# Interpolating vertically in ArcGIS 3D Analyst?

I am working on mapping pollutant concentrations in a pond from point-sampled data. There are 50 sampling locations in the pond (randomly dispersed), and at each location there are three sampling events (=150 total); one at the surface, one in the middle, one at the bottom.

I have created a TIN extent based on depth of pond, and now I would like to "fill" the pond by interpolating volumes of pollutant concentrations from the 150 sample points.

I am trying to do this by applying a spline interpolation through the three sampling events at each of the 50 locations, in order to produce 50 interpolated lines. From there i could apply kriging for each pixel down through the pond profile (although this way does ignore important spatial correlation).

I am stuck at the spline interpolation of the lines.

Is there a way to interpolate between points when the X,Y coordinates are all the same, but the Z coordinate changes?

In other words, how does one do vertical interpolation in 3D analyst?

• Great question. This sounds like trilinear interpolation - if so do the algorithms on that page help? – Stephen Lead Apr 10 '14 at 7:02
• Thanks for the suggestion Stephen, It looks like trilinear interpolation is something I could end up using. I am unfamiliar with this method so I will have to look into it closely, but at the surface my only concern is this: does trilinear interpolation create an interpolated value for every point within the chosen extent? In other words, is the whole volume accounted for by the three linear interpolants of trilinear interpolation, or are there missing values within the produced cube? – Michael S Apr 10 '14 at 9:46
• Sorry, this is way beyond me - hopefully someone with more modelling experience can help. While researching this I came across LeapFrog3D which might help if you're able to purchase a new product – Stephen Lead Apr 10 '14 at 22:38
• One source of error in my project: I was in GCS as my coordinate system, when I should have been in a projected coordinate system which measures distances not by degrees but by defined lengths (meters). My elevation data were in meters, which when taken as degrees caused the cell size to be may too big for interpolation of a raster. Unfortunately I still get that error, even now! I might have to check out some other products (somewhat out of the scope of my project currently, but may well be necessary soon). Thanks! – Michael S Apr 13 '14 at 2:13
• Leapfrog is great. Fantastic actually - very polished interface and quite intuituve. I used the Leapfrog Mining version of the software which shares the same 3D math engine. It can do any sort of 3D interpolation with a multitude of parameters including anisotropy but at a cost of about \$10000 / year. – Jakub Sisak GeoGraphics Apr 15 '14 at 22:33