1. 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

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

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

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

5. 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

6. Part I. Stochastic disaggregation of monthly rainfall amounts

7. 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

8. 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 2 + (1-α)β 2 2 + α(1-α)(β 1 -β 2 ) Max. Likelihood (MLH) Markovian process Mixed- exponential Occurrence model: Intensity model:

9. 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

10. 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

11. 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

12. 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

13. 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

14. Applications A.1 Diagnostic case study –Locations: Tifton, GA and Gainesville, FL –Data: 1923-1999 A.2 Prediction case study –Location: Katumani, Kenya –Data: MOS corrected GCM outputs (ECHAM4.5) –ONDJF (1961-2003)

15. Crop Model: CERES-Maize in DSSATv3.5 Crop: Maize (McCurdy 84aa) Sowing dates: Apr 2 1923 – Tifton Mar 6 1923 – 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: 1923-1996 Simulation Data (Tifton, GA and Gainesville, FL)

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

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

18. Gainesville, FL μ π RmRm 1000Realizations Predicted Yields

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

20. Simulation Data (Katumani, Machakos Province, Kenya) Crop Model: CERES-Maize Crop: Maize (KATUMANI B) Sowing dates (Nov 1 1961) Soil depth :130cm Extr. H 2 O:177.0mm Scenario: Rainfed Simulation period: 1961-2003 Sowing strategy: conditional-forced

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

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

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

24. Statement of the problem RmRmRmRm Climatology, Monthly rainfall

25. RmRmRmRm Variance, Monthly rainfall

26. π μ Intensity Frequency

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

28. Application Location: Katumani, Machakos, Kenya Climate model: ECHAM4.5 (Lat. 15S;Long. 35E) Crop Model: CERES-Maize Crop: Maize (KATUMANI B) Sowing dates (Nov 1 1970) Soil depth :130cm; Extr. H 2 O:177.0mm Scenario: Rainfed Simulation period: 1970-1995 Sowing strategy: conditional-forced

29. Results RmRmRmRm μ Variance, R m μ Variance, μ

30. π

31. Sensitivity of RMSE and correlation of yield

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

33. Bias corrected seasonal rainfall (OND) RmRmRmRm μ π

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

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

36. Inter-annual variability of monthly rainfall for November

37. 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

38. 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…