![Page 1: By: tarun gill Interpolation and evaluation of probable Maximum Precipitation (PMP) patterns using different methods](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697c0201a28abf838cd2486/html5/thumbnails/1.jpg)
by: tarun gill
Interpolation and evaluation of probable Maximum Precipitation (PMP) patterns using different methods
![Page 2: By: tarun gill Interpolation and evaluation of probable Maximum Precipitation (PMP) patterns using different methods](https://reader035.vdocuments.us/reader035/viewer/2022062409/5697c0201a28abf838cd2486/html5/thumbnails/2.jpg)
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.
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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
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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
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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
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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
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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.
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Inverse distance weightedInverse distance weighted
Power value
method
location
View type
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Inverse distance weightedInverse distance weighted
errorstable
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Inverse distance weightedInverse distance weighted
Raster created after interpolation Conversion of raster into contourscomparison
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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
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splinespline
type
shape
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splinespline
errorstable
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splinespline
Raster created after interpolation Conversion of raster into contours
comparison
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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
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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)),
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Ordinary krigingOrdinary kriging
Model type
nugget
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Ordinary krigingOrdinary kriging
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Ordinary krigingOrdinary kriging
Raster created after interpolation Conversion of raster into contourscomparison
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IDW
spline
kriging
comparison
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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.