Depressions, otherwise known as pits, are areas of a landscape wherein flow ultimately terminates without reaching an ocean or the edge of a digital elevation model.
Depressions, Pits, and Sinks¶
Depressions have been called by a variety of names. To clarify this mess, Lindsay (2016) provides a typology. This typology is followed here.
For reference, the original DEM appears as follows:
import richdem as rd import numpy as np beau = rd.rdarray(np.load('imgs/beauford.npz')['beauford'], no_data=-9999) beaufig = rd.rdShow(beau, ignore_colours=, axes=False, cmap='jet', figsize=(8,5.5))
Depression-filling is often used to fill in all the depressions in a DEM to the level of their lowest outlet or spill-point.
The result looks as follows:
beau_filled = rd.FillDepressions(beau, in_place=False) beaufig_filled = rd.rdShow(beau_filled, ignore_colours=, axes=False, cmap='jet', vmin=beaufig['vmin'], vmax=beaufig['vmax'], figsize=(8,5.5))
We can visualize the difference between the two like so:
beau_diff = beau_filled - beau beaufig_diff = rd.rdShow(beau_diff, ignore_colours=, axes=False, cmap='jet', figsize=(8,5.5))
Complete Filling is available via the following commands:
A downside of complete filling is that it replaces depressions with a perfectly flat region with no local gradients. One way to deal with this is to ensure that every cell in the region is raised some small amount, ε, above cells which are closer to a depression’s spill point.
This must be done carefully. In floating-point DEMs, the value ε is non-constant
and must be chosen using the
std::nextafter function. If a depression is too
large, the imposed gradient may result in the interior of the depression being
raised above the surrounding landscape. Using
double instead of
reduces the potential for problems at a cost of twice the space used. If a
problem does arise, RichDEM provides a warning.
We can visualize the difference between the epsilon-filled DEM and the original DEM like so:
beau_epsilon = rd.FillDepressions(beau, epsilon=True, in_place=False) beau_eps_diff = beau_epsilon - beau beaufig_eps_diff = rd.rdShow(beau_eps_diff, ignore_colours=, axes=False, cmap='jet', figsize=(8,5.5))
We can visualize the difference between the epsilon-filled DEM and the completely-filled DEM as follows. Note that elevation increases with distance from the depression’s outlet: this is the effect of the epsilon.
beau_diffeps_diff = beau_epsilon - beau_filled beaufig_diffeps_diff = rd.rdShow(beau_diffeps_diff, ignore_colours=, axes=False, cmap='jet', figsize=(8,5.5))