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COMPILATION OF RAINFALL DATA

COMPILATION OF RAINFALL DATA. TRANSFORMATION OF OBSERVED DATA FROM ONE TIME INTERVAL TO ANOTHER FROM POINT TO AREAL ESTIMATES NON-EQUIDISTANT TO EQUIDISTANT ONE UNIT TO ANOTHER DERIVED STATISTICS MIN./MEAN/MAX. SERIES, PERCENTILES ETC. OBJECTIVES DATA VALIDATION - WHOLE TO PART!!

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COMPILATION OF RAINFALL DATA

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  1. COMPILATION OF RAINFALL DATA • TRANSFORMATION OF OBSERVED DATA • FROM ONE TIME INTERVAL TO ANOTHER • FROM POINT TO AREAL ESTIMATES • NON-EQUIDISTANT TO EQUIDISTANT • ONE UNIT TO ANOTHER • DERIVED STATISTICS • MIN./MEAN/MAX. SERIES, PERCENTILES ETC. • OBJECTIVES • DATA VALIDATION - WHOLE TO PART!! • SUMMARISING LARGE DATA VOLUMES - REPORTING • STAGES OF COMPILATION • DATA VALIDATION - SDDPC, DDPC, SDPC • FINALISATION - SDPC & AFTER CORRECTION/COMPLETION OHS - 1

  2. AGGREGATION TO LONGER INTERVALS • DATA VALIDATION • WHOLE TO PART !! • DAILY TO MONTHLY • DAILY TO YEARLY • SRG / ARG • HOURLY TO DAILY • VARIOUS APPLICATIONS • WEEKLY/TEN-DAILY/MONTHLY • COMPREHENSION OF TEMPORAL VARIATION • REPORTING NEEDS OHS - 2

  3. OHS - 24 OHS - 3

  4. OHS - 4

  5. OHS - 5

  6. OHS - 6

  7. OHS - 7

  8. OHS - 8

  9. Plot of Hourly Rainfall 40 35 30 25 Rainfall (mm) 20 15 10 5 0 01/09/94 02/09/94 03/09/94 04/09/94 05/09/94 06/09/94 07/09/94 08/09/94 09/09/94 10/09/94 11/09/94 Time ANIOR Plot of Daily Rainfall 150 125 100 Rainfall (mm) 75 50 25 0 05/07/94 12/07/94 19/07/94 26/07/94 02/08/94 09/08/94 16/08/94 23/08/94 30/08/94 06/09/94 13/09/94 20/09/94 Time ANIOR Plot of Weekly Rainfall 300 250 200 Rainfall (mm) 150 100 50 0 07/94 08/94 09/94 10/94 11/94 12/94 01/95 02/95 03/95 04/95 05/95 06/95 07/95 08/95 09/95 10/95 Time OHS - 9 ANIOR

  10. Plot of Monthly Rainfall 800 700 600 500 Rainfall (mm) 400 300 200 100 0 06/91 12/91 06/92 12/92 06/93 12/93 06/94 12/94 06/95 12/95 06/96 12/96 06/97 12/97 Time ANIOR Plot of Yearly Rainfall 2,000 1,800 1,600 1,400 1,200 Rainfall (mm) 1,000 800 600 400 200 0 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 Time (Year) OHS - 10 ANIOR

  11. ESTIMATION OF AREAL RAINFALL • HYDROLOGICAL APPLICATIONS • CATCHMENT RAINFALL • AREAL ESTIMATE FOR ADMIN. UNITS • ACTUAL RAIN VOLUME - EQUI. AVERAGE DEPTH • RAINFALL SPATIALLY VARIABLE • VARIABILITY DYNAMIC IN TIME • NO METHOD YIELDS PRECISE ESTIMATE OF THE TRUE VALUE !! OHS - 11

  12. VARIOUS ESTIMATION PROCEDURES • VARIOUS METHODS • ARITHMETIC AVERAGE • USER DEFINED WEIGHTS • THIESSEN POLYGON • KRIGING • PROCESS OF WEIGHTING STATIONS • APPLICABILITY OF METHODS VARIES • TYPE OF RAINFALL - SPATIAL VARIABILITY • SPATIAL DISTRIBUTION OF POINT RAINFALL STATIONS • OROGRAPHICAL EFFECTS OHS - 12

  13. ARITHMETIC AVERAGE • COMPARATIVELY FLATTER AREA • UNIFORM DISTRIBUTION OF RAINFALL STATIONS • UN-WEIGHTED AVERAGING !!! • WEIGHTED AVERAGING • HIGH VARIATION IN DENSITY OF RAINFALL STATIONS IN DIFFERENT AREAS WITHIN THE CATCHMENT OHS - 13

  14. OHS - 14

  15. THIESSEN POLYGON METHOD • REPRESENTATION OF RAINFALL STATIONS PROPORTIONAL TO THEIR AREAL COVERAGE • STEPPED FUNCTION ASSUMED OHS - 15

  16. OHS - 16

  17. THIESSEN WEIGHTS-BILODRA ANIOR .012701 BALASINOR .055652 BAYAD .178597 DAKOR .065945 KAPADWANJ .136940 KATHLAL .076387 MAHISA .096954 MAHUDHA .075515 SAVLITANK .072430 THASARA .034887 VADOL .132929 VAGHAROLI .061064 Sum 1.000000 OHS - 17

  18. OHS - 18

  19. NON-EQUIDISTANT TO EQUIDISTANT • DIGITAL DATA FROM TBR (=Tipping Bucket Raingauge) • TIPS RECORDED AGAINST TIME • NO. OF TIPS AGGREGATED FOR ANY REQUIRED TIME INTERVAL OHS - 19

  20. STATISTICAL INFERENCES • FOR FULL YEARS OR PART WITHIN YEAR • COMPUTE STATISTICS • MINIMUM • MAXIMUM • MEAN • MEDIAN • PERCENTILES OHS - 20

  21. OHS - 21

  22. OHS - 22

  23. ISOHYETAL METHOD (1) • FLAT AREAS: • LINEAR INTERPOLATION BETWEEN STATIONS • CONNECTING POINTS WITH EQUAL RAINFALL: DRAWING ISOHYETS • COMPUTATION OF AREA BETWEEN TWO ADJACENT ISOHYETS • ISOHYETS: P1, P2, P3, ….,Pn AND INTER-ISOHYET AREAS a1, a2, a3, …,an • AREAL RAINFALL FOLLOWS FROM: P= 1/A{½a1(P1+P2)+ ½a2(P2+P3)+ …..+ (½an-1(Pn-1+Pn)} where A = CATCHMENT AREA • BIAS IN CASE ISOHYETS DO NOT COINCIDE WITH CATCHMENT BOUNDARY

  24. ISOHYETAL METHOD (2)

  25. ISOHYETAL METHOD (3) IN HILLY & MOUTAINOUS AREAS • ACCOUNT FOR OROGRAPHIC EFFECTS ON WINDWARD SLOPES OF MOUNTAINS • INTERPOLATION BETWEEN STATIONS IN ACCORDANCE WITH TOPOGRAPHY • DRAWING ISOHYETS PARALLEL TO CONTOUR LINES • REST OF PROCEDURE SIMILAR TO FLAT CATCHMENT BOUNDARY • ISOPERCENTAL METHOD • HYPSOMETRIC METHOD

  26. ISOPERCENTAL METHOD (1) • PROCEDURE: • COMPUTE POINT RAINFALL AS PERCENTAGE OF SEASONAL NORMAL • DRAW ISOPERCENTALS (=LINES OF EQUAL ACTUAL TO SEASONAL RAINFALL RATIO) ON OVERLAY • SUPERIMPOSE OVERLAY ON SEASONAL ISOHYETAL MAP • MARK INTERSECTIONS BETWEEN ISOHYETS AND ISOPERCENTALS • MULTIPLY ISOHYET VALUE WITH ISOPERCENTAL AT ALL INTERSECTIONS = EXTRA RAINFALL VALUES • ADD EXTRA RAINFALL VALUES TO MAP WITH OBSERVED VALUES • DRAW ISOHYETS AND USE PREVIOUS PROCEDURE TO ARRIVE AT AREAL RAINFALL

  27. ISOPERCENTAL METHOD (2)

  28. ISOPERCENTAL METHOD (3)

  29. HYPSOMETRIC METHOD (1) • COMBINATION OF: • PRECIPITATION-ELEVATION CURVE • AREA-ELEVATION CURVE • PRECIPITATION-ELEVATION CURVE • TO BE PREPARED FOR EACH STORM, MONTH, SEASON OR YEAR • AREA-ELEVATION CURVE • TO BE PREPARED ONCE FROM TOPOGRAPHIC MAP • AREAL RAINFALL P =P(zi)A(zi)

  30. HYPSOMETRIC METHOD (2)

  31. RAINFALL INTERPOLATION BY KRIGING AND INVERSE DISTANCE METHOD • PROCEDURE: • A DENSE GRID IS PUT OVER THE CATCHMENT • FOR EACH GRID-POINT A RAINFALL ESTIMATE IS MADE BASED ON RAINFALL OBSERVED AT AVAILABLE STATIONS • RAINFALL ESTIMATE: • STATION WEIGHTS: • KRIGING: BASED ON SPATIAL CORRELATION STRUCTURE RAINFALL FIELD AS FORMULATED IN SEMIVARIOGRAM • INVERSE DISTANCE: SOLELY DETERMINED BY DISTANCE BETWEEN GRIDPOINT AND OBSERVATION STATION

  32. RAINFALL INTERPOLATION BY KRIGING AND INVERSE DISTANCE METHOD 9.2 12.3 7.0 ESTIMATE OF RAINFALL FOR EACH GRIDPOINT BASED ON OBSERVATIONS USING WEIGHTS DETERMINED BY KRIGING OR INVERSE DISTANCE 7.2 9.1 4.0 station DENSE GRID OVER CATCHMENT

  33. RAINFALL INTERPOLATION BY KRIGING (1) • RAINFALL ESTIMATE AT EACH GRIDPOINT: Pe0=w0,k.Pkfor k=1,..,N N=number of stations • PROPERTIES OF WEIGHTS w0,k : • WEIGHTS ARE LINEAR • WEIGHTS LEAD TO UNBIASED ESTIMATE • WEIGHTS MINIMISE ERROR VARIANCE FOR ESTIMATES AT THE GRIDPOINTS • ADVANTAGES OF KRIGING: • PROVIDES BEST LINEAR ESTIMATE FOR RAINFALL AT A POINT • PROVIDES UNCERTAINTY OF ESTIMATE, WHICH IS A USEFUL PROPERTY WHEN OPTIMISING THE NETWORK

  34. RAINFALL INTERPOLATION BY KRIGING (2) • ESTIMATION ERROR e0 AT GRID-LOCATION “0” e0=Pe0-P0 where: Pe0 & P0= est. and true rainfall at “0” resp. • TO QUANTIFY ERROR HYPOTHESIS ON TRUE RAINFALL P0 IS REQUIRED. IN ORDINARY KRIGING ONE ASSUMES: • RAINFALL IN BASIN IS STATISTICALLY HOMOGENEOUS • AT ALL OBSERVATION STATIONS RAINFALL IS GOVERNED BY SAME PROBABILITY DISTRIBUTION • CONSEQUENTLY, AT ALL GRID-POINTS THAT SAME PROBABILITY DISTRIBUTION ALSO APPLIES • HENCE, ANY PAIR OF LOCATIONS HAS A JOINT PROBABILITY DISTRIBUTION THAT DEPENDS ONLY ON DISTANCE AND NOT ON LOCATION

  35. RAINFALL INTERPOLATION BY KRIGING (3) • ASSUMPTIONS IMPLY: • AT ALL LOCATIONS E[P(x1)] = E[P(x1-d)] • COVARIANCE BETWEEN ANY PAIR OF LOCATIONS IS ONLY FUNCTION OF d: COV(d) • UNBIASEDNESS IMPLIES: • E[e0]=0 • so: E[w0,k.Pk]-E[P]=0 or: E[P]{w0,k-1}=0 • hence: w0,k=1 • MINIMISATION OF ERROR VARIANCE se2: • se2=E{(Pe0-P))2] • EQUATING N-FIRST PARTIAL DERIVATIVES OF se2 TO 0 • ADD ONE MORE EQUATION WITH LAGRANGIAN MULTIPLIER TO SATISFY CONDITION w0,k=1 • HENCE N+1 EQUATIONS ARE SOLVED

  36. RAINFALL INTERPOLATION BY KRIGING (4) • SET OF EQ. = ORDINARY KRIGING SYSTEM C.w = D C11………….C1N 1 w0,1 C0,1 C = . . . w = . D = . CN1………….CNN 1 w0,N C0,N 1……………….. 0  1 • STATION WEIGHTS FOLLOW FROM: w =C-1.D Note: C-1is to be determined only once D differs for every location “0” • ERROR VARIANCE: se2 = sP2 - wT.D (which is zero at observation locations)

  37. RAINFALL INTERPOLATION BY KRIGING (5)

  38. RAINFALL INTERPOLATION BY KRIGING (6)

  39. RAINFALL INTERPOLATION BY KRIGING (7)

  40. RAINFALL INTERPOLATION BY KRIGING (8) (semi-)variogram (d) Distance (d)

  41. NETWORK FOR SENSITIVITY ANALYSIS SEMI-VARIOGRAM-MODEL PARAMETERS POINT TO BE ESTIMATED

  42. SEMI-VARIOGRAM MODELS IN SENSITIVITY ANALYSIS Cases 1 = Exp, C0=0, C1=10, a=10 2 = Exp, C0=0, C1=20, a=10 3= Gau, C0=0, C1=10, a=10 4= Exp, C0=5, C1= 5, a=10 5= Exp, C0=0, C1=10, a=20 2 1 4 5 3

  43. SPATIAL COVARIANCE MODELS IN SENSITIVITY ANALYSIS Cases 1 2 3 4 5

  44. NETWORK FOR SENSITIVITY ANALYSIS SEMI-VARIOGRAM-MODEL PARAMETERS POINT TO BE ESTIMATED

  45. SENSITIVITY ANALYSIS, STATION WEIGHTS FOR VARIOUS MODELS Case 1 2 3 4 5 6 SCALE EFFECT: CASE 1 & 2 EFFECT OF SHAPE: CASE 1 & 3 NUGGET EFFECT: CASE 1 & 4 RANGE EFFECT: CASE 1 & 5 KRIGING-INV. DIST: CASE 1 & 6

  46. APPLICATION OF KRIGING AND INVERSE DISTANCE TECHNIQUES • TO APPLY KRIGING: • INSPECT RAINFALL FIELD AND DETERMINE THE VARIANCE OF POINT RAINFALL • DETERMINE THE CORRELATION STRUCTURE • TEST APPLICABILITY OF SEMI-VARIOGRAM MODELS USING APPROXIMATE VALUES OF POINT PROCESS VARIANCE AND CORRELATION DISTANCE a ~ 3d0 • USE APPROPRIATE AVERAGING INTERVAL (LAG-DISTANCE IN KM) FOR DETERMINATION OF SEMI-VARIOGRAM • STORE RAINFALL ESTIMATE-FILE AND VARIANCE-FILE • DISPLAY THE TWO LAYERS ON THE CATCHMENT MAP • INVERSE DISTANCE: • SELECT POWER OF DISTANCE AND STORE ESTIMATE-FILE FOR DISPLAY

  47. SPATIAL CORRELATION STRUCTURE OF MONTHLY RAINFALL DATA BILODRA CATCHMENT

  48. FIT OF SPHERICAL MODEL TO SEMIVARIOGRAM OF BILODRA MONTHLY RAINFALL range a variance C0 +C1 nugget C0

  49. FIT OF SPHERICAL MODEL TO SEMIVARIOGRAM OF BILODRA MONTHLY RAINFALL

  50. FIT OF EXPONENTIAL MODEL TO SEMIVARIOGRAM OF BILODRA MONTHLY RAINFALL

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