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 Daily Rainfall ANIOR Time 20/09/9413/09/9406/09/9430/08/9423/08/9416/08/9409/08/9402/08/9426/07/9419/07/9412/07/9405/07/94 Rainfall (mm) 150 125 100 75 50 25 0 Plot of Weekly Rainfall ANIOR Time 10/9509/9508/9507/9506/9505/9504/9503/9502/9501/9512/9411/9410/9409/9408/9407/94 Rainfall (mm) 300 250 200 150 100 50 0 OHS - 9

10. Plot of Yearly Rainfall ANIOR Time (Year) 9796959493929190898887868584838281 Rainfall (mm) 2,000 1,800 1,600 1,400 1,200 1,000 800 600 400 200 0 OHS - 10

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: P 1, P 2, P 3, ….,P n AND INTER-ISOHYET AREAS a 1, a 2, a 3, …,a n –AREAL RAINFALL FOLLOWS FROM: P= 1/A{½a 1 (P 1 +P 2 )+ ½a 2 (P 2 +P 3 )+ …..+ (½a n-1 (P n-1 +P n )} 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(z i )  A(z i )

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

33. RAINFALL INTERPOLATION BY KRIGING (1) RAINFALL ESTIMATE AT EACH GRIDPOINT: Pe 0 =  w 0,k.P k for k=1,..,N N=number of stations PROPERTIES OF WEIGHTS w 0,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 e 0 AT GRID-LOCATION “0” e 0 =Pe 0 -P 0 where: Pe 0 & P 0 = est. and true rainfall at “0” resp. TO QUANTIFY ERROR HYPOTHESIS ON TRUE RAINFALL P 0 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(x 1 )] = E[P(x 1 -d)] –COVARIANCE BETWEEN ANY PAIR OF LOCATIONS IS ONLY FUNCTION OF d: COV(d) UNBIASEDNESS IMPLIES: –E[e 0 ]=0 –so: E[  w 0,k.P k ]-E[P]=0 or: E[P]{  w 0,k -1}=0 –hence:  w 0,k =1 MINIMISATION OF ERROR VARIANCE s e 2 : –s e 2 =E{(Pe 0 -P)) 2 ] –EQUATING N-FIRST PARTIAL DERIVATIVES OF s e 2 TO 0 –ADD ONE MORE EQUATION WITH LAGRANGIAN MULTIPLIER  TO SATISFY CONDITION  w 0,k =1 –HENCE N+1 EQUATIONS ARE SOLVED

36. RAINFALL INTERPOLATION BY KRIGING (4) SET OF EQ. = ORDINARY KRIGING SYSTEM C.w = D C 11 ………….C 1N 1 w 0,1 C 0,1 C =... w =. D =. C N1 ………….C NN 1 w 0,N C 0,N 1……………….. 0  1 STATION WEIGHTS FOLLOW FROM: w =C -1.D Note: C -1 is to be determined only once D differs for every location “0” ERROR VARIANCE: s e 2 = s P 2 - w T.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) Distance (d) (semi-)variogram  (d)

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

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

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

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

45. SENSITIVITY ANALYSIS, STATION WEIGHTS FOR VARIOUS MODELS 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 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 Case 1 2 3 4 5 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 ~ 3d 0 –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. variance C0 +C1 range a nugget C0 FIT OF SPHERICAL MODEL TO SEMIVARIOGRAM OF BILODRA MONTHLY RAINFALL

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

51. RAINFALL CONTOURS BY KRIGING

52. VARIANCE CONTOURS BY KRIGING

53. RAINFALL CONTOURS BY INVERSE DISTANCE (Power = 2)

54. COMMENTS ON KRIGING BASIC ASSUMPTION IN ORDINARY KRIGING IS SPATIAL HOMOGENEITY OF THE RAINFALL FIELD IN CASE OF OROGRAPHICAL EFFECTS THIS CONDITION IS NOT FULFILLED TO APPLY THE TECHNIQUE, FIRST THE RAINFALL FIELD HAS TO BE NORMALISED KRIGING IS APPLIED ON THE NORMALISED VALUES AFTERWARDS THE GRID-VALUES ARE DENORMALISED. THIS REQUIRES A MODEL FOR PRECIPITATION-ELEVATION RELATION