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

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.

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

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

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

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

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.

Inverse distance weighted Power value method location View type

Inverse distance weighted errors table

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

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

spline type shape

spline errors table

spline comparison Raster created after interpolation Conversion of raster into contours

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

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),

Ordinary kriging Model type nugget

Ordinary kriging

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

IDW comparison kriging spline

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.