Prediction of flash flood hazard impact from Himalayan river profiles

To what extent can we treat topographic metrics such as river long profiles as a long‐term record of multiple extreme geomorphic events and hence use them for hazard prediction? We demonstrate that in an area of rapid mountain erosion where the landscape is highly reactive to extreme events, channel steepness measured by integrating area over upstream distance (chi analysis) can be used as an indicator of geomorphic change during flash floods. We compare normalized channel steepness to the impact of devastating floods in the upper Ganga Basin in Uttarakhand, northern India, in June 2013. The pattern of sediment accumulation and erosion is broadly predictable from the distribution of normalized channel steepness; in reaches of high steepness, channel lowering up to 5 m undercut buildings causing collapse; in low steepness reaches, channels aggraded up to 30 m and widened causing flooding and burial by sediment. Normalized channel steepness provides a first‐order prediction of the signal of geomorphic change during extreme flood events. Sediment aggradation in lower gradient reaches is a predictable characteristic of floods with a proportion of discharge fed by point sources such as glacial lakes.


Introduction
The application of topographic analysis in determining tectonic forcing of landscapes at timescales that bridge the historical (<10 2 years) and geological (>10 6 years) is improving assessment of seismic hazard [Kirby et al., 2008]. Assuming the long-term erosion of rivers in mountain belts can be modeled as a power law function of channel slope versus water discharge (approximated by upstream catchment area [Whipple and Tucker, 1999]), the progressive reduction of channel gradient with upstream area is predictable [Hack, 1960]. However, in the Himalaya, the long profiles of rivers do not decline from their mountain sources asymptotically to the Gangetic Plains but instead exhibit downstream steepening over active fault structures such as the Main Central Thrust [Seeber and Gornitz, 1983]. Quantification of the degree of steepening has enabled differential rock uplift fields and their associated fault structures to be identified in a range of settings [Kirby and Whipple, 2012] with some of the earliest applications in the Himalaya [e.g., Hodges et al., 2004].
Increases in channel gradients via, for example, tectonic forcing will increase unit stream power resulting in higher incision rates. This provides a mechanism by which rivers adjust toward a dynamic steady state between rock uplift and river incision. In rivers where the channel is bound by bedrock surfaces, incision is said to be detachment limited; i.e., changes in channel geometry can only occur due to detachment of rock from the channel boundary [Howard, 1994]. In contrast, where sediment flux exceeds the transport capacity of a river, the system becomes transport limited whereby the river long profile is dictated by the downstream divergence of sediment flux [Whipple and Tucker, 2002]. In this case, the volumetric transport capacity is a power function of unit stream power [Willgoose et al., 1991]. Therefore, as channel gradients decrease (normalized for drainage area), so sediment transport capacity of the river declines and sedimentation is enhanced. However, this transition from bedrock incision into channel alluviation is also a function of grain size and sediment supply rate [Sklar and Dietrich, 1998].
Although channel steepness, normalized for drainage area, has been demonstrated as a proxy for long-term erosion rates [e.g., Kirby and Whipple, 2012], to our knowledge it has not been used as a predictor of the spatial distribution of channel incision during extreme events. Here we exploit a major event which occurred on 16 and 17 June 2013, which devastated the Mandakini River Valley in the upper Ganga basin [Ziegler et al., 2014]; heavy rainfall in the region was augmented by the breaching of a lake on the edge of the Chorabari glacier that enhanced the flood discharge [Dobhal et al., 2013]. Our goal is to determine if the spatial pattern of channel steepness prior to the flooding event in 2013 was consistent with topographic modification along the Mandakini River that occurred during the event.

Methodology
Our topographic analysis of river long profiles in the Mandakini basin normalizes for drainage area by integrating drainage area over flow distance. This method, first suggested by Royden et al. [2000], produces a transformed coordinate, χ (chi), which has dimensions of length . The elevation of the channel can then be plotted against the χ coordinate, and the gradient of the transformed profile in χ elevation space (which we call M χ ) provides a metric that can be used to compare channel segments with different drainage areas.
The chi method is underpinned by the stream power model of channel incision . It applies to bedrock rivers; these may have thin alluvial covering but are defined as rivers where bedrock must be incised in either the bed or banks for the river to change its form [cf. Hancock et al., 1998]; we choose this model because field observations indicate that the Mandakini River was predominantly bedrock prior to the event. This model is an imperfect description of channel incision [e.g., Lague, 2014], and other models have been proposed, including those that incorporate the role of sediment supply [Sklar and Dietrich, 1998] and erosion thresholds [Snyder et al., 2003].
However, even if the stream power incision model is an imperfect description of channel incision, M χ can still be calculated and allows at least a qualitative comparison of the steepness of channel segments relative to their upstream area, from different parts of the channel network. Analytical solutions of the stream power model suggest that M χ will reflect channel erosion even if different segments of the channels are eroding at different rates ; this prediction has been corroborated with comparison to field data Mudd et al., 2014]. The normalized steepness M χ is related to the normalized steepness index, k sn (see Text S1 in the supporting information), which has been used as a proxy for both erosion rates [e.g., Ouimet et al., 2009] and tectonic signals [e.g., Kirby and Whipple, 2012] in the Himalayas. Both chi analysis and the normalized steepness index (k sn ) have been found to correlate well with erosion rates in the nearby Yamuna River which is the basin immediately to the west of the Ganga [Scherler et al., 2014]. We have followed methodology by Mudd et al. [2014] to extract χ (chi) and M χ (Text S1 in the supporting information).

Topographic Analysis of the Mandakini Basin
We focus on the westernmost of the Mandakini upper tributaries; this tributary drains the valley containing the Kedarnath temple and comprises three distinct reaches (Figures 2b and 3a) (see Text S2 in the supporting information). The upper reach has a low-gradient main channel with extensive moraines and glaciers in its headwaters; the M χ value is relatively low (M χ~3 ) (Figures 2b and 3a). Approximately 1 km south of Kedarnath, the river channel steepens downstream and the valley narrows over a distance of around 7 km with M χ values significantly greater (>150%) than the upper reaches (M χ~7 .9) (Figures 2a, 2b, and 3a); this middle reach has gneisses and schists over more granitic rocks in the hanging wall of the Main Central Thrust [Valdiya et al., 1999]. Values of M χ decrease (~4.5) again downstream above the town of Gaurikund (at~6 km in Figure 3a), and the valley also widens from this point.

Impact of Flash Floods
On 16 and 17 June 2013, following sustained heavy rainfall, a series of flash floods caused devastation down the Mandakini Valley and south to the exit of the Ganga from the mountain front near Rishikesh and Haridwar killing approximately 5700 people. Hillslope runoff combined with a lake outburst at the head of the Chorabari glacier caused the remobilization of glacial moraine, hillslope debris, and valley alluvium as debris and mud flows [Dobhal et al., 2013]. The sediment-laden waters devastated infrastructure in two ways, either by burying buildings (aggradation) or by incising and undercutting foundations as the active channel, predominantly composed of either bedrock or moraine material, which responds to incision in detachment limited manner [e.g., Hobley et al., 2011], widened (see Figure S1 in the supporting information). The distribution of sediment aggradation and bedrock incision has been mapped through field observations and repeat satellite imagery in Kedarnath Valley ( Figure S1 in the supporting information).

Discussion
In this example from the western Himalaya, we have explored whether the first-order geomorphic characteristics of the long river profile which are accessible from digital topography can be interpreted as an integrated record of extreme storm events. Estimation for paleoflood deposits in the Alaknanda Valley suggests a mean 55 years repeat interval [Wasson et al., 2013]. However, the erosive record of a circa 13 ka glacial deposit near Rambara indicates that the 2013 floods were the largest since the glacial maxima in the upper Kedarnath Valley.
The results suggest that chi analysis of river channel steepness, via the chi gradient M χ [Royden et al., 2000;Perron and Royden, 2013;Mudd et al., 2014], provides a potentially important methodology for assessing the long-term trajectory of geomorphic change driven by extreme events. In order to relate the chi analysis to the geomorphic signal of this event, we must integrate the spatial pattern of incision and aggradation along with the channel widening and the evidence of a point source for some of the discharge. Embedded within chi analysis is an assumption that channel incision is a function of the discharge divided by the width of the channel; the final form of the stream power law combines an assumption that discharge, Q, is a function of drainage area (Q = k Q A a ) and channel width, w, is also a function of drainage area (w = k w A b ). The m exponent therefore combines the exponents a and b (m = a À b). The exponent b is positive and less than 1 [e.g., Whipple and Tucker, 1999]. If the flood is a point source, then a will be 0 (discharge will not increase downstream) and the m exponent will be negative; that is, incision will decrease downstream as the channel widens, all else being equal. The discharge in the Mandakini during the flood was not exclusively from the breached lake; rainfall during the event was also heavy [Dobhal et al., 2013], so during the event discharge still increased downstream, but the m exponent would be depressed. We suggest this as a component of the explanation of the switch to sediment aggradation in the lower reaches of the channel; this will also be enhanced by a high sediment transport load from reworked moraine. It is possible that much of the evacuation of sediment generated during these extreme events is subsequently mobilized out of the system during more moderate monsoonal discharge [e.g., Hartshorn et al., 2002].
In addition, the stream power law does not account for channel widening [cf. Lague, 2014], and during the event channel widening was widespread. This means that stream power would overpredict erosion rates since it assumes incision will occur over fixed channel geometries. Despite the fact that the chi analysis does not include adjustments for channel widening, areas of channel widening are correlated with area of high M χ , suggesting that in these areas extreme events should expend energy on channel banks in addition to the channel bed [cf. Hartshorn et al., 2002].
A fundamental question in drainage systems is whether it is the extreme geomorphic events that define the long profile of a river channel [Schumm, 1973], and if so, how can we use this information to improve hazard mitigation strategies in these settings. In Ladakh, in the lee of the western Himalaya where long-term erosion rates are slow (~0.01 mm yr À1 ), the impact of extreme monsoonal storms of August 2010 could not be related to the longer-term trajectory of change recorded by the channel profiles [Hobley et al., , 2012. The slowly eroding landscape of Ladakh is clearly transient as much of the river valleys are still occupied by glacial moraine that is dated at circa 100 ka [Owen et al., 2006]; these landscapes may be considered to be "buffered" against the extreme events (in a broad sense Allen [2005]). The 2013 event in the Mandakini River contrasts with the event in Ladakh: in the Mandakini, Mχ has a spatial distribution that mirrors the spatial distribution of damage during the 2013 event. Thus, the Mandakini River follows the "reactive" model of Allen [2005]: its topography, developed over long timescales, appears to relate to the pattern of incision that occurred during a rare, extreme event.

Conclusion
Mapping of the Mandakini River network using a chi analysis demonstrates high M χ values in the upper part of the catchment in the hanging wall of the Main Central Thrust. These data suggest that this structure governs the distribution of differential rock uplift during the time of landscape formation in this valley (10 5 -10 6 years). Following flash floods during the summer of 2013, the valley was devastated by both channel incision and undercutting of infrastructure, and by burial by coarse boulder debris. Enhanced channel incision occurred along the reaches where M χ greatest, compared to sediment aggradation (burial) where steepness is less. Because the spatial distribution of topographic modification was consistent with the long river profile as quantified by chi analysis, we suggest that in the frontal Himalaya topographic analysis could provide a valuable first-order approximation of the future impact of extreme flood events in the frontal Himalaya.