# How to integrate dry wells into groundwater level mapping automatically (inequality constraints on the interpolation)?

I'm interested in automating spatial interpolation of groundwater level measurements. I'm wondering if anyone knows a method for automatically taking into account things like dry wells, where I can't get a depth to water measurement, but where I do know that the depth to water is greater than the depth of the screened interval of the well.

The interpolation would be constrained at that location so that the water table would be below the bottom of the well. In addition to saying things like "the value at $(x_1,y_1) = z_1$" I could also specify "the value at $(x_2, y_2) < z_2$" or "at $(x_3, y_3) > z_3$".

I'd like to know if anyone knows any interpolation algorithms that can do this, and if there are any tools out there to implement them.

• It isn't clear what you need help with, are you looking for code that is already developed to manage this, or are you asking for help understanding what the algorithm should include? Thinking in terms of elevations will help, one measures depth to water, but the data that gets utilized is elevation, so dry wells will have a groundwater elevation of <z2 as you talk about it in your question, with z2 being the bottom of the screen interval. Feb 5 '16 at 17:25
• Right - I do convert to altitude before interpolating. If there is code for this already, of course that would be nice, but any ideas on how to integrate that kind of information into an interpolation algorithm would be welcome, and I could work on the code myself if there aren't already any tools out there. Feb 5 '16 at 17:45
• Automated mapping of the water table is a difficult task. Probably a bigger constraint that should be applied is that it can't rise above the land surface. If you have water level trends in the wells that have gone dry, they can be used with climate data to estimate the current water level. If you can estimate the range of probable level with it truncated by the well depth then you could probably try some kind of stochastic solution. Feb 11 '16 at 2:31
• You're right, keeping it below land surface where there are no surface-water bodies is one of the big challenges to automating it. The thing is, if I was doing it manually I would be making certain assumptions (like adjusting things in areas where the initial interpolation went over land surface to get the water table below) anyway. I guess I just need a systematic way to apply those assumptions that I could program in as pre- and/or post-processing steps, instead of trying to find an interpolator that has that kind of thing as part of the algorithm. Feb 11 '16 at 19:52
• Are you still working on this? I have some suggestions that could help direct your decisions, unfortunately in the end you will need to make a decision about how you correct for any apparent errors that appear and present a justification for what you decide. Mar 9 '16 at 18:20