1. Interpolation and evaluation of probable Maximum Precipitation (PMP) patterns using different methods
by: tarun gill

2. objectives
To convert vector based PMP to raster based PMP using different interpolation methods.
Finding the accuracy of all the methods used.
Determining the best method for interpolation.

3. Different interpolation methods
Predicting values of a certain variable at unsampled location based on the measurement values at sampled locations.
Different interpolation methods
Deterministic methods
Use mathematical functions based on the degree of similarity or degree of smoothing
Geostatistical methods
Use Both mathematical and statistical functions based on spatial autocorrelation

4. Data used Probable maximum precipitation maps
Theoretically the greatest depth of precipitation for a given duration that is physically possible over a drainage area at a certain time of year.
10 sq.miles-6 hour
10 sq.miles-12 hour
Hmr-52 -Standard pmp estimates for united states east of the 105 meridian
Areas -10,200,1000,5000,10000 sq.miles
Duration-6,12,24,48,72hours

5. methodology IDW kriging spline Geostat. analysis
Vectorize and compare with original shapefile
Original PMP shape files
(vector data)
Conversion into raster
Interpolate Using geostatistical wizard
Optimize parameters
Final raster grid

6. Criteria used for the best raster
methodology
Remove a known point from the data
Use the methods to predict its value
Calculate the predicted error
Cross validation
Criteria used for the best raster
Standardized mean nearest to 0
Smallest RMS prediction error

7. INVERSE DISTANCE WEIGHTED
Uses values of nearby points and their distances
Weight of each point is inversely proportional to its distance from that point.
The further away the point the lesser its weight in defining the value at the unsampled location.

8. Inverse distance weighted
Power value
method
location
View type

9. Inverse distance weighted
errors
table

10. Inverse distance weighted
comparison
Raster created after interpolation
Conversion of raster into contours

11. spline
Fits a mathematical function to a specified number of nearest points.
Unknown points are estimated by plotting their position on the spline
minimizes overall surface curvature
Regularised
tension
Redundant values are often ignored

12. spline
type
shape

13. spline
errors
table

14. spline comparison Raster created after interpolation
Conversion of raster into contours

15. Ordinary kriging Z(s) = μ(s) + ε(s),
Specialized interpolation method based on spatial correlation
Takes into account drift and random error
Predicts values based on regression trends
Uses semivaroigram and covariance for trend analysis

16. Trend analysis Covariance semiVariogram C(si, sj) = cov(Z(si), Z(sj)),
γ(si,sj) = ½ var(Z(si) - Z(sj))
Covariance
C(si, sj) = cov(Z(si), Z(sj)),
γ(si, sj) = sill - C(si, sj),

17. Ordinary kriging
Model type
nugget

18. Ordinary kriging

20. Ordinary kriging comparison Raster created after interpolation
Conversion of raster into contours

21. IDW
comparison
kriging
spline

22. Conclusion
Idw is a fast interpolation method but does not give accurate results- “bull’s eye effect”
Usually used for interpolation of high density or regularly spaced points
Spline and kriging coinside better with the original data
ANISOTROPY IS AN IMPORTANT ASPECT AND SHOULD BE TAKEN INTO ACCOUNT IN ALL THE TECHNIQUES.