topic Re: Laplace Finite Difference Equation as a Tool in ArcGIS Spatial Analyst Questions

Laplace Finite Difference Equation as a Tool

HannesZiegler1 — Wed, 12 Aug 2015 19:29:32 GMT

I'm working on my master's thesis and would like to create a groundwater model from well data, so that I can eventually estimate the amount of nitrogen that loads into a nearby estuary through groundwater discharges from septic tanks. There is a formula, called the laplace equation, that defines head in groundwater. A version of this equation, called the laplace finite difference equation is used iteratively to calculate groundwater head if you have some known values of the water table and set up boundary conditions. I was wondering if this is available as a tool for ArcGIS? The governing equation looks like this:

hi,j = (hi+1,j + hi-1,j + hi,j+1 + hi,j-1)/4

where h is the value on a scalar field and i is the column and j is the row of the field.

Thank you

Re: Laplace Finite Difference Equation as a Tool

DanPatterson_Retired — Thu, 03 Sep 2015 03:19:36 GMT

You might want to investigate focal statistics Focal Statistics—Help | ArcGIS for Desktop

and create your own kernel if h is indeed just a scalar value for row/column j,i Otherwise if your data are in raster format, conver it to a numpy array and process it through there or in SciPy's image analysis section

Re: Laplace Finite Difference Equation as a Tool

HannesZiegler1 — Sat, 23 Jan 2016 17:40:40 GMT

Thank you for the response! I actually ended up using numpy arrays in python and processed the rasters through that. It worked really well!