1. Spatial Interpolation of monthly precipitation by Kriging method

2. 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.
range
sill
distance
semivariance
nugget

3. 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

4. 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

5. Study Area: Yadkin River Basin
Location: western NC
Area: 17,775 km2
Dataset for analysis
: monthly scale data from 1968 to 2007
1) precipitation: approximately 45 COOP stations around Yadkin river basin area
2) stream discharge: USGS #

6. Kriging trend: Elevation
The relationship between elevation (m) and annual precipitation (mm)
45 COOP stations
Period: 1968~2007
Positive precipitation trend with elevation

7. Semivariogram with and without trend

8. 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).

9. Kriging method comparison (1) semivariogram
Without topographic trend
“Power” Model
With topographic trend
“ML Matern” Model

10. Kriging method comparison (2) visualization (1km resolution)
w/o trend
-Mean: , SD:33.27
With trend
-Mean: , SD: 34.32

11. Kriging method comparison (3) error analysis
Comparison between observed precipitation and interpolated precipitation

12. Kriging result example (1)
Interpolation of monthly precipitation of 1998 using Ordinary Kringing with trend

13. Kriging result example (2)
Jul. 1975
-The most spatially heterogeneous
- Mean:
- SD: 82.71
Oct. 2000
- The most spatially homogeneous
- Mean: 0.30
- SD: 0.22

14. 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.

15. 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
1971
0.9996
0.9896
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
1977
0.9988
0.8974
1978
1.0000
0.9871
1979
1.0010
0.9554 39
1980
1.0030
0.9925
1981
1982
0.9963
0.8196
1983
0.9958
1984
0.9990
0.9364
1985
0.9933
1986
0.9748
1987
0.9989
0.9771
Slope R2
Available stations
1988
0.9975
0.7924 38
1989
1.0001
0.9798 37
1990
1.0013
0.9712
1991
0.9994
0.9742
1992
0.9995
0.9745 32
1993
0.9937
0.8859
1994
0.9993
0.9862
1995
0.9997
0.9635 28
1996
0.9979
0.9716 31
1997
0.9985
0.9945 34
1998
1.0009
0.9955
1999
1.0003
0.9681 30
2000
0.9944
0.8853
2001
1.0094
0.8950
2002
1.0004
0.9583 35
2003
1.0046
0.9338
2004
1.0063
0.9071
2005
0.8121
2006
1.0039
0.8949 33
2007
1.0166
0.8370 18

16. Monthly precipitation in Yadkin river basin (1968~2007)
- Mean value of interpolated precipitation data
Standard deviation of precipitation within basin
: 0.22 ~ 82.71

17. 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.