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\title{- Supplementary Data - \\ \textbf{Denudation rates across the Pamir based on $^{10}$Be concentrations in fluvial sediments: Dominance of topographic over climatic factors}
\vspace{1em}
\\Earth Surface Dynamics}


\Author[1,2]{Margret C.}{Fuchs}
\Author[1,2]{Richard}{Gloaguen}
\Author[3]{Silke}{Merchel}
\Author[1]{Eric}{Pohl}
\Author[1]{Vasila A.}{Sulaymonova}
\Author[4]{Christoff}{Andermann}
\Author[3]{Georg}{Rugel}


\affil[1]{Remote Sensing Group, Institute of Geology, TU Bergakademie Freiberg, Bernhard-von-Cotta-Strasse 2, 09599 Freiberg, Germany}
\affil[2]{Remote Sensing Group, Helmholtz-Zentrum Dresden-Rossendorf, Helmholtz Institute Freiberg for Resource Technology, Halsbr\"ucker Strasse 34, 09599 Freiberg, Germany}
\affil[3]{Helmholtz-Zentrum Dresden-Rossendorf, Helmholtz Institute Freiberg for Resource Technology, Bautzner Landstrasse 400, 01328 Dresden, Germany}
\affil[4]{Section 5.1 Geomorphology, German Research Centre for Geoscience GFZ, Telegraphenberg, 14473 Potsdam, Germany}


\date{} % uncomment this line to display the current date

%\correspondence{Margret C. Fuchs (fuchsm@mailserver.tu-freiberg.de)}


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%--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
\section{Details on material and methods}
%--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
\label{methods}

\subsection{Beryllium-10-based modern denudation rates}
\label{basics-erosion-rates}

Beryllium-10 concentrations in modern fluvial sediments scale to the rate of landscape lowering by weathering and physical erosion and average the time of exposure to cosmic ray interaction in rock surfaces
\citep{vBlanckenburg2005, Dunai2010}.
The generally dry conditions in Pamir (Fig.~\ref{Fig-CN-regional}) 
suggest weathering to be of less importance in the total erosion budget. In this case, landscape lowering is dominated by the physical material removal at the landscape's surface, which means that denudation rates narrow down to erosion rates \cite[e.g.][]{Dunai2010}, and it may be convenient to use both terms interchangeably in the following.

The relation between the $^{10}$Be concentration in a target mineral and modern denudation rates is based on the fact that the nuclide is produced by cosmic rays at rock surfaces within a rock-characteristic attenuation depth, while material removal brings constantly new material from shielded depth to the surface
\citep{Lal1991, Brownetal1995, vBlanckenburg2005, Dunai2010}. 
Being highest at the rock surface, the $^{10}$Be production decreases approximately exponentially with depth
\citep{Lal1991, Dunne:1999vi, Braucher:2011epsl}. 
The mean attenuation path length z$^{*}$ of cosmic rays in rocks depends on the attenuation coefficient of the nucleonic component ($\sim$160\,g/cm$^{2}$) and the rock density  
\cite[e.g.][]{GossePhillips2001, Balco:2008gp} of the bulk, often polymineral material. 
Accordingly, in silicate rocks z$^{*}$ is typically $\sim$60\,cm  
\citep{Lal1991, vBlanckenburg2005}. 
The $^{10}$Be concentration C is then proportional to the time the mineral grains reside within  z$^{*}$ until being removed from the surface. Consequently, C is inversely proportional to the denudation rate $\varepsilon$ 
\citep{Lal1991, Brownetal1995, vBlanckenburg2005}. 
This relation can be described by:


%% EQUATION EROSION RATES
\begin{equation}\label{erosion rate}
\varepsilon \; =\; \left(\frac{P} {C} - \lambda\right) * z^{*} 
\end{equation}


where $\lambda$ is the decay constant of the nuclide and P its production rate.
To calculate $\lambda$ by

%% EQUATION EROSION RATES
\begin{equation}\label{lambda}
\lambda \; =\; \frac{ln(2)} {t_{1/2}}
\end{equation}


we used the $^{10}$Be half-life (t$_{1/2}$) of (1.387\,$\pm$\,0.012)\,Ma
\citep{Korschinek:2010cz}.
The parameter z$^{*}$ may be treated as a constant when determining basin-wide denudation rates
that averages over local variations in rock densities affecting the attenuation path length. 
The central estimates required for solving the equation are the $^{10}$Be concentration of the sample and the rate of nuclide production at the corresponding location (details given in
sections ~\ref{sampling}, ~\ref{preparation} and ~\ref{prod-shield}).
The equation is valid under steady-state conditions of  $^{10}$Be production and material removal at the surface.
This implies constant conditions over a period that is long compared to the averaging time T$_{ave}$, the time it takes to erode z$^{*}$ and hence, to remove the `cosmogenic memory' of the material
\citep{Brownetal1995, BiermanSteig1996, vBlanckenburg2005, Dunai2010}.

Assuming uniform erodibility,  mineral composition and grain size release of the eroding rock surface, denudation rates represent averages for all upstream surfaces at the basin scale
\citep{BiermanSteig1996, vBlanckenburg2005, Carretier:2009fk}. 
Well-mixed sediment representative of all process domains within the basin  require sample basins large enough to minimize the influence of single and only local processes 
\cite[e.g.][]{vBlanckenburg2005, Niemi:2005epsl, Yanites:2009jg}. 
Although large basins imply longer grain travel times,  nuclide concentrations revealed negligible increases compared to the concentration already acquired at their initial position in non-aggrading basins 
\citep{Carretier:2009fk}.




%--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
\subsection{Sample preparation and $^{10}$Be measurements}
\label{preparation}

The polymineral sediment samples required quartz enrichment before starting chemical cleaning and $^{10}$Be extraction. 
To narrow the grain size fraction, we first sieved the samples to 250\,-\,500\,$\mu$m and 500\,-\,1000\,$\mu$m, and focussed on the 250\,-\,500\,$\mu$m fraction. For two samples (TA28C and TA30P) only the coarser fraction yielded sufficient material.
After magnetic separation and ultrasonic bath, we cleaned the quartz 
with a 1:1 solution of HCl (32\%) and H$_{2}$SiF$_{6}$ (34\%)  
\citep{Brown:1991ui}.  
Inspection of the sample's mineral composition under the binocular revealed relatively high proportions of feldspars (up to 50\%) for most of our samples, even after repeating the partial dissolution for six cycles. 
Feldspars cause bias in quartz results due to differing rates of $^{10}$Be production. Additionally, the lower chemical resistance compared to quartz as well as high aluminum contents affect chemical procedures. This motivated us to introduce a standard feldspar flotation   
\citep{Herber:1969vr} to further enrich the quartz fraction. 
The feldspar flotation was carried out in a solution of 0.2\% HF and pH of 2.4\,-\,2.7 to activate feldspar adherence to bubbles using the foam agent dodecylamine.
 

Atmospheric $^{10}$Be was removed by dissolving 30\% of the extracted quartz fraction with 48\% HF during three cycles.
The BeO separation followed the procedures by 
\cite{Mercheletal1999}.
After the addition of about 300\,$\mu$g of a $^{9}$Be carrier (Phena DD, (3.025\,$\pm$\,0.009)\,$\times$\,10$^{-3}$~$^{9}$Be/g, 
\citealp{Merchel:2008cv}),
samples were totally dissolved using 48\% HF.
The Be extraction from the dissolved quartz included repeated hydroxide precipitation by NH$_{3aq}$, anion  and cation exchanges.
For high Ti-containing samples, Ti was diminished by precipitation of  Ti(OH)$_{4}$ before ignition of Be(OH)$_{2}$ to BeO.
Then, target preparation involved adding Nb (six times of the dry oxide weight).  
AMS measurements were conducted at DREAMS (DREsden AMS, Helmholtz-Zentrum Dresden-Rossendorf, 6 MV, Cu cathode)
using the in-house standard SMD-Be-12  
\citep{Akhmadalievetal2013}
normalized against the 
NIST SRM 4325 standard ($^{10}$Be/$^{9}$Be ratio of (2.79\,$\pm$\,0.03)\,$\times$\,10$^{-11}$, 
\citealp{Nishiizumi:2007kq}). 
A round-robin exercise of AMS facilities
confirmed robust standard calibration and measurement configuration
 \citep{Mercheletal2012}.
Processing blanks were treated and measured parallel to the sediment samples. 
The blank isotope ratios in the order of 0.3\,-\,1.7\% ($^{10}$Be/$^{9}$Be ratio of 2.0\,$\times$\,10$^{-15}$ and 2.1\,$\times$\,10$^{-15}$) were subtracted from the measured ratios of all samples.


%--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
\subsection{Production rates and shielding factor}
\label{prod-shield}

The production of  $^{10}$Be in quartz is primarily dependent on the cosmogenic particle flux from nucleons and muons  \citep{Lal1991, GrangerMuzikar2001} as a function of  the geomagnetic field, altitude and shielding \citep{Lal1991, Brownetal1995, BiermanSteig1996, Stone:2000vn, GossePhillips2001}.
Accounting for the location-specific modulation, reference sea level and high latitude (SLHL) production rates need to be scaled to the conditions at the site of sampling.

In the case of fluvial sediment samples, the cosmogenic nuclide inventory was acquired in source areas of the sediment upstream of the sampled site
 \cite[e.g.][]{Brownetal1995, BiermanSteig1996, Granger:1996tr, vBlanckenburg2005}. Consequently, the calculation of representative production rates requires attention to the hypsometry of the whole basin  \citep{vBlanckenburg2005, Norton:2009ic, Dunai2010}. 
Representative values for the production rate and shielding were calculated raster-cell resolved
for the upstream area of each sampling site based on a ASTER GDEM of 10\,m resolution (see also main text).

% Be-10 production
For each sampled basin, we then calculated $^{10}$Be production rates from neutrons, and fast and stopped muons by raster cell-resolved scaling of a SLHL reference according to \citep{Stone:2000vn}.
We used the SLHL production rate of 4.5\,at/g quartz/yr 
(cf. \citealt{Balco:2008gp} along with the half-life of $^{10}$Be of (1.387\,$\pm$\,0.012)\,$\times$\,10$^{6}$ years,
\citealt{Korschinek:2010cz}) 
and the attenuation parameters according to \cite{Braucher:2003es} and \cite{Siame:2004dm}.

% shielding
Topographic shielding plays an important role in high relief terrain \citep{Dunne:1999vi} as steep slopes reduce the exposure to the cosmic particle flux \cite[e.g.][]{GossePhillips2001, Codilean2006, Norton:2009ic}. Shielding from other sources is considered negligible as glaciated areas are excluded from production rate calculation and vegetation is scarce due to the dry climate and high basin altitudes.
The shielding factor was estimated for each GDEM raster cell based on the horizon line within a 10\,km distance according to the method of \cite{Codilean2006}. 
\cite{Norton:2009ic} found only low underestimation of shielding when using a DEM of 30\,m resolution in steep terrain.  


\section{Details on results}
\subsection{Details on denudation rate parameters}

Denudation rates corrected for the basins proportion of snow and ice cover display an exponential relation with AMS-based $^{10}$Be concentrations (Fig.~\ref{Fig-CN-erosion-parameters}, B) as an expression of the attenuation of cosmic rays in rock surfaces. 


The correction of production rates according to the basin's topographic shielding factors enhance differences between basins. Low altitude areas commonly relate to marginal Pamir basins that are more shielded by steep slopes than plateau-related basins with a high proportion of altitudes above 3600 m a.s.l. and large areas of slopes  ${<}$5\%. 
Consequently, elevated central and eastern basin portions deliver sediments of high $^{10}$Be concentrations (e.g., TA08N) to the river channels due to high production and low shielding. Lowest production rates occur within north-western basins (e.g. TA02A) due to both, high topographic shielding and high snow and ice cover. 
The rates of nuclide production (Tab.~\ref{Tab-CN-results}) are similar, with only $\sim$9\% variability for plateau-related basins (TA08N  and TA30P) and  those of the southern Panj basins (TA23P, TA24O, TA25C and TA28C). 
The shielding corrected production rates in tributary basins indicate a slight decrease (Fig. 2 in supplementary material, C) corresponding to northward lower altitudes and steepened topography.



\newpage{}

%--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
\section{Supplementary figures}
%--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

\subsection{Figure 1: Spatial variations of  $^{10}$Be production rates and topographic shielding}


%% FIGURE Pneutrons
\begin{figure*} [h!]
\begin{center}
\includegraphics[width=0.85\textwidth]{CN-figures-els/Pamir_CN_Fig4_Pn-S_5.pdf}
\caption {Spatial variations of  $^{10}$Be production rates and topographic shielding according to the hypsometry of the Pamir, and individual frequency distributions of production and shielding within sampled basins (cf. Figs.~\ref{Fig-CN-regional} and ~\ref{Fig-CN-basin-TOPO-SLP}). As an example of the spatially variable production, rates are given for the neutron induced $^{10}$Be built-up (CN: cosmogenic nuclide, color code for CN sample locations in map refers to individual basins in the legend of  frequency distribution plots: reddish: southern Pamir margin, greenish: western Pamir margin, blueish: plateau-related basins, cf. Fig.~\ref{Fig-CN-regional}; notation of basins refers to bold fonts used for sample names in Fig.~\ref{Fig-CN-regional} and Tab.~\ref{Tab-CN-sample-location}).}
\label{Fig-CN-basin-Pn-S}
\end{center}
\end{figure*}
%------------------------------



\newpage{}
\subsection{Figure 2: Parameters of denudation rate calculations}

%% FIGURE erosion rate parameters
\begin{figure*} [h!]
\begin{center}
\includegraphics[width=0.9\textwidth]{CN-figures-els/Pamir_CN_Fig6_param-erosion-rates_4.pdf}
\caption {Relationship between basin-wide denudation rates and respective parameters used for calculations and corrections. A: Denudation rates with and without correction for areas covered by permanent snow and ice. B: Exponential relation between denudation and $^{10}$Be concentrations from AMS measurements. C: Low variability of production rates corrected for topographic shielding (color code refers to individual basins in the legend, reddish: southern Pamir margin, greenish: western Pamir margin, blueish: plateau-related basins, cf. Fig.~\ref{Fig-CN-regional}; notation of basins refers to bold fonts used for sample names in Fig.~\ref{Fig-CN-regional} and Tab.~\ref{Tab-CN-sample-location}, shaded areas provide a quick demarcation of margin or plateau-related samples, the sample TA01C between the two units illustrates the integration of both, marginal and plateau-related portions).}
\label{Fig-CN-erosion-parameters}
\end{center}
\end{figure*}



%% REFERENCES

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\bibliography{Pamir-CNerosion.bib}

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