Regardless of where extreme weather occurs, the effects on food availability and price are disproportionately felt by the world's poor. Moreover, crop failures due to extreme weather not only affect those buying and selling in the global marketplace, but also have a direct impact on subsistence farmers. Understanding how such extreme weather events — which are predicted to become more frequent under climate change — affect both yields and total production of the world's staple food crops is thus an issue of both scientific and societal importance. Writing in Nature Climate Change, David Lobell and colleagues1 present results that further our understanding of how maize yields — a crop on which millions depend for food and their livelihoods — respond to hotter days under both drought and non-drought conditions.
Global food markets have become increasingly volatile in recent years. Both supply and demand have contributed to this instability: rising incomes, growing populations and biofuel policies are upping the productivity required from a limited amount of agricultural land, and an almost incomprehensibly intricate set of agricultural support and trade policies within and across countries have historically made the economics of food supply extremely complicated.
Extreme weather events have also played a role. Wheat production in Russia decreased by almost a third last year2, largely due to the summer heatwave, and the unusually high rainfall in Australia this past summer meant that a significant share of the nation's 2010–2011 wheat crop had to be downgraded to 'animal feed' quality. In the near term, the prospects for other major markets look equally pessimistic — the US Department of Agriculture and the United Nations Food and Agricultural Organization have both warned of a significant decrease in yields of Chinese winter wheat this year owing to drought34; a change that could result in the emerging superpower becoming a buyer of wheat on world markets.
Lobell and colleagues1 exploit historical data from over 20,000 field trials of maize conducted in Africa over the past decade or so. The trials were originally conducted to test the resilience of the crop to different environmental conditions and involved varieties that are either currently in use or intended for planting by African farmers. Using daily weather records, the authors matched the yield results for each trial to the daily weather experienced by the plants while growing. They controlled for other factors that might affect the results at each site (such as soil quality) and during each season (such as changing global carbon dioxide concentrations) indirectly in a statistical model. This analysis allowed them to extract the effects of temperature and rainfall on yields.
The results show that each 'degree day' that the crop spends above 30 °C (a unit that reflects both the amount and duration of heat experienced by the plant) depresses yields by 1% if the plants are receiving sufficient water. This sensitivity is similar to that observed for temperate maize varieties in the United States5. However, Lobell and co-workers also show that water availability has an important effect on the sensitivity, with yields decreasing by 1.7% for each degree day spent over 30 °C under drought conditions.
To put these numbers in perspective, they indicate that under non-drought conditions 65% of the area in Africa that is under maize cultivation at present would experience yield losses from a uniform 1 °C warming. Under drought conditions, 100% of the present cultivated area would experience yield losses, with 75% of this area suffering yield losses of at least 20%.
What is most concerning about these results is the empirical confirmation that drought stress significantly amplifies the effects of heat stress. The authors are careful to caution that the field trials on which their results are based use fairly high levels of nitrogen fertilizers, which is not the case in many areas of Africa. Plants under nitrogen stress may react less strongly to temperature stress, suggesting that their results may be an upper bound for what one could expect in actual field settings. However, the close match with the field-based results for temperate maize in the United States5 indicates that this effect is probably minor.
The study raises several issues related to how best to deal with the impacts of climate change on agriculture. It suggests that maize planted in a future Africa characterized by a drier and hotter climate will need to be able to withstand the joint stress imposed by heat and drought, which poses a challenge for the development of new varieties of the crop. But maize is not the only crop available to farmers, so they will most probably shift to growing other crops if maize yields are depressed to the extent that it is no longer profitable. Understanding the heat sensitivity of substitute crops is of prime importance for establishing the optimal sequence of crops that farmers could move to as temperatures rise.
One of the most important aspects of the work by Lobell and colleagues1 is that it offers a new way of obtaining this information from a widely available source of data. Data repositories hold the results of field trials for a variety of crops and locations, and should be exploited in the same fashion to establish an 'atlas of climate sensitivities' for multiple crops in different regions. Finally, social scientists can help crop scientists understand how farmers' decisions may change with climate. Farmers mitigate the effect of a changing climate by adjusting the mix of crops they plant and inputs they use, but these factors are normally held fixed in experimental field trials and computer-based simulation models. Additional interdisciplinary research that takes the human response to changing weather patterns into account will be key to obtaining reliable impact estimates and therefore to designing optimal policy responses.

David B. Lobell et al., Nature Climate Change (March 15, 2011), Nonlinear heat effects on African maize as evidenced by historical yield trials

Nature Climate Change (March 15, 2011)

Nonlinear heat effects on African maize as evidenced by historical yield trials

Nature Climate Change
Published online
New approaches are needed to accelerate understanding of climate impacts on crop yields, particularly in tropical regions. Past studies have relied mainly on crop-simulation models12 or statistical analyses based on reported harvest data34, each with considerable uncertainties and limited applicability to tropical systems. However, a wealth of historical crop-trial data exists in the tropics that has been previously untapped for climate research. Using a data set of more than 20,000 historical maize trials in Africa, combined with daily weather data, we show a nonlinear relationship between warming and yields. Each degree day spent above 30°C reduced the final yield by 1% under optimal rain-fed conditions, and by 1.7% under drought conditions. These results are consistent with studies of temperate maize germplasm in other regions, and indicate the key role of moisture in maize’s ability to cope with heat. Roughly 65% of present maize-growing areas in Africa would experience yield losses for 1°C of warming under optimal rain-fed management, with 100% of areas harmed by warming under drought conditions. The results indicate that data generated by international networks of crop experimenters represent a potential boon to research aimed at quantifying climate impacts and prioritizing adaptation responses, especially in regions such as Africa that are typically thought to be data-poor.

Figures at a glance


Effective adaptation of agriculture to climate change in the developing world will require at least two pieces of information: the relative risks posed by climate change across different locations and cropping systems, which is useful for prioritizing the use of scarce resources devoted to adaptation, and the likely mechanisms of potential damage from climate change, to prioritize among different types of possible solution. For example, a main strategy will probably be breeding for improved abiotic stress, but the particular traits that present the largest opportunities for progress are often unclear56.
Present approaches to addressing both of these needs are limited, especially in developing countries. For example, simulation models have been calibrated mainly in temperate systems, do not include all potentially relevant processes, and are dependent on inputs that prescribe cultivar characteristics, management practices, soil properties and initial conditions, all of which are imperfectly known78. Statistical approaches are frequently limited by the quantity and quality of data used to train them, which results in fairly large uncertainties4, although the data sets available for statistical approaches are improving910.
Here we introduce an empirical approach that relies on newly available data from a network of cropping trials. In this case, we focus on field trials for tropical maize conducted in Africa in 1999–2007 on a network of 123 research stations managed by the International Maize and Wheat Improvement Center (CIMMYT), National Agricultural Research Programs and private seed companies11 (Fig. 1). The original purpose of these trials was to test new varieties across a range of environmental conditions, to identify robust lines for release to farmers. Most trials were carried out under ‘optimal’ management, that is, rain-fed conditions using site-specific agronomic treatments to minimize nutrient, water, disease and other stresses. The second most common treatment was managed drought stress, where the varieties were irrigated in a rain-free period until plants were established, and then irrigation was cut off to induce moisture stress during flowering and grain-filling11. The varieties included in this data set are grown or intended for farmers’ fields throughout Africa, nearly all of which are rain-fed. We refer to each combination of maize variety, station, year and management regime as a single trial.
Figure 1: The study region in Africa.
The study region in Africa.
The circles show locations of crop trials, with the size of the circle indicating the number of trials per site (ranging from 20 to 1,249). Weather stations with daily data for at least some portion of the study period 1999–2007 are marked as crosses. The background map shows elevation, with higher altitudes appearing darker.
For each trial, we recreated the daily temperature and precipitation using thin-plate spline interpolation of daily records from nearby weather stations (see Methods). Various summary statistics of the growing season weather were then computed, including growing degree sums, averages for critical development phases and time spent above critical temperature thresholds. In total, 17,713 trials with optimal management and 3,244 with managed drought stress for the period 1999–2007 were used. The effect of weather on yields was modelled using a linear fixed-effects model, with three weather variables:
where Yi,s,t is the natural logarithm of reported yield (log(yield)) for the ith trial at station s in year tXi,s,t is a vector of climate variables for that trial, a is a vector of coefficients, bs represents an intercept associated with station sct represents an intercept for year t and ε is an error term. The weather variables in Xi,s,t in our initial model included three terms: GDD8,30, the sum of growing degree days between 8°C and 30°C for the growing season (defined as the interval from sowing to 150 days after sowing for each trial), GDD30+, the sum of growing degree days above 30°C, and precanth, total precipitation for the 21-day period centred on anthesis. GDD8,30 represents a typical measure used to predict maize development rates12, and is closely related to average growing-season temperature (Tavg), with a correlation over 0.98 in our sample. GDD30+ is a measure of exposure to temperatures above a threshold at which warming can be quite harmful to growth and reproductive processes13, and is only weakly correlated with Tavg (r=0.49) and GDD8,30 (r=0.45;Supplementary Fig. S1). Precipitation around anthesis is used because maize plants are particularly susceptible to drought stress at this stage614151617. Alternative formulations were tested, with similar results as described in the Supplementary Information. Inclusion of the coefficients bs and ct in equation (1) helps to ensure that any perceived effect of weather is not due to differences between sites or years that may arise from omitted variables. Within sites, omitted variables such as use of fertilizers, herbicides or labour are likely to be uniform, and any variations are assumed orthogonal to weather because the locations of trials were randomized within the experiment station.
We find a highly significant (P<0.01) effect of temperature on maize yields, with clear differences between optimal and drought conditions (Fig. 2a). Both management systems show fairly modest and statistically insignificant (P>0.05) sensitivities to increased degree days between 8°C and 30°C. In contrast GDD30+exhibits a marked negative effect on yields, with the effect larger under drought conditions. As the units of yields are in log, a coefficient of −0.01 (or −0.017) indicates that each additional degree day above 30°C reduces the final yield by 1% (or 1.7%) under optimal (or drought) conditions.
Figure 2: The effect of heat on maize yields.
The effect of heat on maize yields.
a, Regression estimates of the effects of an increase of GDD8,30 and GDD30+ by 1 degree day, using data from trials managed for optimal (n=17,713) or drought (n=3,244) conditions. Error bars indicate 95% confidence interval using robust standard errors clustered by site–year.b, Model estimate of yield impact of 1°C warming for trials at different average growing-season temperatures, using regression equations for trials with optimal or drought management. The lines are the best fits to the mean impact at each temperature level, and the shaded areas show an estimate of the 95% confidence interval using robust standard errors.
The importance of GDD30+ is consistent with the only previous study to our knowledge with a comparable sample size, which focused on temperate maize in the US (ref. 13). As in the optimal management case here, they found that increases in GDD8,30 improved yields but each additional GDD30+ reduced yields by about 1%. In our drought management case, yields are reduced by roughly 1.7% for each additional GDD30+. This demonstrates the importance of moisture status in the response to heat, an insight that is not possible from evaluating data from a single or, as in ref. 13, unknown mixture of management regimes. The interaction between moisture and heat could indicate that the main mechanism of heat damage is by reducing soil moisture and increasing the severity of drought, that the ability of maize to cope with direct effects of heat on cellular processes is dependent on plant water availability status, or both. For example, evaporative cooling is an important mechanism for coping with heat, but can occur only with ample soil moisture18.
The negative impact of GDD30+ found here and elsewhere indicates that daytime warming is more harmful to maize than night-time warming. To corroborate this, we carried out a regression with linear and quadratic terms for growing-season average daily maximum and minimum temperature. The results confirmed that warming is more harmful during the day, and under optimal management warming at night can even be beneficial (Supplementary Fig. S2). This result is probably crop dependent; for instance, recent analysis of rice indicates that night-time warming is more harmful than daytime warming10.
One mechanism of yield loss from daytime heat and moisture stress is damage to reproductive organs. To evaluate this further, a regression with GDD8,30 and GDD30+ split across three stages of the growing season was carried out. The results supported an important role for processes related to flowering, as sensitivity to GDD30+ was highest under optimal management for the 21 days around silking, and under drought management for pre-silking and silking stages (Supplementary Fig. S3).
The net effect of warming on yields was computed for each trial by artificially raising observed temperatures on each day by 1°C, recomputing temperature indices such as GDD8,30, and using the regression equations to predict the new yield. Results were summarized as averages for all trials at a given baseline temperature to assess the nonlinearity of warming effects (Fig. 2b). For optimal management, at present, maize growing below ~23°C in average growing-season temperature tends to gain from warming, owing to positive effects of GDD8,30, whereas yields of maize grown in areas above this baseline temperature tend to decline with warming. Sites above 25°C in average temperature decline quite rapidly, albeit with considerable uncertainty, because of frequent exposure to temperatures above 30°C, with more than 10% yield loss per °C of warming.
Under drought conditions, even the coolest trials are harmed by 1°C warming, with losses exceeding 40% at the hottest sites. Again, this emphasizes the importance of moisture in the ability of maize to cope with heat. Similarly, studies for maize in the US have shown much greater sensitivity to hot days for eastern, rain-fed states than in the western states, where irrigation is much more common13.
The relationships derived from trial data were used to map potential impacts for maize under optimal or drought management across sub-Saharan Africa (Fig. 3). Under optimal management, negative yield impacts were projected for roughly 65% of the area where maize is harvested at present in Africa. All maize areas were projected to exhibit yield declines under drought management, with more than 75% of areas predicted to decline by at least 20% for 1°C warming.
Figure 3: Model estimates of maize yield changes for 1°C warming.
Model estimates of maize yield changes for 1[thinsp][deg]C warming.
ac, Present growing-season average temperature (a) and estimated impacts of 1°C warming for all areas for optimal (b) and drought (c) management. df, Present maize-growing area (fraction of grid cell; ref. 23d) and estimated impacts of 1°C warming for areas with at least 1%of maize (e,f).
It is difficult to relate the management conditions in these trials to those in actual farmers’ fields. One clear difference is that these particular trials use fairly high rates of fertilizer to avoid nitrogen (N) stress, whereas most farmers outside South Africa and Zimbabwe have historically applied little N fertilizer. Nitrogen stress tends to mute the response to other stresses, such as moisture or heat419; thus, the maps in Fig. 3 would exaggerate the impacts on actual farmers under present conditions. However, there are widespread efforts to increase fertilizer rates in Africa to raise average yields20, and this would tend to bring fields closer to the types of heat sensitivity estimated here. For example, previously estimated responses to warming using country-level data in southern Africa4, where fertilizer rates are higher, lie between the estimates for optimal and drought conditions estimated here (Supplementary Fig. S4).
Not all maize varieties will respond similarly to climate change, and indeed shifting varieties represents a key potential means of adaptation. The large data set used here affords the opportunity to examine varietal differences (Supplementary Fig. S5), indicating a potentially important role for variety switching as an adaptive response to climate change, although the appropriate switch depends on moisture conditions.
Overall, our results indicate two important conclusions. First, maize yields in Africa may gain from warming at relatively cool sites, but are significantly hurt in areas where temperatures commonly exceed 30°C. This roughly corresponds to areas with growing season Tavg of 23°C or Tmax of 28°C. These conclusions are in line with previous results from process-based models721 or statistical models in Africa that relied on United Nations Food and Agriculture Organization data4, which showed heterogeneous impacts of climate change that, on average, are quite negative. However, the present study offers more precision than previous studies because of the large sample sizes.
Second, sensitivity to heat is clearly exacerbated in drought conditions, with even the coolest sites hurt by warming in the absence of adequate soil moisture. These results indicate that agronomic measures to improve soil moisture and breeding efforts to produce drought-tolerant crops are not only beneficial for managing present and future risks of drought, but are also probably important strategies to deal with future warming. Conversely, improvements in heat tolerance may limit losses during droughts. Although these conclusions cannot be directly extrapolated to other regions or crops, we believe the approach introduced here has wide applicability in other settings, and for a range of questions that extend beyond the present focus on temperature. For example, international public research organizations, national breeding programmes, and multinational companies possess similar data for many crops and regions.


Daily minimum and maximum temperatures and precipitation for each trial were estimated by interpolation of daily measurements made in the World Meteorological Organization, World Weather Watch Program (obtained from The locations of stations with data are shown in Fig. 1, although many stations have incomplete records over the study period (1999–2007). For each day, a thin-plate spline using latitude (in degrees), longitude (in degrees) and elevation (in kilometres) as predictors was fitted to the available data. Root mean square errors of the model at the World Meteorological Organization sites averaged 1.3°C for mean temperature and 2.7mmday−1 for precipitation, with cross-validated errors of 1.9°C and 4.8mmday−1, respectively.
Growing degree days were estimated from daily Tmin and Tmax at each site as:
where t is an individual time step (hour) within the growing season, Tt is the average temperature during this time step (determined by interpolating between Tmin and Tmax with a sin curve) and N is the number of hours between sowing and maturity. Only a small subset of sites reported maturity date, and therefore we could not use trial-specific growing season lengths without omitting a large fraction of the data. The average length to maturity for reporting sites (150 days or 3,600h) was therefore used for all sites. GDD8,30 corresponds to equation (2) with Tbase=8°C, and Topt=30°C, which is based on established values for maize12, whereas GDD30+ corresponds to equation (2) with Tbase=30°C, and  . Daily errors in T estimates will largely cancel when aggregating to growing-season sums, but any residual error will tend to attenuate the regression coefficients toward zero.
Several proxies for soil moisture availability were tested, including precipitation for the 21 days around anthesis (a period commonly viewed as critical to maize17), precipitation before anthesis, the difference between precipitation and total potential evapotranspiration before anthesis, and precipitation for the entire growing season. All gave similar results for temperature sensitivity, as did a model without any precipitation term, as well as a model with the measured anthesis–silking interval for the trial, which is a good indicator of moisture stress and a strong predictor of final yield1519 (see Supplementary Fig. S6).
In the linear mixed model in equation (1), the coefficients bs and ct can be treated as either fixed effects, where each site and year has its own independent intercept, or random effects, where the effects are viewed as derived from a Gaussian distribution (that is, bs~N(0,σb2)). We use the more conservative fixed-effects approach, but results were nearly identical when using random effects. Results were also similar when using actual yields instead of log-transformed yields. Log yields were used to account for the skewed distribution of yields (Supplementary Fig. S1), as commonly done and supported in this case by a theta parameter of 0.5 for the Box–Cox power transformation.
A potential problem when using standard regression is that, if model errors are not independent, the inferred confidence intervals can be overly optimistic. In this context, it is likely that trials conducted for a particular year in a particular station were all affected by the same omitted variables, and therefore errors will not be independent. To account for this, we clustered standard errors by site–year, and use these more conservative estimates of standard errors throughout.
Finally, we note that none of the regression models or impacts shown in Fig. 3 considers fertilization effects of elevated carbon dioxide levels. These effects are expected to be small for C4 crops such as maize, for which photosynthesis rates do not respond to higher ambient carbon dioxide22, but may be important under drought conditions when all crops show improved water-use efficiency with elevated carbon dioxide.

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