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/( )= –Gage 2 = 0.35/( )= –Gage 3 = 1.40/( )= 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.