1. Crop-Weather Models Observed soybean yields (GA yield trials) vs. seasonal rainfall, temperature, simulated yields

2. 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

3. Crop Model Concept after Rabbinge, 1993

4. DSSAT v4.02.0

5. The Challenge: The Scale Mismatch Problem

6. Information Pathways predicted crop yields observed climate predictors ?

7. Information Pathways downscaled dynamic model stochastic generator crop model (observed weather) crop model (hindcast weather) analog years predicted crop yields statistical climate model statistical yield model observed climate predictors categorize

8. 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

9. Stochastic Disagregation of Monthly Rainfall Data for Crop Simulation Studies Stochastic disaggregation, and deterministic bias correction of GCM outputs for crop simulation studies

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

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

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

13. Stochastic disaggregation of monthly rainfall amounts

14. Rainfall amounts and frequency prediction Katumani, Machakos Province, Kenya Skill of the MOS corrected GCM data OND

15. 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

16. 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:

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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)

23. 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)

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

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

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

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

28. 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

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

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

31. Bias correction of daily GCM outputs (precipitation)

32. Statement of the problem RmRmRmRm Climatology, Monthly rainfall

33. RmRmRmRm Variance, Monthly rainfall

34. π μ Intensity Frequency

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

36. 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

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

38. π

39. Sensitivity of RMSE and correlation of yield

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

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

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

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

44. Inter-annual variability of monthly rainfall for November

45. Extracting Useful Information from Daily GCM Rainfall for Cropping System Modeling

46. Temporal mismatch… Seasonal Climate Forecasts Cropping system models Yield forecasts, water balance etc. <<<GAP>>> Daily Weather Sequences  Cropping system models require daily weather inputs

47. GCM Rainfall vs. Observed Rainfall Ines and Hansen (2006). Agric. For. Meteorol. Mean amount (mm d -1 ) Intensity (mm wd -1 ) Frequency (wd d -1 ) Obs GCM Source: wikipedia

48. Weather within Climate Hypothesis Maize Yield (kg ha -1 ) Years Correlation=0.65 “Observed” yield Uncorrected ECHAM4.5 GCM BIAS Machakos Southern Province, Katumani, Kenya Cropping season: Oct-Feb (Maize crop)

49. Deterministic Bias Correction GCM ensemble members Bias correction of daily outputs Crop simulation models (DSSAT) Weather Realizations Crop forecasts >> >>

50. Bias Correction of Daily GCM Rainfall (a)-correcting frequency (b)-correcting intensity Ines and Hansen (2006) Hansen et al. (2006) can be varied

51. BC-GCM Rainfall vs. Observed Rainfall Ines and Hansen (2006). Agric. For. Meteorol. Mean amount (mm d -1 ) Intensity (mm wd -1 ) Frequency (wd d -1 ) Source: wikipedia

52. Dry spell length (days) Cum. Frequency Yield, kg ha -1 During Anthesis (Nov 15-Dec 31), for 25 years BIAS BC-Obs BIAS Uncorr-Obs

53. Sample Bias-Corrected (BC) Rainfall (mm) Day of Year (year: 1995) Member 1-corr Observed Cropping season Member 1-uncorr mm  BC fails to correct the temporal structure of daily rainfall

54. Corrected Monthly Rainfall Frequency after BC R=0.06 R=0.74 Observed Mean24Mem Observed Before After Mean24Mem

55. Combined BC-DisAg Stochastic disaggregation GCM ensemble members Bias correction of daily outputs Crop simulation models (DSSAT) Weather Realizations Crop forecasts >> >>

56. Simulated Number of Dry days (Nov. 15-Dec. 31) R 2 =0.49 R 2 =0.45 RAWBC BC-DisAg2

57. 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)

58. 1 – rainfall freq information derived from indv. members 2 – mean rainfall freq information derived from ensem. members year Maize Yield (kg ha -1 ) Performance of the information extracted from daily GCM rainfallMethodR(-)MBE (Mg ha -1 ) d(-)MSE (Mg ha -1 ) 2 MSE R (Mg ha -1 ) 2 MSE S (Mg ha -1 ) 2 Uncorrected0.61-2.35-1.146.611.065.55 BC only 0.70-1.040.501.950.861.09 BC-DisAg10.63-0.410.631.221.010.21 BC-DisAg20.73-0.200.740.910.790.12

59. 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.

60. Linear Programming Subject to:

61. Definition of terms Z = value of overall performance x j = level of activity j c j = increase in Z that would result from each unit increase in level of activity j b i = amount of resource i that is available for allocation to activities j a ij = amount of resource i consumed vy each unit of activity j

62. Example Max Z = 2x 1 + 3x 2 Subject to: x 1 ≤ 4 2x 2 ≤ 12 3x 1 + 2x 2 ≤ 18 Non-negativity constraint: x 1 ≥ 0; x 2 ≥ 0

63. Graphical solution 1234 5 6789100 1234 5 6789 0 x 1 ≤ 4 2x 2 ≤ 12 x1x1 x2x2 3x1 + 2x 2 ≤ 18 FEASIBLE REGION (0,0) (0,6) (2,6) (4,3) Z max = 2x 1 + 3x 2

64. Non-Linear Programming Subject to:

65. Graphical solution; linear constraints 1234 5 6789100 1234 5 6789 0 x1x1 x2x2 FEASIBLE REGION

66. Graphical solution; non-linear constraint 1234 5 6789100 1234 5 6789 0 x1x1 x2x2 FEASIBLE REGION

67. Crop-water management Example: Bata Minor, Bhakra Irrigation System, Kaithal, Haryana, India IRRIGATION SYSTEM Physical properties (soil, water quality, GW depth … ) Management practices (water, crop mgt … ) WEATHER WEATHER EXTERNAL CONSTRAINTS We can explore options in agricultural and water management Need to characterize and understand these complexities INPUT INPUT OUTPUT OUTPUT Yield, water balance, water productivities … NEED to develop a regional model (deterministic-stochastic)

68. RS-simulation model framework Pink: INVERSE MODELING Red: FORWARD MODELING

70. STUDY AREA Snapshot of Kaithal Irrigation Circle (Landsat 7ETM+)

75. Crop-water management optimization model Objective function Subject to water availability Decision variables: Water management Decision variables: Crop management By definition: Soil properties Salinity

76. Crop-water management Optimization Take the relaxed constraints Where: Fitness function:

77. Optimized wheat yields Current Optimized Current scenario

78. Crop-water management options Note: A Rainfall of 91 mm was recorded during the simulation period a In terms to T a /T p (irrigation scheduling criterion) b In terms of emergence dates