Interpolation of current flow data

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02-05-2013 07:25 AM
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New Contributor III
Hello,

I have a dataset of current flow data (x,y,z), collected by a vessel-mounted ADCP over 11 transects, which were spaced by 300m. Normally I would use Matlab to post-process and interpolate these data. In Matlab I would apply the griddata function, which creates a uniform meshgrid (dimensions defined by myself) and applies linear interpolation, which I smooth at the end.

I would like to recreate the results in ArcGIS 10.0, but I am struggling a bit as I'm not entirely sure which interpolation to use.
Initially I thought the creation of TINs would come closest to what I've done in Matlab, but I think my data are not scattered enough (being formed by straight transect lines) and I'm ending up with a very jagged appearance and bad edge effects.
I then tried the natural neighbour interpolation and the result was closer to my Matlab results, but the surface was not very smooth. IDW gave ok results, but I would prefer the resulting surface to include the measured values. Hence I applied the Spline function, but it overestimated the values in some areas. Kriging at the end gave a reasonable good result.

I was now wondering if anyone here worked with current flow data and could give some advice on how to best interpolate these in ArcGIS. As far as I understand (please apologize if I'm wrong and correct if required) is a linear interpolation fairly simple and straight forward calculating the value of a point between two known points and thus differs from available interpolation options in ArcGIS, which are all distance weighted. Accordingly I'm hesitating to apply a distance weighted interpolation as I'm not entirely sure what the effect on my data will be.

Your help and advice will be highly appreciated!

Best regards,
Astrid
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Occasional Contributor III
Astrid,
I wholeheartedly agree and think that basing your decision of an appropriate interpolation model on the error is very good statistical practice. A Kriging model is a good choice because you are directly modeling (via the semivariogram) and thus, incorporating, the spatial process into the estimate. I am curious if you are using the Kriging model in Spatial Analyst or Geostatistical Analyst? The Geostatistical Analyst software is quite impressive and if you are not using it and have access I would recommend redoing your analysis. It will not take long and you will be able to more precisely model the spatial process, error (nugget) and account for any potential anisotropy (directional variation). 

Sometimes given high "small distance spatial variation" splines can have wildly divergent values but nothing like you are observing. The spline results are very suspect and sounds like a bug, which are becoming alarming common.

I am quite happy that you ferreted out the fact that sometimes people utilize a model because it is computationally easy or just because "it has always be done this way" and nobody has ever questioned it. Sometimes these methodological decisions are a legacy and quite dated.

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Occasional Contributor III
Did you adjust the tension (weight) and neighborhood (Number of points) in the Thin Plate Spline function? A high enough tension parameter should return values at your points. The neighborhood size can effect results as well. A smaller neighborhood is not trying to fit a spline across as much potential variability. The default parameters do not necessarily fit you problem.

Regardless of what MATLAB methodology you implemented, a linear fit interpolation is generally, not a very good choice. If you misspecify a Kriging model and omit the error term you essentially get a linear approximation (decomposed linear regression), which is not considered a good thing. Do you have a strong justification of your previous methodology that provides a theoretical basis to recreate it in ArcGIS?

Please do not double post within the forum (posted in both Spatial Statistics and Spatial Analyst).
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New Contributor III
Dear Jeffrey,

thanks for your prompt reply and sorry for the double posting of this thread! I tried the Spline function and adjusted weight and number of points, but am ending up with really odd output values. My data should be in a range of 0 to 4.5, but the Spline output ranges in some cases from -400 to +800. This occurs for the regularized as well as the tension spline type and I'm not entirely sure why it happens. The data work fine with Kriging and the model output looks good, with a mean error close to zero (-0.001) and RMS standardized close to 1 (please correct if this interpretation is wrong).

I do not have a theoretical basis which provides a good reason to replicate the method used in Matlab in ArcGIS. I only assumed that linear interpolation is required as everyone, who I know is handling current flow data, is using it - basically a fairly bad reason. I had a few discussions with oeanographers today, asking why linear interpolation is so commonly used with current flow data. The general reply was: because it is simple and easy. So no deeper theory behind it. Accodingly I decided now to use kriging. My sampling area is only 6 km^2, which means that the difference might not have a huge effect either. Additionally the stats behind it support the model prediction, thus it is acceptable.

Would you agree with this?

Best regards,
Astrid
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Occasional Contributor III
Astrid,
I wholeheartedly agree and think that basing your decision of an appropriate interpolation model on the error is very good statistical practice. A Kriging model is a good choice because you are directly modeling (via the semivariogram) and thus, incorporating, the spatial process into the estimate. I am curious if you are using the Kriging model in Spatial Analyst or Geostatistical Analyst? The Geostatistical Analyst software is quite impressive and if you are not using it and have access I would recommend redoing your analysis. It will not take long and you will be able to more precisely model the spatial process, error (nugget) and account for any potential anisotropy (directional variation). 

Sometimes given high "small distance spatial variation" splines can have wildly divergent values but nothing like you are observing. The spline results are very suspect and sounds like a bug, which are becoming alarming common.

I am quite happy that you ferreted out the fact that sometimes people utilize a model because it is computationally easy or just because "it has always be done this way" and nobody has ever questioned it. Sometimes these methodological decisions are a legacy and quite dated.

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New Contributor III
Dear Jeffrey,

I firstly used Kriging as part of the Spatial Analyst Tools, but soon figured out that the Geostatistical Analyst, as you said, provides a much wider range of adjustments and also a far better visualisation of the model fitting and number crunching related to the statistical output. Hence I'm going to continue using the Geostatistical Wizard.

Thanks a lot for your help, advice and support of this final decision! It's very much appreciated. I found the thought of possibly using a wrong interpolation and hence creating data out of the blue, which would then also form a base for further work, pretty scary! But this definitely confirmed my decision of using Kriging for the interpolation.

Many thanks,
Astrid
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