Stochastic Disagregation of Monthly Rainfall Data for Crop Simulation Studies
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Stochastic Disagregation of Stochastic Disagregation of Monthly Rainfall Data for Crop Monthly Rainfall Data for Crop Simulation Studies Simulation Studies Amor VM Ines and James W Hansen Amor VM Ines and James W Hansen International Institute for Climate Prediction International Institute for Climate Prediction The Earth Institute at Columbia University The Earth Institute at Columbia University Palisades, NY, USA Palisades, NY, USA Stochastic disaggregation, and Stochastic disaggregation, and deterministic bias correction of deterministic bias correction of GCM outputs for crop simulation GCM outputs for crop simulation studies studies
description
Stochastic Disagregation of Monthly Rainfall Data for Crop Simulation Studies. Stochastic disaggregation, and deterministic bias correction of GCM outputs for crop simulation studies. Amor VM Ines and James W Hansen International Institute for Climate Prediction - PowerPoint PPT Presentation
Transcript of Stochastic Disagregation of Monthly Rainfall Data for Crop Simulation Studies
Stochastic Disagregation of Monthly Stochastic Disagregation of Monthly Rainfall Data for Crop Simulation Studies Rainfall Data for Crop Simulation Studies
Amor VM Ines and James W HansenAmor VM Ines and James W Hansen
International Institute for Climate PredictionInternational Institute for Climate Prediction
The Earth Institute at Columbia UniversityThe Earth Institute at Columbia University
Palisades, NY, USAPalisades, NY, USA
Stochastic disaggregation, and Stochastic disaggregation, and deterministic bias correction of GCM deterministic bias correction of GCM outputs for crop simulation studies outputs for crop 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
liza
tio
ns
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
liza
tio
ns
Crop forecasts
<<<Bridging the GAP>>><<<Bridging the GAP>>>
• To present stochastic disaggregation, and deterministic bias correction as methods for generating daily weather sequences for crop simulation models
• To evaluate the performance of the two methods using the results of our experiments in Southeastern US (Tifton, GA; Gainesville, FL) and Katumani, Machakos Province, Kenya.
Objectives
Part I. Stochastic disaggregation of monthly rainfall amounts
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
NOTE: Used long-term NOTE: Used long-term conditionalconditional means of TMAX,TMIN,SRAD means of TMAX,TMIN,SRAD
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 in the intensity modelmodel
π = Rπ = Rm m / μ/ μwe condition we condition pp0101, p, p1111 from the from the
frequency and auto-correlation frequency and auto-correlation equationsequations
……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 ((RRmm/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 Skill of the MOS corrected GCM datacorrected GCM data
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)
Part II. 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 Bias corrected 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 successful? Is the procedure the procedure applicable in applicable in every situation?every 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
Conclusions
• Stochastic disaggregation:
– Conditioning the outputs to match target monthly rainfall totals works better than conditioning the inputs of the weather generator:
– i) it tends to minimize the variability of monthly rainfall within realizations;
– ii) tends to reproduce better the historic intensity and frequency;
– iii) requires fewer realizations to achieve a given level of accuracy in crop yield prediction
• Deterministic bias correction of daily GCM precip:
– There are useful information hidden in daily GCM outputs
– Extracting them entails interpreting the data according to the GCM climatology then correcting them based on observed climatology
• Overall, the success of stochastic disaggregation or bias correction of GCM outputs for crop yield prediction depends greatly on the skill of the GCM
THANK YOU…THANK YOU…
