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.