by: tarun gill

Interpolation and evaluation of probable Maximum Precipitation (PMP) patterns using different methods

objectivesobjectives

To convert vector based PMP to raster To convert vector based PMP to raster based PMP using different interpolation based PMP using different interpolation methods.methods.

Finding the accuracy of all the methods Finding the accuracy of all the methods

used.used.

Determining the best method for Determining the best method for interpolation.interpolation.

InterpolationInterpolation

•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

10 sq.miles-6 hour 10 sq.miles-12 hour

Data usedData usedProbable maximum Probable maximum precipitation mapsprecipitation 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.milesDuration-6,12,24,48,72hours

Conversion into raster

•Interpolate Using geostatistical wizard •Optimize parameters•Final raster grid

methodologymethodology

Original PMP shape files(vector data)

IDW

kriging spline

Geostat. analysis

Vectorize and compare with original shapefile

methodologymethodology

•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 WEIGHTEDINVERSE DISTANCE WEIGHTED

•The further away the point the lesser its weight in defining the value at the unsampled location.

•Uses values of nearby points and their distances

•Weight of each point is inversely proportional to its distance from that point.

Inverse distance weightedInverse distance weighted

Power value

method

location

View type

Inverse distance weightedInverse distance weighted

errorstable

Inverse distance weightedInverse distance weighted

Raster created after interpolation Conversion of raster into contourscomparison

splinespline

•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

•Redundant values are often ignored

•Regularised•tension

splinespline

type

shape

splinespline

errorstable

splinespline

Raster created after interpolation Conversion of raster into contours

comparison

Ordinary krigingOrdinary 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 analysisTrend analysis

γ(si, sj) = sill - C(si, sj),

semiVariogramγ(si,sj) = ½ var(Z(si) - Z(sj))

CovarianceC(si, sj) = cov(Z(si), Z(sj)),

Ordinary krigingOrdinary kriging

Model type

nugget

Ordinary krigingOrdinary kriging

Ordinary krigingOrdinary kriging

Raster created after interpolation Conversion of raster into contourscomparison

IDW

spline

kriging

comparison

ConclusionConclusion

•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.