Lap trinh va ung dung Chaper I

8/8/2019 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

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