How to calculate the average velocity over the flowpath length?

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I’m working on building a GIS based groundwater travel time distribution (TTD) model similar to the one developed by Schilling and Wolter (2007)http://lilt.ilstu.edu/ewpeter/GEO435/Readings/2012/Schilling_Kelly.pdf.

The conceptual model of cell TTD is illustrated below (Schilling and Wolter, 2007).


As you knowVelocity = -k (dh/dl)/n

I have calculated the velocity using raster calculator. I used the permeability values from the soil map as a substitute for hydraulic conductivity, the slope from the DEM as substitute for hydraulic gradient (dh/dl) and porosity (n) one value only from literature. I calculated the distance till the nearest river using Euclidean Distance.


After getting the velocity and the distance, I can easily calculate the time using raster calculator. However, it is not straightforward like this. Schilling & Wolter (2007) described how to calculate the time as follows “The time needed for groundwater in each 5-m cell to travel from the cell to the stream network was then determined by averaging all the individual cell velocities over the

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