creating hydrogrphically correct dems

[Rich Shepard]

On Mon, 4 Oct 1999, Matt.Wilkie wrote:

> I'm not sure which document this is, do you mean the one titled
> "Introduction to GRASS GIS Software"?

  Yes.
 
> It's not that I couldn't find anything to work with our data, but rather
> difficulty in finding papers which -explain- what the approaches are and
> how they work and what their limitations are. Most of the docs/sites I
> have found basically say chuck your data into this hole here, and that
> hole over there will spit out the thing you're looking for.

  Aha! Yes, I'm rather fond of understanding what I'm doing, too. There's a
large literature on interpolation methods and algorithms.

  I'll take a short break from what I should be doing and post some
information to the entire list, too. The following is a summary from the
Vertical Mapper document, Chapter 3: Building Grid Files.

  Numeric grids are created using mathematical routines collectively called
interpolation techniques. Four of these techniques are:

  - Inverse Distance Weighing (IDW)
  - Triangulation With Smoothing (TIN)
  - Natural Neighbor (NN)
  - Retangular (or Bilinear)

  Each technique creates a characteristic surface of information estimated
from scattered point measurements/observations. The user must decide which
is the most "appropriate" surface for the gridded data. For example,
triangulation is most commonly applied to elevation data since it is a
technique that uses the slope between data points to estimate new grid
values. On the other hand, IDW is used when the estimated surface is best
represented by a weighted average of the original values, for example, data
recording contaminants in groundwater.

  Interpolation vs. Modeling:

  Both are mathematical tools used to create grids from points. Both build
grids and assign values to each grid cell from an underlying point table.

  Interpolation methods are used to build grids that are an estimation of
the same variable as the underlying points. Each new grid cell, therefore,
has the same unit of measurement as the point value. For example, TIN is
used to estimate new grid elevations in meters from a table of scattered
point elevation also in meters.

  In contrast, modeling techniques create grids of derived values. For
example, the Huff modeler uses (in a business example, but natural systems
work the same way) store locations and their relative "attractiveness" to
calculate grid values measuring the probability of customer patronage. The
calculated value is derived from a mathematical relationship (the model)
that makes use of a number of different variables. This is appropriate, for
instance, when looking at estimated erosion potential from a series of
connected subbasins.

  I'm not going into more detail about each interpolation and modeling
technique. That's left as an exercise for the reader. :-)

  References for further reading:

  Watson, D.F. 1992. Contouring: A Guide to The Analysis and Display of
	Spatial Data. Tarrytown, NY: Elsevier Science, Inc. 321 pp.

  Jones, T.A., D.E. Hamilton, C.R. Johnson. 1986. Contouring Geologic
	Surfaces With The Computer. New York, NY: Van Nostrand Reinhold
	Company. 314 pp.

For TIN:

  Akima, H. 1978. A method for bivariate interpolation and smooth surface
	fitting for irregularly distributed data points. ACM Transactions on
	Mathematical Software, 4(2):148-159.

For NN:

  Gold, C.M. and T. Roos. Surface modeling with guaranteed consistency -- an
	object-based approach. IGIS '94, Proceedings of the International
	Workshop on Advanced Research in Geographic Information Systems,
	Lecture Notes in Computer Science 884: Springer-Verlag, pp 70-87.

Happy hunting!
 
Rich

Dr. Richard B. Shepard, President

                       Applied Ecosystem Services, Inc. (TM)
              Making environmentally-responsible mining happen. (SM)         
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