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How to Generate Theissen Weights
Example 8 – Supplement
Theissen Weights
• Theissen polygons represent nearest neighbor areas
• If one knows gage locations in an XY coordinate system and one has a grid of points that uniformily sample a watershed area, then the fraction of points nearest a particular gage divided by the total points representing the wateeshed is a good approximation of the Theissen weight.
Using Freeware
• Concept is to use freeware to generate the grid of points on the watershed, then use Excel to compute the fraction of points assigned to each gage.
• Obviously if you have real tools to do this job (ArcGIG, AutoCAD, etc.) then the process here is a waste of time.
• If you are software poor, then this method will keep you in the race!
G3DATA
• Software you will need– G3DATA a freeware utility to find XY
coordinates on a PDF image.• SURFER, AutoCAD, or any digitizing software
would also work just fine.
– Excel to compute the distances from points in G3DATA and calculate the approximate weights.
Example 8S: Find Theissen Weights for Watershed
• Example – Suppose the
circles represent rain gages
– What weights to assign to each gage?
Theissen Polygons
• What weights to assign to each gage?
• Theissen polygons would produce areas close to those shown.– How about a
semi -automated method?
Generate Points on the Watershed
• Step 1– Use G3DATA to
generate XY coordinates for the watershed boundary.
– Record separately the gage locations
Start G3DATA
• Step 1:G3DATA– Set XY limits– Get gage
locations, read from “processing information” and enter into an Excel spreadsheet.
Record Gage Locations
• Step 1:G3DATA– Set XY limits– Get gage
locations, read from “processing information” and enter into an Excel spreadsheet.
Generate Boundary
• Step 2:G3DATA– Get the boundary XY
coordinates– Run around boundary
in clockwise direction– Start at outlet (for
consistency)
Populate Interior Points
• Step 2:G3DATA– Now mark a few
interior points, try to distribute across the interior, use about 100 points or so.
Save the Points, Check File
• Step 3: Prepare for Distance Calculations– Here is the
G3DATA file.– All points are XY
coordinates within the watershed.
Points into Excel
• Step 4: Paste into Excel– Set up a
distance table– Find distances
from watershed points to each gage
– Min distance chooses gage
Results
• So the approximate Theissen weights for this example are:– Gage 1 = 35%– Gage 2 = 13%– Gage 3 = 52 %
• So as a validity check will use the polygons.
Conventional Polygons
• Polygon approach– In practice the polygons can get hard to draw,
especially as gages are added and deleted.– Keeping the points in a file is pretty trivial.– Point here is to validate the method
Drawing Rules
• Step 1: Draw the polygons– Join each gage by a line segment– Mark the segment bisector– Pass segments through the bisectors to
isolate parts of the area that are closest to a gage.
Three Gage Assignments
• Gage 1 = Red
• Gage 2 = Blue
• Gage 3 = Green
Find Polygon Areas
• Import into Acrobat and measure the areas of each polygon.
• Unit conversion unnecessary – after ratios.
Compute Gage Area Ratios
• Results in Acrobat Pro “inch” units– Gage 1 = 0.98 sq. in.– Gage 2 = 0.35 sq. in.– Gage 3 = 1.40 sq. in.
• Now compute gage weights:– Gage 1 = 0.98/(0.98+1.40+0.35)= 0.358– Gage 2 = 0.35/(0.98+1.40+0.35)= 0.128– Gage 3 = 1.40/(0.98+1.40+0.35)= 0.513
Report Results
• Convert to percentages (and rounding)
• Now compute gage weights:– Gage 1 = 36%– Gage 2 = 13%– Gage 3 = 51%
• These results are essentially the same!
Summary
• Advantage comes when gage network changes.
• If using Theissen polygons, have to redraw and re-measure areas– Not particularly hard, but complex Theissen
polygon systems can result – drawing them is challenging.
• If using the shortest distance method, simply enter the new gage locations.