by: tarun gill

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. Interpolation • 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. 10 sq.miles-6 hour 10 sq.miles-12 hour 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. 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. IDW Geostat. analysis Original PMP shape files (vector data) • Interpolate Using geostatistical wizard • Optimize parameters • Final raster grid Vectorize and compare with original shapefile kriging spline Conversion into raster methodology

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

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. Power value method location View type Inverse distance weighted

9. errors table Inverse distance weighted

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

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. type shape spline

13. errors table spline

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

15. 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 Ordinary kriging Z(s) = μ(s) + ε(s),

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

17. Model type nugget Ordinary kriging

18. Ordinary kriging

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

21. IDW kriging spline comparison

22. 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. Conclusion