Spatial and temporal variation in jökulhlaup hydraulics and sediment transport

The 25 km long Hraundalur valley became inundated within ∽3 hours (Fig. 4). Mean frontal velocity was ∽2.3ms^–1, although this varied with a much slower frontal velocity upslope of the major channel construction. Since channel geometry is fixed, water stage is a proxy for discharge, and this attenuated very rapidly downstream (Fig. 5). It is interesting to note that the rate of rise to peak stage is generally consistent between sites and coincident with the timing of peak discharge (Fig. 2), but that the magnitude of peak stage and subsequent stage recession rates vary considerably (Fig. 5). Peak stage magnitude generally decreases and peak stage duration generally increases with distance downstream. However, a few exceptions occur where hydraulic ponding causes a prolonged peak stage and in zones of narrow channel width where the hydrograph becomes very flashy (Fig. 5).

Fig. 4. Schematic illustration of the time to inundation by glacial outburst floods (jökulhlaups) from Kverkfjöll of the Kverkfjallarani bedrock landscape. The main northeast-trending valley is Hraundalur. Floods routing northwest were of a lower discharge and of slower frontal velocity than the Hraundalur example.

Fig. 5. Spatial and temporal variation in relative water depth (m) of a 100 000m³ s^–1 jökulhlaup routing along Hraundalur, Kverkfjallarani. Note prolonged peak stage in areas of hydraulic ponding, and general downstream attenuation. This model run considers 100% water flow. x scale is time (hours) since flood initiation. Note y scale (m) varies between graphs.

At peak stage (after 2 hours), supercritical flow predominated in proximal reaches, was intermittent in medial reaches, and generally absent from distal reaches (Fig. 6a). On the rising stage, after 1.5 hours, a number of high-magnitude flow phenomena can be described. These include: mid-valley islands causing flow acceleration and a meandering thalweg (Fig. 6b); temporary hydraulic ponding where flow spills over low divides between mid-channel islands and where valley constrictions dramatically reduce channel widths (Fig. 6c); and very steep water surface gradients between flow depths upstream of a severe construction that are up to an order of magnitude greater than flow depths immediately downstream (Fig. 6c). Inundation of tributary valleys and other backwater sites therefore largely depends on flow depth. The rapidly varied nature of flow conditions is further illustrated by the contrast between over-bank and backwater flow shear stress (Fig. 6d).

Fig. 6. Examples of 2D hydrodynamic model output and GIS-based calculations of (a) flow regime at peak stage after 2 hours, (b) flow velocity after 1 hr 30 min, (c) flow depth at peak stage and (d) shear stress after 1 hour. Note that diagrams do not necessarily pertain to the same model run, nor to the same hydrograph stage.

Sediment transport comprised suspended load and bed load, and is discriminated by the calibre of material entrained at a given shear stress. Suspended load, which in the Hraundalur jökulhlaup comprised volcaniclastic scoria, spatter, pumice, tuff fragments and pillow lava blocks (Reference Carrivick, Russell, Tweed and TwiggCarrivick and others, 2004b), persists over the duration of the flood hydrograph within both relatively deep and shallow flows (Fig. 7). While suspended load transport was sustained in the upper reaches of Hraundalur, it became discontinuous in the lower reaches due to a dissipation of flow energy. In contrast, bed load transport was highly variable in space and time and occurred only in the relatively deep main channel (Fig. 7). Additionally, bed load transport featured pulses and become rapidly exhausted after peak discharge. Net sediment gain and loss per grid cell was modelled as a mass change and infers erosion or deposition. Note that bed elevation change was not modelled. Mass changes in sediment were predominantly negative, i.e. erosional, except for within hydraulically ponded zones and marginal embayments (Fig. 8). Some mid-channel deposition occurred immediately downstream of islands (Fig. 8).

Fig. 7. Spatial and temporal variation in suspended load and bed load. The total of all sediment fractions is presented only. Note that suspended load persists in phase with the water hydrograph, but bed load is extremely transient and exhibits pulses. x scale is time (hours) since flood initiation. Note y scale (m) varies between graphs.

Fig. 8. Net gain and loss of pre-existing sediment, i.e. erosion and deposition, after 1, 3 and 5 hours. Each grid cell initially contained a total mass of 8000 kg of sediment of uniform depth.

Association of modelled hydraulics with field-mapped landforms and sediments

Ranges of hydraulic parameters can be defined for each landform type, in a manner similar to that presented by Reference O’ConnorO’Connor (1993) and Reference Benito and O’ConnorBenito and O’Connor (2003) for the Bonneville and Missoula megafloods, for example. Figure 9 clearly show that erosional landforms are associated with much higher flow depths, flow velocities, shear stresses and stream powers than depositional landforms. These ranges define both maximum and minimum thresholds of hydraulic parameters within which landform types are located. It is clear that there is no unique range of hydraulics associated with particular landform type, i.e. many of the ranges overlap (Fig. 9). Indeed, depositional and erosional ranges also overlap. This is because of the transient nature of hydraulic parameters, particularly due to turbulence and the development of spatially discordant supercritical flow.

Fig. 9. Conceptual diagram illustrating a quantitative hierarchy of landforms based on a range of hydraulic conditions associated with each landform type. Landforms are arranged from those associated with deeper, faster and more powerful flows to those associated with shallower, slower and less energetic flows. The hierarchy is thus gorges, scoured bedrock, cataracts, valley-fill deposits, bars and terraces, and slackwaters. Data points and ranges are displayed for maximum values recorded in that landform area.

Landform group hydraulics allows a quantitative hierarchy of landforms to be proposed. This hierarchy is ordered from landforms situated in zones of deep, fast and high-energy flow to landforms situated in shallow, slow and low-energy flow. Gorges are at the top of this hierarchy and are characterized by mean shear stresses and stream powers of 100–3400Nm^–2 and 3500–20 000 Wm^–2 respectively (Fig. 9). Scoured bedrock surfaces extend over a far greater spatial area than gorges, which of course are linear features, but exhibit rather more stable flows as illustrated by smaller ranges and lower standard deviations of depths, velocities, shear stresses and stream powers (Fig. 9). Stream powers associated with scoured bedrock surfaces are 300– 18 500Wm^–2, and thus approach maximum values associated with gorges. Cataracts occur where hydraulic conditions are similar though less varied in comparison to scoured bedrock surfaces. This is because cataracts are localized down-cuts into bedrock, and therefore flow will always be accelerating through these zones. Consequently, flow depths within cataract zones range from just 4.0–7.5m over cataracts in comparison to 3–11.3m on scoured bedrock (Fig. 9). A further factor to explain the range of flow depths associated with scoured bedrock zones is that some probably experience hydraulic ponding. Spillways, which are not show in Figure 9, are similar to cataracts but overtop topographic divides. Flow depths and velocities have low variance within spillway zones, with mean values varying from 5 mand 10 ms^–1, respectively. Shear stresses and stream powers associated with spillways are low, with mean values of 200–500Nm^–2 and 310–830Wm^–2 respectively. Channel reaches with valley-fill deposits are associated with a range of flow depths that are similar to those of scoured bedrock zones. This is again attributed to the fact that valley-fill surfaces occur within the main channel and are therefore subjected to main flow hydraulics, which include both rising and falling stages of a flood hydrograph. However, in contrast to scoured bedrock reaches, valley-fill zones are located in reaches of shallow gradient. They have flow velocities of 6–11ms^–1, which are much less and of a tighter range than the flow velocities of 7–16ms^–1 of scoured bedrock zones

(Fig. 9). Shear stresses of valley fill zones are low, with mean values ranging from 140–450Nm^–2. The importance of whether reach-scale flow is accelerating or decelerating, as determined primarily by gradient in the absence of topographic widening or narrowing, is therefore again highlighted. Slackwater deposits are characterized by maximum flow depths < 8m and maximum flow velocities of < 4ms^–1 (Fig. 9). However, mean flow depths and mean flow velocities in slackwater areas are < 2m and < 2ms^–1 respectively. Thus, calculations of flow depths and flow velocities between different slackwater zones have a low standard deviation (1.25 and 0.5 respectively), illustrating relatively similar flow conditions at all locations. Mean shear stresses and mean stream powers within slackwater locations are less than 100 Nm^–2 and 4000Wm^–2 respectively, although some values recorded are at least an order of magnitude greater (Fig. 9). Nonetheless, shear stress and stream powers within individual slackwater zones have a low range, implying spatially homogenous flow conditions at a particular site. Slackwater zones therefore have lowest flow depths, lowest flow velocities and lowest shear stresses and stream powers of any landform class (Fig. 9). Slackwater zones thus fall at the bottom of the proposed hierarchy.

Spatial and temporal variation in jökulhlaup hydraulics and sediment transport

The large difference between frontal flow velocity (Fig. 4) and main body velocity is attributed to the relative decrease of form roughness with increasing discharge and hence greater flow depths. Main body velocity became faster and at peak stage, highly varied, as characterized by frequent hydraulic jumps between subcritical and supercritical flow regimes (Fig. 6a). The transition between the two regimes would have been a zone of turbulence, high-pressure and potential for high-magnitude fluvial phenomena such as cavitation and plucking (Reference Whipple and HancockWhipple and others, 2000). These zones have been attributed to the production of, for example, cataracts, gorges and bedrock steps (e.g. Reference Carrivick, Russell and TweedCarrivick and others, 2004a; Reference Carrivick and TwiggCarrivick, 2005), but precise mechanisms and hydraulic parameters of bedrock erosion remain unquantified. Supercritical flow predominates in narrow, steep channels and subcritical flow in wide, shallow reaches (Fig. 6a). However, supercritical flow also persists at some channel margins and around islands (Fig. 6a). Supercritical flow zones at channel margins in Kverkfjallarani correspond to a gap between valley floor lava flows and valley walls (Reference Carrivick, Russell and TweedCarrivick and others, 2004a), and in all cases reflect localized flow acceleration.

Peak discharge through Kverkfjallarani apparently attenuated very rapidly, due to high channel roughness where Manning’s n ∽ 0:05–0.1m^1/3 (Reference Carrivick, Russell, Tweed and TwiggCarrivick and others, 2004b). High roughness is a result of flow depths of the order of the height of form elements, in this case 1–2 m. Longitudinal energy losses were also caused by recirculation of water in backwater areas. Some of these backwaters are marginal to the main channel, for example, within tributary valley mouths (Fig. 6b), but others are caused by temporary hydraulic ponding upslope of topographic constrictions between mid-valley islands. Mid-valley islands thus caused flow acceleration, which would exacerbate streamlining processes and lateral variations in erosional capability.

Main channel flows remain relatively stable, despite rising stage, because backwaters accommodate water mass and thus help dissipate flow energy and to attenuate main channel discharge. Backwaters can also develop a surging flow, as flow laps over-bank in successive waves (Fig. 6d). Waves may also be produced from upstream ponding, as continued discharge periodically causes overtopping of shallow topography. Temporary hydraulic ponding in Kverkfjallarani could have been responsible for the deposition of valley-fill sediments (Reference Carrivick, Russell and TweedCarrivick and others, 2004a, Reference Carrivick, Russell, Tweed and Twiggb) and for longitudinal transitions between erosional and depositional zones (Carrivick, 2005). If ponding leaves palaeostage indicators (PSIs), flood reconstructions using PSIs could erroneously calculate flood hydraulics by assuming that those PSIs relate to channel flow. For example, boulder run-ups are common along Hraundalur (Reference Carrivick, Russell, Tweed and TwiggCarrivick and others, 2004b).

Suspended load comprised highly friable volcaniclastic material (Reference Carrivick, Russell and TweedCarrivick and others, 2004a, Reference Carrivick, Russell, Tweed and Twiggb), which is a feature shared by dilute lahars. This material is of relatively low density and therefore, for given clast sizes, becomes much more readily entrained than non-volcaniclastic material. Flows may thus approach hyperconcentrated rheology (∽20% sediment by volume), and suspended load transport persists over the entire hydrograph (Fig. 7). In contrast, bed load comprises 1–2m basalt boulders plucked from subaerial lava, and hyaloclastite conglomerates (Carrivick and others, 2004b). Bed load therefore ensues only after a critical entrainment threshold has been reached, but also only where a suitable supply of sediment exists. Modelled bed load appears discontinuous, in pulses and is exhausted (Fig. 7) due to transient hydraulic conditions, as described above, but also because sediment was supply-limited, both in terms of volume and calibre.

Sedimentary character therefore exerts a strong control on the hydraulics of bedrock jökulhlaups, with feedbacks between sediment entrainment, flow density, flow hydraulics, particularly bed shear stress and thus capacity for erosion. The largest Hraundalur jökulhlaup was predominantly erosional (Fig. 8). Disparate deposition occurs marginally, in association with embayment and tributary mouths, laterally as bars and terraces and within the main channel in association with topographic islands and zones of hydraulically ponded water (Fig. 8). It is suggested that deposition could occur within a channel if flow velocity is decreasing, even if absolute velocity at a point within that channel section is sufficient for transport. Therefore it is rather important for landscape change to know if flow is accelerating or decelerating through a given reach, rather than just to calculate point measurements of flow velocity. It is an important output of this paper that the modelled net gains and losses of sediment (Fig. 8) closely resemble field-mapped erosional and depositional landforms (Fig. 3), demonstrating the ability of this model to simulate rapid landscape change due to high-magnitude outburst floods.

Kverkfjöll jökulhlaups produce landforms and sediments analogous to those ascribed to the Missoula, Bonneville and Altai megafloods (Reference Carrivick, Russell and TweedCarrivick and others, 2004a, Reference Carrivick, Russell, Tweed and Twiggb, Reference Carrivick and Twigg2005). A comparison of the Hraundalur jökulhlaup hydraulics with those of the Missoula, Bonneville and Altai megafloods is given by Reference Carrivick and RushmerCarrivick (2006) and therefore is not repeated here. Rather, this paper will compare modelled Hraundalur jökulhlaup hydraulics with mapped landforms and sediments in Hraundalur, Kverkfjallarani.

Association of modelled hydraulics with field-mapped landforms and sediments

Figure 9 illustrates that a wide range of flow conditions are experienced in areas of erosional landforms, specifically gorges, scoured bedrock and cataracts. This is suggested as erosional landforms are situated within a main channel and become inundated throughout the whole duration of an outburst flood. Therefore, both high and low stage flows inundate main channel and erosional zones, giving a far greater variability in all hydraulic parameters than depositional zones, specifically valley-fill areas, bars and terraces and slackwaters (Fig. 9). In contrast, areas marginal to a main channel such as bedrock alcoves and tributary valley mouths only become inundated at high stage and with relatively low flow depths. Flow velocities are also lower in marginal areas, being well aside from the thalweg. More complex analysis of hydraulic output is required to ascribe hydrograph stage to landform generation, but some indication can be given by the maximum values recorded for each landform type. Maximum values are 1–2 orders of magnitude greater for erosional landforms than depositional landforms (Fig. 9).

By describing a hierarchy of landforms, it is suggested that a landform evolution persists due to high-magnitude outburst floods with increasing flow erosion, and thus with increasing flow energy. The exact magnitude of this flow energy is dependant upon routeway geology. In Kverkfjallarani, landform evolution due to high-magnitude outburst floods is dominated by erosion (Fig. 8), i.e. with incision and relief exaggeration, the ultimate expression of which is gorges (Fig. 9). However, all of the eroded material must end up somewhere, and the apparent disproportionate areas of deposition imply that the majority of sediment is simply flushed out of the system, beyond the mouth of Hraundalur. This has important implications for sediment delivery during periods of deglaciation (when glacier instability and meltwater production are heightened, and volcanic activity is stimulated by rapid ice-unloading) to the north-central area of Iceland, and indeed to the north coast of Iceland.