3.1. Climatic characterization
As a starting point for the study, a climate analysis of the reference stations used was carried out to observe the behaviour of the variables throughout the year (Table 3). The minimum temperatures are not shown, because it will be shown below that when both precipitation and maximum temperature are included in the analysis the minimum temperature did not contribute additional information about the crop yield.
Table 3. Mean monthly maximum temperature and cumulative monthly precipitation during the study period (1979–2006)
| ||Month||Maximum temperature|
| || ||1||2||3||4||5||6||7||8||9||10||11||12|
| ||S.B.||− 0.1||1.9||7.9||15.1||21.1||26.4||28.5||27.3||23.5||16.5||9.1||2.2|
|China||Che.||− 2||2.6||9.8||18.7||25.2||28.7||29.9||28.8||24.3||17.3||7||− 0.6|
| ||Cha.||− 1.9||2.3||9.4||18.7||25.2||28.8||30.2||29.3||25.1||17.6||7.4||0.1|
| || ||1||2||3||4||5||6||7||8||9||10||11||12|
In Argentina, the five selected localities behaved in similar ways in the months between May and October. These months were the driest in the study period, with values of accumulated precipitation close to 50 mm. In the remaining months, the accumulated precipitation exceeded 100 mm and reached values of as much as 150–200 mm. Precipitation in Argentina has a high regional variability. Regional precipitation exhibits a very well defined annual cycle in the north and northeast. It exhibits a uniform distribution with small maxima during spring and autumn in the east central area and northeast Argentina. Precipitation in the south is scarce (Hoffmann, 1975; Schwerdtfeger, 1976).
The greatest annual precipitation during most months was registered in Formosa. The yearly accumulated average was 1419 mm. The results for Reconquista showed that most precipitation occurred during the transition months. The annual accumulated value was 1162.5 mm. The total annual precipitation for Córdoba was 917.9 mm; the low rainfall during the winter months was reflected in this value. In Rosario, the greatest accumulations were observed in the months of April to May and November to December. The annual accumulation value recorded was 943 mm. In Junín, the winter months exhibited the lowest values. The annual accumulated total was 993.9 mm.
The five reference stations for Argentina were similar in their temperature regime. These stations had hot summers and cool winters. A distinctive annual wave according to the geographical location (north–south) was exhibited by the recorded values. During summer, those values ranged between 28 and 34 °C, whereas in winter the values fluctuated between 14 and 24 °C.
The precipitation values for Brazil differed across stations. The greatest variability throughout the year in accumulated precipitation was exhibited by the two northernmost stations, Vilhena and Campo Grande. A difference between the summer (wet) and winter (dry) months was exhibited by these stations. Throughout the entire year, in Vilhena the total accumulated precipitation was 1719.6 mm and in Campo Grande 1080.1 mm.
Curitiba did not show great within-year variation, resulting in a cumulative annual total of 1180.6 mm. Irai and San Luis Gonzaga, the two southernmost stations, exhibited less intra-annual variability. The annual accumulation for the two stations exceeded 1800 mm.
The maximum temperature values also revealed differences between the stations located in the north and those located more to the south. Vilhena and Campo Grande exhibited little variability throughout the year, with amplitude of 4 °C. A strong annual difference was shown by the three stations in the south. Curitiba had the greatest amplitude, a value of 12 °C. The two remaining stations exhibited very similar behaviour, with an amplitude of 10 °C degrees.
In the United States, the five stations showed similar precipitation regimes. Columbia exhibited an average annual accumulation of 1013.7 mm. In Peoria the annual accumulation was 862 mm. Toledo presented the same pattern observed for Columbia, with an accumulation of 848 mm. throughout the year. For South Bend, the value of accumulation was 950 mm. Birmingham, the southernmost United States station included in the study, exhibited a different precipitation regime and an annual accumulation of 1370 mm.
Maximum temperatures for the stations analysed exhibited a strong annual pattern. Maximum winter temperatures were less than 5 °C. Maximum temperatures during the summer exceeded 30 °C.
For the purposes of this study, China had been divided into two areas. The northern area containing the Chaoyang and Chengde stations and the southern area swith Han Shou and Bijie stations. The two northern stations had very similar regimes and almost identical accumulation values for monthly precipitation. The winters were very dry, whereas the summers were wet. Throughout the year, the accumulated precipitation was relatively low, near 450 mm. The southern stations exhibited the same annual pattern, but specific values differ. The winter months were dry, but the extremes of the north were not reached. The summer months were wetter. The annual precipitation accumulation in Han Shou was 1295 mm and in Bijie 860 mm.
The maximum temperature again revealed differences between the north and the south. All the stations exhibited a distinct annual pattern (wave). At the northern stations, the winter months exhibited maximum temperatures less than 0 °C. Summer maximum temperature reached 30 °C. At the southern stations, variability was not as strong because winters were less harsh.
Based on the behaviour observed at the different stations, it was decided to represent the variables in the regions by area averages of the reference season data. In Brazil and China, the analysis was carried out for two areas, a northern zone and a southern zone. The analyses for Argentina and the United States focussed on one area for each country (Table 4).
Table 4. Monthly values of maximum temperature and accumulated precipitation regional for the average of reference stations
|Chi N||− 2.0||2.5||9.6||18.7||25.2||28.8||30.1||29.1||24.7||17.5||7.2||− 0.3|
3.2. Regional climate environment
In this part of the study the maximum temperature and the monthly precipitation accumulation were considered together in order to compare ranges and annual behaviour between regions (Figures 1 and 2). In Argentina, September marks the start of the corn cycle (Cs). This agricultural season is 9 months long and includes the three main stages of crop development: planting, flowering and harvest. The start of planting was generally characterized by maximum temperatures that were not extremely high and by low precipitation (50 mm on average). However, this lack of rainfall was quickly made up by the average accumulation values in the following months, especially during the flowering stage (December-January-February). In the ensuing harvest months, temperatures began to drop. Precipitation remained at the same value except during the last month of harvest (Ce), when precipitation values fell abruptly. Soya bean has a cycle that lasts for 7 months. Since the beginning of the cycle (Ss) in November, the precipitation values surpassed 100 mm in most months. The exception was harvest time in May (Se).
In the northern Brazil area, the months involved in both growing seasons presented the same temperature range. Recorded amounts of precipitation were greatest at the start of both cycles in November (Cs-Ss) and in the following months. A difference occurred during the harvest stage, where the recorded accumulation decreased and reached values near 50 mm. The average for the southern stations exhibited higher temperatures at the start of both cycles and ended with lower values at harvest time. Precipitation values during all of the cycle surpassed 100 mm and reached their maximum during flowering.
When the behaviour of the average values for reference stations in the United States was analysed it could be clearly seen that the range in the maximum temperature values was very different from that seen for Argentina and Brazil. During the planting and flowering months, the temperatures showed a greater range and very low variation in precipitation. During the course of the year, the temperature increased in a stepped way. The same sort of increase occurred with precipitation, which reached a maximum during the spring months, generally during May (Ss). The maximum temperature occurred in July to August (flowering months), accompanied by high precipitation values.
For China, the average of both stations in the north was unusual. The transition months (spring for planting and autumn for harvest) had the same values both for maximum temperature and for precipitation. The maximum temperature exhibited wide variation. These values were below 0 °C in winter and reached 30 °C in summer (flowering). Precipitation varied from the dry season to the warm months (the accumulated precipitation reached 100 mm.).
For the average of the southern stations, the shape of the curve changed. Maximum temperatures were higher than the temperatures recorded at the northern stations during the winter months. No difference between the two areas was observed for the warm months. In this case precipitation also varied from the dry winter to the wet warm season, but in this region the precipitation surpassed 150 mm (associated with flowering).
The previous analyses revealed that the studied crops were exposed to a wide range of precipitation and maximum temperatures during their development. The data exhibited different patterns of relationships between precipitation and maximum temperature.
To complete the study, the behaviour of the precipitation during each cycle was analysed in terms of the regional averages for each zone. The average precipitation values and standard deviations are shown in Table 5. Similarly, Table 6 indicates the average values and standard deviation of detrended crop yields.
Table 5. Mean values of accumulated precipitation during the growing season (in millimetres) and standard deviation value
|Precipitation (mm)||Corn||Soya bean|
Table 6. Mean and standard deviation of the corn and soya bean yields in the four countries studied
|Yield (kg ha)||Corn||Soya bean|
When both tables are analysed, it can be seen that the regions with most precipitation accumulation (both in Brazil) had the most variability. The regions with the greatest yield (United States and Argentina) also exhibited substantial variability, i.e. the yield reflected rainfall characteristics.
To compare the adaptability or climatic efficiency of the crops in the areas, this property will be represented by deriving a coefficient relating precipitation to crop yields. The variability along the record of the coefficient is shown in Figures 3 and 4. In addition, the type of yield for each cycle is highlighted. The 27 growing areas were divided into three groups: high (h), medium (m) and low (l) yield, each of them with nine cycles. In each country the thresholds that separated in categories were different, they depended of the yield values.
It could be seen that the two areas in Brazil had the lowest adaptability for corn, whereas the adaptability was highest in the United States and the northern region of China. On the other hand, the variability of this ‘index’ was determined by the variability of the precipitation more than by the range of the yields. This fact was evident because the ranges (high, low and medium) were distributed throughout the years in random way, without differentiating between maximum or minimum values of the adaptability coefficient.
In the case of soya beans, the index showed that northern Brazil and China had the lowest adaptability to rain, although Brazil showed a change in the 1990s, when the year-to-year variability also increased. This latter behaviour was shared by southern Brazil. The maximum adaptability was recorded for the United States, Argentina and northern China.
3.4. The crop yield—climatic variables relation
As a part of the study of the relationship between crop yields and climate variables, multiple regression analysis was carried out. The parameters used in this methodology represented regional average climate variables in each one of the zones defined previously.
Multiple regression models were developed based on specifications found in study by Thompson (1962). The author modelled corn yields for different states of the United States from 1930 to 1962. The model included climate variables: precipitation and temperatures. This kind of model has been adopted by several others such as Schlenker and Roberts (2006) and Tannura et al. (2008).
In the first multiple regression model, the yield (Y) was modelled by three study variables: the accumulated precipitation (pp) during the growing season and the average values of the maximum temperature (Tx) and minimum temperature (Tn) throughout the entire cycle:
The difference between the original yield and the yield predicted was represented by δ.
The existing dependence between precipitation and monthly maximum temperature was studied for each of the different stages of development of the crop and for the entire cycle of the regional averages. In the cases where the relationship between temperature and precipitation was significant, the effect was filtered out and the analysis was performed with the part of the maximum temperatures that was not explained by precipitation. Table 7 shows the correlation coefficients between the variables.
Table 7. Correlation coefficient of regional averages of maximum temperature and precipitation on the growth stages
| ||Corn||Soya bean|
| ||Growing stage||Planting||Flowering||Harvest||Growing stage||Planting||Flowering||Harvest|
|Arg||− 0.157||− 0.292||−0.329||− 0.131||− 0.297||−0.608||− 0.23||− 0.089|
|Bra N||0.28||0.186||0.034||0.018||0.266||0.186||0.037||− 0.16|
|Bra S||− 0.265||−0.333||− 0.307||− 0.282||−0.41||−0.333||− 0.108||−0.368|
|USA||− 0.272||−0.41||−0.577||− 0.26||−0.40||−0.432||−0.547||− 0.26|
|Chi N||− 0.142||− 0.119||−0.475||− 0.189||− 0.192||− 0.119||−0.369||− 0.097|
|Chi S||0.136||0.069||− 0.14||−0.621||− 0.104||0.256||−0.601||− 0.139|
The second model was similar to the first, but it excluded the minimum temperature. In this two-variable model, the relationship between the variables used was more controlled, Tx′ represented the part of the maximum temperature that was not explained by the precipitation:
The last model used examined the behaviour of precipitation (pp) and the maximum temperature (Tx) during each of the three stages into which the growing season was divided (planting—flowering—harvest). At this point, the linear relationship existing between the variables involved at each stage was filtered again. The equation for this model was:
Because the third theoretical model gave the best fit to the crop yield data, these results were presented mainly in tables and figures. The results for the others theoretical models only were commented on. Table 8 shows the values of the regression coefficients for the third model (Equation (3)).
Table 8. Values of the coefficients an (with n = 0, …, 6) of the third linear regression model that includes the maximum temperatures and precipitation in the stages of crops
| || ||a0||a1||a2||a3||a4||a5||a6|
|Arg||Corn||13371.5||0.46||1.94||0.23||27.3||− 330.6||− 83.7|
| ||Soya bean||7050.9||− 0.07||1.40||− 0.55||− 54.3||− 82.6||− 66.5|
|Bra N||Corn||1100.0||− 0.40||− 0.07||− 1.51||61.1||36.2||− 63.4|
| ||Soya bean||2633.2||− 0.21||0.03||− 0.36||− 66.0||− 6.7||43.3|
|Bra S||Corn||3251.1||0.41||0.68||− 0.79||− 69.1||10.0||− 0.6|
| ||Soya bean||3446.3||0.00||1.41||− 0.36||− 111.1||− 75.5||126.3|
|Chi N||Corn||4322.9||0.01||0.69||0.57||− 50.0||− 45.8||32.6|
| ||Soya bean||1495.9||0.68||− 0.08||0.44||0.5||1.7||− 27.0|
|Chi S||Corn||3984.6||− 0.68||− 0.11||1.50||− 22.0||− 67.2||17.6|
| ||Soya bean||521.9||0.14||0.11||− 0.31||19.3||4.0||− 2.0|
|USA||Corn||16021.5||− 1.23||− 0.78||− 1.71||144.3||− 483.3||129.0|
| ||Soya bean||4377.7||− 0.34||− 0.28||− 0.24||42.2||− 115.2||4.0|
The coefficient of determination (R2) was used to measure of the goodness of fit of the theoretical models. This coefficient measured the rate of change (percent) of crop yield that could be explained by climatic variables.
3.4.1. Corn crops
Table 9 shows the mean crop yield values of the regions, along with their standard deviations. These values were displayed according to the yield generated by the theoretical model that includes the maximum temperature and precipitation during each stage. The last column shows the value of the coefficient of determination.
Table 9. Mean values of the original yield and standard deviation
| ||Average||Deviation||Deviation||Rest||R2 (%)|
|Soya bean|| || |
Beginning with the analysis for Argentina, the third linear regression model showed that the precipitation values and maximum temperatures, evaluated by stages, explained 58% of the crop yield variability. Figure 5 shows a better fit to the generated yield, mainly in the ‘peaks’ observed in the record at different stages. A better fit was obtained near the end of the period, but the observed variability was not well represented at the beginning.
Figure 5. Detrended yield of corn in four producing regions (solid line) and yield generated according to the third linear regression model with the maximum temperature and precipitation data in the three stages of crop development (dotted line)
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For the model applied to the regional average for northern Brazil, the coefficient of determination reached a value of 29%. Figure 5 shows that the variability displayed by the crop yield was well represented. However, the ‘peaks’ in the crop yield were not as well represented by the model.
For the southern area of Brazil, when the regression model was used with the climatic variables represented by stages, the fit improved noticeably relative to that of the other models. The coefficient of determination showed that the values of accumulated precipitation (stage-wise fit) and the averages of their maximum temperatures represented 48% of the variability of the crop yield of corn.
For the United States, when the third linear regression model was used the results showed that the use of accumulated precipitation and of average maximum temperatures explained 73% of the variability in yield. Figure 5 shows the resulting regression and the observed yield values. This model fitted the variability, as well as the ‘peaks’ of extreme yield.
For the northern region of China, the values of the coefficient of determination did not differ between the theoretical models that used the data from the cycles and the regression model that uses the data of the variables in the stages. The value of coefficient of determination in all cases was around 35%.
For southern China, using the third model according to stages increased the resulting variability, but the model was still unable to represent extremes. In this case, precipitation and temperature only explained 25% of the variability in the efficiency of corn production.
3.4.2. Soya bean crops
The theoretical regression model (specifically, the third model) applied to the soyabean crop in Argentina exhibited an increased coefficient of determination. The model successfully represented the variability of the crop, including extreme cycles such as 1988–1989, 1997–1998 and 2003–2004.
For the northern part of Brazil, theoretical models did not represent the yield as well. The third model according to stages could not fit such cases of extreme yield as the 1990–1991, 2000–2001, 2002–2003 and 2004–2005 growing seasons. For the southern part of Brazil, the performance of this model was better than it was for the northern part. The variables included explained 56% of the variability in soya bean crop yield.
The United States data exhibited behaviour similar to that observed for corn crops in Argentina. A stage-level theoretical regression model yielded a coefficient of determination of 56%.
For northern China, the theoretical models did not adequately represent the variability in the yields of soya bean. The value of the coefficient of determination was 8% when stage-level model was used. Results for the southern part of China did not differ greatly from those for the northern part.