Lap trinh va ung dung Chaper I
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Transcript of Lap trinh va ung dung Chaper I
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Chapper I: Graph & Interpolar
Programming & Application
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Part I: Graph
Wind & Flow Rose
Field vector
Historgram Other plot
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Wind & Flow Rose
O
Vector
North (y)
East (x)
( , )
Math angle:
arctan 2[ , ]Flow angle:
arctan 2[ , ]
Wind angle:
arctan 2[ , ]
v v u v
u v
v u
v u
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Wind & Flow Rose
YR-MO-DA HH-MM-SSEas Nor Mag Dir
mm/s deg mm/s deg
20/04/2010 18:30:00 -144 214
20/04/2010 18:45:00 -35 123
20/04/2010 19:00:00 -5 10
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Field Vector
Name X Y Deg Speed
Centennial -104.8 39.6 157.5 28
Cortez -108.7 37.3 202.5 20
Durango -107.8 37.3 202.5 26
Springfield -102.6 37.4 202.5 35
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How to ???
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Histogram
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Part II: Spatial Analysis
World file
Digitizing
Interpolar: IDW
Kriging
Natural Neibour
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World file
A world file is a plain text
computer data file used by
GIS to georeference rastermap images.
The file specification was
introduced by ESRI.
http://en.wikipedia.org/wiki/Plain_texthttp://en.wikipedia.org/wiki/Data_filehttp://en.wikipedia.org/wiki/Georeferencehttp://en.wikipedia.org/wiki/Raster_graphicshttp://en.wikipedia.org/wiki/ESRIhttp://en.wikipedia.org/wiki/ESRIhttp://en.wikipedia.org/wiki/Raster_graphicshttp://en.wikipedia.org/wiki/Georeferencehttp://en.wikipedia.org/wiki/Data_filehttp://en.wikipedia.org/wiki/Data_filehttp://en.wikipedia.org/wiki/Data_filehttp://en.wikipedia.org/wiki/Plain_texthttp://en.wikipedia.org/wiki/Plain_texthttp://en.wikipedia.org/wiki/Plain_text -
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World file
Line 1: A: pixel size in the x-direction in map units/pixel
Line 2: D: rotation about y-axis
Line 3: B: rotation about x-axis
Line 4: E: pixel size in the y-direction in map units, almost
always negative.
Line 5: C: x-coordinate of the center of the upper left pixel
Line 6: F: y-coordinate of the center of the upper left pixel
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Example
0.00068664550781250889 (size of pixel in x direction)
1.9907765865908334e-011 (rotation term for row)
-1.7190550058712099e-018 (rotation term for column)
-0.00067648625587322258 (size of pixel in y direction)
104.67807769775386 (x coordinate of centre of upper leftpixel in map units)
11.178063629472314(y coordinate of centre of upper left
pixel in map units)
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Invert Distance Weighting (IDW)
1
1
1 1
n
i i
i
n
i j
i j
Z w Z
w
c d c d
IDW assumes thateach measuredpoint has a localinfluence that
diminishes withdistance.
It weights thepoints closer to
the predictionlocation greaterthan those fartheraway.
http://_geostatistical_wizard_colon_searching_neighborhood_dialog_box1407990.click%28%29/http://_geostatistical_wizard_colon_searching_neighborhood_dialog_box1407990.click%28%29/ -
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Invert Distance Weighting (IDW)
Power of interpolation => RMSPE
min
Searching strategy
Limit of IDW ???
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Kriging method
This method produces
visually appealing
maps from irregularly
spaced data.
Kriging attempts to
express trends
suggested in data.
EX: High points might beconnected along a
ridge rather than
isolated by bull's-eye
type contours.
Semivariogram(distance h) = 0.5 * average[
(value at location i value at location j)2 ]
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Variogram
Orgin
Lag Distance
Va
riogram
No correlation
2
( )
12 ( ) [ ( ) ( )]
( ) N hh z u z u h
N h
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Trend
Lag Distance
Variogram
No correlation
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Some Definition
2
,
,
, ,
Semivariogram:
Covariance:
Link:
1[ ]
2
[ ]
i j i j
i j i j
i j i j
E Z Z
C E Z Z
C Sill
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Kriging method
1
2
[ ] min
n
i i
i
Z w Z
E Z Z
2 2 2
2
1 1 1
, 0 , 0
1 1 1
, 0 ,
1 1
, 0,
1 1
[ ] [ ] 2 [ ] [ ] [ ]
[ ] 2 [ ] [ ]
2
[ ]2
n n n
i j i j i i
i j i
n n n
i j i j i i
i j i
n n
j i j i
j ii
n n
j i j i
j i
E Z Z E Z E Z E Z E Z
w w E Z Z w E ZZ E Z
w w C w C C
E Z Z w C C
w
w C C
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Thiessen polygons (Voronoi diagram)
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Natural Neighbor
1
n
ii i i
i
A Z w Z w
A
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Nearest Neighbor
Selects the valueof the nearestpoint, and doesnot consider the
values of otherneighboringpoints at all.
The algorithm isvery simple to
implement, and iscommonly usedin 3D rendering.
http://en.wikipedia.org/wiki/3D_renderinghttp://en.wikipedia.org/wiki/3D_renderinghttp://en.wikipedia.org/wiki/3D_renderinghttp://en.wikipedia.org/wiki/3D_renderinghttp://en.wikipedia.org/wiki/3D_renderinghttp://en.wikipedia.org/wiki/3D_rendering -
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Which Methods ?
Few
Kriging, Polynomial Regression, RadialBasis Function
Small Kriging, Radial Basis Function
Medi
um
Triangulation with Linear Interpolation
Large
Minimum Curvature, Triangulation withLinear Interpolation
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Reference
http://www.statios.com/Resources/04-variogram.pdf
http://www.statios.com/Resources/05-kriging.pdf
http://www.cee.vt.edu/ewr/environmental/teach/smprimer/kriging/kriging.html
http://dilbert.engr.ucdavis.edu/~suku/nem/nem_intro/node3.html
http://gis.enr.state.nc.us/sid/bin/zhelpworld_nofrm.htm
http://www.statios.com/Resources/04-variogram.pdfhttp://www.statios.com/Resources/04-variogram.pdfhttp://www.statios.com/Resources/05-kriging.pdfhttp://www.statios.com/Resources/05-kriging.pdfhttp://www.cee.vt.edu/ewr/environmental/teach/smprimer/kriging/kriging.htmlhttp://www.cee.vt.edu/ewr/environmental/teach/smprimer/kriging/kriging.htmlhttp://dilbert.engr.ucdavis.edu/~suku/nem/nem_intro/node3.htmlhttp://dilbert.engr.ucdavis.edu/~suku/nem/nem_intro/node3.htmlhttp://gis.enr.state.nc.us/sid/bin/zhelpworld_nofrm.htmhttp://gis.enr.state.nc.us/sid/bin/zhelpworld_nofrm.htmhttp://gis.enr.state.nc.us/sid/bin/zhelpworld_nofrm.htmhttp://gis.enr.state.nc.us/sid/bin/zhelpworld_nofrm.htmhttp://dilbert.engr.ucdavis.edu/~suku/nem/nem_intro/node3.htmlhttp://dilbert.engr.ucdavis.edu/~suku/nem/nem_intro/node3.htmlhttp://www.cee.vt.edu/ewr/environmental/teach/smprimer/kriging/kriging.htmlhttp://www.cee.vt.edu/ewr/environmental/teach/smprimer/kriging/kriging.htmlhttp://www.statios.com/Resources/05-kriging.pdfhttp://www.statios.com/Resources/05-kriging.pdfhttp://www.statios.com/Resources/05-kriging.pdfhttp://www.statios.com/Resources/04-variogram.pdfhttp://www.statios.com/Resources/04-variogram.pdfhttp://www.statios.com/Resources/04-variogram.pdf