Stochastic Disagregation of Monthly Rainfall Data for Crop Simulation Studies Amor VM Ines and James W Hansen International Institute for Climate Prediction The Earth Institute at Columbia University Palisades, NY, USA Stochastic disaggregation, and deterministic bias correction of GCM outputs for crop simulation studies

Linkage to crop simulation models Seasonal Climate Forecasts Crop simulation models (DSSAT) Crop forecasts <<<GAP>>> Daily Weather Sequence

a) Stochastic disaggregation Monthly rainfall Stochastic disaggregation Crop simulation models (DSSAT) Weather Realizations Crop forecasts GCM ensemble forecasts Stochastic weather generator >> >>

b) Bias correction of daily GCM outputs 24 GCM ensemble members Bias correction of daily outputs Crop simulation models (DSSAT) Weather Realizations Crop forecasts >> >>

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<=p c ? x f(x) Generate ppt.=0 p c =p 01 p c =p 11 Wet-day non-ppt. parameters: μ k,1 ; σ k,1 Dry-day non-ppt. parameters: μ k,0 ; σ k,0 Generate today’s non- ppt. variables Generate uniform random number Precipitation sub-modelNon-precipitation sub- model (after Wilks and Wilby, 1999) Generate a non- zero ppt. (Begin next day)INPUT OUTPUT

Precipitation sub-model p 01 =Pr{ppt. on day t | no ppt. on day t-1} p 11 =Pr{ppt. on day t | ppt. on day t-1} f(x)=α/β 1 exp[-x/β 1 ] + (1-α)/β 2 exp[-x/β 2 ] μ= αβ 1 + (1-α)β 2 σ 2 = αβ (1-α)β α(1-α)(β 1 -β 2 ) Max. Likelihood (MLH) Markovian process Mixed- exponential Occurrence model: Intensity model:

Long term rainfall frequency: First lag auto-correlation of occurrence series: π=p 01 /(1+p 01 -p 11 ) r 1 =p 11 -p 01

Temperature and radiation model zAzB z(t)=[A]z(t-1)+[B]ε(t) z k (t)=a k,1 z 1 (t-1)+a k,2 z 2 (t-1)+a k,3 z 3 (t-1)+ b k,1 ε 1 (t)+b k,2 ε 2 (t)+b k,3 ε 3 (t) b k,1 ε 1 (t)+b k,2 ε 2 (t)+b k,3 ε 3 (t) T k (t)= μ k,0 (t)+σ k,0 z k (t); if day t is dry μ k,1 (t)+σ k,1 z k (t); if day t is wet Trivariate 1 st order autoregressive conditional normal model NOTE: Used long-term conditional means of TMAX,TMIN,SRAD

Decomposing monthly rainfall totals R m =μ x π Dimensional analysis: where: R m - mean monthly rainfall amounts, mm d -1 μ - mean rainfall intensity, mm wd -1 π - rainfall frequency, wd d -1

Conditioning weather generator inputs μ = R m /π we condition α in the intensity model π = R m / μ we condition p 01, p 11 from the frequency and auto-correlation equations …and other higher order statistics

Conditioning weather generator outputs First step: Iterative procedure - by fixing the input parameters of the weather generator using climatological values, generate the best realization using the test criterion |1-R mSim /R m | j <= 5% Second step: Rescale the generated daily rainfall amounts at month j by (R m /R mSim ) j

Applications A.1 Diagnostic case study –Locations: Tifton, GA and Gainesville, FL –Data: A.2 Prediction case study –Location: Katumani, Kenya –Data: MOS corrected GCM outputs (ECHAM4.5) –ONDJF ( )

Crop Model: CERES-Maize in DSSATv3.5 Crop: Maize (McCurdy 84aa) Sowing dates: Apr – Tifton Mar – Gainesville Soils: Tifton loamy sand #25 – Tifton Millhopper Fine Sand – Gainesville Millhopper Fine Sand – Gainesville Soil depth: 170cm; Extr. H 2 O:189.4mm – Tifton 180cm; Extr. H 2 O:160.9mm – Gainesville 180cm; Extr. H 2 O:160.9mm – Gainesville Scenario: Rainfed Condition Simulation period: Simulation Data (Tifton, GA and Gainesville, FL)

Sensitivity of RMSE and correlation of yield Tifton, GAGainesville, FL A.1 Diagnostic Case RmRmRmRm π μ

Gainesville, FL Sensitivity of RMSE and R of rainfall amount, frequency and intensity at month of anthesis (May) RmRmRmRm μ π RmRmRmRm π μ

Gainesville, FL μ π RmRm 1000Realizations Predicted Yields

A.2 Case study: Katumani, Machakos Province, Kenya Skill of the MOS corrected GCM data OND

Simulation Data (Katumani, Machakos Province, Kenya) Crop Model: CERES-Maize Crop: Maize (KATUMANI B) Sowing dates (Nov ) Soil depth :130cm Extr. H 2 O:177.0mm Scenario: Rainfed Simulation period: Sowing strategy: conditional-forced

Sensitivity of RMSE and correlation of yield π1 (Conditioned) R m (Hindcast) π2 (Hindcast) R m +π2

R m (Hindcast) R m + π2 π1 (Conditioned) π2 (Hindcast)

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

Statement of the problem RmRmRmRm Climatology, Monthly rainfall

RmRmRmRm Variance, Monthly rainfall

π μ Intensity Frequency

Proposed bias correction (a)-correcting frequency (b)-correcting intensity

Application Location: Katumani, Machakos, Kenya Climate model: ECHAM4.5 (Lat. 15S;Long. 35E) Crop Model: CERES-Maize Crop: Maize (KATUMANI B) Sowing dates (Nov ) Soil depth :130cm; Extr. H 2 O:177.0mm Scenario: Rainfed Simulation period: Sowing strategy: conditional-forced

Results RmRmRmRm μ Variance, R m μ Variance, μ

π

Sensitivity of RMSE and correlation of yield

Comparison of yield predictions using disaggregated, MOS-corrected monthly GCM predictions, and bias- corrected daily gridcell GCM simulations

Bias corrected seasonal rainfall (OND) RmRmRmRm μ π

Comparison of MOS corrected and bias corrected seasonal rainfall (OND)

Why are we successful? Is the procedure applicable in every situation? Inter-annual correlation (R) of monthly rainfall

Inter-annual variability of monthly rainfall for 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…