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| Titel |
Reducing scale dependence in TOPMODEL using a dimensionless topographic index |
| VerfasserIn |
A. Ducharne |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1027-5606
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| Digitales Dokument |
URL |
| Erschienen |
In: Hydrology and Earth System Sciences ; 13, no. 12 ; Nr. 13, no. 12 (2009-12-14), S.2399-2412 |
| Datensatznummer |
250012073
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| Publikation (Nr.) |
 copernicus.org/hess-13-2399-2009.pdf |
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| Zusammenfassung |
| This paper stems from the fact that the topographic index used in TOPMODEL is
not dimensionless. In each pixel i in a catchment, it is defined as
xi=ln(ai/Si), where ai is the specific contributing area per unit contour length and Si is the topographic slope. In the SI unit
system, ai/Si is in meters, and the unit of xi is problematic. We
propose a simple solution in the widespread cases where the topographic index
is computed from a regular raster digital elevation model (DEM). The pixel
length C being constant, we can define a dimensionless topographic index
yi=xi-lnC. Reformulating TOPMODEL equations to use yi
instead of xi helps giving the units of all their terms and emphasizes the
scale dependence of these equations via the explicit use of C outside from
the topographic index, in what can be defined as the transmissivity at
saturation per unit contour length T0/C. The term lnC defines the
numerical effect of DEM resolution, which contributes to shift the spatial
mean x of the classical topographic index when the DEM cell size
C varies. A key result is that both the spatial mean y of the
dimensionless index and T0/C are much more stable with respect to DEM
resolution than their counterparts x and T0 in the classical
framework. This shows the importance of the numerical effect in the
dependence of the classical topographic index to DEM resolution, and reduces
the need to recalibrate TOPMODEL when changing DEM resolution. |
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