Interpolate along the length of a river with 'diffusion interpolation with barriers'

Question

I'm involved with a project where I'm tasked with interpolating water quality data along a winding river (around 500km long but with a focus of a ~100km reach). I'm working mostly with phosphorus concentration values ranging from 0.0015-9.413 The data comes from water quality monitoring stations that I have snapped to within the river boundary (which I have been using as a break line). These stations are fairly sporadically spaced, some are within a few hundred meters but there are long stretches of several km without data.

I've been asked for a number of interpolations that span the majority of the river length but have run into some problems.
After doing some research the interpolation method most recommended for this type of problem seems to be  'diffusion interpolation with barriers'. I've run a number of test interpolations with small sections of the river with test points spaced much closer than most of the actual monitoring stations . I've played with various settings within the tool including various bandwidth values but have run into a problem where the resulting raster contains long stretches without data (as seen in the attached .png). The ideal output would encompass the majority of the river without any gaps in the interpolated raster. How would I fix this problem? Is it simply a matter of further increasing the bandwidth size (I've done tests with bandwidth values ranging from  10-10,000)?

Interpolation_Test.png

TimHodson_1-1633989334344.png

SamHopkins · Answer

Kernel Interpolation can slow to a standstill if your barrier is too complicated.  You should be able to resolve this by running Simplify Polygon on your barrier to reduce the number of vertices.  That should get Kernel Interpolation working fast again.

We had already simplified the polygon, but following your advice I simplified it further. It helped immensely and the resulting raster finally encompassed the entire length of the reach. The resulting cell values were not ideal but this is a still a great step forward.

Eric6346 · Answer

Kernel Interpolation can slow to a standstill if your barrier is too complicated.  You should be able to resolve this by running Simplify Polygon on your barrier to reduce the number of vertices.  That should get Kernel Interpolation working fast again.

SamHopkins · Answer

The problem is probably that the bandwidth is too small.  You can only make a prediction at a location if there is an input point within the bandwidth distance.

You should also look into Kernel Interpolation with Barriers.  It generally outperforms Diffusion Interpolation with Barriers.

We've actually already switched to Kernel interpolation over Diffusion as  ourresults seemed to be a bit better.

We've tried to boost the bandwidth to an appropriate level, but so far either tool has just frozen after increasing the bandwidth to anything over about 15,000 m (even with vastly increased cell sizes). The problem is that some of our stations are separated by 25+ km. Do you have an idea why the tool would simply freeze? Last night I left a model running overnight only to find it stuck at the raster creation stage at 0%.

Do you have any advice on how we might reduce processing time while still allowing the interpolation to encompass this large area, or do you think our goal may be too ambitious with our current methods?