crop-weather models observed soybean yields (ga yield trials) vs. seasonal rainfall, temperature,...

Crop-Weather Models

0 2 4 6 8

Rainfall (mm/d)

25 27 29 31 33

Max Temp Average (C)

y = 0.9204x + 202.61

R2 = 0.81

0 1000 2000 3000 4000

Simulated Yield (kg/ha)

Observed soybean yields (GA yield trials) vs. seasonal rainfall, temperature, simulated yields

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)

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

Stochastic disaggregation of monthly rainfall amounts

Rainfall amounts and frequency predictionKatumani, 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 corrected GCM Skill of the MOS corrected GCM datadata

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

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

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 corrected GCM Skill of the MOS corrected GCM datadata

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)

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 corrected Bias 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 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

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

Extracting Useful Information from Daily GCM Rainfall for Cropping System Modeling

Temporal mismatch…

Seasonal Climate

Forecasts

Cropping system models

Yield forecasts, water balance

<<<GAP>>><<<GAP>>>

Daily Weather

Sequences

Cropping system models require daily weather inputs

Ines and Hansen (2006). Agric. For. Meteorol.

Mean amount(mm d-1)

Intensity(mm wd-1)

Frequency(wd d-1)

Obs GCM

Source: wikipedia

1970 1975 1980 1985 1990 1995

Base Yield

Mean24

Weather within Climate Hypothesis

Correlation=0.65“Observed” yield

Uncorrected ECHAM4.5GCM

Machakos Southern Province, Katumani, Kenya

Cropping season: Oct-Feb (Maize crop)

Deterministic Bias Correction

GCM ensemble members

Crop simulation

models (DSSAT)

lizati

Crop forecasts

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

Ines and Hansen (2006). Agric. For. Meteorol.

Mean amount(mm d-1)

Intensity(mm wd-1)

Frequency(wd d-1)

Source: wikipedia

1971 1974 1977 1980 1983 1986 1989 1992 1995

Observed BC Uncorr

RBC-Obs=0.71

RUncorr-Obs=0.65

0 10 20 30 40

Dry Spell Length (days)

observed

Dry spell length (days)

During Anthesis (Nov 15-Dec 31),for 25 years

BIASBC-Obs

BIASUncorr-Obs

Sample Bias-Corrected (BC) Rainfall (mm)

1 16 31 46 61 76 91 106

Day of Year (year: 1995)

Member 1-corr

Observed

Croppingseason

1 16 31 46 61 76 91 106

Member 1-uncorr

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

R² = 0.551

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

Before

Combined BC-DisAg

Stochastic disaggregation

GCM ensemble members

Crop simulation

models (DSSAT)

lizati

Crop forecasts

Simulated Number of Dry days (Nov. 15-Dec. 31)

Realizations Obs Mean_Realizations

R2=0.49 R2=0.45

R2=0.45

RAW BC

BC-DisAg2

0 5 10 15 20 25 30 35 40 45 50

Observed Uncorrected GCM runs

0 5 10 15 20 25 30 35 40 45 50

Observed Bias Corrected GCM runs

0 5 10 15 20 25 30 35 40 45 50

Observed BC - Disaggregated GCM runs

Mean GCM

Mean observed

Dry spell length

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)

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

)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

Max Z c x

ij j ii j

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

0x1 ≤ 4

2x2 ≤ 12

x2 3x1 + 2x2 ≤ 18

FEASIBLE REGION

(4,3)Zmax = 2x1 + 3x2

Non-Linear Programming

Max Z c x

ij ii j

0jx , j

Subject to:

Graphical solution; linear constraints

1 2 3 4 5 6 7 8 9 100

FEASIBLE REGION

Max Z c x

Graphical solution; non-linear constraint

1 2 3 4 5 6 7 8 9 100

FEASIBLE REGION

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

February 4, 2001 March 8, 2001

Classification

0.5 1 1.5 2 2.5 3 3.5 4 4.5

ETa, mm

0.5 1 1.5 2 2.5 3 3.5 4 4.5

ETa, mm

Cropped area

GA solution to the regional inverse modeling

<=1.91.9-2.12.1-2.32.3-2.52.5-2.7 >2.7

ETa, mm

SWAPGA

<=2.92.9-3.13.1-3.33.3-3.53.5-3.73.7-3.9>3.9

ETa, mm

SWAPGA

<=1.9 1.9-2.1 2.1-2.3 2.3-2.5 2.5-2.7 >2.7

ETa, mm

SWAPGA

<=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

SWAPGA

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

max iN

1Z max Y

i Si 1

1Ir Qave

1min 1 1max

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

1LL Ir UL

SLL 1 Qave

SUL (1 )Qave

2N 2 N

i imaxi 1 1 i 1

1 1fitness Max Y Ir Limit

Crop-water management Optimization

Take the relaxed constraints

Where:

Fitness function:

Average water supply, mm

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

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