Generating weather data for agricultural applications                                         September 2011
Why do we sometimes need synthetic dailyweather?• Synthetic: weather records that are statistically the same as (orsimilar...
Weather generationWhich variables, and how often?• Plant growth models       Daily: rainfall, max and min temperatures, so...
Rainfall generation• Rainfall is a major determinant of agriculture globally• Difficult to model well; most rainfall gener...
How do weather generators work?• Very many different weather generators have been built andapplied, often using similar pr...
A common method of generating rainfall The chance of rain depends on whether it rained yesterday (a “first- order Markov c...
Is today wet?Yesterday was dry: Pi (w | d) = 0.3Generate a random number R, distributeduniformly between 0 and 1          ...
If today is wet, how much rain falls?                   Use a two-parameter gamma                   probability distributi...
What about temperatures and solarradiation?For example, WGEN (a common generator) takes into account:• serial correlation•...
Weather generator parametersDepending on the weather generator, a set of parameters for anysite might include long-term me...
What is the “minimum” set of climatevariables for generating daily data?Depends on the methods used, but could include:• M...
MarkSim is a tool that combines a dailyweather generator with climate surfaces ofthe common variables (rainfall, tmax andt...
Climate surfaces in MarkSim v1About 10,000 stations for Latin America 7,000 stations for Africa4,500 stations for Asia Dif...
A Few Pixels of METGRID for Africa: Near Limuru-1.083   36.583 1981   54   44   84 210 177     42   18   23   24   54 118 ...
140              Northvil e              120              100                80Rainfall mm                60              ...
Northville                                      Southville                   150    JAN                                   ...
Northville                                Southville                 150   JAN                                 150   AUG  ...
Standardisation of Climate NormalsStandard climate normalstillaber 14.180    1.430   209   0.   1.   1.   3. 18. 55. 119. ...
MarkSim the rainfall generator• Based on a third-order Markov process: probability of      rain on any day is dependent on...
Probability of a Wet DayThe probability of a day being wet is                                    -1                 P(W/D1...
1.0                         0.8                         0.6Cumulative Probability                         0.4             ...
Sampling Model ParametersFor each year of generated rainfall required, the baseline probits are randomlysampled from a 12-...
Baseline Rainfall Probit Resampling: Tillabery, Niger     Mean      Rep 1     Rep 2                         (000)   001   ...
GAMMA DISTRIBUTIONS                                  SHAPE (P) AND LOCATION (AV)                      0.3                 ...
Historical Rainfall Data: Mangalore, western India----1988 MANGALORE/BAJPE    IN 12.917    74.883 102   JAN FEB MAR APR MA...
Historical Rainfall Data: Antofagasta, Chile----1988 ANTOFAGASTA/CERRO CL-23.433 -70.433 120   JAN FEB MAR APR MAY JUN JUL...
(1)                      200                                       GUATEMALA                                      TOTAL 11...
ANNUAL VARIANCE OF RAINFALL FOR THREE SITES                       50                                                      ...
Combining climate surfaces and the weather generator to providedaily weather data that are characteristic of any location•...
Weather typing~10,000 weather stations with > 12 years daily rainfall data    Lat, long, elevation    Long-term monthly te...
Generating daily weather               Pick a location: lat, long (elevation)       Read the climate surface to find long-...
Where do the MarkSim v1 modelparameters come from?From climate grids, or from the user directly:• Monthly rainfall amounts...
ApplicationsWeather data to drive crop, livestock, household, ecosystemmodelsproviding information on   • system performa...
Simulated Cereal Yields at Three Sites                         1.0                                              Til abery ...
Versions of MarkSimVersion 1.0 GIS-based CD edition (2002)   • Getting old   • Some known problems with the code and the c...
Versions of MarkSimVersion 1.7 MarkSimGCM batch mode (late 2011)   • Run MarkSimGCM as a DLL and an EXE (depending on OS) ...
Generating weather data for agricultural applications
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Generating weather data for agricultural applications

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CCAFS workshop titled "Using Climate Scenarios and Analogues for Designing Adaptation Strategies in Agriculture," 19-23 September in Kathmandu, Nepal.

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Generating weather data for agricultural applications

  1. 1. Generating weather data for agricultural applications September 2011
  2. 2. Why do we sometimes need synthetic dailyweather?• Synthetic: weather records that are statistically the same as (orsimilar to) historical records• Needed to fill data gaps, for interpolation, for long-termsimulations, for short-term simulations, for help in simulating futurescenarios• To drive models of agricultural processes: growth anddevelopment of plants, of animals, pests & diseases, …
  3. 3. Weather generationWhich variables, and how often?• Plant growth models Daily: rainfall, max and min temperatures, solar radiation (or sunshine hours)• Livestock and ecosystem models Weekly, monthly• Special purpose models < 1 day time step: wind speed, leaf wetness, etc
  4. 4. Rainfall generation• Rainfall is a major determinant of agriculture globally• Difficult to model well; most rainfall generators severely under-estimate monthly and annual variance• In risk studies, tails of the distributions (especially the lower) areof particular importance: impacts on household incomes, foodsecurity, …  Need for representative rainfall generation
  5. 5. How do weather generators work?• Very many different weather generators have been built andapplied, often using similar principles• They use sequences of pseudo-random numbers to operate; asequence that is “seeded” will eventually repeat itselfSame seed  same random number sequence  same weathersequence
  6. 6. A common method of generating rainfall The chance of rain depends on whether it rained yesterday (a “first- order Markov chain”): Pi (w | w) = 1 – Pi (d | w) Pi (w | d) = 1 – Pi (d | d) Y esterday T oday S tate wet 1 wet 1 1001101000101110 … dry 0 2 dry 0 wet 1 34 2 3 1 dry 0 4
  7. 7. Is today wet?Yesterday was dry: Pi (w | d) = 0.3Generate a random number R, distributeduniformly between 0 and 1 Y esterday T oday S tateIf R < 0.3, today is wet wet 1 wet 1 1 dry 0 2 dry 0 wet 1 3 dry 0 4
  8. 8. If today is wet, how much rain falls? Use a two-parameter gamma probability distribution, defined by • a shape parameter p • a scale (or location) parameter av
  9. 9. What about temperatures and solarradiation?For example, WGEN (a common generator) takes into account:• serial correlation• cross correlations on the same day, and on one day and the previous day Mean SRGenerated from monthly meansand monthly standard deviations dry (northern hemisphere) wet 1 365 Day of year
  10. 10. Weather generator parametersDepending on the weather generator, a set of parameters for anysite might include long-term means for • Monthly rainfall amounts • Number of rain days per month • Monthly max and min temperatures, averages and standard deviations • Monthly solar radiation, averages and standard deviationsWhere might these come from, for a site?• Historical daily data for several years for these variables• Climate surfaces based on station data, with interpolationtechniques used to fill in the “grid”
  11. 11. What is the “minimum” set of climatevariables for generating daily data?Depends on the methods used, but could include:• Monthly rainfall amounts – from climate grids• Number of rain days per month• Monthly average max and min temperatures – from climategrids, standard deviations from regressions• Monthly solar radiation – can be estimated from • sunshine hours, day length, and 2 empirical parameters, or • daily maximum and minimum air temperatures, latitude, longitude, and various empirical parameters
  12. 12. MarkSim is a tool that combines a dailyweather generator with climate surfaces ofthe common variables (rainfall, tmax andtmin), and uses climate typing to estimatethe full parameter set of the model
  13. 13. Climate surfaces in MarkSim v1About 10,000 stations for Latin America 7,000 stations for Africa4,500 stations for Asia Different resolutions 10’ pixel 2.5’ pixel 2.5’ pixel 10’ pixel 10’ pixel 0 Climate 270 Phase 90 Angle 180
  14. 14. A Few Pixels of METGRID for Africa: Near Limuru-1.083 36.583 1981 54 44 84 210 177 42 18 23 24 54 118 83 17.7 18.3 18.5 17.9 16.6 15.2 14.5 14.8 16.1 17.4 17.2 17.1 13.0 13.3 12.0 9.8 9.2 10.1 10.2 10.9 12.8 12.3 10.2 11.0-1.083 36.750 2072 52 46 97 224 182 45 18 27 26 62 139 85 17.2 18.0 18.3 17.7 16.6 15.2 14.2 14.6 16.1 17.2 16.9 16.7 13.3 14.0 12.5 9.8 9.4 9.8 10.3 10.8 12.9 12.1 10.1 10.8-1.083 36.917 1676 47 42 101 233 181 43 21 30 29 67 148 79 19.0 19.7 20.1 19.8 19.0 17.4 16.5 16.8 18.1 19.4 18.9 18.5 13.8 15.1 13.3 10.5 10.0 10.7 11.0 10.9 13.2 12.7 10.3 11.4-1.083 37.083 1493 36 32 96 212 137 27 15 19 18 61 147 77 19.7 20.2 21.1 21.1 20.1 18.6 17.5 18.0 19.5 20.5 20.0 19.6 14.7 16.1 14.0 11.0 10.4 11.3 11.0 11.4 13.5 13.1 10.6 12.0
  15. 15. 140 Northvil e 120 100 80Rainfall mm 60 40 20 0 Jan Mar May Jul Sep Nov 140 Southvil e 120 100 80Rainfall mm 60 40 20 0 Jan Mar May Jul Sep Nov
  16. 16. Northville Southville 150 JAN 150 JAN DEC FEB DEC FEB 100 100 NOV MAR NOV MAR 50 50OCT APR OCT APR SEP MAY SEP MAY AUG JUN AUG JUN JUL JUL Rotation of climate record based on 12-point Fourier transform Convert 12 monthly values to a series of sine & cosine functions and subtract the first phase angle
  17. 17. Northville Southville 150 JAN 150 AUG DEC FEB JUL SEP 100 100 NOV MAR JUN OCT 50 50OCT APR MAY NOV SEP MAY APR DEC AUG JUN MAR JAN JUL FEB
  18. 18. Standardisation of Climate NormalsStandard climate normalstillaber 14.180 1.430 209 0. 1. 1. 3. 18. 55. 119. 181. 73. 13. 0. 0. 24.7 27.5 30.8 33.2 34.0 32.1 29.2 27.5 28.9 30.4 28.5 25.3 15.8 16.8 16.8 15.1 13.8 12.5 10.8 9.8 11.0 14.5 16.1 16.1Standardised climate normals – rotated through the first phase angle of the Fourier-transformed monthly rainfall datatillaber 14.180 1.430 209 3.4554 170. 131. 19. 10. 0. 6. 0. 5. 0. 12. 36. 89. 27.9 28.0 30.1 29.6 26.5 24.5 26.1 29.6 32.4 34.0 33.1 30.3 10.0 10.2 13.1 15.8 16.1 15.9 16.2 17.2 15.8 14.3 13.1 11.5
  19. 19. MarkSim the rainfall generator• Based on a third-order Markov process: probability of rain on any day is dependent on occurrence of rain on the three previous days• To model observed rainfall variances in parts of the tropics and subtropics, some of the parameters of the rainfall model are randomly sampled• The model has been fitted to more than 9000 data sets world-wide and has been extensively tested• May model parameters offer some insight into the nature of long-term climate change?
  20. 20. Probability of a Wet DayThe probability of a day being wet is -1 P(W/D1D2D3) = Φ (bi + ai-1d1 + ai-2d2 + ai-3d3)Where: -1Φ is the inverse of the probit functionbi is the monthly probit of a wet day following 3 consecutive dry daysam are binary coefficients for rain (1) or no rain (0) on day mdm are lag constants. -1The probability of a wet day following three dry days is Φ (bi) -1The probability of a wet day following three wet days is Φ (bi + d1 + d2 + d3)
  21. 21. 1.0 0.8 0.6Cumulative Probability 0.4 0.2 0.0 -3 -2 -1 0 1 2 3 Normal Probability (Probit)
  22. 22. Sampling Model ParametersFor each year of generated rainfall required, the baseline probits are randomlysampled from a 12-dimensional normal distribution: * b i = si RNi + bi, i=1,12Where: *bi is the sampled value of bi, the baseline probability of rain.si is the standard deviation of bI (from the fitting of the model).RNi is a random normal number.The sampled baseline monthly probabilities are correlated using the correlationmatrix of raindays per month.
  23. 23. Baseline Rainfall Probit Resampling: Tillabery, Niger Mean Rep 1 Rep 2 (000) 001 010 011 100 101 110 111 +d1 +d2 +d1+d2 +d3 +d1+d3 +d2+d3 +d1+d2+d3______________________________________________________________________________J -4.76 -4.99 -5.32 :F -2.75 -2.74 -2.01 :M -2.49 -2.31 -2.26 :A -2.03 -2.71 -1.66 :M -1.31 -0.93 -1.17 :J -0.78 -1.25 -1.00 -0.90 –0.87 –0.77 –0.91 –0.81 –0.78 –0.68J -0.38 -0.35 -0.79 :A -0.25 -0.39 -0.59 :S -0.72 -0.90 -0.94 :O -1.56 -1.83 -2.14 :N -2.68 -2.61 -2.91 :D -2.91 -3.03 -2.33 :d1 0.10d2 0.13d3 0.09______________________________________________________________________________
  24. 24. GAMMA DISTRIBUTIONS SHAPE (P) AND LOCATION (AV) 0.3 P = 0.5 AV = 5.0 0.2 (Mean = 10.0) 0.1 0.0 P = 1.5 AV = 5.0 0.2 (Mean = 3.3) 0.1 0.0PROBABILITY DENSITY P = 5.5 AV = 5.0 0.4 (Mean = 0.9) 0.3 0.2 0.1 0.0 0 3 6 9 12 15 18 21 24 27 30 RAINFALL (mm)
  25. 25. Historical Rainfall Data: Mangalore, western India----1988 MANGALORE/BAJPE IN 12.917 74.883 102 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1 0 0 0 0 7 0 170 10 0 90 0 0 2 0 0 0 0 2 330 350 140 260 510 0 0 3 0 0 0 20 0 120 150 140 550 350 0 0 4 0 0 0 0 0 20 30 170 80 2 0 0 5 0 0 0 0 0 20 540 500 6 0 0 0 6 0 0 0 0 0 860 80 430 0 230 0 0 7 0 0 0 0 0 140 5 10 0 90 0 0 8 0 0 0 0 3 700 400 20 0 0 10 0 9 0 0 0 0 01010 70 50 540 0 0 010 0 0 0 0 0 520 0 430 250 0 0 011 0 0 0 8 0 450 350 90 1 0 0 012 0 0 0 10 3 710 400 220 6 0 0 013 0 0 0 0 0 2301000 170 0 0 0 014 0 0 0 0 0 5 930 10 3 0 0 015 0 0 0 0 0 330 270 250 110 0 0 016 0 0 0 30 0 130 60 140 4 0 0 417 0 0 0 40 0 830 690 760 290 0 0 018 0 0 0 0 20 18013201010 350 0 0 019 0 0 0 4 0 50 290 250 160 0 0 020 0 0 0 0 0 270 300 60 200 0 0 021 0 0 0 0 20 730 620 50 310 0 0 022 0 0 0 0 1 60 550 130 190 0 0 023 0 0 0 0 0 250 680 150 50 0 0 024 0 0 0 0 0 170 30 0 10 0 0 025 0 0 0 0 01150 90 3 50 10 0 026 0 0 0 0 90 750 380 4 370 70 0 027 0 0 0 0 0 820 30 20 330 0 0 028 0 0 0 0 20 100 10 60 50 0 0 029 0 0 0 0 0 250 20 50 1 0 0 030 0 0 0 8 210 210 0 110 0 0 031 0 0 70 240 20 0 0
  26. 26. Historical Rainfall Data: Antofagasta, Chile----1988 ANTOFAGASTA/CERRO CL-23.433 -70.433 120 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 2 0 0 0 0 0 4 0 0 0 0 0 0 * 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 010 0 0 0 0 0 0 0 0 0 0 0 011 0 0 0 0 0 0 0 0 0 0 0 012 0 0 0 0 0 0 0 0 0 0 0 013 0 0 0 0 0 0 0 0 0 0 0 014 0 0 0 0 0 0 0 0 0 0 0 015 0 0 0 0 0 0 0 0 0 0 0 016 0 0 0 0 0 0 0 0 0 0 0 017 0 0 0 0 0 0 0 0 0 0 0 018 0 0 0 0 0 0 0 0 0 0 0 019 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 0 0 021 0 0 0 0 0 0 0 0 0 0 0 022 0 0 0 0 0 0 0 0 0 0 0 023 0 0 0 0 0 0 0 0 0 0 0 024 0 0 0 0 0 0 0 0 0 0 0 025 0 0 0 0 0 0 0 0 0 0 0 026 0 0 0 0 0 0 0 0 0 0 0 027 0 0 0 0 0 0 0 0 0 0 0 028 0 0 0 0 0 0 0 0 0 0 0 029 0 0 0 0 0 0 0 0 0 0 0 030 0 0 0 0 0 0 0 0 0 0 031 0 0 0 0 0 0 0
  27. 27. (1) 200 GUATEMALA TOTAL 1175 mm (n=38) 100RAINFALL (mm) 0 PALMIRA (2) TOTAL 993 mm 200 (n=52) 100 RAINFALL (mm) 0 TILLABERY (3) TOTAL 483 mm 200 (n=35) 100 RAINFALL (mm) 0 J F M A M J J A S O N D
  28. 28. ANNUAL VARIANCE OF RAINFALL FOR THREE SITES 50 HISTORICAL WGEN 40 MarkSim TOMM 30 ANNUAL RAINFALL VARIANCE X 1000 20 10 0 GUATEMALA PALMIRA, TILLABERY, CITY COLOMBIA NIGER
  29. 29. Combining climate surfaces and the weather generator to providedaily weather data that are characteristic of any location• MarkSim v1 on CD-ROM, data for Latin America, Africa, Asia (2002)• The original MarkSim calibration data station map
  30. 30. Weather typing~10,000 weather stations with > 12 years daily rainfall data Lat, long, elevation Long-term monthly temp Estimate rainfall model parameters Monthly diurnal temp range Monthly rainfallCluster analysis in 36-D space, giving ~700 climate clustersCalculate regression coefficients for rainfallmodelparameters for each cluster Store in cluster files
  31. 31. Generating daily weather Pick a location: lat, long (elevation) Read the climate surface to find long-term means Read cluster coverage to find cluster number Read cluster files for regression coefficients Reconstitute rainfall model parametersGenerate daily rainfall; generate daily temps from long-term means Generate daily solar radiation from temps Application
  32. 32. Where do the MarkSim v1 modelparameters come from?From climate grids, or from the user directly:• Monthly rainfall amounts• Monthly average max and min temperaturesFrom the climate typing clusters:• Number of rain days per month• Monthly correlation matrix of raindays per month• Baseline normal probabilities (probits) of a wet day followingthree dry days and the “lag parameters”Derived parameters:• Monthly solar radiation
  33. 33. ApplicationsWeather data to drive crop, livestock, household, ecosystemmodelsproviding information on • system performance with respect to technological, climate, policy changes • constraint identification and characterisation • identification of possible intervention points • answer “what-if” questions relating to risk, sustainability, trade-offs
  34. 34. Simulated Cereal Yields at Three Sites 1.0 Til abery (mil et) Guatemala City 0.8 (maize) 0.6 PalmiraCUMULATIVE PROBABILITY 0.4 (maize) 0.2 Historical weather "Interpolated" weather 0.0 0 1 2 3 4 5 6 7 GRAIN YIELD (t/ha)
  35. 35. Versions of MarkSimVersion 1.0 GIS-based CD edition (2002) • Getting old • Some known problems with the code and the climate grids • Support?Version 1.5 MarkSimGCM (2011) • Google-Earth based web application that generates data in relation to future climates from GCMs as well as data for “current conditions” • Many v1 bugs fixed, data produced in DSSAT weather file format
  36. 36. Versions of MarkSimVersion 1.7 MarkSimGCM batch mode (late 2011) • Run MarkSimGCM as a DLL and an EXE (depending on OS) • Can then be run as part of the DSSAT v4.5 system or of any other model systemVersion 2 MarkSim2012 • Use an expanded gauge dataset (~54,000 stations) to refit MarkSim globally • Will incorporate the features of MarkSimGCM and AR5 climate dataVersion 3 onwards • Current research ideas: improve temperature simulation; data filling; utilising satellite data in places where gauge data are sparse; MarkSim spatial

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