# Model help:TopoFlow-DEM Smoother

## TopoFlow-DEM Smoother

This routine creates a "profile-smoothed" DEM from an input DEM.

Symbol | Description | Unit |
---|---|---|

S | slope | - |

A | area | - |

c | parameter in Flint's law equation | - |

p | parameter in Flint's law equation | - |

## Notes

The columns and rows of the pixels on a watershed's main channel are read from the "profile file" and then a nonlinear least-squares regression is used to find the parameters c and p in a slope-area power-law relationship Flint's law (S = c A^{p})that best fit the elevations and areas for these main-channel pixels. These parameters are then used together with the grid of contributing areas in an iterative procedure that creates a new DEM by assigning new, floating-point elevations to every pixel in the original DEM. The elevations in the new DEM should be close to those in the original DEM, but there will no longer be abrupt stair-step features and flats along profiles within which slopes are zero (due to poor vertical resolution and integer-rounding). Instead, the elevations and slopes will decrease smoothly along every channel streamline while remaining close to the original elevations.

Well-defined and smoothly-varying slopes along streamlines is important when using the kinematic wave method of flow routing.

This algorithm is based on an implicit assumption of spatial homogeneity in both the geology and climate, which may not be satisfied for many DEMs. However, the parameters c and p are not treated as universal values but are determined on a case by case basis from the input channel profile data. The value of p will typically be slightly greater than 0.5.

Note that errors in slope, S, along a channel as measured between grid cells in a DEM can be very large, especially in DEMs for which elevations have been rounded to the nearest foot or meter. For example, with 10-meter grid cells and a vertical resolution of one meter, the minimum resolvable, nonzero slope is 0.1, whereas the actual slope could be less than 0.00001. This factor of 10,000 difference represents an enormous error. However, contributing area, A, measured from a DEM depends only on the horizontal resolution and therefore the relative error in A is very small for basins that are much larger than the grid cell size. It follows that even if Flint's law is only an approximation, using it to compute channel slopes from areas is likely to be more accurate than measuring slopes between grid cells in the DEM. Also, because of the inverse relationship between S and A, the relative error in A is smallest for the larger basins where the measured error in S is largest.

## Uses ports

This will be something that the CSDMS facility will add

## Provides ports

This will be something that the CSDMS facility will add

## Main equations

A list of the key equations. HTML format is supported; latex format will be supported in the future

## Notes

Any notes, comments, you want to share with the user

Numerical scheme

## Examples

An example run with input parameters, BLD files, as well as a figure / movie of the output

Follow the next steps to include images / movies of simulations:

- Upload file: https://csdms.colorado.edu/wiki/Special:Upload
- Create link to the file on your page: [[Image:<file name>]].

See also: Help:Images or Help:Movies

## Developer(s)

## References

Peckham, S.D. (2009) A new algorithm for creating DEMs with smooth elevation profiles, extended abstract, *Proceedings of Geomorphometry 2009*, Zurich, Switzerland, p. 34-37, R. Purves, S. Gruber, T. Hengl, R. Straumann (Eds).

## Links

**Related Help Pages**

**Model Metadata**