Transcript Inverse distance weighted method

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.
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
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
10 sq.miles-6 hour
10 sq.miles-12 hour
methodology
IDW
Geostat. analysis
Originaland
PMPcompare
shape
Vectorize
withfiles
original
(vector
data)
shapefile
kriging
spline
•Interpolate Using
geostatistical wizard
•Optimize parameters
•Final raster grid
Conversion into raster
methodology
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
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
Raster
comparison
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
•Redundant values are
often ignored
•Regularised
•tension
spline
type
shape
spline
errors
table
spline
Raster
comparison
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
semiVariogram
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
Raster
comparison
created after
interpolation
Conversion of raster
into contours
comparison
IDW
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.