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). enter image description here

As you know Velocity = -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 flowpath length from the cell to the stream”

enter image description here

So, in order to calculate the time, I have to calculate the average velocities over the flowpath length which I don’t know how to do. It would be much appreciated if you can help me in this regard.

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    Your work appears inconsistent. If you truly calculated velocity (not just speed), you can see that the groundwater rarely flows in a straight line towards its discharge point. Thus the Euclidean distance has little relevance. You need to track the flow down flow lines instead and, at each cell, record the cumulative time and cumulative distance from the discharge point. That's what Schilling & Wolter are saying. (BTW, this is not an average velocity, it's an average speed.) You can adapt a costdistance or pathdistance calculation to do this. – whuber Aug 30 '13 at 15:28
  • @whuber Many thanks for your help and detailed reply. I do agree with you the Euclidean distance was not the right choice. What about using the flow length to calculate the distance and using the flow accumulation as the weight raster with a null value for the river network (i.e. cells with flow accumulation values >=100000 for example)? It would be much appreciated if you can explain in more detail how can I use cost distance and path distance to calculate the travel time? – shiny Sep 2 '13 at 2:33

If you have the flowpaths identified and a velocity surface, perhaps zonal statistics could work for you. The tool calculates statistics (mean, median, etc.,) on values of a raster within the zones of another dataset. http://resources.arcgis.com/en/help/main/10.1/index.html#//009z000000w7000000

  • If you need to identify groundwater flowpaths, and Euclidean distance is appropriate, you could use Near (Analysis) to determine flowpath of a source to the nearest point of the river. – mwil Aug 30 '13 at 13:25
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    In general that will not work unless the "source" is very close to the river, because Euclidean distance is not appropriate. – whuber Aug 30 '13 at 15:29
  • @whuber I agree, but I saw above that Euclidean was used to get the distance to stream. I have only used cost or path distance for this type of analysis - but I have only worked with surface - and not with groundwater. – mwil Aug 30 '13 at 15:45
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    Your experience with surface water flow is applicable here, because the model the OP uses is so greatly simplified that it is identical to a surface water flow model. (The model is two dimensional, flow is advective only, the hydraulic gradient equals the topographic gradient, the porosity is constant, and--although this is not stated--the transmissivity tensor is isotropic.) – whuber Aug 30 '13 at 15:49
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    @whuber Thanks for looking at the whole question, and for your detailed explanation. Obviously it wasn't my question, but it's great to learn/think about. – mwil Aug 30 '13 at 16:18

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