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t itle. A Web-based Rainfall Atlas for Southern Africa. Walter Zucchini, Oleg Nenadi ć , Günther Kratz, University of Göttingen. toc. Outline:. Purpose of the Atlas What the Atlas offers Development and calibration of daily rainfall model Interpolation of daily rainfall model parameters

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  1. title A Web-based Rainfall Atlas for Southern Africa Walter Zucchini, Oleg Nenadić, Günther Kratz, University of Göttingen

  2. toc Outline: • Purpose of the Atlas • What the Atlas offers • Development and calibration of daily rainfall model • Interpolation of daily rainfall model parameters • Computing rainfall statistics via simulation • Information transfer • Summary

  3. 1 - purpose 1. Purpose of the rainfall atlas • A water resources decision support system for: • hydrologists & civil engineers • water resource planners • ecologists & conservationists • town planners • agricultural planners & farmers

  4. 2 – annual and monthly 2. What the Atlas offers • Annual and monthly statistics: • Means, standard deviations, coefficients of variation • Selected percentiles: 1%, 5%, 10%, 25%, 50%, 75%, 95% and 99% • Average number of rain days • Average rain per day on rain days • Average number of rain days in July • Rain depth in July: 90th percentile

  5. 2 – storm-related 2. What the Atlas offers • Storm-related statistics: • One-, two- and five-day storm percentiles • Percentage of rain attributable to storms • Annual one-day storm 75th percentile • One-, two- and five-day annual storm percentiles at the selected site

  6. 2 – dry-run probabilities 2. What the atlas offers • Daily dry-run probabilities: • P(no rain) in 5, 10,15, 20, 25, 30 consecutive days • Dry-run probabilities starting 3 September displayed as maps • Dry-run probabilities starting 3, 8, 13, 18, 23, 28 September for the selected site

  7. 2 – sundry statistics 2. What the atlas offers • Sundry statistics: • Day with minimum/maximum probability of rain • Day with minimum/maximum mean rain • Index of seasonality and its standard deviation • Day of year with maximum mean rainfall • Day in year with - maximum / minimum probability of rain, - maximum / minimum mean rain • Seasonality index and its standard deviation

  8. 2 – rainfall generator 1.) Select site - click on the imagemap,or -enter the coordinates. 4.) #{years event occured} #{years generated} ^ P(event) = ... t 1 2 3 365 d d d d State 1: “ dry day “ Discrete ... 2.) part ? w w w w State 2: “ wet day “ W | D ... ? Continuous Amount of rainfall W | W 3.) Compute required estimate on wet days part Generate rainfall 0.6 0.6 0.4 0.5 0.4 0.5 0.3 0.4 0.4 0.3 dweibull(x, 3, 2) 0.3 dweibull(x, 3, 2.5) dweibull(x, 3, 2.8) dweibull(x, 3, 2) 0.3 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.0 0.0 0.0 0.0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 x x x x table of sequences Generate artificial rainfall sequences Import generated sequence and regard as a long historical record 2. What the atlas offers • Computing additional rain-related probabilities andstatistics: e.g. P(10mm<Julyrain<25mm & no consecutive 5-day dry run)

  9. 3 – rain properties • mixed discrete-continuous distribution • seasonal January • serial correlation - wet/dry sequences are dependent - depths on wet days are approx. independent July 3. Development and calibration of a daily rainfall model • Properties of daily rainfall: depth D DW WD DWD D DW DW W day

  10. Parameters:(discrete part) seasonal ... t 1 2 3 365 Discrete part(Markov chain) d d d d State 1: “dry day“ ... w w w w State 2: “wet day“ Amount of rainfall on wet days ... Continuous part Scale parameter: seasonal a30 a31 a32 f31 f32 CV Parameters:(continuous part) Weibull Distribution Shape parameter: non-seasonal 3. Development and calibration of a daily rainfall model 3 – model summary • Daily rainfall model:

  11. 4. Interpolation of the daily rainfall model parameters 4 – interpolation gradient aspect roughness Parameters for the calibrates sites exposure Calibrated sites (5070) kriging with externaldrift Topographic features 1.5 km Interpolated parameters Resolution:one minute of degree • McNeill, L. (1994) "Topics in Interpolation and Smoothing of Spatial Data"

  12. ... t 1 2 3 365 d d d d State 1: “ dry day “ Discrete ... part ? w w w w State 2: “ wet day “ W | D ... ? Continuous Amount of rainfall W | W on wet days part 0.6 0.6 0.4 0.5 0.4 0.5 0.3 0.4 0.4 0.3 dweibull(x, 3, 2) 0.3 dweibull(x, 3, 2.5) dweibull(x, 3, 2.8) dweibull(x, 3, 2) 0.3 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.0 0.0 0.0 0.0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 x x x x 5. Computing rainfall statistics via simulation 5 – generating Artificial rainfall sequence (5000 yrs) Model 1,825,000 times(5000 years) 16 Parameters Empirical statistics (~ 950) Site x Simulation for each of the 424,646 sites • ~ 1 GB zip-compressed ASCII-Files • 950 statistics for each of the 425,000 sites Database

  13. Image database: 126x100 px 255x203 px 1065x842 px 443x355 px 693x550 px Database • ~ 5000 maps in 5 different sizes • Site database: • Extract statistics for individiual sites into separate small files 6. Information transfer 6 – data preparation • Data preparation:

  14. 1daymax 2daymax 5daymax 1daymax 2daymax 5daymax 1% 5% 10% 25% 50% 75% 90% 95% 99% 50% 75% 90% 95% 99% 50% 75% 90% 95% 99% AMDW0 AMDW1 AMDW2 PHDW1 PHDW2 AMWW0 AMWW1 AMWW2 PHWW1 PHWW2 AMMU0 AMMU1 AMMU2 PHMU1 PHMU2 CV 6. Information transfer 6 – data structure • Data Structure: Mean SD CV PercentilesRain per Rainday Stormdays Storm PercentageStormrain ANNUAL 1% 5% 10% 25% 50% 75% 90% 95% 99% Mean SD CV PercentilesRain per Rainday Stormdays Storm PercentageStormrain Exc. prob. MONTHLY 10mm 25mm 50mm 75mm100mm 125mm 150mm 200mm DAILY Dry run probability 5 days 10 days 15 days 20 days 25 days 30 days PARAMETERS Cities Rivers Altitude Max.mean Max.prob. Min.mean Max.mean SI-mean SI-SD OTHER DATA

  15. 6. Information transfer 6 – image database • Image Database: Select required maps Default output: Thumbnail maps Optional (click on map): Enlarged maps

  16. 6. Information transfer 6 – enlarged map • Enlarged map: P( December rain exceeds 50 mm )

  17. 3.) 1.) Select site - click on the imagemap,or -enter the coordinates. 2.) PHP-Script Complete form to select required statistics • Form is parsed to a PHP-script that - reads the appropriate data • - displays output in tabular form. Site database 6. Information transfer 6 – site database 4 – site db • Site Database:

  18. 226.51, 18.88, 145.06, 23.59, 30.37, 12.21, .00, 13.89, .00, 76.51, 24.45, 100.83 53.96, 81.27, 31.12, 171.45, 50.10, .00, .00, .00, 43.42, 72.81, 66.05, 118.14 179.01, 112.36, 26.58, 45.48, .00, 29.85, .00, 1.49, 70.57, 51.51, 79.20, 46.24 80.98, 65.22, 79.65, 37.07, 9.45, 16.64, .00, .00, 14.24, 12.10, 93.48, 32.54 74.04, 94.55, 114.12, 19.48, .00, 12.75, .00, .00, 24.29, 37.89, 132.92, 9.55 119.22, 95.87, 63.25, 16.48, 16.98, 22.74, 2.06, 20.58, 15.05, 72.41, 10.52, 163.70 63.73, 114.85, 42.44, 60.57, 20.75, 13.50, 5.15, .00, .00, 88.90, 84.76, 41.51 190.08, 72.40, 24.94, 76.73, 1.46, .00, 19.68, 41.67, 49.01, 40.11, 19.83, 92.12 9.38, 149.84, 75.36, 74.41, 34.14, .00, 5.23, .38, 8.29, 119.32, 42.96, 82.64 77.47, 100.23, 49.83, 38.09, 27.55, .00, .00, 12.24, 47.47, 38.92, 45.76, 110.10 142.16, 29.03, 33.75, 30.55, 3.48, .00, .66, .00, .52, 17.62, 67.83, 72.54 81.34, 113.30, 64.12, 33.67, 20.68, 2.27, .00, .00, 9.26, 54.96, 43.60, 112.95 49.23, 13.82, 74.85, 110.18, 22.16, 13.90, .00, 6.45, 42.82, 41.49, 19.54, 154.54 20.03, 72.16, 88.68, 12.28, 2.82, 15.89, .00, 13.89, 22.01, 40.30, 153.63, 82.06 54.55, 194.19, 83.60, 97.55, 97.83, 16.07, .00, 18.96, .00, 115.44, 95.29, 71.92 149.98, 67.02, 136.87, 32.96, 43.36, .00, .00, 51.70, 9.13, 38.79, 149.05, 44.24 167.97, 115.73, 162.58, 38.53, 42.31, 32.51, .00, 13.27, 10.16, 43.18, 74.03, 173.93 21.90, 97.11, 191.01, 95.62, 6.64, .00, .00, .00, 27.18, 18.48, 20.26, 110.75 78.92, 44.84, 54.04, 61.50, 8.24, .00, 12.31, .00, 9.45, 17.76, 70.26, 145.69 65.01, 58.61, 5.94, 60.34, 19.59, 20.63, 29.73, 9.11, 18.73, 88.42, 67.95, 144.73 106.60, 45.84, 77.13, 34.41, .00, 9.49, 22.11, .00, 63.23, 112.51, 46.40, 56.95 291.16, 93.36, 69.01, .00, 21.81, 12.31, 9.78, .00, 3.72, 115.79, 79.09, 89.58 59.15, 89.01, 49.03, 37.98, 27.75, 1.83, 15.01, 18.02, 101.02, 7.20, 120.96, 68.30 166.16, 89.21, 101.28, 20.79, .00, 8.15, .00, .00, 11.61, 30.00, 130.31, 49.88 73.47, 86.60, 61.16, 90.00, 7.30, 10.82, 37.60, 10.15, 13.78, 36.50, 81.16, 93.10 153.91, 36.13, 105.36, 10.70, 6.41, 17.98, 13.36, 13.39, 17.16, 143.32, 68.13, 63.62 49.68, 56.38, 91.31, 86.98, 35.80, 2.23, 14.11, 18.27, 26.20, 16.68, 220.09, 152.47 144.44, 121.14, 70.75, 19.39, 22.04, .00, .00, .00, 12.07, 24.07, 53.56, 185.57 57.26, 63.27, 59.93, 49.16, 16.43, 18.90, .00, 8.21, 94.36, 45.20, 60.49, 127.39 117.39, 120.27, 57.09, 61.80, 9.95, .00, .00, .00, 1.37, 11.07, 105.13, 78.79 50.58, 109.14, 72.15, 60.39, 7.85, .00, .00, 56.65, 45.77, 104.37, 99.55, 37.46 184.01, 135.06, 67.59, 57.15, .00, 4.61, 75.12, 5.41, 40.47, 88.16, 46.93, 107.63 208.35, 94.20, 108.65, 61.82, 11.66, .00, 30.03, .00, 56.13, 23.22, 91.10, 84.35 59.16, 93.85, 42.86, 79.03, .00, .00, .00, 11.46, 38.11, 105.50, 66.44, 88.65 141.92, 100.95, 65.00, 44.76, 19.07, 8.01, .00, 20.50, 19.49, 55.18, 92.67, 52.30 92.25, 177.40, 40.39, 11.40, 3.91, 7.07, .00, 25.78, 32.77, 99.02, 174.17, 122.54 63.80, 89.12, 98.13, 2.66, 15.57, .00, .00, 26.57, 53.00, 41.06, 95.80, 75.86 88.64, 120.34, 79.53, 80.50, 7.34, 3.58, .00, 22.77, 58.60, 34.75, 64.89, 50.96 67.44, 115.74, 31.25, 17.71, 5.78, 17.97, .00, 6.40, 32.67, 13.05, 125.80, 141.69 79.54, 158.87, 77.54, 86.19, .00, .00, 7.80, .00, 3.82, 50.36, 106.71, 79.39 98.74, 4.32, 122.17, 37.11, .00, 21.44, 3.41, .00, 124.17, 66.15, 42.81, 186.01 81.56, 85.27, 108.23, 84.91, 20.04, 2.10, .00, .00, 51.76, 35.43, 91.84, 52.10 184.37, 36.50, 95.56, 92.34, 56.70, 4.15, 7.19, .00, 36.89, 145.08, 60.68, 97.69 92.34, 74.18, 47.86, 17.78, 6.65, 10.02, .00, 1.09, 7.73, 33.64, 84.11, 116.24 51.55, 10.14, 93.87, 103.69, 13.00, 33.23, .00, 72.39, 55.84, 32.03, 62.11, 112.05 116.54, 124.80, 81.54, 62.31, 21.62, 34.76, 5.94, .00, 43.96, 34.01, 85.33, 46.53 120.00, 54.58, 178.64, 101.52, 33.93, .00, .00, 19.23, 67.16, 142.55, 48.12, 143.76 55.05, 104.72, .00, 60.85, 26.48, .00, .00, .00, 11.94, 29.73, 31.80, 93.04 176.05, 180.19, 178.17, 49.90, 40.02, .00, .00, 60.41, 24.36, 59.95, 55.56, 178.01 186.56, 71.69, 88.45, 92.61, 10.19, .00, .56, 6.25, 31.92, 28.50, 75.82, 73.21 63.58, 46.73, 150.71, 50.61, 30.86, 8.18, 11.44, 11.38, 28.54, 12.35, 120.78, 52.00 45.60, 60.38, 145.87, 100.39, 12.99, .00, 1.10, .00, 9.42, 151.67, 80.92, 54.25 69.04, 66.50, 109.81, 70.05, 18.97, .00, .00, 60.34, .00, 44.52, 156.14, 125.05 51.13, 172.45, 32.18, 52.15, 1.86, 98.07, .00, .00, 30.68, 137.95, 57.29, 139.13 47.13, 6.44, 61.19, 74.98, 46.73, .00, .00, 19.78, 11.45, 47.91, 60.04, 146.54 197.22, 39.63, 20.27, 71.92, .00, .00, 13.18, 1.82, 20.12, 38.54, 15.28, 92.29 162.26, 100.22, 97.05, 68.06, 16.49, 11.82, .00, .00, 25.50, 80.63, 64.93, 66.41 113.89, 135.50, 81.88, 20.49, 60.81, 14.38, 14.48, .00, .00, 53.05, 31.83, 72.83 51.66, 90.35, 29.77, 69.97, 13.26, .00, 4.34, 12.78, 61.97, 139.20, 65.27, 74.99 62.89, 49.23, 111.10, 28.57, 10.73, .00, .00, 2.33, 23.83, 186.12, 50.75, 114.29 174.59, 92.82, 115.81, 40.59, 70.44, .00, .00, 10.55, 119.16, 130.44, 29.36, 156.97 45.27, 62.57, 55.35, 6.60, .73, .00, 22.57, 30.98, 11.73, 34.91, 172.51, 174.46 81.97, 97.13, 73.62, 156.15, 24.36, 5.31, .00, .00, 33.78, 58.49, 73.11, 53.72 76.43, 68.09, 119.21, 29.77, 40.92, 8.81, .00, .00, .00, 44.92, 55.46, 16.06 68.48, 44.41, 67.24, 79.03, 23.17, .00, .00, 6.30, 18.64, 74.47, 85.01, 134.96 147.06, 34.90, 29.26, 30.91, 19.66, 53.00, 6.93, 15.99, 4.41, 105.07, 42.49, 140.58 54.83, 72.96, 13.60, 49.62, 28.02, 13.84, .00, 13.77, 3.49, 20.81, 42.68, 41.30 141.16, 74.86, 73.50, 20.14, 13.57, 2.11, .00, .00, 29.20, 25.66, 57.93, 77.72 85.62, 168.29, 64.83, 25.62, 39.92, 7.52, 23.82, 30.60, 40.00, 74.63, 24.82, 50.68 81.02, 47.71, 61.35, 29.65, .00, 19.38, 15.87, 14.84, 34.09, 84.19, 3.) Generated sequences 2.) daily monthly annual Generated sequences can be displayed or downloaded html zip gz txt Select options 6. Information transfer 6 – rain simulator 4 – site db • Rain simulator: 1.) Select site - click on the imagemap,or -enter the coordinates.

  19. 7 - summary Summary The Atlas offers a large repository ofmaps and statistics. High spatial resolution: 1 minute of degree (approx. 1.5 km). Simulation facility allows computation of additional statistics. Freely accessible via Internet. Computations carried out on server; no special software required. Current version located at Institute for Statistics and Econometrics server http://134.76.173.220/rainfall/ (Feedback and suggestions are welcome!)

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