Stochastic Disagregation of Monthly Rainfall Data for Crop Simulation Studies

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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)

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)

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<=pc?

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

1 10 100 1000

No. of realizations

1 10 100 1000

No. of realizations

1 10 100 1000

No. of realizations

1 10 100 1000

No. of realizations

piTifton, GA Gainesville, FL

A.1 Diagnostic Case

Gainesville, FLGainesville, FL

Sensitivity of RMSE and R of rainfall amount, frequency and intensity at month of anthesis (May)

1 10 100 1000

No. of realizations

1 10 100 1000

No. of realizations

1 10 100 1000

No. of realizations

1 10 100 1000

No. of realizations

1 10 100 1000

No. of realizations

1 10 100 1000

No. of realizations

RRmmμμ ππ

1922 1932 1942 1952 1962 1972 1982 1992

Base Yield Predicted

R=0.79

1922 1932 1942 1952 1962 1972 1982 1992

R=0.71

1922 1932 1942 1952 1962 1972 1982 1992

R=0.79

Gainesville, FL

1000 1000 RealizationsRealizations

Predicted Yields

A.2 Case study: Katumani, Machakos Province, Kenya

O N D J F

Months

Rainfall amount

Rainfall frequency

1960 1965 1970 1975 1980 1985 1990 1995 2000

Observed GCM_Hindcasts

R=0.62

Skill of the MOS Skill of the MOS corrected GCM datacorrected GCM data

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

Sowing strategy: conditional-forced Sowing strategy: conditional-forced

1 10 100 1000

No. of realizations

ha-1 Rm

Rm+pi2

1 10 100 1000

No. of realizations

Rm+pi2

π1 (Conditioned)π1 (Conditioned)

RRmm (Hindcast) (Hindcast)

π2 (Hindcast)π2 (Hindcast)

RRmm+π2+π2

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Rm+pi2

RRmm (Hindcast) (Hindcast)

RRmm+ π2+ π2π1 (Conditioned)π1 (Conditioned)

π2 (Hindcast)π2 (Hindcast)

Part II. Bias correction of daily GCM outputs (precipitation)

jan feb mar apr may jun jul aug sep oct nov dec

obs123456789101112131415161718192021222324mean24

Statement of the problem

Climatology, Monthly rainfall

obs123456789101112131415161718192021222324mean24

Variance, Monthly Variance, Monthly rainfallrainfall

obs123456789101112131415161718192021222324mean24

IntensityIntensity

FrequencyFrequency

Proposed bias correction

GCM GCMj 0

(x / )F(x; , ) 1 exp

Historical Historicalj 0

(x / )F(x; , ) 1 exp

F(xGCM)

XHistorical

F(xHistorical)=F(xGCM)

x1GCM’

Historical

GCM GCMj 0

(x / )F(x; , ) 1 exp

Historical Historicalj 0

(x / )F(x; , ) 1 exp

F(xGCM)

XHistorical

F(xHistorical)=F(xGCM)

x1GCM’

Historical

0.0 Xmax

Daily rainfall, mm

F(xhistorical=0.0)

Empirical Distribution

0.0 Xmax

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

Sowing strategy: conditional-forced Sowing strategy: conditional-forced

Results

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Uncorr

RRmm μμ

Variance, Rm Variance, μμ

Uncorr

0 4 8 12 16 20 24

Realizations

Uncorr

0 4 8 12 16 20 24

Realizations

Uncorr

1970 1975 1980 1985 1990 1995

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

1970 1975 1980 1985 1990 1995

GGr=0.43

1970 1975 1980 1985 1990 1995

-1 Obs

GG r=0.74

1970 1975 1980 1985 1990 1995

d-1 Obs

GGr=0.74

Bias Bias corrected corrected seasonal seasonal rainfall (OND)rainfall (OND)

1970 1975 1980 1985 1990 1995

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)

Bias corrected

Uncorrected

Intesity

Bias corrected

UncorrectedFrequency

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

1969 1974 1979 1984 1989 1994

Observed

Bias corrected

Uncorrected

Intensity

1969 1974 1979 1984 1989 1994

Observed

Bias corrected

Uncorrected

Frequency

1969 1974 1979 1984 1989 1994

m d-1 Observed

Bias corrected

Uncorrected

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…

Stochastic Disagregation of Monthly Rainfall Data for Crop Simulation Studies

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