Erodibility controls on the vertical and horizontal scalings of topography : a case study in the Himalayas

Understanding the scaling properties of topography in actively uplifting areas is a major issue in quantitative geomorphology. Analytical formulations of non-glaciated landscape evolution clearly demonstrate that metrics such as local relief or drainage density are explicitly related to the spatial distribution of tectonic uplift, precipitation, erodibility and local slope across the landscape. However, in most regions, these parameters are seldom documented with enough resolution and precision to allow a systematic and statistically significant investigation of their relationships with both horizontal and vertical scaling properties of topography. A notable exception is the Himalaya of central Nepal, where the last 20 years of tectonic and geomorphological research have produced one of the densest regional data-set and documented major gradients in uplift and precipitation across the range [e.g. Lavé and Avouac, 2001; Bookhagen and Burbank, 2006]. The purpose of our study is to use this data in order to develop a detailed investigation of the influence of the erodibility parameter in controlling the structure and texture of the landscape. We first build on the derivation of total catchment relief of Tucker and Whipple [2002] to include the contribution of precipitation in addition to uplift, erodibility. Then, by minimizing the misfit between observed and predicted catchment relief, we assess the erodibility parameter for each second or third order catchment in our area of investigation. The resultant erodibility map (1) matches the distribution of geological units and (2) reveals a number of interesting second order patterns, such as along-strike fluctuations in the Lesser Himalayas and a significant decrease in erodibility coincident with the location of the MCT zone. This latter result possibly highlights the effect of intense schistosity and fracturation on large scale erosion efficiency [Molnar et al., 2007]. Then to assess the influence of erodibility on landscape horizontal wavelength, we compute for each catchment a normalized roughness. This morphological index has the advantage of being unbiased by arbitrary definitions of channel inception or local relief. As predicted by theoretical formulations, we observe that both the horizontal wavelength and vertical relief of the landscape are sensitive to the U/K ratio. Our results suggest that, in combination with usual metrics based on the vertical development of the landscape (i.e. channel or hillslope gradients), the analysis of the variability in horizontal wavelengths holds a significant potential to resolve uplift and erodibility in tectonically active areas.