Geophysical Research Letters
Supporting Information for Title – “Prediction of flash-flood hazard impact from Himalayan river profiles”
Authors- R. Devrani1, V. Singh1, S. M. Mudd2 and H. D. Sinclair2
1
Department of Geology, Chhatra Marg, University of Delhi, Delhi - 110007, India
2
School of GeoSciences, University of Edinburgh, Drummond Street, Edinburgh EH8 9XP
Corresponding author: R. Devrani, Department of Geology, Chhatra Marg, University of
Delhi, Delhi - 110007, India. (rahuldevrani18@gmail.com)
Contents on this file
Text S1 to S2
Figures S1 to S2
Text S1
Theory
The transformed coordinate  (dimensions length) is calculated with (Royden and Perron,
2013):
𝑥
𝐴
0
𝜒 = ∫𝑥 (𝐴(𝑥)
)
𝑏
𝑚/𝑛
𝑑𝑥,
(1)
where x [dimensions length, dimensions henceforth denoted as [M]ass [L]ength and [T]ime
in square brackets] is the flow distance from the outlet, xb [L] is the flow distance at the
outlet, A [L2] is the drainage area, A0[L2] is a reference drainage area introduced to ensure the
integrand is dimensionless, and m and n are empirical constants.
The choice of the integrand in equation (1) is informed by a simple model of channel incision
called the stream power law (e.g., Howard and Kerby 1983, Whipple and Tucker, 1999)
𝐸 = 𝐾𝐴𝑚 𝑆 𝑛 ,
(2)
where E [L T-1] is the erosion rate, S [dimensionless] is the slope and K is an erodibility
coefficient with dimensions that depend on the exponent m. If river incision can be described
by this equation, then a steady state, ‘graded’ channel profile will be linear in -elevation
space. In a more complex channel network characterised by variability in factors such as
climate, rock uplift and lithology, the -elevation plots comprise a series of linear segments
that reflect changing erosion rates determined by these variables (Royden and Perron, 2013).
These segments can be described by:
1/𝑛
𝑈
𝑧(𝑥) = 𝐵𝜒 + (𝐾(𝐴
0
)𝑚
)
𝜒,
(3)
where z(x) [L] is elevation. Equation (3) is a linear equation with an intercept of Bχ [L] and a
slope [dimensionless] we call Mχ, or the gradient in -elevation space:
1/𝑛
𝑈
𝑀𝜒 = (𝐾(𝐴
0
)𝑚
)
(4)
In channels with fluvial incision that can be described with the stream power law (equation
(2)), the gradient in -elevation plots is closely related to the normalized channel steepness
(ksn), which has been used by a number of authors as an indicator of relative channel incision
rates (e.g. Hodges et al., 2004; Kirby and Whipple, 2012):
𝑈
𝑀𝜒 = (𝐾(𝐴
0
1/𝑛
)
)𝑚
= 𝑘𝑠𝑛 𝐴0 −𝑚/𝑛 .
(5)
The chi coordinate was calculated by integrating drainge area along the channel form a
baselevel at Rudraprayag (Fig. 1A). The reference drainage area was chosen as 1000 m2. This
value does not affect the relative values or spatial distribution of Mχ but it does affect the
absolute values of  and Mχ (see equations (1) and (4)). Whereas the normalized steepness
index, ksn, is calculated using a reference value for the m/n ratio (the ‘normalized’ denotes
that a reference m/n was used, usually 0.45; e.g., Kirby and Whipple, 2012), we calculate the
m/n ratio based on the topography at the site. Perron and Royden (2013) demonstrated that if
the m/n ratio is correct, the profiles of tributaries should be collinear with each other and the
main stem channel.
We found a regional m/n value by testing for collinearity across 8 tributaries in the upper
Mandakini basin, both above and below the MCT (tributaries were: Basti Damaar Gaad,
Kyunja Gaad, Kaakda Gaad and Lastar Gaad below downstream of the MCT and
Vasukiganga, Mandakini, Kaliganga and Madyamaheshwar Ganga upstream of the MCT).
Best fit m/n ratios were similar for upstream and downstream of the MCT (upper and lower
quartile m/n values across all 8 tributaries were 0.5 and 0.275). Upstream of the MCT, the
95% confidence bounds of median m/n were 0.325 and 0.4, with a median of 0.35. This m/n
value (0.35) was used to calculate Mχ. The code for performing these tests is available
through the Community Sediment Dynamics Modeling Systems (CSDMS) website:
http://csdms.colorado.edu/wiki/Model:Chi_analysis_tools).
Once m/n was determined, we used the algorithm of Mudd et al. (2014) to identify segments
within the channel network with different values of Mχ. This method tests all possible
contiguous segments in a channel network and selects the most likely segment transitions
using the Aikake Information Criterion (AIC; Aikake 1974), which is a statistical technique
that rewards goodness of fit while at the same time penalizing over fitting. In addition, the
Mudd et al. (2014) method uses Monte Carlo sampling to provide uncertainty estimates of the
location of channel segments, the gradient in chi space (Mχ) and the most likely value of m/n.
Our objective was to determine if the channel configuration prior to the event was consistent
with the pattern of topographic change in the channels, thus we did not perform the chi
analysis that included a point source of water. Additionally, there are no reliable estimates on
the discharge of the flood and its relative discharge contribution relative to runoff from
rainfall.
Text S2
The Mandakini catchment is a tributary of the Alaknanda River in the upper reaches of the
Ganga river basin (Fig 1). It is approximately 60 km long and traversed in its upper reaches
by the Main Central Thrust (MCT) (Valdiya et al., 1999; Fig. 2A).
We first constrained the most likely m/n ratio for tributaries both upstream and downstream
of the MCT, since this structure separates lesser and greater Himalayan lithologies. Upstream
of the MCT, we find that the best fit m/n ratio lies between 0.35 and 0.4. We find similar, but
slightly lower m/n ratios downstream of the MCT (between 0.275 and 0.325).
We extracted -elevation profiles within the Mandikani basin using a m/n ratio of 0.35 (Fig.
2A). The M value for the Mandakini channel network demonstrates a steepening of channels
to the northwest of the MCT linked to differential rock uplift across this structure as recorded
in the Nepalese Himalaya (Hodges et al., 2004). These anomalously high M values are
recorded in all the neighbouring valleys in the hanging wall of the MCT, with the highest
values at varying locations up the valley (Fig. S2b); the exact distribution of the steepest
reaches will also be influenced by lithology and glaciation (eg. Hobley et al., 2010).
Figure S1
S1. (a) Showing pre-event Bhuvan image around Kedarnath Township, where red polygon
represents boundary of the Kedarnath Township. (a´´) Pro-event Bhuvan image Extreme
event affected area near Kedarnath Township, showing erosive work of the Mandakini River,
mass movement system and reactivated low order streams. The indication of the valley
widening is clearly visible in the upstream and downstream of the Kedarnath Township
Light yellow area represents area of sedimentation in Kedarnath Township, for further colour
coded reference see legend.
(b) Pre-event Bhuvan image in downstream of Kedarnath
Township, covering the Garuriya Township. (b´´) Post –event Bhuvan image showing highly
eroded course of the Mandakini River. Though, much sedimentation was not visible in this
reach, but there is a slight increase in channel width. (c) Pre-event Bhuvan image of the
Ghindurupani and Rambara Township, which is downstream of the Garuriya Township. (c´´)
Post-event Bhuvan image of the Ghindurupani and Rambara Township;,showing massive
erosion done by the Mandakini River. Present reach exhibits highest degree of channel and
valley widening. This segment of the Mandakini River also witnessed highest devastation in
terms of social prospective, where the Rambara Township was totally swept away. . 3
(a´,b´,c´) Post event Bhuvan images, mainly showing location of major geomorphic features
and field photograph.
Figure S2
S2 (a) strictly focuses on the Kaliganga and Madhyamaheshwar Ganga River basin and
downstream streches of the Mandakini River after its confluence with the respective
tributaries (refer Fig.2 for location) where white colour rectangle represents location for Fig.
S2 b,c,d,e,f,g and h. (b) Red colour arrow shows erosive work done by the Kaliganga River.
The left hillslope is highly affected by the mass-movements. (c) The right hillslope is
completely affected by the mass-movements (represented by red line), where small red
arrows represent erosive work by the Kaliganga River. (d) Deposition of boulders during
extreme event by the Mandakini River. The sediment deposit could combine result of the
sediment flux from the Mandakini and Kaliganga River. This stretch lies between the
confluences of the Kaliganga and Madhyamaheshwar Ganga River with the Mandakini River.
(e) Confluence of the Madhyamaheshwar Ganga River with the Mandakini River, where big
boulders represents deposition done by the Madhyamaheshwar Ganga River during extreme
event. The black dotted rectangle represents Fig. S2f. (f) A downstream view of the
Madhyamaheshwar Ganga River towards confluence with the Mandakini River. Where, a
structure is wrecked by the boulders brought by the Madhyamaheshwar Ganga. (g)
Widespread of the boulders brought down by the Madhyamaheshwar Ganga, the highest
deposited boulder mound is upto 12 m from present river base level. Note the red colour
ellipse marking man for scale. (h) High magnitude of deposition by the Mandakini River,
where boulders are shoved into first storey of a structure.
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