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Crop-Weather Models
0
1000
2000
3000
4000
0 2 4 6 8
Rainfall (mm/d)
Yie
ld (
kg
/ha
)
0
1000
2000
3000
4000
25 27 29 31 33
Max Temp Average (C)
Yie
ld (k
g/h
a)
y = 0.9204x + 202.61
R2 = 0.81
0
500
1000
1500
2000
2500
3000
3500
4000
0 1000 2000 3000 4000
Simulated Yield (kg/ha)
Obs
erve
d Yi
eld
(kg/
ha)
Observed soybean yields (GA yield trials) vs. seasonal rainfall, temperature, simulated yields
0
1
2
3
4
5
Gra
in y
ield
(M
g/h
a)
0 200 400 600 800OND precipitation (mm)
The Challenge
• Nonlinearity. Crop response to environ-ment nonlinear, non-monotonic.
• Dynamics. Crops respond not to mean conditions but to dynamic interactions:– Soil water balance– Phenology
Crop Model Concept
2b. N-limited
3. Actual
1. Potential
pests, disease,micronutrients,toxicities
H, T, crop charac-teristics
water2a. Water-limited
??????
soil N dynamics,plant N use,stress response
photosynthesis,respiration,phenology
water balance,transpiration,stress response
Level of production Processes
nitrogen
after Rabbinge, 1993
DSSAT v4.02.0
The Challenge:The Scale Mismatch Problem
• Crop models:
– Homogeneous plot spatial scale
– Daily time step (w.r.t. weather)
• GCMs:
– Spatial scale 10,000-100,000 km2
– Sub-daily time step, BUT... Output meaningful only at (sub)seasonal scale
• Spatial averaging within GCM distorts daily variability important to crop response
• Temporal scale problem more difficult than spatial scale
Information Pathways
predicted crop yields
observed climate predictors
?
Information Pathways
downscaleddynamicmodel
stochasticgenerator
crop model(observedweather)
crop model(hindcast weather)
analogyears
predicted crop yields
statisticalclimatemodel
statisticalyield model
observed climate predictors
categorize
Linking Approaches
• Classification and analog methods (e.g., ENSO phases)
• Synthetic daily weather conditioned on forecast: stochastic disaggregation
• (Corrected) daily climate model output
• Statistical function of simulated response
Stochastic Disagregation of Monthly Stochastic Disagregation of Monthly Rainfall Data for Crop Simulation Studies Rainfall Data for Crop Simulation Studies Stochastic disaggregation, and deterministic Stochastic disaggregation, and deterministic
bias correction of GCM outputs for crop bias correction of GCM outputs for crop simulation studies simulation studies
Linkage to crop simulation models
Seasonal Climate
Forecasts
Crop simulation
models (DSSAT)
Crop forecasts
<<<GAP>>><<<GAP>>>
Daily Weather
Sequence
a) Stochastic disaggregation
Monthly rainfall
Stochastic disaggregation
Crop simulation
models (DSSAT)
Wea
ther
Rea
lizat
ions
Crop forecasts
GCM ensemble forecasts
Stochastic weather
generator
<<<Bridging the GAP>>><<<Bridging the GAP>>>
b) Bias correction of daily GCM outputs
24 GCM ensemble members
Bias correction of daily outputs
Crop simulation
models (DSSAT)
Wea
ther
Rea
lizat
ions
Crop forecasts
<<<Bridging the GAP>>><<<Bridging the GAP>>>
Stochastic disaggregation of monthly rainfall amounts
Rainfall amounts and frequency predictionKatumani, Machakos Province, Kenya
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
O N D J F
Months
R
Rainfall amount
Rainfall frequency
0
200
400
600
800
1000
1960 1965 1970 1975 1980 1985 1990 1995 2000
Year
Sea
son
al R
ain
fall
, m
m
Observed GCM_Hindcasts
R=0.62
Skill of the MOS corrected GCM Skill of the MOS corrected GCM datadata
OND
Structure of a stochastic weather generator
u
f(u)
u<=pc?
x
f(x)
Generate ppt.=0
pc=p01
pc=p11Wet-day non-ppt. parameters: μk,1; σk,1
Dry-day non-ppt. parameters: μk,0; σk,0
Generate today’s non-ppt. variables
Generate uniform random number
Precipitation sub-model Non-precipitation sub-model(after Wilks and Wilby, 1999)
Generate a non-zero ppt.
(Begin next day)
INPUTINPUT
OUTPUTOUTPUT
Precipitation sub-model
pp0101=Pr{ppt. on day t | no ppt. on day t-1}=Pr{ppt. on day t | no ppt. on day t-1}
pp1111=Pr{ppt. on day t | ppt. on day t-1}=Pr{ppt. on day t | ppt. on day t-1}
f(x)=α/βf(x)=α/β11 exp[-x/β exp[-x/β11] + (1-α)/β] + (1-α)/β22 exp[-x/β exp[-x/β22]]
μ= αβμ= αβ11 + (1-α)β + (1-α)β22
σσ22= αβ= αβ1122 + (1-α)β + (1-α)β22
2 2 + α(1-α)(β+ α(1-α)(β11-β-β22))
Max. Likelihood (MLH)
Markovian process
Mixed-exponential
Occurrence model:Occurrence model:
Intensity model:Intensity model:
Long term rainfall frequency:Long term rainfall frequency:
First lag auto-correlation First lag auto-correlation of occurrence series:of occurrence series:
π=pπ=p0101/(1+p/(1+p0101-p-p1111))
rr11=p=p1111-p-p0101
Temperature and radiation model
zz(t)=[AA]zz(t-1)+[BB]ε(t)
zzkk(t)=a(t)=ak,1k,1zz11(t-1)+a(t-1)+ak,2k,2zz22(t-1)+a(t-1)+ak,3k,3zz33(t-1)+(t-1)+
bbk,1k,1εε11(t)+b(t)+bk,2k,2εε22(t)+b(t)+bk,3k,3εε33(t)(t)
TTkk(t)=(t)=
μμk,0k,0(t)+σ(t)+σk,0k,0zzkk(t); if day t is dry(t); if day t is dry
μμk,1k,1(t)+σ(t)+σk,1k,1zzkk(t); if day t is wet(t); if day t is wet
Trivariate 1st order autoregressive conditional normal model
Decomposing monthly rainfall totals
RRm m =μ x π=μ x π
Dimensional analysis:Dimensional analysis:
where:where:
RRmm - mean monthly rainfall amounts, mm d - mean monthly rainfall amounts, mm d-1-1
μ μ - mean rainfall intensity, mm wd - mean rainfall intensity, mm wd-1-1
ππ - rainfall frequency, wd d - rainfall frequency, wd d-1-1
mm mm wd= x
d wd d
Conditioning weather generator inputs
μ = Rμ = Rm m /π/π we condition we condition αα in the intensity model in the intensity model
π = Rπ = Rm m / μ/ μwe condition we condition pp0101, p, p1111 from the frequency and from the frequency and
auto-correlation equationsauto-correlation equations
……and other higher order statisticsand other higher order statistics
Conditioning weather generator outputs
First step:First step:Iterative procedure - by fixing the input parametersIterative procedure - by fixing the input parametersof the weather generator using climatological values, of the weather generator using climatological values, generate the best realization using the test criterion generate the best realization using the test criterion
|1-R|1-RmSimmSim/R/Rmm||jj <= 5% <= 5%
Second step:Second step: Rescale the generated daily rainfall amountsRescale the generated daily rainfall amountsat month j by at month j by (R(Rmm/R/RmSimmSim))jj
Applications
A.1 Diagnostic case studyA.1 Diagnostic case study– Locations: Locations: Tifton, GATifton, GA and and Gainesville, FLGainesville, FL– Data: 1923-1999Data: 1923-1999
A.2 Prediction case studyA.2 Prediction case study – Location: Location: Katumani, KenyaKatumani, Kenya– Data: MOS corrected GCM outputs (ECHAM4.5)Data: MOS corrected GCM outputs (ECHAM4.5)– ONDJF (1961-2003)ONDJF (1961-2003)
Crop Model: CERES-Maize in DSSATv3.5Crop Model: CERES-Maize in DSSATv3.5
Crop: Maize (McCurdy 84aa)Crop: Maize (McCurdy 84aa)
Sowing dates: Sowing dates: Apr 2 1923 – TiftonApr 2 1923 – Tifton
Mar 6 1923 – GainesvilleMar 6 1923 – Gainesville
Soils: Soils: Tifton loamy sand #25 – TiftonTifton loamy sand #25 – Tifton
Millhopper Fine Sand – GainesvilleMillhopper Fine Sand – Gainesville
Soil depth: Soil depth: 170cm; Extr. H170cm; Extr. H22O:189.4mm – TiftonO:189.4mm – Tifton
180cm; Extr. H180cm; Extr. H22O:160.9mm – GainesvilleO:160.9mm – Gainesville
Scenario: Rainfed ConditionScenario: Rainfed Condition
Simulation period: 1923-1996Simulation period: 1923-1996
Simulation Data(Tifton, GA and Gainesville, FL)
Sensitivity of RMSE and correlation of yield
1000
1500
2000
2500
3000
1 10 100 1000
No. of realizations
RM
SE
, kg
ha-1
Rm
alpha
pi
1000
1500
2000
2500
3000
1 10 100 1000
No. of realizations
RM
SE
, kg
ha-1
Rm
alpha
pi
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 10 100 1000
No. of realizations
R
Rm
alpha
pi
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 10 100 1000
No. of realizations
RRm
alpha
piTifton, GA Gainesville, FL
A.1 Diagnostic Case
RRmm
ππ
μμ
Gainesville, FLGainesville, FL
Sensitivity of RMSE and R of rainfall amount, frequency and intensity at month of anthesis (May)
0
0.5
1
1.5
2
2.5
1 10 100 1000
No. of realizations
RM
SE
, m
m d
-1
Rm
Mui
Pi
0
0.2
0.4
0.6
0.8
1
1.2
1 10 100 1000
No. of realizations
R
Rm
Mui
Pi
0
1
2
3
4
5
6
7
8
9
10
1 10 100 1000
No. of realizations
RM
SE
, m
m w
d-1
Rm
Mui
Pi
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1 10 100 1000
No. of realizations
R
Rm
Mui
Pi
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
1 10 100 1000
No. of realizations
RM
SE
, w
d d
-1
Rm
Mui
Pi
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1 10 100 1000
No. of realizations
R
Rm
Mui
Pi
RRmmμμ ππ
RRmm
ππ
μμ
0
2000
4000
6000
8000
10000
1922 1932 1942 1952 1962 1972 1982 1992
Year
Yie
ld,
kg h
a-1
Base Yield Predicted
R=0.79
0
2000
4000
6000
8000
10000
1922 1932 1942 1952 1962 1972 1982 1992
Year
Yie
ld,
kg h
a-1
Base Yield Predicted
R=0.71
0
2000
4000
6000
8000
10000
1922 1932 1942 1952 1962 1972 1982 1992
Year
Yie
ld,
kg h
a-1
Base Yield Predicted
R=0.79
Gainesville, FL
μ
π
Rm
1000 1000 RealizationsRealizations
Predicted Yields
A.2 Case study: Katumani, Machakos Province, Kenya
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
O N D J F
Months
R
Rainfall amount
Rainfall frequency
0
200
400
600
800
1000
1960 1965 1970 1975 1980 1985 1990 1995 2000
Year
Sea
son
al R
ain
fall
, m
m
Observed GCM_Hindcasts
R=0.62
Skill of the MOS corrected GCM Skill of the MOS corrected GCM datadata
OND
Simulation Data(Katumani, Machakos Province, Kenya)
Crop Model: CERES-Maize Crop Model: CERES-Maize
Crop: Maize (KATUMANI B)Crop: Maize (KATUMANI B)
Sowing dates (Nov 1 1961)Sowing dates (Nov 1 1961)
Soil depth :Soil depth :130cm Extr. H130cm Extr. H22O:177.0mmO:177.0mm
Scenario: Rainfed Scenario: Rainfed
Simulation period: 1961-2003Simulation period: 1961-2003
Sowing strategy: conditional-forced Sowing strategy: conditional-forced
Sensitivity of RMSE and correlation of yield
1000
1200
1400
1600
1800
2000
1 10 100 1000
No. of realizations
RM
SE
, kg
ha-1 Rm
pi1
Rm+pi2
pi2
0.1
0.2
0.3
0.4
0.5
0.6
1 10 100 1000
No. of realizations
R
Rm
pi1
Rm+pi2
pi2
π1 (Conditioned)π1 (Conditioned)
RRmm (Hindcast) (Hindcast)
π2 (Hindcast)π2 (Hindcast)
RRmm+π2+π2
0
1000
2000
3000
4000
5000
6000
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Year
Yie
ld,
kg h
a-1
Obs
Rm0
1000
2000
3000
4000
5000
6000
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Year
Yie
ld,
kg h
a-1
Obs
pi2
0
1000
2000
3000
4000
5000
6000
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Year
Yie
ld,
kg h
a-1
Obs
pi10
1000
2000
3000
4000
5000
6000
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Year
Yie
ld,
kg h
a-1
Obs
Rm+pi2
RRmm (Hindcast) (Hindcast)
RRmm+ π2+ π2π1 (Conditioned)π1 (Conditioned)
π2 (Hindcast)π2 (Hindcast)
Bias correction of daily GCM outputs (precipitation)
0
1
2
3
4
5
6
jan feb mar apr may jun jul aug sep oct nov dec
Month
Mea
n m
oth
ly r
ain
fall
, m
m d
-1
obs123456789101112131415161718192021222324mean24
Statement of the problem
RRmm
Climatology, Monthly rainfall
0
20
40
60
80
100
120
140
jan feb mar apr may jun jul aug sep oct nov dec
Month
Var
ian
ce,
(mm
d-1
)2
obs123456789101112131415161718192021222324mean24
RRmm
Variance, Monthly Variance, Monthly rainfallrainfall
0
2
4
6
8
10
12
jan feb mar apr may jun jul aug sep oct nov dec
Month
Mea
n r
ain
fall
in
ten
sity
, m
m w
d-1
obs123456789101112131415161718192021222324mean24
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
jan feb mar apr may jun jul aug sep oct nov dec
Month
Mea
n r
ain
fall
fre
qu
ency
, w
d d
-1
obs123456789101112131415161718192021222324mean24
ππ
μμ
IntensityIntensity
FrequencyFrequency
Proposed bias correction
x j1
GCM GCMj 0
(x / )F(x; , ) 1 exp
j!
x j1
Historical Historicalj 0
(x / )F(x; , ) 1 exp
j!
F(xGCM)
XGCM
XHistorical
F(xHistorical)=F(xGCM)
x1GCM’
GCM
Historical
x1GCM
x j1
GCM GCMj 0
(x / )F(x; , ) 1 exp
j!
x j1
Historical Historicalj 0
(x / )F(x; , ) 1 exp
j!
F(xGCM)
XGCM
XHistorical
F(xHistorical)=F(xGCM)
x1GCM’
GCM
Historical
x1GCM
1.0
0.0 Xmax
0.0
F(x)
Daily rainfall, mm
F(xhistorical=0.0)
Empirical Distribution
1.0
0.0 Xmax
0.0
F(x)
Daily rainfall, mm
F(xhistorical=0.0)
Empirical Distribution
(a)-correcting frequency
(b)-correcting intensity
Application
Location: Katumani, Machakos, Kenya Location: Katumani, Machakos, Kenya
Climate model: ECHAM4.5 (Lat. 15S;Long. 35E)Climate model: ECHAM4.5 (Lat. 15S;Long. 35E)
Crop Model: CERES-Maize Crop Model: CERES-Maize
Crop: Maize (KATUMANI B)Crop: Maize (KATUMANI B)
Sowing dates (Nov 1 1970)Sowing dates (Nov 1 1970)
Soil depth :Soil depth :130cm; Extr. H130cm; Extr. H22O:177.0mmO:177.0mm
Scenario: Rainfed Scenario: Rainfed
Simulation period: 1970-1995Simulation period: 1970-1995
Sowing strategy: conditional-forced Sowing strategy: conditional-forced
Results
0
1
2
3
4
5
6
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
Mea
n m
on
thly
rai
nfa
ll,
mm
d-1
Obs
EG
GG
Uncorr
0
30
60
90
120
150
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
Var
ian
ce,
(mm
d-1
)2
Obs
EG
GG
Uncorr
0
2
4
6
8
10
12
14
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
Mea
n r
ain
fall
in
ten
sity
, m
m w
d-1
RRmm μμ
Variance, Rm Variance, μμ
0
50
100
150
200
250
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
Var
ian
ce,
(mm
wd
-1)2
0
50
100
150
200
250
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Obs
EG
GG
Uncorr
0.0
0.2
0.4
0.6
0.8
1.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
Mea
n r
ain
fall
fre
qu
ency
, w
d d
-1
Obs
EG
GG
Uncorr
ππ
1000
1500
2000
2500
3000
0 4 8 12 16 20 24
Realizations
RM
SE
, kg
ha-1
EG
GG
Uncorr
0.3
0.4
0.5
0.6
0.7
0 4 8 12 16 20 24
Realizations
R
EG
GG
Uncorr
Sensitivity of RMSE and correlation of yield
0
1000
2000
3000
4000
5000
6000
1970 1975 1980 1985 1990 1995
Year
Yie
ld,
kg h
a-1
Obs
Bias corrected, GG
Disaggregated, Rm
R GG =0.69
R Rm =0.58
Comparison of yield predictions using disaggregated, MOS-corrected monthly GCM predictions, and bias-corrected daily gridcell GCM simulations
0
2
4
6
8
10
12
14
1970 1975 1980 1985 1990 1995
Year
Mea
n r
ain
fall
in
ten
sity
, m
m w
d-1
Obs
GGr=0.43
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1970 1975 1980 1985 1990 1995
Year
Mea
n r
ain
fall
fre
qu
ency
, w
d d
-1 Obs
GG r=0.74
0
1
2
3
4
5
6
7
8
1970 1975 1980 1985 1990 1995
Year
Mea
n r
ain
fall
am
ou
nt,
mm
d-1 Obs
GGr=0.74
Bias corrected Bias corrected seasonal seasonal rainfall (OND)rainfall (OND)
RRmm
μμ
ππ
0
1
2
3
4
5
6
7
8
1970 1975 1980 1985 1990 1995
Year
Mea
n m
on
thly
rai
nfa
ll,
mm
d-1 Observed
MOS corrected
Bias corrected GG
R_MOS=0.59R_BCGG=0.74
Comparison of MOS corrected and bias corrected seasonal rainfall (OND)
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
R
Bias corrected
Uncorrected
Intesity
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
R
Bias corrected
UncorrectedFrequency
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
R
Bias corrected
UncorrectedR m
Why are we Why are we successful? Is the successful? Is the procedure procedure applicable in every applicable in every situation?situation?
Inter-annual Inter-annual correlation (R) of correlation (R) of monthly rainfallmonthly rainfall
0
5
10
15
20
25
1969 1974 1979 1984 1989 1994
Year
Rain
fall
in
tesit
y,
mm
wd-1
Observed
Bias corrected
Uncorrected
Intensity
0.0
0.2
0.4
0.6
0.8
1.0
1969 1974 1979 1984 1989 1994
Year
Rain
fall
fre
qu
en
cy,
wd
d-1
Observed
Bias corrected
Uncorrected
Frequency
0
2
4
6
8
10
12
14
16
1969 1974 1979 1984 1989 1994
Year
Mean
mo
nth
ly r
ain
fall
, m
m d-1 Observed
Bias corrected
Uncorrected
R m
Inter-annual Inter-annual variability of variability of monthly rainfall monthly rainfall for Novemberfor November
Extracting Useful Information from Daily GCM Rainfall for Cropping System Modeling
Temporal mismatch…
Seasonal Climate
Forecasts
Cropping system models
Yield forecasts, water balance
etc.
<<<GAP>>><<<GAP>>>
Daily Weather
Sequences
Cropping system models require daily weather inputs
GCM
Rai
nfal
l vs.
Obs
erve
d Ra
infa
ll
Ines and Hansen (2006). Agric. For. Meteorol.
Mean amount(mm d-1)
Intensity(mm wd-1)
Frequency(wd d-1)
Obs GCM
Source: wikipedia
0
1
2
3
4
5
6
1970 1975 1980 1985 1990 1995
Th
ou
san
ds
Base Yield
Mean24
Weather within Climate Hypothesis
Mai
ze Y
ield
(kg
ha-1
)
Years
Correlation=0.65“Observed” yield
Uncorrected ECHAM4.5GCM
BIAS
Machakos Southern Province, Katumani, Kenya
Cropping season: Oct-Feb (Maize crop)
Deterministic Bias Correction
GCM ensemble members
Bias correction of daily outputs
Crop simulation
models (DSSAT)
Wea
ther
Rea
lizati
ons
Crop forecasts
<<<Bridging the GAP>>><<<Bridging the GAP>>>
Bias Correction of Daily GCM Rainfall
(a)-correcting frequency
(b)-correcting intensity
Ines and Hansen (2006)Hansen et al. (2006)
10 0 0GCM ,m obs ,m obsx F F x .
1'i obs ,m GCM ,m ix F F x
can be varied
BC-G
CM R
ainf
all v
s. O
bser
ved
Rain
fall
Ines and Hansen (2006). Agric. For. Meteorol.
Mean amount(mm d-1)
Intensity(mm wd-1)
Frequency(wd d-1)
Source: wikipedia
0
1
2
3
4
5
6
1971 1974 1977 1980 1983 1986 1989 1992 1995
Th
ou
sa
nd
s
Observed BC Uncorr
RBC-Obs=0.71
RUncorr-Obs=0.65
0.0
0.2
0.4
0.6
0.8
1.0
0 10 20 30 40
Cu
mu
lativ
e F
req
uen
cy
Dry Spell Length (days)
observed
GCM
Dry spell length (days)
During Anthesis (Nov 15-Dec 31),for 25 years
BIASBC-Obs
BIASUncorr-Obs
Sample Bias-Corrected (BC) Rainfall (mm)
0
10
20
30
40
50
60
70
80
90
1 16 31 46 61 76 91 106
121
136
151
166
181
196
211
226
241
256
271
286
301
316
331
346
361
0
10
20
30
40
50
60
70
80
90
1 16 31 46 61 76 91 106
121
136
151
166
181
196
211
226
241
256
271
286
301
316
331
346
361
Day of Year (year: 1995)
Member 1-corr
Observed
Croppingseason
0
10
20
30
40
50
60
70
80
90
1 16 31 46 61 76 91 106
121
136
151
166
181
196
211
226
241
256
271
286
301
316
331
346
361
Member 1-uncorr
mm mm
BC fails to correct the temporal structure of daily rainfall
Corrected Monthly Rainfall Frequency after BC
R² = 0.004
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
R² = 0.551
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Threshold: 0mm
R=0.06
R=0.74
Observed
Observed
Before
After
Combined BC-DisAg
Stochastic disaggregation
GCM ensemble members
Bias correction of daily outputs
Crop simulation
models (DSSAT)
Wea
ther
Rea
lizati
ons
Crop forecasts
<<<Bridging the GAP>>><<<Bridging the GAP>>>
Simulated Number of Dry days (Nov. 15-Dec. 31)
0
10
20
30
40
50
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
Realizations Obs Mean_Realizations
0
10
20
30
40
50
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
Realizations Obs Mean_Realizations
0
10
20
30
40
50
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
Realizations Obs Mean_Realizations
R2=0.49 R2=0.45
R2=0.45
RAW BC
BC-DisAg2
0.0
0.1
0.2
0.3
0.4
0.5
0 5 10 15 20 25 30 35 40 45 50
Observed Uncorrected GCM runs
0.0
0.1
0.2
0.3
0.4
0.5
0 5 10 15 20 25 30 35 40 45 50
Observed Bias Corrected GCM runs
0.0
0.1
0.2
0.3
0.4
0.5
0 5 10 15 20 25 30 35 40 45 50
Observed BC - Disaggregated GCM runs
Mean GCM
Mean observed
a b c
Dry spell length
Prob
abili
ty
PDF of dry spell lengths (days) during anthesis period (Nov. 15-Dec. 31) from a) uncorrected, b) BC only and c) BC-DisAg2 (best trial).
Dry spell length distributions (Nov. 15-Dec. 31)
0
1
2
3
4
5
6
1970 1975 1980 1985 1990 1995
Observed Uncorrected BC BC-DisAg1 BC-DisAg2
1 – rainfall freq information derived from indv. members
2 – mean rainfall freq information derived from ensem. members
year
Mai
ze Y
ield
(kg
ha-1
)Performance of the information extracted from daily GCM rainfall
MethodMethodRR(-)(-)
MBE MBE (Mg ha(Mg ha-1-1))
dd(-)(-)
MSE MSE (Mg ha(Mg ha-1-1))22
MSEMSERR
(Mg ha(Mg ha-1-1))22
MSEMSESS (Mg ha(Mg ha-1-1))22
UncorrectedUncorrected 0.610.61 -2.35-2.35 -1.14-1.14 6.616.61 1.061.06 5.555.55
BC onlyBC only 0.700.70 -1.04-1.04 0.500.50 1.951.95 0.860.86 1.091.09
BC-DisAg1BC-DisAg1 0.630.63 -0.41-0.41 0.630.63 1.221.22 1.011.01 0.210.21
BC-DisAg2BC-DisAg2 0.730.73 -0.20-0.20 0.740.74 0.910.91 0.790.79 0.120.12
Lessons learned…
• Simultaneous Bias Correction (BC) of GCM rainfall frequency and intensity improves the “weather within climate” information contained in the daily GCM rainfall, however-
• BC does not correct the temporal structure of daily GCM rainfall… GCM daily rainfall are highly auto-correlated.
• Combined BC-DisAg improves the temporal structure of daily rainfall hence improved the simulations of dry spell lengths and frequency, thus improving the systematic bias in the simulated yields.
Linear Programming
1
N
j jj
Max Z c x
1 1
M N
ij j ii j
a x b
0jx , j
Subject to:
Definition of terms
Z = value of overall performance
xj = level of activity j
cj = increase in Z that would result from each unit increase in level of activity j
bi = amount of resource i that is available for allocation to activities j
aij = amount of resource i consumed vy each unit of activity j
Example
Max Z = 2x1 + 3x2
Subject to:
x1 ≤ 4
2x2 ≤ 12
3x1 + 2x2 ≤ 18
Non-negativity constraint:
x1 ≥ 0; x2 ≥ 0
Graphical solution
1 2 3 4 5 6 7 8 9 100
12
34
56
78
910
0x1 ≤ 4
2x2 ≤ 12
x1
x2 3x1 + 2x2 ≤ 18
FEASIBLE REGION
(0,0)
(0,6)
(2,6)
(4,3)Zmax = 2x1 + 3x2
Non-Linear Programming
1
j
Np
jj
Max Z c x
1 1j
M Np
ij ii j
a x b
0jx , j
Subject to:
Graphical solution; linear constraints
1 2 3 4 5 6 7 8 9 100
12
34
56
78
910
0
x1
x2
FEASIBLE REGION
1
j
Np
jj
Max Z c x
Graphical solution; non-linear constraint
1 2 3 4 5 6 7 8 9 100
12
34
56
78
910
0
x1
x2
FEASIBLE REGION
1
j
Np
jj
Max Z c x
Crop-water management Example: Bata Minor, Bhakra Irrigation System, Kaithal, Haryana, India
IRRIGATION SYSTEMIRRIGATION SYSTEM
Physical properties (soil, Physical properties (soil, water quality, GW water quality, GW depthdepth……))
Management practices Management practices (water, crop mgt(water, crop mgt……))
WEATHERWEATHER
EXTERNAL EXTERNAL CONSTRAINTSCONSTRAINTS
We can explore We can explore options in agricultural options in agricultural and water and water managementmanagement
Need to characterize and Need to characterize and understand these complexitiesunderstand these complexities
INPUTINPUT
OUTPUTOUTPUT
Yield, water balance, Yield, water balance, water productivitieswater productivities……
NEED to develop a regional modelNEED to develop a regional model(deterministic-stochastic)(deterministic-stochastic)
RS-simulation model framework
Pink: INVERSE MODELING
Red: FORWARD MODELING
STUDY STUDY AREAAREA
Snapshot of Kaithal Irrigation Circle (Landsat 7ETM+)
ETa in Bata Minor from SEBAL analysis
ETa, mm ETa, mm
m m
February 4, 2001 March 8, 2001
2.90
2.48
2.06
1.64
1.22
0.80
4.20
3.44
2.68
1.92
1.16
0.40
Classification
0
5
10
15
20
25
0.5 1 1.5 2 2.5 3 3.5 4 4.5
ETa, mm
Rel
. fre
qu
ency
, %
0
5
10
15
20
25
0.5 1 1.5 2 2.5 3 3.5 4 4.5
ETa, mm
Rel
. fre
qu
ency
,%
February 4, 2001 March 8, 2001
Cropped area
Cropped area
GA solution to the regional inverse modeling
0
10
20
30
40
50
60
<=1.91.9-2.12.1-2.32.3-2.52.5-2.7 >2.7
ETa, mm
Re
l. fr
eq
ue
nc
y, %
SEBAL
SWAPGA
0
10
20
30
40
50
60
<=2.92.9-3.13.1-3.33.3-3.53.5-3.73.7-3.9>3.9
ETa, mm
Re
l. fr
eq
ue
nc
y
SEBAL
SWAPGA
0
10
20
30
40
50
60
<=1.9 1.9-2.1 2.1-2.3 2.3-2.5 2.5-2.7 >2.7
ETa, mm
Rel
. fre
quen
cy, %
SEBAL
SWAPGA
0
10
20
30
40
50
60
<=2.9 2.9-3.1 3.1-3.3 3.3-3.5 3.5-3.7 3.7-3.9 >3.9
ETa, mm
Rel
. fre
quen
cy, %
SEBAL
SWAPGA
February 4, 2001 March 8, 2001
System characteristics derived by GA
* The mean and standard deviation were derived independently, so the values depended on the range between their prescribed maximum and minimum values.
** Sowing dates were represented by emergence dates in Extended SWAP.
Stochastic variables Mean Standard deviation (soil parameter)* 0.0212 0.0252 n (soil parameter) 1.4144 0.0381 Emergence date** November 22 7 days Depth to groundwater 434.6 cm 33.5 cm Irrigation scheduling 0.72 0.28 Irrigation quality 2.4 dS m-1 0.74 dS m-1
N
max iN
i 1
1Z max Y
NM
N
i Si 1
1Ir Qave
N
1min 1 1max
1min 1 1max
2min 2 2max
2min 2 2max
2 2 2 2i 1 1 2 2 3 3 4 4 i
Ir f ( , ), ( , ), ( , ), ( , ) ¥ ¥ ¥ ¥
2 2 2i 1 1 2 2 5 5 i
Y f ( , ), ( , ), ( , ) ¥ ¥ ¥
S SQave f Qc,Qgw
Crop-water management optimization model
Objective function
Subject to water availability
Decision variables:Water management
Decision variables:Crop management
By definition: Soil properties
Salinity
N
ii 1
1LL Ir UL
N
SLL 1 Qave
SUL (1 )Qave
2N 2 N
i imaxi 1 1 i 1
1 1fitness Max Y Ir Limit
N Nk
l ll
Crop-water management Optimization
Take the relaxed constraints
Where:
Fitness function:
Average water supply, mm
Yie
ld,
kg h
a-1
Optimized wheat yields
Current
Optimized
Current scenario
Best management options Water Water management a Crop management b
Available, mm 200 0.68 0.03 Nov. 11 12 300 0.73 0.28 Nov. 11 20 400 0.88 0.13 Nov. 26 2 500 0.93 0.06 Nov. 18 10 600 0.94 0.06 Nov. 18 19
Crop-water management options
Note: A Rainfall of 91 mm was recorded during the simulation periodNote: A Rainfall of 91 mm was recorded during the simulation period
a a In terms to TIn terms to Taa/T/Tpp (irrigation scheduling criterion) (irrigation scheduling criterion)
bb In terms of emergence dates In terms of emergence dates