I'm having trouble understanding the method for creating a cartographic depth to water index and seek some guidance. I'm using ArcGIS Pro 2.3, but equally happy with ArcMap desktop.
The method is outlined in Murphy, Ogilvie and Arp (2009) "Topographic Modelling of Soil Moisture Conditions: A comparison and verification of two Models" European Journal of Soil Science 60, p. 94-109.
The model takes two inputs: streams and a slope grid. Excerpt from paper below:
"An iterative function finds the cumulative slope value associated with the least slope path from the cell in the landscape to a surface water cell. That is, the function explores each possible path from the cell in the landscape to a surface water feature across the slope grid and sums the cell slope values along those paths (cumulative slope values). The function takes account of whether the path crosses a cell parallel to the cell boundaries or diagonally by using a multiplier, a. Therefore, the path of least cumulative slope will be identified on the basis of both slope and distance, the cumulative slope value tending to increase with both for any possible path.
The cumulative slope value associated with the least slope path is then multiplied by the grid cell size (resolution) and assigned to the cell in the landscape. This is carried out for each cell. The result is a DTW grid, formally derived from:
where dz/dx is the slope of a cell, i represents a cell along the path, a is 1 when the path crosses the cell parallel to the cell boundaries and 1.414214 when it crosses diagonally and xc is the grid cell size [m].
Because the cumulative values over the whole path of axc and dx will be approximately equal, the index value approximates the elevation difference between the cell in the landscape and the hydrologic source cell (the cumulative value of dz over the whole path).
In this process, all surface water features (lakes, streams, rivers) are assumed to have a DTW value of 0. Lower values indicate wetter soils. Values tend to increase away from surface water features into the landscape, indicating drier soils. DTW increases more rapidly in steeper terrain (greater slope values) and more slowly in flatter terrain (smaller slope values).
So, from this, I understood the streams and slope to be inputs into a cost function and that the output is multiplied by the cell resolution. Firstly, I couldn't decide on whether cost or path distance would be better, and if using Path, in which input would the slope be best (i.e. cost raster?, surface raster? vertical factor?) Both seem to take account of the horizontal or diagonal travel mentioned in the paper.
However, I feel like there's more to it than that. Essentially the method is trying to calculate depth to the water table, and my results are looking nothing like that. The last two paragraphs are not making a lot of sense to me. What am I missing?