Tectonic control on the persistence of glacially sculpted topography

One of the most fundamental insights for understanding how landscapes evolve is based on determining the extent to which topography was shaped by glaciers or by rivers. More than 104 years after the last major glaciation the topography of mountain ranges worldwide remains dominated by characteristic glacial landforms such as U-shaped valleys, but an understanding of the persistence of such landforms is lacking. Here we use digital topographic data to analyse valley shapes at sites worldwide to demonstrate that the persistence of U-shaped valleys is controlled by the erosional response to tectonic forcing. Our findings indicate that glacial topography in Earth's most rapidly uplifting mountain ranges is rapidly replaced by fluvial topography and hence valley forms do not reflect the cumulative action of multiple glacial periods, implying that the classic physiographic signature of glaciated landscapes is best expressed in, and indeed limited by, the extent of relatively low-uplift terrain.


Variability in cross-sectional valley shape
Approximately 2.5 million valley cross sections were automatically extracted from digital elevation models for this study. Mean exponents of power-laws fitted to these cross-sections plotted against bins of rock uplift or erosion rates define robust trends. The mean power-law exponents derived from our automated, global analysis are slightly lower than, but generally in good agreement with those found in the literature 16,17,18 . For example, a mean exponent of 1.87 (min = 1.03, max = 3.5) was found for 49 valley cross profiles in the Tien Shan Mountains 19 . While we identified large glacial valleys with long turnover time to have the highest exponents ( Supplementary Fig. 2), our study sites are dominated by smaller valleys, which explains the lower mean exponents found with our approach. However, our power-law exponents have high variability in both glacial and fluvial landscapes (Supplementary Fig. 1).
Standard deviations are high for the 20 rock uplift bins in Supplementary Fig. 1a, but the histograms in Supplementary Fig. 1b show nonetheless that the entire distributions of powerlaw exponents shift towards higher exponents with decreasing rock uplift rates. To further test whether the large scatter is due to natural variability of cross-sectional valley shape or due to methodological issues we compared the distribution of the 3000 exponents automatically

Comparison of rock uplift and erosion rate datasets
The erosion rates 1 for Westland shown in Fig. 3c are much lower than rock uplift rates 7 reported for the same area (shown in Fig. 3a), which are generally in good agreement with other sources for Westland 22,23,24,25 . The erosion rates 1 are also generally lower in comparison to values reported in studies 6,7,8,26,27,28,29 for the regions shown in Figs. 3c (study areas depicted in Supplementary Figs. 3 to 5) and 4 (study areas depicted in Supplementary Fig. 6).
The difference in magnitude may be due to the timescales involved or the techniques employed to create the gridded erosion rate dataset 1 . Despite the differences in magnitude, the spatial patterns of erosion 1 and rock uplift 8 are generally similar. Hence we use the erosion dataset as an indicator of the general long-term distribution of erosion rates that facilitates comparisons of spatial patterns among different study sites (e.g., Fig. 3c).
The exponent-rock uplift relation for Westland (Fig. 3a) differs from the exponent-erosion trend (Fig. 3c) due to differences in the rock uplift 8 and erosion 1 data sources. Valley shape exponents decrease with increasing erosion rates from 0.3 to about 3.5 mm yr -1 , a relationship that holds for 98% of the study area ( Supplementary Fig. 3). However, for the highest erosion rates in the erosion dataset the exponents increase in the vicinity of Mt. Cook ( Supplementary   Fig. 8), in an area that constitutes about 2% of the study area but hosts an erosion rate gradient from 3.5 to about 5.5 mm yr -1 . The Mt. Cook region experienced stronger post-LGM glacial advances than other parts of Westland 30 , probably due to its exceptionally high topography.
This may have prevented a full transition from U-shaped to V-shaped valleys since the LGM in this area. In addition, the limited spatial distribution of these high erosion rates in New Zealand differs from other studies where high rates extend over much more extensive areas 8,22 . The zone with high erosion rates near Mt. Cook arises from only a few erosion grid cells, some which are located northwest of the Alpine Fault (the downthrown block) that are anomalously portrayed as having erosion rates > 3.5 mm yr -1 . A gridding artifact may be 13 responsible for the anomalous positioning of some of the high erosion rate grid cells, as this area accounts for little more than a single 3 x 3 cell neighborhood quadrat on the erosion rate grid, the standard neighborhood used for raster data manipulation. We suspect that the anomalous exponent-erosion rate trend for the Mt. Cook area shown in Supplementary Fig. 8 results either from differences in glacial history or a gridding effect. Thus, we have omitted this region from the analysis used to generate Fig. 3c.