As part of my request/justification to go to the UC I had to fend off the claim from management that Manifold can't do surfaces as well as ArcGIS (3D Analyst), this was partly my fault for not using Manifold to generate surfaces for random points (I'd been using Surfer to achieve this), I commonly use boreholes and water well records as sources, mainly because I had not investigated thoroughly the variety of methods and models available in Manifold. With the incentive of dismissing the 'ArcGIS is better than Manifold' carrot dangling in front of me it didn't take me long to figure out that using Kriging with the Linear variogram in Manifold produces much better results for this kind of randomly placed data.

The reason for the comment from management related to a surface that was generated by another consultant using IDW interpolation with 3D Analyst. I used the Kriging/Linear method on the same data and to be honest I don't think either IDW or Kriging produced results that weren't far from the mark. This quote of a quote felt quite relevant in this case:

"Interpolation is a black art, and interpolation methods should never be trusted. Careful researchers always interpolate several times using different methods, and choose the result they dislike least." ~ Roger Bivand

Isn't it about time Manifold added IDW as another interpolation method? I'd have thought it being in ESRI products already would be reason enough.

Actually Brian, I am less interested in IDW, and more interested in the ability to create a variogram. IDW and kriging are of little use personally, unless you can see the variogram to determine the spatial structure of the data. Therefore, I either use another product for geostatistics, or create my variogram in SQL. Its alittle ugly, but it does in fact work :-)

That said, IDW is really computationally easy to do, and should be incorporated into Manifold.

I agree creating variograms would be a good addition - some of us would have to get studying to understand the nuances of tweaking them and the subsequent results they produce

I sent my suggestion to Sales for IDW in any case.

I heard another quote:

"everyone believes the results of a model, except the guy who developed the model"

Great quote ... I think this should be a standard disclaimer added to all GIS maps and outputs

'All models are wrong, but some of them are useful'

These books are good:

Smoothing Methods in Statistics

Applied Smoothing Techniques for Data Analysis

Hi Art,

do you have or would you be wiling to post the code in SQL that use to create variogram?

m

Your management is quite correct in some respects. Manifold certainly does not provide such a range of interpolators as Surfer and may be 3D Analyst ( i have not had the pleasure of the latter).

There are several issues with performing interpolation in Manifold:

Firstly, the range of interpolators available is very limited.

Secondly, there is next-to- no documentation about those interpolators that are provided. There are no descriptions of Median Polish Kriging or Gravity Kriging or constrained triangulatiom (fortunately i recommended the latter and have the original paper on it, but for anyone else DEST may be a complete mystery). At the very least there should be a bibliographic reference to papers where these interpolators were first described. An online search the other day to try and discover what Median Polish Kriging was and whether or not it was better of worse than general kriging, only returned the Manifold Help file entry.

Thirdly, there is very little control over how interpolation is carried out for those interpolators that allow this, unlike in Surfer (eg using search sectors, minimum datapoints per sector, search radii, duplicate datapoint rejection, search anisotropy, breaklines, and discontinuiuties etc).

Finally, the way dimensions of the arrayed data domain are set up is data dependant. It is not currently possible to specify the exact geographic positioning of array point coloums and point rows, or the orientation of rows and columns.

The algorithmns used by Surfer are taken from Numerical Recipes in C+ (or C). Manifold would do well to do the same.

Dream no small dreams for they have no power to change the minds of men. - After Johann Wolfgang von Goethe

FWIW, 'Constrained triangulation' just means that the Delaunay criterion is relaxed in order to incorporate existing spatial features (i.e. lines and area boundaries). So the mesh gets the existing line segments, with those taking priority over those that would be generated based on the the minimizing circle thing with Delaunay triangulation. This is in the manual - but you can't blame Manifold for using their own terminology, there simply aren't lay-terms for some of these things.

Manifold has used things from Numerical Recipes. Full stop. But the issue of referencing is moot. Some of these things can be figured out and the need to refer to others is a personal call - Manifold reference Snyder and Brewer (and probably others) - it's not a particular agenda IMO, it's just that there really is a disconnect between math-world and lay-world and the stereotypical GIS technician does very little to bridge the gap.

My mistake, i meanttriangulation adjusted for contours - not constrained triangulatio.

Some of the algorithms used may be quite obvious and others can be figured out as you put it, but this is not the same as a full documentation and transparency. Both are essential if you are required to justify a result to a client or in a scienfific publication. I am not suggesting Manifold publishes the code for the algorithms its uses, only a textual description and the mathematical basis of them. The Surfer 7 or 8 handbook provides a good model for doing this.

Dream no small dreams for they have no power to change the minds of men. - After Johann Wolfgang von Goethe

I agree Nick that there should be more information on the algorithms used.

Another issue is the Auto model setting - as I go through this QA/QC procedure for this surface the more I realize I shouldn't ever use this setting as I have no way of knowing what model Manifold decides on and how it arrives at this choice. An improvement that I'll send to Manifold would be to at least automatically add details, in the Description field of a Surface, on what model was chosen when using the Auto setting.

I don't see why the surface creation algorithms get singled out for this need. I don't see anyone questioning the projection algorithms or similar. I think it's more about our habitual assumptions regarding algorithms vs. tools we take for granted. The ever present *Manifold should do X* problem is covered by Suggestions.

"at least automatically add details, in the Description field of a Surface, on what model was chosen when using the Auto setting."

But this information, along with kriging parameters, does appear in the Notes pane when the interpolated surface is active, does it not?

does appear in the Notes pane when the interpolated surface is active, does it not?

Yes it does, thanks for the pointer.

IDW is one of the ones that should ne added, maybe together with spline, but idw the lack of idw and other is a limitation.

The list should include the following interpolators/estimators:

Regularised spline with tension

Barnes's objective analysis

Cressman analysis

Weaver analysis

Minimum curvature

Shephard's method

Inverse distance-to-a-power

Radial basis functions

Block kriging

Conventional kriging with ability to define search parameters such shape and anisotropy of search area, search sectors etc.

Polynomial regression

ANUDEM

Dream no small dreams for they have no power to change the minds of men. - After Johann Wolfgang von Goethe

Those interpolators are also interesting

Regards

Personally I use functions from R to perform spatial interpolation. The algorithms there are clearly spelled out and you have quite a bit of control over different parameters for each of the models. I haven't tried to link the functions into Manifold yet, though. Also, there is a full suite of functions for semivariogram construction and modeling, as well as different flavors of kriging.

For BCowper per "I used the Kriging/Linear method on the same data and to be honest I don't think either IDW or Kriging produced results that weren't far from the mark." Could this have been due to a surface trend in the data that wasn't removed prior to interpolation? Just curious.

As far as an IDW interpolator in Manifold, the gravity model is an IDW model. I don't know their exact form of the function they implement but the results it gave me were very similar to an IDW using a squared distance in the denominator.

hi, I was wondering whether any more information has come out about what exactly the gravity model is doing. I think this option stands out from the others in that I have at least some idea of the techniques being used by familiar methods like kriging, but I'm unfamiliar with what a gravity model could stand for although I would agree that it does seem to mimic an IDW model.

thanks!

About the IDW method, otherwise known outside of ESRI circles as Shepard's method

http://en.wikipedia.org/wiki/Inverse_distance_weighting

Dream no small dreams for they have no power to change the minds of men. - After Johann Wolfgang von Goethe

but is gravity indeed doing idw?