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.