Spatial Interpolation of monthly precipitation by Kriging method

Kriging method

Kriging is one of the spatial interpolation algorithm and falls within the field of geostatistics.

Kriging is known to be more realistic spatial behavior of the climate variables.

Semivariogram

- The fundamental tool of kriging

- This concept explains how quickly spatial autocorrelation falls off with increasing distance.

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Types of Kriging

Ordinary kriging - uses a random function model of spatial

correlation to calculated a weighted linear combination of the available samples to predict the response for an unmeasured location.

Simple kriging

Universal kriging

Cokriging

Kriging analysis example Compare Kriging method with and without considering

elevation as a trend.

Find the best Kriging model in semivariogram.

Choose the best method and do spatial interpolation of monthly precipitation: 45 COOP stations from 1968 to 2007.

Produce 1km resolution spatially interpolated precipitation map for each time step.

Calculate the mean precipitation of each month in Yadkin river basin

Study Area: Yadkin River Basin

Location: western NC Area: 17,775 km2 Dataset for analysis

: monthly scale data from 1968 to 20071) precipitation: approximately 45 COOP stations around Yadkin river basin area2) stream discharge: USGS # 0212999

Kriging trend: Elevation

The relationship between elevation (m) and annual precipitation (mm)

45 COOP stations Period: 1968~2007 Positive precipitation trend with

elevation

0

500

1000

1500

2000

2500

0 200 400 600 800 1000 1200

Elevation (m)

Pre

cip

itat

ion

(m

m)

1968196919701971197219731974197519761977197819791980198119821983198419851986198719881989199019911992199319941995199619971998199920002001200220032004200520062007

Semivariogram with and without trend

Semivariogram with trend

"ML“: Maximum Likelihood "REML“: Restricted Maximum Likelihood

parameter estimation

“ML matern” is the best fitted correlation function for both jan00 and feb00 (with the lowest AIC and maximum likelihood value).

Kriging method comparison (1) semivariogram

Without topographic trend

“Power” Model

With topographic trend

“ML Matern” Model

Kriging method comparison (2) visualization (1km resolution)

w/o trend-Mean: 122.69, SD:33.27

With trend-Mean: 121.99, SD: 34.32

Kriging method comparison (3) error analysis

Comparison between observed precipitation and interpolated precipitation

Jan00 w/o trend

y = 1.0065xR2 = 0.9584

0

20

40

60

80

100

120

140

160

180

200

220

0 20 40 60 80 100 120 140 160 180 200 220

Observed

Inte

rpo

late

d

Jan00 with trend

y = 1.0015xR2 = 0.9987

0

20

40

60

80

100

120

140

160

180

200

220

0 20 40 60 80 100 120 140 160 180 200 220

Observed

Inte

rpo

late

d

Kriging result example (1)

Interpolation of monthly precipitation of 1998 using Ordinary Kringing with trend

Kriging result example (2)

Jul. 1975-The most spatially heterogeneous - Mean: 204.76- SD: 82.71

Oct. 2000- The most spatially homogeneous- Mean: 0.30- SD: 0.22

Kriging error analysis (1)

Step 1: Monthly interpolations are sampled at the location of each precipitation stations.

Step 3: Aggregate monthly data to annual scale both observed and interpolated data.

Step 4: Linear regression between observed and interpolated data.

1968-2007 annual precipitation

y = 0.9997x

R2 = 0.9783

0

500

1000

1500

2000

2500

0 500 1000 1500 2000 2500

Observed

Inte

rpo

late

d

Kriging error analysis (2)  Slope R2 Available stations

1968 0.9979 0.9932 40

1969 0.9999 0.9901 41

1970 1.0005 0.9708 40

1971 0.9996 0.9896 40

1972 0.9994 0.9804 36

1973 0.9965 0.9192 35

1974 0.9998 0.9806 37

1975 1.0001 0.9780 38

1976 0.9993 0.9667 40

1977 0.9988 0.8974 37

1978 1.0000 0.9871 41

1979 1.0010 0.9554 39

1980 1.0030 0.9925 36

1981 1.0010 0.9932 41

1982 0.9963 0.8196 39

1983 0.9996 0.9958 41

1984 0.9990 0.9364 38

1985 0.9990 0.9933 40

1986 0.9979 0.9748 38

1987 0.9989 0.9771 39

  Slope R2 Available stations

1988 0.9975 0.7924 38

1989 1.0001 0.9798 37

1990 1.0013 0.9712 37

1991 0.9994 0.9742 38

1992 0.9995 0.9745 32

1993 0.9937 0.8859 32

1994 0.9993 0.9862 32

1995 0.9997 0.9635 28

1996 0.9979 0.9716 31

1997 0.9985 0.9945 34

1998 1.0009 0.9955 31

1999 1.0003 0.9681 30

2000 0.9944 0.8853 32

2001 1.0094 0.8950 37

2002 1.0004 0.9583 35

2003 1.0046 0.9338 30

2004 1.0063 0.9071 32

2005 1.0013 0.8121 30

2006 1.0039 0.8949 33

2007 1.0166 0.8370 18

Monthly precipitation in Yadkin river basin (1968~2007)

0

50

100

150

200

250

300

350

Jan-

68

Jan-

70

Jan-

72

Jan-

74

Jan-

76

Jan-

78

Jan-

80

Jan-

82

Jan-

84

Jan-

86

Jan-

88

Jan-

90

Jan-

92

Jan-

94

Jan-

96

Jan-

98

Jan-

00

Jan-

02

Jan-

04

Jan-

06

Year

pcp

(m

m)

- Mean value of interpolated precipitation data- Standard deviation of precipitation within basin

: 0.22 ~ 82.71

Conclusion

Kriging interpolation considering elevation as a trend is better fitted than without trend method.

Ordinary Kringing with elevation as a trend produces spatially well interpolated precipitation data.

The interpolated precipitation data by this method can be useful input data for hydrologic modeling, especially distributed model.