COMPILATION OF RAINFALL DATA

HYDROLOGY PROJECTTechnical Assistance

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


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


OHS - 24

Plot of Hourly Rainfall

ANIOR

Time11/09/9410/09/9409/09/9408/09/9407/09/9406/09/9405/09/9404/09/9403/09/9402/09/9401/09/94

Rai

nfal

l (m

m)

40

35

30

25

20

15

10

5

0

OHS - 3


Plot of Daily Rainfall

ANIOR

Time20/09/9413/09/9406/09/9430/08/9423/08/9416/08/9409/08/9402/08/9426/07/9419/07/9412/07/9405/07/94

Rai

nfal

l (m

m)

150

125

100

75

50

25

0

OHS - 4


Plot of Weekly Rainfall

ANIOR

Time10/9509/9508/9507/9506/9505/9504/9503/9502/9501/9512/9411/9410/9409/9408/9407/94

Rai

nfal

l (m

m)

300

250

200

150

100

50

0

OHS - 5


Plot of Ten-daily Rainfall

ANIOR

Time01/10/9501/08/9501/06/9501/04/9501/02/9501/12/9401/10/9401/08/94

Rai

nfal

l (m

m)

350

300

250

200

150

100

50

0

OHS - 6


Plot of Monthly Rainfall

ANIOR

Time12/9706/9712/9606/9612/9506/9512/9406/9412/9306/9312/9206/9212/9106/91

Rai

nfal

l (m

m)

800

700

600

500

400

300

200

100

0

OHS - 7


Plot of Yearly Rainfall

ANIOR

Time (Year)9796959493929190898887868584838281

Rai

nfal

l (m

m)

2,000

1,800

1,600

1,400

1,200

1,000

800

600

400

200

0

OHS - 8


Plot of Hourly Rainfall

ANIOR

Time11/09/9410/09/9409/09/9408/09/9407/09/9406/09/9405/09/9404/09/9403/09/9402/09/9401/09/94

Ra

infa

ll (m

m)

40

35

30

25

20

15

10

5

0

Plot of Daily Rainfall

ANIOR

Time20/09/9413/09/9406/09/9430/08/9423/08/9416/08/9409/08/9402/08/9426/07/9419/07/9412/07/9405/07/94

Rai

nfa

ll (m

m)

150

125

100

75

50

25

0

Plot of Weekly Rainfall

ANIOR

Time10/9509/9508/9507/9506/9505/9504/9503/9502/9501/9512/9411/9410/9409/9408/9407/94

Rai

nfa

ll (m

m)

300

250

200

150

100

50

0

OHS - 9


Plot of Yearly Rainfall

ANIOR

Time (Year)9796959493929190898887868584838281

Rai

nfa

ll (

mm

)

2,000

1,800

1,600

1,400

1,200

1,000

800

600

400

200

0

Plot of Monthly Rainfall

ANIOR

Time12/9706/9712/9606/9612/9506/9512/9406/9412/9306/9312/9206/9212/9106/91

Ra

infa

ll (m

m)

800

700

600

500

400

300

200

100

0

Plot of Ten-daily Rainfall

ANIOR

Time01/10/9501/08/9501/06/9501/04/9501/02/9501/12/9401/10/9401/08/94

Ra

in

fa

ll (m

m)

350

300

250

200

150

100

50

0

OHS - 10


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


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


• 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

N

iitNttttat P

NPPPP

NP

1321

1)(

1

ti

N

iiNtNtttwt Pc

NPcPcPcPc

NP

1

332211

1)....(

1

OHS - 13


Areal Daily Rainfall - Arithmetic Average

BILODRA CATCHMENT RAINFALL

Time15/10/9401/10/9415/09/9401/09/9415/08/9401/08/9415/07/9401/07/9415/06/94

Rai

nfal

l (m

m)

250

225

200

175

150

125

100

75

50

25

0

Equal Station Weights BILODRA

Station weights BALASINOR = 0.0909 DAKOR = 0.0909 KAPADWANJ = 0.0909 BAYAD = 0.0909 MAHISA = 0.0909 MAHUDHA = 0.0909 SAVLITANK = 0.0909 THASARA = 0.0909 VAGHAROLI = 0.0909 VADOL = 0.0909 KATHLAL = 0.0909

Sum = 0.999

OHS - 14


• THIESSEN POLYGON METHOD* REPRESENTATION OF RAINFALL STATIONS

PROPORTIONAL TO THEIR AREAL COVERAGE

* STEPPED FUNCTION ASSUMED

N

iit

iNt

Ntttat P

A

AP

A

AP

A

AP

A

AP

A

AP

13

32

21

1 )(

OHS - 15


OHS - 16


Areal Average Daily Rainfall (Thiessen Weights)


Time15/10/9401/10/9415/09/9401/09/9415/08/9401/08/9415/07/9401/07/9415/06/94

Rai

nfal

l (m

m)

250

225

200

175

150

125

100

75

50

25

0

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


Areal Daily Rainfall - Arithmetic Average


Time15/10/9401/10/9415/09/9401/09/9415/08/9401/08/9415/07/9401/07/9415/06/94

Ra

infa

ll (

mm

)250

225

200

175

150

125

100

75

50

25

0

Areal Average Daily Rainfall (Thiessen Weights)


Time15/10/9401/10/9415/09/9401/09/9415/08/9401/08/9415/07/9401/07/9415/06/94

Ra

infa

ll (

mm

)

250

225

200

175

150

125

100

75

50

25

0

OHS - 18


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


STATISTICAL INFERENCES

• FOR FULL YEARS OR PART WITHIN YEAR– COMPUTE STATISTICS

* MINIMUM

* MAXIMUM

* MEAN

* MEDIAN

* PERCENTILES

OHS - 20


Min., Mean and Max. Ten-daily Rainfall During Monsoon Months

Min. - Max. & 25 & 90 %iles Mean Median

Time979695949392919089888786858483828180797877767574737271706968676665646362

Rai

nfa

ll (m

m)

400

350

300

250

200

150

100

50

0

OHS - 21


Year Min. Max. Mean Median 25 %ile 90 %ile1961 34.54 170.39 99.6 81.03 39.36 158.471962 5.6 237.6 78.9 8.6 8.4 197.51963 0 177.44 53.0 0 0 119.11964 0 157.2 39.7 20.7 1.7 69.61965 0 237 56.3 8 0 110.61966 0 151 31.4 0 0 981967 0 270 75.9 26 6 1581968 0 211 63.0 0 0 1851969 0 128 49.2 30 0 871970 0 287 120.7 50 0 2321971 0 118.5 53.1 7 0 1141972 0 99.6 29.9 7 2.6 83.31973 0 330.4 110.8 34.8 17 322.61974 0 51 16.5 5 1.5 31.21976 0 333.4 108.8 38.2 0 234.21977 0 175.4 67.6 18 7 1641978 0 324 90.3 36 16 1231979 0 282 46.0 0 0 671980 0 43 15.3 0 0 421981 0 198 81.0 65.5 16 115.51982 0 144 38.5 0 0 691983 0 256 84.7 54 12 2191984 0 265 87.0 19.5 7.5 231.51985 0 140.5 36.9 3 0 1271986 0 170 38.4 0 0 94.51987 0 287 38.5 0 0 331988 0 300 99.0 50 3 2071989 0 140 72.3 44.5 9 138.51990 5 211.5 91.1 38.5 10 203.51991 0 361.5 56.7 4 0 41.51992 0 298 72.2 3 0 1341993 0 336.5 75.7 8 0 2691994 0 249 121.1 85 58.5 241.51995 0 276.5 85.9 9.5 0 2641996 0 309 81.9 52.5 13.5 1091997 0 391 105.7 23 10 242.5

Full Period 0 391 68.7OHS - 22


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


ISOHYETAL METHOD (2)ISOHYETAL METHOD (2)ISOHYETAL METHOD (2)ISOHYETAL METHOD (2)

12.3

9.2

9.1

7.2

7.0

4.0

12

10

10

8

8

6

6

4

4

Legend

station12 mm

10 mm8 mm

6 mmisohyet


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


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


ISOPERCENTAL METHOD (2)ISOPERCENTAL METHOD (2)ISOPERCENTAL METHOD (2)ISOPERCENTAL METHOD (2)


ISOPERCENTAL METHOD (3)ISOPERCENTAL METHOD (3)ISOPERCENTAL METHOD (3)ISOPERCENTAL METHOD (3)


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)


HYPSOMETRIC METHOD (2)HYPSOMETRIC METHOD (2)HYPSOMETRIC METHOD (2)HYPSOMETRIC METHOD (2)

rainfall (mm)

ele

vati

on

(m

+M

SL

)

ele

vati

on

(m

+M

SL

)

Basin area above given elevation (%)0 100

zi

P(zi)

Δz

ΔA(zi)

Precipitation-elevation curve Hypsometric curve


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

N

1kkk,00 P.wPe


12.3

9.2

9.1

7.2

7.0

4.0station

ESTIMATE OF RAINFALL FOR EACH GRIDPOINT BASED ON

OBSERVATIONS USING WEIGHTS DETERMINED BY KRIGING OR

INVERSE DISTANCE

ESTIMATE OF RAINFALL FOR EACH GRIDPOINT BASED ON

OBSERVATIONS USING WEIGHTS DETERMINED BY KRIGING OR

INVERSE DISTANCE

DENSE GRID OVER CATCHMENT

DENSE GRID OVER CATCHMENT

RAINFALL INTERPOLATION BY KRIGING AND RAINFALL INTERPOLATION BY KRIGING AND INVERSE DISTANCE METHODINVERSE DISTANCE METHOD

RAINFALL INTERPOLATION BY KRIGING AND RAINFALL INTERPOLATION BY KRIGING AND INVERSE DISTANCE METHODINVERSE DISTANCE METHOD


RAINFALL INTERPOLATION BY KRIGING (1)

• RAINFALL ESTIMATE AT EACH GRIDPOINT:

Pe0=w0,k.Pk for 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



• 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



• 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



• 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-1 is to be determined only once

D differs for every location “0”

• ERROR VARIANCE: se

2 = sP2 - wT.D (which is zero at observation locations)


RAINFALL INTERPOLATION BY KRIGING (5)RAINFALL INTERPOLATION BY KRIGING (5)RAINFALL INTERPOLATION BY KRIGING (5)RAINFALL INTERPOLATION BY KRIGING (5)

1

r0

Distance d

Exponential spatial correlation functionExponential spatial correlation function

Exponential spatial correlationfunction:

r(d) = r0 exp(- d / d0)

Exponential spatial correlationfunction:

r(d) = r0 exp(- d / d0)

0

0.37r0

d0

co

rrela

tio

n


C0 + C1

C1

Nugget effectNugget effect

Distance da

Exponential covariance functionExponential covariance function

Covariance function:

C(d) = C0 + C1 for d = 0

C(d) = C1 exp(- 3d / a) for d > 0

Covariance function:

C(d) = C0 + C1 for d = 0

C(d) = C1 exp(- 3d / a) for d > 0

Range = aRange = a (C(a) = 0.05C1 0 )(C(a) = 0.05C1 0 )




C0 + C1

Distan ce da

Exponentialvariogram

Exponentialvariogram

Variogram function:

(d) = 0 for d = 0

(d) = C0 + C1 (1- exp(- 3d / a) for d > 0

Variogram function:

(d) = 0 for d = 0

(d) = C0 + C1 (1- exp(- 3d / a) for d > 0

Rang e = aRang e = a

Nug get effectNug get effect

P2P

2

C0

(a) C0 + C1Sil lS il l



0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Spherical model

Gaussian model

Exponential model

Distance (d)

(sem

i-)v

ario

gra

m

(d)


126

128130

132

134136

138

140

142144

146

60 62 64 66 68 70 72 74 76 78 80

1

2

34

56

7

Point to be estimated

X-direction

Y-d

irec

tion POINT TO BE

ESTIMATED

POINT TO BE ESTIMATED

NETWORK FOR SENSITIVITY ANALYSIS NETWORK FOR SENSITIVITY ANALYSIS SEMI-VARIOGRAM-MODEL PARAMETERSSEMI-VARIOGRAM-MODEL PARAMETERS NETWORK FOR SENSITIVITY ANALYSIS NETWORK FOR SENSITIVITY ANALYSIS

SEMI-VARIOGRAM-MODEL PARAMETERSSEMI-VARIOGRAM-MODEL PARAMETERS


SEMI-VARIOGRAM MODELS IN SENSITIVITY SEMI-VARIOGRAM MODELS IN SENSITIVITY ANALYSISANALYSIS

SEMI-VARIOGRAM MODELS IN SENSITIVITY SEMI-VARIOGRAM MODELS IN SENSITIVITY ANALYSISANALYSIS

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16 18 20

Distance (d)

d

11

22

33

44

55

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

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


SPATIAL COVARIANCE MODELS IN SPATIAL COVARIANCE MODELS IN SENSITIVITY ANALYSISSENSITIVITY ANALYSIS

SPATIAL COVARIANCE MODELS IN SPATIAL COVARIANCE MODELS IN SENSITIVITY ANALYSISSENSITIVITY ANALYSIS

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 20

Distance (d)

Co

vari

ance

C(d

)

Cases

1

2

3

4

5

Cases

1

2

3

4

5


126

128130

132

134136

138

140

142144

146

60 62 64 66 68 70 72 74 76 78 80

1

2

34

56

7

Point to be estimated

X-direction

Y-d

irec

tion POINT TO BE

ESTIMATED

POINT TO BE ESTIMATED

NETWORK FOR SENSITIVITY ANALYSIS NETWORK FOR SENSITIVITY ANALYSIS SEMI-VARIOGRAM-MODEL PARAMETERSSEMI-VARIOGRAM-MODEL PARAMETERS NETWORK FOR SENSITIVITY ANALYSIS NETWORK FOR SENSITIVITY ANALYSIS

SEMI-VARIOGRAM-MODEL PARAMETERSSEMI-VARIOGRAM-MODEL PARAMETERS


SENSITIVITY ANALYSIS, STATION WEIGHTS SENSITIVITY ANALYSIS, STATION WEIGHTS FOR VARIOUS MODELSFOR VARIOUS MODELS

SENSITIVITY ANALYSIS, STATION WEIGHTS SENSITIVITY ANALYSIS, STATION WEIGHTS FOR VARIOUS MODELSFOR VARIOUS MODELS

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1 2 3 4 5 6 7

stations

sta

tio

n w

eig

ht

Exp C0=0, C1=10, a=10

Exp C0=0, C1=20, a=10Gau C0=0, C1=10, a=10

Exp C0=5, C1=5, a=10Exp C0=0, C1=10, a=20

Inverse distance p=2

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


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


Correlation Correlation function

Distance [km]1009080706050403020100

Co

rre

latio

n c

oef

fici

en

t

1

0.8

0.6

0.4

0.2

0

SPATIAL CORRELATION STRUCTURE OF MONTHLY SPATIAL CORRELATION STRUCTURE OF MONTHLY RAINFALL DATA BILODRA CATCHMENTRAINFALL DATA BILODRA CATCHMENT

SPATIAL CORRELATION STRUCTURE OF MONTHLY SPATIAL CORRELATION STRUCTURE OF MONTHLY RAINFALL DATA BILODRA CATCHMENTRAINFALL DATA BILODRA CATCHMENT


Semivariance Semivariogram function Distance

1,2001,0008006004002000

Sem

ivar

ianc

e (m

m2)

30,000

28,000

26,000

24,000

22,000

20,000

18,000

16,000

14,000

12,000

10,000

8,000

6,000

4,000

2,000

variance C0 +C1variance C0 +C1

range arange a

nugget C0nugget C0

FIT OF SPHERICAL MODEL TO SEMIVARIOGRAM OF FIT OF SPHERICAL MODEL TO SEMIVARIOGRAM OF BILODRA MONTHLY RAINFALLBILODRA MONTHLY RAINFALL



Semivariance Semivariogram function Distance

1009080706050403020100

Sem

ivar

ian

ce (m

m2)

5,000

4,500

4,000

3,500

3,000

2,500

2,000

1,500

1,000

500

0




Semivariance Semivariogram function

Distance1009080706050403020100

Sem

ivar

ianc

e (m

m2)

5,000

4,500

4,000

3,500

3,000

2,500

2,000

1,500

1,000

500

0

FIT OF EXPONENTIAL MODEL TO SEMIVARIOGRAM OF FIT OF EXPONENTIAL MODEL TO SEMIVARIOGRAM OF BILODRA MONTHLY RAINFALLBILODRA MONTHLY RAINFALL

FIT OF EXPONENTIAL MODEL TO SEMIVARIOGRAM OF FIT OF EXPONENTIAL MODEL TO SEMIVARIOGRAM OF BILODRA MONTHLY RAINFALLBILODRA MONTHLY RAINFALL


RAINFALL CONTOURS BY KRIGINGRAINFALL CONTOURS BY KRIGINGRAINFALL CONTOURS BY KRIGINGRAINFALL CONTOURS BY KRIGING


VARIANCE CONTOURS BY KRIGINGVARIANCE CONTOURS BY KRIGINGVARIANCE CONTOURS BY KRIGINGVARIANCE CONTOURS BY KRIGING


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

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


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

COMPILATION OF RAINFALL DATA

Documents

density of rainfall

areal estimatesnonequidistant

thiessen weightsbilodra

anotherfrom point

precise estimate

equidistantdigital data

timeno method

objectivesdata validation