How to Generate Theissen Weights

Example 10 – 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 10S: 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.