compilation of rainfall data
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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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
• 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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
• 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
HYDROLOGY PROJECTTechnical Assistance
OHS - 16
HYDROLOGY PROJECTTechnical Assistance
Areal Average Daily Rainfall (Thiessen Weights)
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
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
HYDROLOGY PROJECTTechnical Assistance
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
Ra
infa
ll (
mm
)250
225
200
175
150
125
100
75
50
25
0
Areal Average Daily Rainfall (Thiessen Weights)
BILODRA CATCHMENT RAINFALL
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
STATISTICAL INFERENCES
• FOR FULL YEARS OR PART WITHIN YEAR– COMPUTE STATISTICS
* MINIMUM
* MAXIMUM
* MEAN
* MEDIAN
* PERCENTILES
OHS - 20
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
ISOPERCENTAL METHOD (2)ISOPERCENTAL METHOD (2)ISOPERCENTAL METHOD (2)ISOPERCENTAL METHOD (2)
HYDROLOGY PROJECTTechnical Assistance
ISOPERCENTAL METHOD (3)ISOPERCENTAL METHOD (3)ISOPERCENTAL METHOD (3)ISOPERCENTAL METHOD (3)
HYDROLOGY PROJECTTechnical Assistance
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)
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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-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)
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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 )
RAINFALL INTERPOLATION BY KRIGING (6)RAINFALL INTERPOLATION BY KRIGING (6)RAINFALL INTERPOLATION BY KRIGING (6)RAINFALL INTERPOLATION BY KRIGING (6)
HYDROLOGY PROJECTTechnical Assistance
RAINFALL INTERPOLATION BY KRIGING (7)RAINFALL INTERPOLATION BY KRIGING (7)RAINFALL INTERPOLATION BY KRIGING (7)RAINFALL INTERPOLATION BY KRIGING (7)
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
HYDROLOGY PROJECTTechnical Assistance
RAINFALL INTERPOLATION BY KRIGING (8)RAINFALL INTERPOLATION BY KRIGING (8)RAINFALL INTERPOLATION BY KRIGING (8)RAINFALL INTERPOLATION BY KRIGING (8)
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)
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
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
FIT OF SPHERICAL MODEL TO SEMIVARIOGRAM OF FIT OF SPHERICAL MODEL TO SEMIVARIOGRAM OF BILODRA MONTHLY RAINFALLBILODRA MONTHLY RAINFALL
HYDROLOGY PROJECTTechnical Assistance
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
FIT OF SPHERICAL MODEL TO SEMIVARIOGRAM OF FIT OF SPHERICAL MODEL TO SEMIVARIOGRAM OF BILODRA MONTHLY RAINFALLBILODRA MONTHLY RAINFALL
FIT OF SPHERICAL MODEL TO SEMIVARIOGRAM OF FIT OF SPHERICAL MODEL TO SEMIVARIOGRAM OF BILODRA MONTHLY RAINFALLBILODRA MONTHLY RAINFALL
HYDROLOGY PROJECTTechnical Assistance
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
HYDROLOGY PROJECTTechnical Assistance
RAINFALL CONTOURS BY KRIGINGRAINFALL CONTOURS BY KRIGINGRAINFALL CONTOURS BY KRIGINGRAINFALL CONTOURS BY KRIGING
HYDROLOGY PROJECTTechnical Assistance
VARIANCE CONTOURS BY KRIGINGVARIANCE CONTOURS BY KRIGINGVARIANCE CONTOURS BY KRIGINGVARIANCE CONTOURS BY KRIGING
HYDROLOGY PROJECTTechnical Assistance
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)
HYDROLOGY PROJECTTechnical Assistance
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
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