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Climate change and agriculture: impacts onwheat and corn yields in France

Catherine Benjamin and Ewen Gallic

Faculté des sciences économiques, Université de Rennes 1

Jeudi 28 novembre 2013 - Aber Wrac’h

Introduction Model Results Conclusion

1 Introduction

2 ModelYieldsClimate DataData AggregationIncluding Weather Variability

3 ResultsEstimationSimulation

4 Conclusion

Ewen Gallic Climate change and agriculture: impacts on wheat and corn yields in France - 2/48


1 Introduction



4 Conclusion



Climate is changing ;Agriculture as a prime area :

I direct impacts on yields,I consquences on global markets, on prices, on world food

supply, on food security, . . . ;Objective of this study: measuring the impact of weatheron wheat and corn yields in France.



corn wheat

0

20

40

60

80

1960 1970 1980 1990 2000 20101960 1970 1980 1990 2000 2010Year

Per

cent

age China

FranceIndiaUSAArgentinaBrazilIndonesiaMexicoUkraine

Source : FAOSTAT.

Figure 1: Top world producers of wheat and corn, in percentage ofglobal production



1 Introduction



4 Conclusion



Yields

1 Introduction



4 Conclusion



Yields

A wide literature;With mixed conclusions :

I positive global effects shown for some (Aggarwal andMall 2002; Deschênes and Greenstone 2007),

I negative global effects for others (Parry et al. 2004; Jonesand Thornton 2003) ;

Different aims:I forecasting (Fischer et al. 2005; Deschenes and Kolstad

2011),I determining influent factors of yield variation (Reidsma,

Ewert, and Lansink 2007),I quantification of different effects (Almaraz et al. 2008).



Yields

Yields modelsTwo types of models :

I agronomic based ones (e.g. Tubiello and Fischer (2007)),I regression based ones (e.g. Schlenker and Roberts (2008)).

Strengths Weaknesses

Agronomic • Distribution of weather • Small scale• CO2 Fertilizer effects • A lot of missing effects

Regression • Large scale • Annual data• Ease of calculation • Large dataset needed

Table 1: Strengths and weaknesses of agronomic and regressionbased models



Yields

Model estimatedFrom Deschênes and Greenstone (2007):

yct = αc + γt + X>ctβ +∑

iθifi(W ict) + εct , (1)

yct : yields or profits ;αc : individual specific effects ;γt : year fixed effects ;Xct : observable determinants of farmland values, varyingwith time t ;W ict : annual realization of the i th weather variable ;εct : a residual error.



Yields

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6000

7000

8000

9000

10000

1990 1995 2000 2005 2010Year

Yie

lds

(kh/

ha)

Crop ● ●Corn Wheat

Source : DISAR.

Figure 2: Corn and wheat yields evolution in France (1990–2011).



Yields

7000800090001000011000

Yields

(a) Corn.

4000

6000

8000

Yields

(b) Wheat.Source : DISAR.

Figure 3: Average annual yields (1990–2011, kg ha−1) .



Yields

Yields are observed on a yearly basis, and data are spatiallyaggregated ;Two issues :

I How can one aggregate weather data?I How can one incorporate variability of weather with an-

nual data?



Climate Data

1 Introduction



4 Conclusion



Climate Data

Weather Data Description

Average daily temperature and precipitation ;210 weather stations ;Source : NOAA ;From 1990 to 2011.



Climate Data

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0km 100km 200kmN

Figure 4: French weather stations



Data Aggregation

1 Introduction



4 Conclusion



Data Aggregation

Intuitive idea

1. Divide France with multiple rectangles ;

2. Estimate temperature and precipitation for each centroidof the rectangles;

3. Averaging for each département.



Data Aggregation

Intuitive idea

1. Divide France with multiple rectangles ;

Figure 5: France divided in multiple rectangles

2. Estimate temperature and precipitation for each centroidof the rectangles;




Data Aggregation

Intuitive idea

1. Divide France with multiple rectangles ;2. Estimate temperature and precipitation for each centroid

of the rectangles;




Data Aggregation

Intuitive idea

1. Divide France with multiple rectangles ;2. Estimate temperature and precipitation for each centroid

of the rectangles;3. Averaging for each département.



Data Aggregation

Two methods used to estimate the values of temperatureand precipitations at unobserved locations:

I ordinary kriging for temperature (Guillot (2004)),I trivariate thin-plate splines for precipitation (McKenney

et al. (2006)).



Data Aggregation

Temperature

Let Z = (z1, . . . , zn)> be a spatial random variable ;Observations are made at location (s1, . . . , sn) ;Let z(s) be the realization of Z (s) at location s.An estimation of Z (s0), at site s0 is given by :

Z (s0) =n∑

i=1λiZ (si) = λ>Z

with λi providing a minimum variance unbiased estimator.



Data Aggregation

Then, the kriging weights λ must satisfy

E[Zs0 − Zs0

]= 0

minλi

{V[Zs0 − Zs0

],λ ∈ Rn

}.



Data Aggregation

Unbiased estimator, assuming E(Z) = m :

E[Zs0 − Zs0

]= 0

⇔n∑

i=1λiE [Zsi ]− E [Zs0 ] = 0

⇔ mn∑

i=1λi −m = 0

⇔n∑

i=1λi = 1.

⇔ λ1 = 1.



Data Aggregation

Minimum variance : λ solution of[V[Z ] 11> 0

] [λµ

]=[Cov(Zs0 ,Z)

1

].

Details



Data Aggregation

The covariance function is defined as

C (h) = Cov [Z (s),Z (s + h)] ,

where h is the distance between s and s + h ;A parametric form is used :

C (h) = σ2 · ρ(h),

with σ2 the limit of the variogram tending to infinity lagdistance and ρ(·) a covariance function ;



Data Aggregation

The variogram function is given by

γ(h) = 12V [Z (s)− Z (s + h)]

And estimated using

γ(h) = 12nh

nh∑i=1

(Z (si)− Z (si + h))2 ,

where nh is the number of observations separated by h.



Data Aggregation

The spherical covariance function was used :

ρ(h) =

1− 32

hφ

+ 12

(hφ

)3, h < φ

0, h ≤ φ,

where φ is a scale parameter.



Data Aggregation

Precipitation

Let us assume that precipitation depend on both location(s, identified by longitude and latitude) and elevation (q)(as in Boer (2001)) ;Then the measurements can be viewed as

z(si , qi) = f (si , qi) + ε(si , qi), i = 1, . . . , n,

where f (·) is a trivariate function and ε(si , qi) are randomerrors.



Data Aggregation

The trivariate function f (·) can be estimated by minimizingn∑

i=1{z(si , qi)− f (si , qi)}+ λJ2(f ),

where J2(f ) is a penalty functional measuring the smooth-ness of f (·) and λ is a parameter controlling for the trade-off between the fit and the smoothness of f (·). Both canbe estimated.



Data Aggregation

The solution is given by

f (s) =4∑

j=1αjφj(s) +

n∑i=1

βiΨ(hi),

where α and β are unknown parameters vectors, φi arelinearly independent polynomials (φ1 = 1, φ2 = lon, φ3 =lat, φ4 = q), Ψ = h, and

hi =√

(lon− loni)2 + (lat− lati)2 + (q − qi)2



Including Weather Variability

1 Introduction



4 Conclusion




Temperature-related measures

Climate variability is not included because of yields obser-vation frequency ;Growing degree days measure a heat accumulation ;A definition is given by Deschênes and Greenstone (2007)

GDD =

0 si h ≤ 8h − 8 si 8 < h ≤ 3224 si h > 32

,

where h is the daily mean temperature.




Precipitation-related measures

To try to incorporate precipitation variability, another setof variables is created :

I # of wet days over a period (month or growing season),I # of consecutive dry days over a period ;

A day is considered wet at a given location if the totalprecipitation exceeds 0.01 inch.



1 Introduction



4 Conclusion



Estimation

1 Introduction



4 Conclusion



Estimation

AVG

GDDMonths

GDDComplete Growing

season

Figure 5: Different models.



Estimation

Four estimated models:

I pooling

yct = δ +∑

iθi fi(W ict) + εct (2)

I individual fixed effects

yct = αc +∑


I time fixed effects

yct = γt +∑


I individual and time fixed effects

yct = αc + γt +∑




Estimation

Four estimated models:I pooling

yct = δ +∑


I individual fixed effects

yct = αc +∑


I time fixed effects

yct = γt +∑


I individual and time fixed effects

yct = αc + γt +∑




Estimation

Only one selected model for each crop :I wheat: individual and time fixed effects, where weather

data is aggregated for each month, and with temperaturein degrees Celsius ;

I corn: individual fixed effects, where weather data is ag-gregated for each month, and with temperature in growing-degree days.



Estimation

Temperature effects

Table 2: Summary of effects of temperature on yields∆ yields in responseto an increase of thevariable

Variable

Wheat

↘ Temp. in February↘ Temp. in July↘ Temp. sup. in August↗ Temp. in April∩ Temp. in August (threshold at 21◦C)

Corn ↗ Temp. in April∩ Temp. in June (threshold at 250 GDD)



Estimation

Precipitation effectsTable 3: Summary of effects of precipitation on yields

∆ yields in responseto an increase of thevariable

Variable

Wheat

↘ # of wet days in May↘ Precip. in June∪ Precip. in January (threshold at 110.9 mm)∪ Precip. in July (threshold at 191.82 mm)

∩ # of wet days in February (threshold at 16.3days)

Corn

↗ Precip. in April↗ # of wet days in June↘ Precip. in May∩ Precip. in June (threshold at 99.5 mm)∩ Precip. in August (threshold at 92.2 mm)∪ # of wet days in May (threshold at 16.6 days)∪ # of wet days in July (threshold at 15 jours)



Simulation

1 Introduction



4 Conclusion



Simulation

S−10,3+3◦ C

S−10,2+2◦ C

S−10,1

+1◦ C−10% precipitation

S0,3+3◦ C

S0,2+2◦ C

S0,1

+1◦ C

+0% precipitation

Figure 6: Simulated climate scenarios



Simulation

Table 4: Yields variations under different climate scenario

+1◦ C +2◦ C +3◦ C

∆ precip. Wheat Corn Wheat Corn Wheat Maïs

0%Mean −7.2% 0.0% −15.6% −3.0% −25.0% −7.5%S.D. (2.0%) (11.6%) (4.8%) (11.8%) (8.4%) (11.9%)Min. −10.7% −19.% −22.8% −22.8% −37.4% −27.9%Max. −5.4% 17.1% −11.56% 13.8% −18.7% 9.1%

−10%

Mean −6.8% −1.3% −15.1% −4.3% −24.5% −8.9%S.D. (2.1%) (11.4%) (4.8%) (11.6%) (8.4%) (11.8%)Min. −10.0% −20.2% −22.1% −23.8% −36.7% −29.0%Max. −5.0% 15.8% −11.4% 12.6% −18.3% 7.8%



Simulation

−1.88

1.06

0.61

−1.44

1.86−0.03

−0.14

2.86

2.75

−2.77−3.24

−0.053.54

−2.27

−3.29

−19.180.56

17.091.28

2.34

6.28

−2.81

1.41−0.42

−2.61

0.43

0.21

2.24

−2.31

0.25

0.34

0.73

−1.98

−0.83 1.12

0km 100km 200km

N % change−20 and 00 and 20NA

(a) +0% precipitation, +1◦C.

−2.84

−0.38

−0.49

−2.6

0.15−1.35

−1.41

1.24

0.95

−4.24−4.49

−1.492.17

−3.71

−4.38

−20.17−0.03

15.82−0.41

0.67

4.6

−3.58

−0.17−1.85

−4.09

−1.37

−1.32

0.58

−2.64

−1.14

−1.28

−0.78

−3.18

−2.31 −0.61

0km 100km 200km

N% change

−40 and −20−20 and 00 and 20NA

(b) −10% precipitation, +1◦C.

Figure 7: Average variation of corn yield response to climatechange



Simulation

−11.18

−1.6

−6.12

−9.28

−9.33−10.78

−6.25

2.57

−6.32

−14.87−14.13

−3.263.15

−12.74

−15.06

−27.95−8.55

9.14−2.95

−3.69

−7.91

−13.38

−3.46−5.05

−14.33

−6.75

−4.24

−1.36

−13.54

−7.12

−5.26

−4.26

−12.71

−7.55 −6.3

0km 100km 200km

N% change

−40 and −20−20 and 00 and 20NA


−12.15

−3.04

−7.23

−10.45

−11.05−12.1

−7.53

0.94

−8.12

−16.33−15.38

−4.71.78

−14.18

−16.16

−28.94−9.15

7.86−4.64

−5.36

−9.59

−14.15

−5.03−6.48

−15.81

−8.55

−5.76

−3.03

−13.87

−8.51

−6.88

−5.77

−13.91

−9.02 −8.03

0km 100km 200km

N% change

−40 and −20−20 and 00 and 20NA


Figure 8: Average variation of corn yield response to climatechange



Simulation

−5.53−5.41

−6.21

−6.34

−9.72

−8.45−7.48

−7.08

−9.18

−6.02

−6.5−7.92

−10.72

−7.31−7.58

−8.43

−8.52

−6.33−8.53

−8.47

−5.56

−7.44

−6.6−6.4

−7.95

−6.85

−5.59

−5.89

−6.9

−5.75

−7.85

−6.2

−5.98−5.61

−8.96 −8.9

−7.41

0km 100km 200km

N % change−20 and 0NA


−5 −5.3

−5.54

−5.8

−9.42

−7.96−7.07

−6.64

−8.86

−5.53

−5.88−7.94

−9.99

−6.84−7.13

−7.91

−7.96

−5.69−7.87

−7.98

−5.11

−6.93

−6.21−6.1

−7.65

−6.06

−5.4

−5.37

−6.26

−5.32

−7.18

−5.63

−5.69−5.22

−8.67 −8.27

−6.93

0km 100km 200km

N % change−20 and 0NA


Figure 9: Average variation of wheat yield response to climatechange



Simulation

−18.88−18.66

−21.87

−21.2

−32.67

−28.63−26.91

−23.63

−31.38

−20.39

−23.67−26.4

−37.44

−25.75−25.21

−30.15

−30.17

−25.91−28.61

−29.72

−19.34

−25.02

−22.67−22.2

−26.44

−23.4

−18.82

−19.96

−23.29

−19.26

−27.64

−21.4

−20.06−18.87

−30.95 −31.2

−27.27

0km 100km 200km

N % change−40 and −20−20 and 0NA


−18.35−18.55

−21.21

−20.67

−32.37

−28.15−26.5

−23.19

−31.07

−19.91

−23.05−26.42

−36.7

−25.28−24.76

−29.62−29.61

−25.27−27.95

−29.22

−18.89

−24.51

−22.28−21.9

−26.14

−22.62

−18.63

−19.44

−22.66

−18.83

−26.97

−20.83

−19.78−18.48

−30.65 −30.56

−26.79

0km 100km 200km

N % change−40 and −20−20 and 0NA


Figure 10: Average variation of wheat yield response to climatechange



1 Introduction



4 Conclusion



Agriculture is vulnerable to climate fluctuations ;We estimated the variation of yields in France using panelmodels ;Mixed results:

I globally negative effects for wheat,I standard deviation too large for corn ;

Some limits to keep in mind:I producers can’t adapt by changing their crops,I CO2 mitigation effects are not taken into account,I neither is irrigation


Références I

Aggarwal, P.K. and R.K. Mall (2002). “Climate Change and Rice Yields inDiverse Agro-Environments of India. II. Effect of Uncertainties in Scenariosand Crop Models on Impact Assessment”. English. In: Climatic Change52.3, pp. 331–343. issn: 0165-0009. doi: 10.1023/A:1013714506779.Almaraz, Juan Jose et al. (2008). “Climate change, weather variability andcorn yield at a higher latitude locale: Southwestern Quebec”. In: Climaticchange 88.2, pp. 187–197.Boer, E. (2001). “Kriging and thin plate splines for mapping climate vari-ables”. In: International Journal of Applied Earth Observation and Geoin-formation 3.2, pp. 146–154. issn: 03032434.Deschênes, Olivier and Michael Greenstone (2007). “The economic impactsof climate change: evidence from agricultural output and random fluctu-ations in weather”. In: The American Economic Review 97.1, pp. 354–385.Deschenes, Olivier and Charles Kolstad (2011). “Economic impacts of cli-mate change on California agriculture”. In: Climatic Change 109.1, pp. 365–386.

http://dx.doi.org/10.1023/A:1013714506779

Références IIFischer, Günther et al. (2005). “Socio-economic and climate change im-pacts on agriculture: an integrated assessment, 1990-2080”. In: Philosoph-ical Transactions of the Royal Society B: Biological Sciences 360.1463,pp. 2067–2083. doi: 10.1098/rstb.2005.1744.Guillot, Gilles (2004). Introductin à la geostatistique. Institut NationalAgronomique de Paris-Grignon.Jones, Peter G and Philip K Thornton (2003). “The potential impacts ofclimate change on maize production in Africa and Latin America in 2055”.In: Global Environmental Change 13.1, pp. 51 –59. issn: 0959-3780. doi:10.1016/S0959-3780(02)00090-0.McKenney, Daniel W et al. (2006). “The development of 1901–2000 his-torical monthly climate models for Canada and the United States”. In:Agricultural and Forest Meteorology 138.1, pp. 69–81.Parry, M.L et al. (2004). “Effects of climate change on global food pro-duction under SRES emissions and socio-economic scenarios”. In: GlobalEnvironmental Change 14.1. Climate Change, pp. 53 –67. issn: 0959-3780.doi: 10.1016/j.gloenvcha.2003.10.008.

http://dx.doi.org/10.1098/rstb.2005.1744

http://dx.doi.org/10.1016/S0959-3780(02)00090-0

http://dx.doi.org/10.1016/j.gloenvcha.2003.10.008

Références III

Reidsma, Pytrik, Frank Ewert, and Alfons Oude Lansink (2007). “Analysisof farm performance in Europe under different climatic and managementconditions to improve understanding of adaptive capacity”. English. In:Climatic Change 84.3-4, pp. 403–422. issn: 0165-0009. doi: 10.1007/s10584-007-9242-7.Schlenker, Wolfram and Michael J Roberts (2008). Estimating the impactof climate change on crop yields: The importance of nonlinear temperatureeffects. Tech. rep. National Bureau of Economic Research.Tubiello, Francesco N. and Günther Fischer (2007). “Reducing climatechange impacts on agriculture: Global and regional effects of mitigation,2000–2080”. In: Technological Forecasting and Social Change 74.7. Green-house Gases - Integrated Assessment, pp. 1030 –1056. issn: 0040-1625.doi: 10.1016/j.techfore.2006.05.027.

http://dx.doi.org/10.1007/s10584-007-9242-7

http://dx.doi.org/10.1007/s10584-007-9242-7

http://dx.doi.org/10.1016/j.techfore.2006.05.027

References

Ordinary Kriging: minimum varianceMinimum variance is obtained by solving the followin program:minλ

{V[Zs0 − Zs0

],λ ∈ Rn

}s.c. λ1 = 1

V[Zs0 − Zs0

]= V [Zs0 ] + V

[Zs0

]− 2Cov(Zs0 , Zs0)

= V [Zs0 ] + V[λ>Z

]− 2Cov

(Zs0 ,λ

>Z)

= V [Zs0 ] + λ>V[Z ]λ− 2λ>Cov (Zs0 ,Z) .


References

Ordinary Kriging: minimum variance II

The program can be rewritten as

⇔ minλ

L =V [Zs0 ] + λ>V[Z ]λ

− 2λCov (Zs0 ,Z)− 2µ(λ>1− 1),

with µ the Lagrange multiplier.


References

Ordinary Kriging: minimum variance III

The first-order conditions are∂L∂λ

= 0∂L∂µ

= 0

⇔

2V[Z ]λ− 2Cov(Zs0 ,Z) + 2µ1 = 02λ1− 2 = 0.


References

Ordinary Kriging: minimum variance IV

The kriging weights (λ) are solution of the following system[V[Z ] 11> 0

] [λµ

]=[Cov(Zs0 ,Z)

1

],

i.e.

V(Z)λ = Cov(Zs0 ,Z)− µ1⇔ λ = [V(Z)]−1 (Cov(Zs0 ,Z)− µ1) .


References

Ordinary Kriging: minimum variance V

Then, the variance can be written as

V[Zs0 − λ>Z

]=V[Zs0 ] + λ> (Cov(Zs0 ,Z)− µ1)

− 2λ>Cov(Zs0 ,Z).

Return to Temperature


References

Estimation of J2(f )

The parameter J2(f ) can be estimated with

J2(f ) =∫ +∞

−∞

∫ +∞

−∞

(∂2f∂x2

)2

+ 2(∂2f∂x∂y

)2

+(∂2f∂y2

)2 dxdy

Return to Precipitation


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