Int J Biometeorol DOI 10.1007/s00484-014-0834-4
ORIGINAL PAPER
The role of climatic variables in winter cereal yields: a retrospective analysis Qunying Luo & Li Wen
Received: 10 July 2013 / Revised: 5 April 2014 / Accepted: 8 April 2014 # ISB 2014
Abstract This study examined the effects of observed climate including [CO2] on winter cereal [winter wheat (Triticum aestivum), barley (Hordeum vulgare) and oat (Avena sativa)] yields by adopting robust statistical analysis/modelling approaches (i.e. autoregressive fractionally integrated moving average, generalised addition model) based on long time series of historical climate data and cereal yield data at three locations (Moree, Dubbo and Wagga Wagga) in New South Wales, Australia. Research results show that (1) growing season rainfall was significantly, positively and non-linearly correlated with crop yield at all locations considered; (2) [CO2] was significantly, positively and non-linearly correlated with crop yields in all cases except wheat and barley yields at Wagga Wagga; (3) growing season maximum temperature was significantly, negatively and non-linearly correlated with crop yields at Dubbo and Moree (except for barley); and (4) radiation was only significantly correlated with oat yield at Wagga Wagga. This information will help to identify appropriate management adaptation options in dealing with the risk and in taking the opportunities of climate change.
Keywords Atmospheric CO2 concentration . Autoregressive fractionally integrated moving average . Generalised additive model . Season and non-season rainfall . Seasonal temperature . Radiation . Winter cereal yields
Q. Luo (*) University of Technology, Sydney, PO Box 123, Broadway, Sydney, NSW 2007, Australia e-mail: [email protected] L. Wen Office of Environment and Heritage, Sydney, NSW 2000, Australia
Introduction Climate is one of the major driving forces of economically important crops. The effects of past climate (climate trend) on crop production have long been studied by adopting statistical modelling (empirical) approaches based on historical climate and crop yields data. Thompson (1969) statistically analysed the relationship between weather and corn production in the corn belt of the USA. Swanson and Nyankori (1979) quantified the effects of weather and technology on both corn and soybean yield trends in the USA. A recent study by Lobell and Asner (2003) studied the relation between climate variation and corn and soybean yields at the county level. Adams et al. (2003) utilised an empirical approach to study climate change impacts on a wide range of crops in California including broad acre crops and horticultural crops. Lobell et al. (2007) analysed the relationship between crop yield and three common climate variables (rainfall, maximum/minimum temperature) for 12 major Californian horticultural and economic crops based on historical production and climate data for the period 1980–2003. A recent study by Liu et al. (2010) analysed the contribution of observed climate trend and agronomic (variety, fertiliser and irrigation) factors to wheat and corn yields by using both mechanistic crop modelling and regression modelling approaches in the Northern China Plain based on long time series (1981–2005) of historical climate, production and management information. Peltonen-Sainio et al. (2010) undertook more detailed statistical analyses in examining the effects of climate variables (temperature, rainfall, solar radiation and evapotranspiration) on crop yields by considering crop key phenophases (i.e. sowing, seedling, flowering and maturity). While these studies significantly enhanced the understanding of the relationship between climate and agricultural technologies with crop yield, they did not consider the contribution of increased atmospheric CO2 concentration [CO2] to crop yield trends.
Int J Biometeorol
Atmospheric [CO2] is a fundamental requirement for crops to synthesise carbohydrate. Both [CO2] and crop yields have shown an increasing trend over the last century (Amthor 1998; Solomon et al. 2007). Few studies have looked at the effects of observed increase in atmospheric [CO2] on the improvement of crop yields although some experimental studies have been conducted in investigating the CO2 fertilisation effects (CFE) on crop production worldwide (Kimball et al. 2002; Ainsworth and Long 2005; Ziska 2008). Amthor (1998) analysed the effects of historical [CO2] on wheat yield in the UK and found that the increase in atmospheric [CO2] is insignificant to wheat yield in that country. Lobell and Field (2008) estimated CFE on worldwide major crop (rice, wheat and corn) yields and found that mean estimates of CFE were consistent with values from experimental studies, but standard deviations were significantly larger than those from experiment. McGrath and Lobell (2011) derived CFE in dry conditions using historical crop (corn and soybean) yield data at the county level from wet and dry years in America. It was found that approximately 50 years of increasing [CO2] resulted in a 9 and 14 % improvement of yield in dry conditions for corn and soybean, respectively, which are similar to estimates derived from free air CO2 enrichment studies. Winter cereals (wheat, barley and oat) are major winter crops in New South Wales (NSW), Australia, in terms of their proportion by area (85–95 % for the period 1993–2006) and their production quantity compared to other winter crops such as canola and pulse [NSW Department of Primary Industry (DPI) 2007]. There are limited studies in Australia in analysing the effects of past climate on crop yield. Nicholls (1997) quantified the contribution of past climate and atmospheric [CO2] on national wheat yield trend and found that the contribution of increased [CO2] to yield trend is insignificant. However, as noted in Amthor (1998), Nicholls (1997) underestimated the contribution of increased atmospheric [CO2] on Australian wheat yield because of the de-trend processes (first difference approach) applied to both yield and climate variables prior to statistical analysis. In fact, CO2 effects were included in the trend term, therefore, were removed by the de-trend procedures. This motivated us to reinvestigate the effects of increased atmospheric [CO2] along with major climate factors on winter cereal crop yields by adopting rational, appropriate and robust research procedures and methodologies such as the autoregressive fractionally integrated moving average (ARFIMA). Another motivation of this research is that much finer scale (shire level/statistical local area scale, which is equivalent to county scale) long time series of yield data are available across the NSW cereal belt, compared with the national scale as used in Nicholls (1997). Therefore, this research aims to identify key climate variables including atmospheric [CO2], which influence cereal crop yields, and to quantify their relationships or functional forms (i.e. positive vs. negative, linear vs. non-linear) with cereal
yields at a local scale. This study presents a robust methodological framework for empirically estimating the effects of environmental variables, especially CFE, on crop yields.
Materials and methods Study sites Three shires [Moree (−29.49°, 149.85°), Dubbo (−32.27°, 148.62°), Wagga Wagga (−35.13°, 147.31°)] in a transect from northeast to southeast of the NSW grain belt were chosen. These three shires are good representatives of NSW grain production areas in terms of geographical distribution, rainfall areas and contribution to this state’s winter cereal production. Moree belongs to the northern farming system (NFS) and has a summer-dominant rainfall pattern. Clay soil is common in the NFS. Wagga Wagga belongs to the southern forming systems (SFS) and has a winter-dominant rainfall pattern. Red-brown earth is the common soil in the SFS. Dubbo is situated between Moree and Wagga Wagga, and rainfall is uniformly distributed throughout the year. There is a distinctive difference in soil moisture at sowing between the two farming systems due to the different soil types they have. Data sources and preparation Time series of crop yields Historical winter cereal (wheat, barley and oat) yields at statistical local area (shire) scale were obtained from Fitzsimmons (2004) and NSW DPI. The length of historical yield records varies by crops and locations (Table 1). Figure 1 shows the time series of winter cereal crop yields and production areas at the three sites. Crop yields present an increasing trend over the study period. The production area shows either an increasing trend or fluctuation throughout the period studied depending on location and crop species. The barley production area is very low in the first half of the study period for all study locations.
Table 1 Data types and length used in this study Locations
Historical yield Wheat
Barley
Oat
Climate and atmospheric [CO2]
Moree 1922–2006 1945–2006 1936–2001 Location and Dubbo 1922–2006 1933–2006 1924–2006 crop specific Wagga Wagga 1922–2006 1922–2006 1922–2006
Int J Biometeorol 4.0
140
3.5
80
350
3.0
120
3.0
70
2.5
100
2.0
80
1.5
60
1.0
40
0.5
150
100
0.5
50
0.0
0
0.0
350
4.0
300
3.5
Moree
3.5
200
2.0 150
1.5
100
1.0
0.0
0
35
4.0
30
3.5
16
3.0
14
15 10
Wagga Wagga
18
12
2.5
10
2.0
8
1.5
6
1.0
4
0.5
2
0
0.0
0
0.0
0
20
4.0
18
3.5
0.0
8
4.0
3.5
7
3.5
3.0
6
3.0
2.5
5
2.0
10
0
5
50
Moree
20
0.5
2.0
1.0
30
20
20
1.5
40
1.5 1.0
25
2.5
50
2.0
0.5
0.5
4.0
Oats Yield (t/ha)
250
2.5
4
Oats Yield (t/ha)
Barley Yield (t/ha)
3.0
Dubbo
3.0 Barley Yield (t/ha)
4.0
Production Area (000 ha)
1.0
60
2.5
Dubbo
16 14
2.5
12
2.0
10
1.5
8
1.5
3
1.0
2
0.5
1
0.5
2
0.0
0
0.0
0
1.0
6 4
Wagga Wagga
Production Area (000 ha)
1.5
90
Production Area (000 ha)
200
Wagga Wagga
30 25
3.0 20
2.5 2.0
15
1.5
10
1.0 5
0.5 0.0
Production Area (000 ha)
2.0
Barley Yield (t/ha)
250
Oats Yield (t/ha)
2.5
Production Area (000 ha)
300
Dubbo
Wheat Yield (t/ha)
160
3.5
Production Area (000 ha)
4.0
400
Production Area (000 ha)
3.0
450
Wheat Yield (t/ha)
Moree
Production Area (000 ha)
Wheat Yie.ld (t/ha)
3.5
Production Area (000 ha)
4.0
0
Fig. 1 Time series of winter cereal yields and production areas
Environment (e.g. climate, atmospheric [CO2]) and management (e.g. fertiliser application rates, adoption of new cultivars) are key determinants of final crop yields. To quantify the effects of observed environmental change on crop productivity, management effect needs to be filtered first. Previous studies employed autoregressive integrated moving average processes [ARIMA (p, d, q), where p, d and q are nonnegative integers that refer to the order of the autoregressive, integrated and moving average parts of the model] to remove positive trends caused by the improvement of agricultural production level (Nicholls 1997; Lobell and Field 2008; McGrath and Lobell 2011). However, some environmental variables such as ambient [CO2] also show constant increases; and their potential positive effects are indistinguishable by the ARIMA procedure. While the application of ARIMA to crop yield time series removes the effect of production improvement, any potential positive effect of such environmental factors is also filtered by this procedure. In other words, the ARIMA process is useful to investigate the impacts of stochastic environmental factors such as rainfall and temperature, but powerless for constantly increasing or decreasing factors, such as ambient [CO2]. We illustrate this point by using an easily understandable simulated dataset in the Appendix.
It is reasonable to assume that agronomic management influences on cereal yield generally occur at a much lower frequency than environmental influences (Baigorria et al. 2008). Thus, production improvements introduce long-term persistence (or memory) in yield time series. Long memory is a form of non-linear dynamics that describes the autocorrelation structure of a time series at long lags, in that a process with long memory displays distinct but non-periodic cyclical patterns. By generalising the widely used ARIMA to allow the degree of differencing [i.e. the term d in ARIMA (p, d, q)] to take fractional values, autoregressive fractionally integrated moving average, ARFIMA (p, d, q) processes are known to be capable of modelling long-run persistence (Hosking 1981). The ARFIMA (p, d, q) models have been applied in diverse fields such as financial time series (e.g. Lo 1991; Meade and Maier 2003), meteorological time series (e.g. Bloomfield 1992; Cohn and Lins 2005) and hydrological time series (e.g. Montanari et al. 1997; Wang et al. 2007). The model for an ARFIMA (p, d, q) for a time series yt with mean μ can be written as equation (1), which was described in Baum and Wiggins (2000) ΦðLÞð1−LÞd ðyt −μÞ ¼ ΘðLÞεt ; εt e i:i:d: 0; δ2
ð1Þ
Int J Biometeorol
where L is the backshift operator, i.e. Φ(L)=1−ϕ1L−… −ϕpLp, Θ(L)=1+ξ1L+…+ξqLq, and (1−L)d is the fractional differencing function defined by ð1−LÞd ¼
∞ X k¼0
Γ ðk −d ÞLk Γ ð −d ÞΓ ðk þ 1Þ
ð2Þ
with k the lag, Г(.) denoting the gamma function and d is the long memory parameter, which is allowed to be any real (noninteger) value. In this study, we first test the long-term persistence property in the crop yield time series and calculate the maximum likelihood estimators of the parameters of ARIMA (p, d, q) model using the “fracdiff” package (Reisen et al. 2006) in the R statistic environment (R Development Core Team 2012). The results show that all yield series exhibit the phenomenon of long-term memory (i.e. 0
ORIGINAL PAPER
The role of climatic variables in winter cereal yields: a retrospective analysis Qunying Luo & Li Wen
Received: 10 July 2013 / Revised: 5 April 2014 / Accepted: 8 April 2014 # ISB 2014
Abstract This study examined the effects of observed climate including [CO2] on winter cereal [winter wheat (Triticum aestivum), barley (Hordeum vulgare) and oat (Avena sativa)] yields by adopting robust statistical analysis/modelling approaches (i.e. autoregressive fractionally integrated moving average, generalised addition model) based on long time series of historical climate data and cereal yield data at three locations (Moree, Dubbo and Wagga Wagga) in New South Wales, Australia. Research results show that (1) growing season rainfall was significantly, positively and non-linearly correlated with crop yield at all locations considered; (2) [CO2] was significantly, positively and non-linearly correlated with crop yields in all cases except wheat and barley yields at Wagga Wagga; (3) growing season maximum temperature was significantly, negatively and non-linearly correlated with crop yields at Dubbo and Moree (except for barley); and (4) radiation was only significantly correlated with oat yield at Wagga Wagga. This information will help to identify appropriate management adaptation options in dealing with the risk and in taking the opportunities of climate change.
Keywords Atmospheric CO2 concentration . Autoregressive fractionally integrated moving average . Generalised additive model . Season and non-season rainfall . Seasonal temperature . Radiation . Winter cereal yields
Q. Luo (*) University of Technology, Sydney, PO Box 123, Broadway, Sydney, NSW 2007, Australia e-mail: [email protected] L. Wen Office of Environment and Heritage, Sydney, NSW 2000, Australia
Introduction Climate is one of the major driving forces of economically important crops. The effects of past climate (climate trend) on crop production have long been studied by adopting statistical modelling (empirical) approaches based on historical climate and crop yields data. Thompson (1969) statistically analysed the relationship between weather and corn production in the corn belt of the USA. Swanson and Nyankori (1979) quantified the effects of weather and technology on both corn and soybean yield trends in the USA. A recent study by Lobell and Asner (2003) studied the relation between climate variation and corn and soybean yields at the county level. Adams et al. (2003) utilised an empirical approach to study climate change impacts on a wide range of crops in California including broad acre crops and horticultural crops. Lobell et al. (2007) analysed the relationship between crop yield and three common climate variables (rainfall, maximum/minimum temperature) for 12 major Californian horticultural and economic crops based on historical production and climate data for the period 1980–2003. A recent study by Liu et al. (2010) analysed the contribution of observed climate trend and agronomic (variety, fertiliser and irrigation) factors to wheat and corn yields by using both mechanistic crop modelling and regression modelling approaches in the Northern China Plain based on long time series (1981–2005) of historical climate, production and management information. Peltonen-Sainio et al. (2010) undertook more detailed statistical analyses in examining the effects of climate variables (temperature, rainfall, solar radiation and evapotranspiration) on crop yields by considering crop key phenophases (i.e. sowing, seedling, flowering and maturity). While these studies significantly enhanced the understanding of the relationship between climate and agricultural technologies with crop yield, they did not consider the contribution of increased atmospheric CO2 concentration [CO2] to crop yield trends.
Int J Biometeorol
Atmospheric [CO2] is a fundamental requirement for crops to synthesise carbohydrate. Both [CO2] and crop yields have shown an increasing trend over the last century (Amthor 1998; Solomon et al. 2007). Few studies have looked at the effects of observed increase in atmospheric [CO2] on the improvement of crop yields although some experimental studies have been conducted in investigating the CO2 fertilisation effects (CFE) on crop production worldwide (Kimball et al. 2002; Ainsworth and Long 2005; Ziska 2008). Amthor (1998) analysed the effects of historical [CO2] on wheat yield in the UK and found that the increase in atmospheric [CO2] is insignificant to wheat yield in that country. Lobell and Field (2008) estimated CFE on worldwide major crop (rice, wheat and corn) yields and found that mean estimates of CFE were consistent with values from experimental studies, but standard deviations were significantly larger than those from experiment. McGrath and Lobell (2011) derived CFE in dry conditions using historical crop (corn and soybean) yield data at the county level from wet and dry years in America. It was found that approximately 50 years of increasing [CO2] resulted in a 9 and 14 % improvement of yield in dry conditions for corn and soybean, respectively, which are similar to estimates derived from free air CO2 enrichment studies. Winter cereals (wheat, barley and oat) are major winter crops in New South Wales (NSW), Australia, in terms of their proportion by area (85–95 % for the period 1993–2006) and their production quantity compared to other winter crops such as canola and pulse [NSW Department of Primary Industry (DPI) 2007]. There are limited studies in Australia in analysing the effects of past climate on crop yield. Nicholls (1997) quantified the contribution of past climate and atmospheric [CO2] on national wheat yield trend and found that the contribution of increased [CO2] to yield trend is insignificant. However, as noted in Amthor (1998), Nicholls (1997) underestimated the contribution of increased atmospheric [CO2] on Australian wheat yield because of the de-trend processes (first difference approach) applied to both yield and climate variables prior to statistical analysis. In fact, CO2 effects were included in the trend term, therefore, were removed by the de-trend procedures. This motivated us to reinvestigate the effects of increased atmospheric [CO2] along with major climate factors on winter cereal crop yields by adopting rational, appropriate and robust research procedures and methodologies such as the autoregressive fractionally integrated moving average (ARFIMA). Another motivation of this research is that much finer scale (shire level/statistical local area scale, which is equivalent to county scale) long time series of yield data are available across the NSW cereal belt, compared with the national scale as used in Nicholls (1997). Therefore, this research aims to identify key climate variables including atmospheric [CO2], which influence cereal crop yields, and to quantify their relationships or functional forms (i.e. positive vs. negative, linear vs. non-linear) with cereal
yields at a local scale. This study presents a robust methodological framework for empirically estimating the effects of environmental variables, especially CFE, on crop yields.
Materials and methods Study sites Three shires [Moree (−29.49°, 149.85°), Dubbo (−32.27°, 148.62°), Wagga Wagga (−35.13°, 147.31°)] in a transect from northeast to southeast of the NSW grain belt were chosen. These three shires are good representatives of NSW grain production areas in terms of geographical distribution, rainfall areas and contribution to this state’s winter cereal production. Moree belongs to the northern farming system (NFS) and has a summer-dominant rainfall pattern. Clay soil is common in the NFS. Wagga Wagga belongs to the southern forming systems (SFS) and has a winter-dominant rainfall pattern. Red-brown earth is the common soil in the SFS. Dubbo is situated between Moree and Wagga Wagga, and rainfall is uniformly distributed throughout the year. There is a distinctive difference in soil moisture at sowing between the two farming systems due to the different soil types they have. Data sources and preparation Time series of crop yields Historical winter cereal (wheat, barley and oat) yields at statistical local area (shire) scale were obtained from Fitzsimmons (2004) and NSW DPI. The length of historical yield records varies by crops and locations (Table 1). Figure 1 shows the time series of winter cereal crop yields and production areas at the three sites. Crop yields present an increasing trend over the study period. The production area shows either an increasing trend or fluctuation throughout the period studied depending on location and crop species. The barley production area is very low in the first half of the study period for all study locations.
Table 1 Data types and length used in this study Locations
Historical yield Wheat
Barley
Oat
Climate and atmospheric [CO2]
Moree 1922–2006 1945–2006 1936–2001 Location and Dubbo 1922–2006 1933–2006 1924–2006 crop specific Wagga Wagga 1922–2006 1922–2006 1922–2006
Int J Biometeorol 4.0
140
3.5
80
350
3.0
120
3.0
70
2.5
100
2.0
80
1.5
60
1.0
40
0.5
150
100
0.5
50
0.0
0
0.0
350
4.0
300
3.5
Moree
3.5
200
2.0 150
1.5
100
1.0
0.0
0
35
4.0
30
3.5
16
3.0
14
15 10
Wagga Wagga
18
12
2.5
10
2.0
8
1.5
6
1.0
4
0.5
2
0
0.0
0
0.0
0
20
4.0
18
3.5
0.0
8
4.0
3.5
7
3.5
3.0
6
3.0
2.5
5
2.0
10
0
5
50
Moree
20
0.5
2.0
1.0
30
20
20
1.5
40
1.5 1.0
25
2.5
50
2.0
0.5
0.5
4.0
Oats Yield (t/ha)
250
2.5
4
Oats Yield (t/ha)
Barley Yield (t/ha)
3.0
Dubbo
3.0 Barley Yield (t/ha)
4.0
Production Area (000 ha)
1.0
60
2.5
Dubbo
16 14
2.5
12
2.0
10
1.5
8
1.5
3
1.0
2
0.5
1
0.5
2
0.0
0
0.0
0
1.0
6 4
Wagga Wagga
Production Area (000 ha)
1.5
90
Production Area (000 ha)
200
Wagga Wagga
30 25
3.0 20
2.5 2.0
15
1.5
10
1.0 5
0.5 0.0
Production Area (000 ha)
2.0
Barley Yield (t/ha)
250
Oats Yield (t/ha)
2.5
Production Area (000 ha)
300
Dubbo
Wheat Yield (t/ha)
160
3.5
Production Area (000 ha)
4.0
400
Production Area (000 ha)
3.0
450
Wheat Yield (t/ha)
Moree
Production Area (000 ha)
Wheat Yie.ld (t/ha)
3.5
Production Area (000 ha)
4.0
0
Fig. 1 Time series of winter cereal yields and production areas
Environment (e.g. climate, atmospheric [CO2]) and management (e.g. fertiliser application rates, adoption of new cultivars) are key determinants of final crop yields. To quantify the effects of observed environmental change on crop productivity, management effect needs to be filtered first. Previous studies employed autoregressive integrated moving average processes [ARIMA (p, d, q), where p, d and q are nonnegative integers that refer to the order of the autoregressive, integrated and moving average parts of the model] to remove positive trends caused by the improvement of agricultural production level (Nicholls 1997; Lobell and Field 2008; McGrath and Lobell 2011). However, some environmental variables such as ambient [CO2] also show constant increases; and their potential positive effects are indistinguishable by the ARIMA procedure. While the application of ARIMA to crop yield time series removes the effect of production improvement, any potential positive effect of such environmental factors is also filtered by this procedure. In other words, the ARIMA process is useful to investigate the impacts of stochastic environmental factors such as rainfall and temperature, but powerless for constantly increasing or decreasing factors, such as ambient [CO2]. We illustrate this point by using an easily understandable simulated dataset in the Appendix.
It is reasonable to assume that agronomic management influences on cereal yield generally occur at a much lower frequency than environmental influences (Baigorria et al. 2008). Thus, production improvements introduce long-term persistence (or memory) in yield time series. Long memory is a form of non-linear dynamics that describes the autocorrelation structure of a time series at long lags, in that a process with long memory displays distinct but non-periodic cyclical patterns. By generalising the widely used ARIMA to allow the degree of differencing [i.e. the term d in ARIMA (p, d, q)] to take fractional values, autoregressive fractionally integrated moving average, ARFIMA (p, d, q) processes are known to be capable of modelling long-run persistence (Hosking 1981). The ARFIMA (p, d, q) models have been applied in diverse fields such as financial time series (e.g. Lo 1991; Meade and Maier 2003), meteorological time series (e.g. Bloomfield 1992; Cohn and Lins 2005) and hydrological time series (e.g. Montanari et al. 1997; Wang et al. 2007). The model for an ARFIMA (p, d, q) for a time series yt with mean μ can be written as equation (1), which was described in Baum and Wiggins (2000) ΦðLÞð1−LÞd ðyt −μÞ ¼ ΘðLÞεt ; εt e i:i:d: 0; δ2
ð1Þ
Int J Biometeorol
where L is the backshift operator, i.e. Φ(L)=1−ϕ1L−… −ϕpLp, Θ(L)=1+ξ1L+…+ξqLq, and (1−L)d is the fractional differencing function defined by ð1−LÞd ¼
∞ X k¼0
Γ ðk −d ÞLk Γ ð −d ÞΓ ðk þ 1Þ
ð2Þ
with k the lag, Г(.) denoting the gamma function and d is the long memory parameter, which is allowed to be any real (noninteger) value. In this study, we first test the long-term persistence property in the crop yield time series and calculate the maximum likelihood estimators of the parameters of ARIMA (p, d, q) model using the “fracdiff” package (Reisen et al. 2006) in the R statistic environment (R Development Core Team 2012). The results show that all yield series exhibit the phenomenon of long-term memory (i.e. 0
