Using ArcGIS Pro to calculate required height of debris dam structure in stream when expected volume to retain is known

Question

I have the locations of potential debris dam structures to be placed in a stream and know the contributing watershed area and the estimated debris volume (in m3) that would flow down that watershed and out to the structure in a given flood event. I now need to calculate what height the dam needs to be to retain that volume of material.

Is there a method using Geoprocessing tools in ArcGIS Pro that would help me calculate this?

Answer 1

I have used the polygon volume tool in 3d Analyst, with an iterator (height field) to report volumes below the plane.

Draw you dam structure in the proposed location. Determine the lowest and highest possible levels from the surface. In the screen shot below 1120 and 1800. Use the model builder to iterate from low to high, using the reference plane height value, passing the updated reference place to the polygon volume. Append the result from each iteration to a result file.

Answer 2

First challenge is to 'construct' earth dam itself, let's do it using @whuber idea. Add minimum and maximum elevation values to location line connecting same elevation contours:

Convert line to raster and expand it by few cells, call it DAM_FLAT_TOP. We need dam to be flat on the top for trucks/cars access. Expand it by 1 cell and call it BIGGER_TOP. Compute Euclidean distance to DAM_FLAT_TOP and use raster calculator to compute intermediate raster called SLOPES:

43.0-"e_Distance"/2

43 here is average of [55,32], 2 defines the slopes of dam, i.e. rise/run here is 1/2.

Compute new DEM using:

Con("SLOPES" > "DEM","SLOPES","DEM")

Use Hydrology Fill to compute depth and extent of old and new depressions:

Con("FILLED" > "new_DEM",1) ---> LAKES
Con("FILLED" > "new_DEM","FILLED" - "new_DEM") ---> DEPTH

Isolate just one lake upstream from dam:

CostAllocation_sa("BIGGER_TOP", "LAKES", "thisLake")

Note the use of BIGGER_TOP.

Run zonal statistics as table to get volume of that lake:

in this case it is 4.620094*79812 = 368738

So, modify script below to get accurate elevation estimate for your target volume. Note extra bonus: compare new DEM with original to estimate amount of earthwork required. You might pick another dam location if too much work needed.

from arcpy.sa import *
from arcpy import env
env.overwriteOutput = True
env.workspace = "in_memory"
bottom,top = 32.0,55.0
targetVolume = 250000

eDistance = Raster('e_Distance')
DEM = Raster("DEM")
bigTOP = Raster("BIGGER_TOP")
outTable = "in_memory/abc"
arcpy.management.Delete("in_memory")
while True:
    arcpy.management.Delete("in_memory")
    mid = (top+bottom)/2
    SLOPES = mid - eDistance/2
    newDEM = Con(SLOPES > DEM, SLOPES,DEM)
    newDEM.save("Filled")
    Filled = Fill(newDEM)
    LAKES = Con(Filled>newDEM,1)
    LAKES.save("LAKES")
    DEPTH = Con(Filled>newDEM,Filled-newDEM)
    DEPTH.save("DEPTH")
    del Filled
    thisLake = CostAllocation(bigTOP, "LAKES", "", "", "", "Value")
    thisLake.save("thisLake")
    arcpy.gp.ZonalStatisticsAsTable_sa("thisLake", "Value", "DEPTH", outTable, "DATA", "MEAN")
    A,D = arcpy.da.TableToNumPyArray(outTable,("AREA","MEAN"))[0]
    volume = A*D
    arcpy.AddMessage("Current volume = %i" %volume)
    if top-bottom <0.1:break
    if volume>targetVolume:top=mid
    else:bottom=mid
arcpy.management.Delete("in_memory")
arcpy.AddMessage("Use elevation of %s" %mid)

Script messages:

Current volume = 408901
Current volume = 90259
Current volume = 212356
Current volume = 299914
Current volume = 253515
Current volume = 232290
Current volume = 242747
Current volume = 248087
Current volume = 250793
Use elevation of 41.298828125

As one can see it took 9 iterations to find solution with 10cm accuracy for possible range of values equal to 33m(!)