Chapter 10 The effect of topography on ash-cloud surge generation and propagation

Abstract The relationship between valley morphology and ash-cloud surge development for 12 pyroclastic density currents (PDCs) at Soufrière Hills Volcano (SHV), Montserrat is investigated. Channel slope, sinuosity and cross-sectional area were measured from high-resolution digital elevation models (DEMs) using geographical information system (GIS) software; and were compared to geometric parameters of the deposits. The data illustrate three surge-generation regimes: a proximal area of rapid expansion; a medial deflation zone; and a steadier distal surge ‘fringe'. The extent to which these regimes develop varies with flow volume. For larger flows, within the proximal and medial regimes, a strong inverse correlation exists between surge detachment and valley cross-sectional area. Surge detachment is also correlated with observed and modelled flow velocities. Areas of topography-induced increases in velocity are interpreted to result in more pervasive fragmentation and fluidization, and thus enhanced surge generation. Distally, surge deposits appear as fringes with decaying extents, indicative of more passive expansion and decreasing velocity. The results indicate that surge mobility and detachment are a complex product of flow mass flux and topography, and that future efforts to model dense–dilute coupled flows will need to account for and integrate several mechanisms acting on different parts of the flow.

The development and subsequent decoupling of dilute, turbulent ash-cloud surges from dense basal pyroclastic flows is poorly understood, unpredictable and often results in deadly consequences. Ash-cloud surges can have a significant lateral component of motion, and have been known to detach and move independently from their parent flows (Fisher 1995). For example, decoupled pyroclastic surges were responsible for fatalities at Mt Pelée, Martinique in 1902 (Fisher & Heiken 1982); Unzen, Japan on 3 June 1991 (Yamamoto et al. 1993); at Soufrière Hills Volcano (SHV), Montserrat on 25 June 1997 (Loughlin et al. 2002a, b); and at Merapi Volcano, Indonesia on 18-19 December 1930, 22 November 1994and October -November 2010(Bourdier & Abdurachman 2001Smithsonian Institution 2011;Jenkins et al. 2013). Several of these events, and their resultant deposits, have been well described and their dynamics analysed in detail retrospectively. However, it remains the case that a more generalized understanding of how such dense -dilute coupled flows behave and propagate given an array of likely eruption scenarios and terrain characteristics is still beyond our capabilities.
A variety of geophysical flow models exist for simulating the dense concentrated parts of pyroclastic density currents (PDCs) (Sheridan et al. 2004;Kelfoun & Druitt 2005;Patra et al. 2005;Kelfoun et al. 2009) or for simulating the dilute ash-cloud surges (Ishimine 2005). However, because these models use simplified rheological laws that capture the bulk flow behaviour, they cannot model the dense basal avalanches and ash-cloud surges as a coupled dense -dilute system. Complex multiphase models that capture the dynamics of both the turbulent fluid and the intergranular interactions within PDCs have the potential to model the decoupling of surges (e.g. Takahashi & Tsujimoto 2000;Todesco et al. 2002;Dartevelle et al. 2004;Valentine et al. 2011), but these models are computational expensive and, as such, are currently impractical for use in many hazard mapping applications.
In contrast, mapping tools based on simplified empirical relationships, such as LAHARZ or PYROFLOW, have shown success (Wadge et al. 1998;Wadge 2009;Widiwijayanti et al. 2008) at both simulating the expected inundation from dense basal avalanches and, to a first order, delineating the probable ash-cloud surge extent. These models have the advantage of being computationally simple, making them more suitable for use in hazard mapping during ongoing volcanic crisis. Several simple methods have been employed to estimate the ash-cloud surge delineation. Widiwijayanti et al. (2008) used a horizontal buffer of uniform distance applied to the modelled dense basal avalanche. The buffer distance was determined by statistically analysing mapped deposits, and setting the buffer distance equal to 90 (700 m wide) and 50% (500 m wide) confidence limits. Wadge et al. (1998), Wadge (2009) and Widiwijayanti et al. (2008) also employed a simple one-dimensional (1D) model for lateral motion of the ash-cloud surge from the dense basal avalanche. The model considers the sedimentation of clasts and entrainment of air as the surge moves laterally away from the dense basal avalanche; therefore the limits of surge inundation are drawn where the bulk density of the surge falls below that of ambient air. They do not, however, capture the complex physics associated with flow emplacement, and, in cases where they have been applied, the need for improved reliability in delineating ash-cloud surge inundation has been highlighted (SAC 2007).
Our understanding of these coupled flows remains very incomplete. For development of dense -dilute coupled geophysical models, the key processes to be incorporated can be guided by observed field relationships between dense basal avalanches, ash-cloud surges and topography. A number of field studies investigate the morphology and granulometry of single events in great detail (e.g. Loughlin et al. 2002b;Charbonnier & Gertisser 2008;Komorowski et al. 2010;Lube et al. 2011;Komorowski et al. 2013), but few aggregate many events in order to extract general information and investigate similarities and differences between PDCs. Complex field relationships that result from the spatial and temporal variability of PDCs need to be reliably distilled in order to understand key physical processes which apply generically and which can be incorporated into dense-dilute coupled models. In this work, we characterize the effect of topography on PDC deposit distribution, with the objective of gleaning a better understanding of ash-cloud surge-generation and detachment mechanisms associated with block-and-ash flows (BAFs) from lava-dome collapse. Our work addresses the need to extract generic relationships by comparing the ash-cloud surge-inundation patterns of several events, a number of which actually inundate the same drainage systems. Commonalities between these events in the same drainage provide the framework for a generic topography-based model, while discrepancies between the events observed here highlight the important role of PDC volume and/ or mass flux. It is envisaged that the relationships found here can be utilized to inform models that deal with ash-cloud surge generation, ranging from those that involve complex geophysics to those that are empirically based.

Previous work
First, we clarify our use of terminology: PDCs are understood to be density-stratified currents (Valentine 1987), which, to varying degrees, develop high concentration, dense undercurrents (pyroclastic flows or dense basal avalanches) and dilute, turbulent, overriding ash clouds (pyroclastic surges or ash-cloud surges). PDCs may form from lava dome collapses, such as at Unzen (Yamamoto et al. 1993;Fujii & Nakada 1999), and Merapi (Voight et al. 2000;Bourdier & Abdurachman 2001); from column collapses, such as at Mount Vesuvius, Italy (Bullard 1962;Lirer et al. 1973); or from directed blasts as at Mount St Helens, Washington, USA (Kieffer 1981;Moore & Sisson 1981); and the Boxing Day event at SHV Voight et al. 2002). This work largely deals with PDCs generated by lava-dome collapse, but also includes two events that are, to some degree, transitional and include an explosive component. Thus, we refer to the high concentration undercurrent as the dense basal avalanche and the overriding dilute component as the ash-cloud surge. We also use the term BAF to refer to the entire PDC generated from lava-dome collapse; this encompasses both the dilute and dense components. The detached pyroclastic surge area is the area inundated by the ash-cloud surge outside the footprint covered by the dense basal avalanche. The total ashcloud surge area is thus the area covered by the dense basal avalanche plus the detached pyroclastic surge area. A number of processes have been proposed to contribute to the generation of ash-cloud surges and these include: (1) elutriation of fine particles and gas from the basal avalanche (Fisher 1979;Wilson 1980); (2) entrainment of ambient air into the flow and subsequent thermal expansion of the mixture (McTaggart 1960;Sparks 1976;Wilson & Walker 1982); (3) particle collision and disintegration (comminution and release of gas from pressurized clasts) (Sparks et al. 1978;Fujii & Nakada 1999;Dufek & Manga 2008); (4) turbulent diffusion across a boundary layer (Denlinger 1987;Burgisser & Bergantz 2002); and (5) explosive decompression of the pressurized dome (Woods et al. 2002). Conversely, Doyle et al. (2008) modelled dense basal avalanches as developing out of dilute currents through mass transfer by sedimentation to the base of the current. With respect to ash-cloud surge generation specifically associated with BAFs, several studies (Ishida et al. 1980;Denlinger 1987;Fujii & Nakada 1999) have proposed models with an intermediate fluidization zone between the dense basal avalanche and the ash-cloud surge. Ash-cloud surge generation is thus considered within a framework of particle transport (by upwards gas flow or interparticle collisions) from the basal avalanche into the intermediate fluidization zone, followed by the subsequent turbulent suspension of fluidized particles into the ash-cloud surge.
Decoupling of pyroclastic surges has been well documented and a range of behaviour noted. Ash-cloud surges are known to detach and overrun dense basal avalanches after traversing a break in slope, as at Mount Ngauruhoe, New Zealand (Nairn & Self 1978), Santiaguito Volcano, Guatemala (Rose et al. 1977), and Merapi (Bourdier & Abdurachman 2001;Lube et al. 2011;Jenkins et al. 2013). Surges may separate from valley-confined flows when steep topography or barriers are encountered, as was Cross-sectional profiles were extracted every 100 m (dashed profiles ¼ 500 m), with the inset showing a representative cross-sectional profile. BAF widths were measured across the 100 m profile lines used to measure the underlying channels (black solid and dashed lines). Areas were measured by dividing the BAF into segments using the profile lines, and measuring the area of each segment between the profile lines. The black box shows the detached surge area measured for the 1500 m profile line.  (Yamamoto et al. 1993;Fujii & Nakada 1999) and SHV (Loughlin et al. 2002b). For the 25 June 1997 SHV BAF described in detail by Loughlin et al. (2002b), detachment of ash-cloud surges was found to occur at valley bends and constrictions, and was related to the slope of the channel, and was enhanced by depositional filling. Cole et al. (2002), analysing data collated from 14 SHV flows, found  that there was no evident relationship between the percentage area covered by the detached ash-cloud surge deposit and the total volume of the BAF deposit; that is, large-volume BAFs did not necessarily produce relatively more extensive surge deposits than did small-volume flows. In view of this, surge development and extent was attributed to variations in topographical effects, temperature and dome pore pressure. Steep valley slopes were suggested to enhance air entrainment, resulting in the heating and thermal expansion of the surge cloud, and valley volume capacity was related to the ability of channels to contain the ash-cloud surges. High pore pressures in collapsing dome rock sourced from deep within the dome (as opposed to the collapse of degassed dome carapace) have been invoked by a number of authors to explain surge development by generating large quantities of fine ash (e.g. at Unzen, Sato et al. 1992;at Merapi, Bourdier & Abdurachman 2001;Komorowski et al. 2013;and at SHV, Cole et al. 2002;Loughlin et al. 2002b;Woods et al. 2002). However, at Merapi, surge detachment was also shown to be highly volume-dependent, with large-volume, long-runout BAFs most likely to produce detaching surge clouds (Bourdier & Abdurachman 2001). Analysis of ash-cloud surge detachment from BAFs during the June 2006 eruption at Merapi showed a more passive channel overflow process controlled primarily by valley crosssectional area, rate of channel confinement (the change in crosssectional area with distance) and channel sinuosity (

Valley morphology
Using GIS software in conjunction with digital elevation models (DEMs) allows for the rapid, precise and reproducible measurement of channel morphology. Multiple DEMs exist for the island of Montserrat, with horizontal spacings of 1-10 m and vertical resolutions of 15 cm -10 m (Table 10.1) (Wadge & Isaacs 1988;SAC 2011). GIS tools allow for the precise and hydrologically correct delineation of stream networks, as well as true 'pathlength' measurements that fully account for sinuosity and elevation changes. Five primary drainage systems were investigated in this work ( Fig. 10.1): the Belham Valley, Mosquito Ghaut, Tuitt's Ghaut, the Tar River Valley and the White River Valley. Longitudinal valley thalweg profiles were extracted for each drainage, with average valley slopes ranging from about 4 to 108. A series of latitudinal (cross-sectional) profiles measured at 100 m intervals were also collected for each valley ( Fig. 10.2). The cross-sectional profiles were drawn with intentionally liberal lengths (0.5 -1 km) in order to fully capture the geometry of adjacent channel banks. While these cross-sectional profiles appear to intersect in Figure 10.2, the actual profile data were limited during processing to only include the bank-to-bank profile information. Valley depth, width, wetted perimeter, cross-sectional area and sinuosity were measured for each profile. A summary of the average valley characteristics can be found in Table 10.2. The Tar River Valley is the steepest, with an average slope of 108, and also broadest, but it is relatively straight (low sinuosity). The Belham Valley, of particular importance for hazard management because of its proximity to an inhabited residential zone and the Montserrat Volcano Observatory (MVO), is relatively long, sinuous and shallow, with an average slope of only 5-68.

Temporal changes
By comparing DEMs from different periods, it is possible to identify areas of time-averaged erosion or deposition. Elevation gains (deposition) and losses (erosion) over the last 15 years can be seen in Figure 10.3. While small geolocation errors result in minor gains and losses appearing over the entire map, it is obvious that areas inundated by PDCs (the hashed region in Fig. 10.3) have experienced net gains of as much as 100-140 m in elevation due to deposition, especially in proximal areas. The formation of new coastline is also apparent, especially where the Tar River Valley, Tuitt's Ghaut and the White River Valley reach the sea. Topographical changes during an ongoing eruptive crisis can have important hazard implications, as in-filled valleys are less able to contain subsequent flows and steeper average drainage slopes can increase flow mobility. These changes are also important to note for modelling purposes. Many mass-flow models simulate flows over natural terrain using DEMs, and the uncertainty due to the DEM collection method, interpolation method, resolution and post-DEM topography changes should be considered (e.g. Darnell et al. 2010;Stefanescu et al. 2010a, b). The average valley measurements for the Belham Valley in Table 10.2 record the changes in valley characteristics between subsequent DEMs. The Belham Valley has steepened from an average slope of 5.648 in 1995 to 5.988 in 2010, narrowed by 127 m on average, and shallowed by an average of 25 m due to deposition, mainly in the proximal areas (Tyer's Ghaut area). Tyer's Ghaut has more than 30 m of infill in some locations with total volumetric infill of the order of 5.8 Â 10 6 m 3 ).

Pyroclastic flow and ash-cloud surge deposits
Overview Since the beginning of the eruption, there have been approximately 50 BAFs with volumes .1 Â 10 6 m 3 and 15 BAFs with volumes .5 Â 10 6 m 3 . There are 20 events, ranging in volume from 0.2 Â 10 6 to 210 Â 10 6 m 3 , with mapped deposits. Twelve of these mapped flow deposits were chosen for this study (Table 10.3). Only BAFs originating from dome-collapse events or predominantly dome-collapse events were included. Some events were excluded due to lack of separate basal avalanche and ash-cloud surge maps (e.g. 17 September 1996), lack of channelization for much of the flow (no corresponding valley to measure, e.g. 3 August 1997), because they had a major lateral blast component (e.g. 26 December 1997, 3 December 2008) or because a significant portion of the flow entered the sea (e.g. 20 May 2006, 12 July 2003). The 8 January 2010 event was included despite also being associated with a Vulcanian explosion because it exhibited characteristics that were somewhat transitional in nature between typical pumice flows from Vulcanian fountain collapse and typical BAFs. Pumice clasts accounted for only 5 wt% by volume of the deposits and, while an eruption column reached 8.3 km, the PDC was sourced from the dome summit . The 8 January 2007 event may have had similar origins as it also contained minor pumiceous component (Hards et al. 2008;Loughlin et al. 2010). Furthermore, the morphology of these flow deposits resembled the BAFs from domecollapse events included in this study. These events also represent the only flows to inundate the Belham Valley, which, from a hazards perspective, is especially important to investigate.  The 25 June 1997 surge-derived flow (while included in the figures herein to avoid distortion of the deposit maps) was not measured as part of the ash-cloud surge, as this part of the flow exhibited a unique generation mechanism and different flow dynamics to the rest of the surge (Druitt et al. 2002;Loughlin et al. 2002b). The 21 September 1997 BAF entered two valleys; most of the flow was contained within Tuitt's Ghaut, but some of the BAF entered White's Ghaut. The volume distribution between these valleys is unknown, and BAF measurements were primarily compared to those from Tuitt's Ghaut. Flows from both discrete single-pulse events and sustained dome collapses were included. Discrete events were generally smaller in volume, and consisted of only one pulse or package of flow material (e.g. 5 June 1997). Sustained dome collapses lasted up to 9 h and usually produced large-volume BAFs with many pulses (e.g. 25 June 1997, 21 September 1997).
All the BAFs studied herein are well constrained by volume estimates (with most having separate volume estimates for the dense basal avalanche and the ash-cloud surge components), inundated areas and height/length (H/L) mobility measurements (Table 10.3). Apart from volumes and height dropped, which were extracted from several different sources 2010a;Hards et al. 2008;Loughlin et al. 2010), all other values were measured using tools within ArcGIS. Because lengths and areas were measured automatically with GIS tools,  (a, b), the sustained surge area is highly negatively correlated with the valley cross-sectional area; that is, the area of detached surge is highest where the valley is narrowest. For small-volume or discrete BAFs (c), the detached surge area is slightly positively correlated with the valley cross-sectional area; that is, the surge spreads to fill the confines of the valley, but does not spill out. September 1997 BAF entered more than one valley, the correlation around the detached surge peak (D.S.P.) is therefore also shown. Fig. 10.10. The critical valley cross-sectional area is dependent on BAF volume. When the channel constricts below the critical cross-sectional area, the ash-cloud surge often detaches from the dense basal avalanche. The critical cross-sectional area is approximately 1 Â 10 23 of BAF volume. The 21 September 1997 BAF (indicated) entered two valleys, with its volume distributed between the two channels. they differ slightly from older published values that used other measurement techniques, usually on paper maps. The volume of the BAFs deposits included in this study range from 0.2 Â 10 6 to 14.3 Â 10 6 m 3 .
Of critical importance to predicting surge detachment and inundation is the volume partitioning that occurs between the dense basal avalanche and the ash-cloud surge. This partitioning is a complex and poorly understood phenomena that probably depends on many factors, including the explosivity of the eruption, the overpressurization of dome rock, and the size and lithology of the particles involved. Large-volume BAFs do not necessarily produce extensive detached surge deposits ( Fig. 10.4a). However, a relationship is observed between the total ash-cloud surge area and the dense basal avalanche volume ( Fig. 10.4b); that is, large-volume dense basal avalanches produce ash-cloud surges that cover extensive areas. Voluminous surge clouds are also more likely to detach significantly ( Fig. 10.4c). Likewise, dense basal avalanches that cover extensive areas are more likely to have large detached surge areas ( Fig. 10.4d). It is therefore difficult to estimate what area might be impacted by a detached surge based only on the BAF collapse volume, but large-volume dense basal avalanches that cover extensive areas are more likely to have ash-cloud surges that detach significantly and cover large areas. This points to possible topographical controls on the detachment of surges, instead of merely volume control.
In addition to the measurements in Table 10.3, each deposit was measured along the 100 m-spacing latitudinal profile lines used to measure valley topography. The width of the deposits of the dense basal avalanche and ash-cloud surges were measured at each profile, and respective inundation areas were also measured for each area segment (areas between two consecutive profile lines) (Fig. 10.2). The maximum elevation and average slope (extending laterally away from the valley axis) over which the ashcloud surge passed was also recorded for each profile. The deposit measurements for all 12 studied deposits were then compared to the cross-channel measurements of the valleys from the appropriate pre-event DEM. For example, the 5 June 1997 deposit measurements were compared to the 10 m DEM of 1995. For illustrative purposes, the relationships found for all studied events are shown in the following figures using only a subset of the events (the 8 January 2010, 25 June 1997 and 5 June 1997 flows), as these provide the clearest examples of the findings discussed throughout.

Deposit morphology
From the ash-cloud surge deposit distributions, several features are immediately apparent. For moderate-to large-volume (.1 Â 10 6 m 3 ) events (which are usually sustained collapses in nature), the data identify three dominant surge regimes: (1) a rapid proximal zone of surge expansion and detachment; (2) a medial deflation zone where the surge extent rapidly diminishes; and (3) a steadier, decaying, distal surge 'fringe' (Fig. 10.5). Proximally (region 1) and medially (region 2), the surge can overspill the channel and spread laterally from the main flow. Alternatively, it  can detach completely and travel in other quite different directions, as happened on 25 June 1997 (Fig. 10.5b). Region 1 and 2 also correspond to the tree blow-down zone and building damage recorded for some events, which indicate dynamic pressures .7 kPa (Cole et al. 2002). Distally (region 3), the surge appears as a narrow fringe adjacent to the dense basal avalanche, and usually remains channelized (e.g. 8 January 2010, Fig. 10.5a), sometimes overtopping channels by a few tens of metres around bends in the channel (e.g. 25 June 1997, Fig. 10.5b). Trees in the distal area remain standing, indicating dynamic pressures ,3 kPa (Cole et al. 2002).
For small-volume (,1 Â 10 6 m 3 ) or discrete pulse events (e.g. 5 June 1997), there is often a small proximal region (region 2) of surge detachment that persists for a few hundred metres. Distally (region 3), however, the surge deposits are minimal and only detach from the dense basal avalanche around channel bends (Fig. 10.5).
These proximal, medial and distal surge regimes are compared with both peak surge detachment and valley slope in Figure 10.6 for the 8 January 2010 event. On slopes greater than 108 (region 1), surge detachment increases until it reaches peak surge detachment at around 108; on slopes from 5 to 108 (region 2), the slope detachment decreases until it reaches the beginning of the surge 'fringe' (the distal region) at around 58 (region 3); and on slopes less than 58 (region 3), the surge is present only as a narrow fringe. These relationships are observed for all the moderate-to large-volume events.
The cumulative curves for the detached surge area along the flow path for all the events in this study do show some variations ( Fig. 10.7). The first-order distinction between surge development and detachment patterns suggests systematic differences between the moderate-to large-volume or sustained events and the smallvolume or discrete events. Moderate-to large-volume events clearly show the three surge regions outlined above, whereas the curves for small-volume events only exhibit the declining surge inundation (region 2) and the distal surge 'fringe' (region 3) (Fig. 10.7).

Valley cross-sectional area
The data show a strong negative correlation between valley crosssectional area and detached surge area for the 8 January 2010 and  (Calder 1999) except where noted. † Loughlin et al. (2002b). This is the velocity of the pyroclastic flow in the corresponding region, not the velocity of the pyroclastic surge. ‡ Molle (2012). 25 June 1997 events (Fig. 10.8a, b); that is, the area of detached surge is greatest where the valley is most constricted. This relationship is observed for all moderate-to large-volume or sustained events (Fig. 10.9), except for the 30 March 1997 BAF in the White River Valley. This flow was the first to inundate the White River Valley, the deepest recorded valley (Table 10.2). Because the 21 September 1997 BAF entered more than one valley, it was more difficult to relate detached surge area to crosssectional area along the entire length of the flow. For this reason, the area around the detached surge peak was correlated with crosssectional area and also plotted in Figure 10.9. A critical crosssectional area can also be identified from this data. The surge detaches from the dense basal avalanche where the valley crosssectional area falls below 1200 m 2 for the 8 January 2010 BAF and 6800 m 2 for the larger-volume 25 June 1997 BAF. There is a strong correlation between critical cross-sectional area and BAF volume for all moderate-to large-volume BAFs (Fig. 10.10). The critical cross-sectional area is approximately 1 Â 10 23 of the BAF volume. The detached surge area from the 5 June 1997 event is either not correlated or is very weakly positively correlated with the valley cross-sectional area (Fig. 10.8c); that is, the surge expands within the valley, but does not spill out. This was the case for all other small-volume events investigated herein (Fig. 10.9).
The extent of topography surmounted by the detached ashcloud surges is another parameter of interest. Therefore, the maximum elevation that the 8 January 2010 and 25 June 1997 surges surmounted at each latitudinal profile line was determined ( Fig.  10.11). This maximum surge elevation profile was then compared with the valley thalweg profile, valley bank profiles, and longitudinal stream profiles (contour lines parallel to the valley thalweg) at 20 and 50 m above the valley thalweg. In essence, the 20 and 50 m contours represent the positions of hypothetical surge clouds with a uniform thickness of 20 or 50 m, if the surge merely filled topography as it descended the drainage. Choosing somewhat arbitrary horizontal or vertical distances from the valley thalweg is a common method of estimating possible surge indunation limits. The difference between the actual maximum surge elevation profile, the maximum valley bank and the longitudinal stream profiles highlights areas where the surge surmounted significant elevation and was not simply infilling topography. For moderate-to largevolume events, the maximum detached surge area is colocated with peaks in surge elevation (Fig. 10.11).

Sinuosity
Detached surge area was also compared to valley sinuosity. Sinuosity was measured at each 100 m-spacing latitudinal profile line, by measuring both the straight-line and along-valley length for the preceding 200 m section. Sinuosity is given as the ratio of the along-valley distance divided by the straight-line distance. The data show a possible relationship between valley sinuosity and the 25 June 1997 detached surge area (Fig. 10.12), and identify a peak in sinuosity preceding the peak detached surge. For many moderate-to large-volume events, there was a possible relationship between peak sinuosity and peak detached surge. The peak in sinuosity (valley bend) either preceded the peak surge detachment by approximately 100 m or coincided with the peak surge detachment. Loughlin et al. (2002b) identified the same valley bend preceding the detachment of the ash-cloud surge. Comparing sinuosity to deposit metrics was difficult for several reasons: the maximum valley sinuosity (the biggest valley bend) often occurred in more distal regions and did not, therefore, correspond to any changes in surge detachment (i.e. White River Valley events). Many small -moderate BAFs were not mobile enough to encounter these distal valley bends, and large-volume BAFs had probably decelerated to such a degree that even large increases in sinuosity could not produce surge detachment. The effect of sinuosity on surge detachment is, therefore, also highly dependent on other factors such as PDC velocity and thickness. Some valleys did not show appreciable sinuosity (i.e. Tar River Valley).  Calder (1999) and Loughlin et al. (2002b). (c) The 5 June 1997 detached surge area with observed velocity estimates from Calder (1999). See Table 10.4 for observed velocity specifics, and Table 10.5 for TITAN2D model parameters. Proximal (1), medial (2) and distal (3) flow regimes are noted. D.S.P., detached surge peak; E.D.S., end of major detached surge.

Velocity
Comparing PDC velocity profiles with ash-cloud surge distribution would probably be informative; however, velocity estimates are notoriously difficult to obtain, and exist only for a few events (Table 10.4). In many cases, the velocities are averaged over the entire flow path or averages are obtained for discrete sections of the flow path. The 12 May 1996 event, for instance, has velocity estimates for two 0.2 km sections along the flow path (in addition to a flow path average velocity), but these estimates only occur in the distal regions of the flow, with no estimates of velocity near the peak in ash-cloud surge detachment (Calder 1999). However, a few events have enough data to make useful comparisons (Table 10.4). The 8 January 2010 event has a few preliminary velocity estimates obtained from video analysis (Molle 2012) (Fig. 10.13a); the 25 June 1997 event has several point velocity estimates for the second and third flow pulses, as well as an average estimate of the proximal surge velocity (Loughlin et al. 2002b) (Fig. 10.13b); and the 5 June 1997 event has several segments with average velocities obtained from video and seismic signal analysis (Calder 1999) (Fig. 10.13c). As seen in Figure 10.13, observed velocity estimates show a strong positive correlation with detached surge area for moderate-to large-volume events. That is, in areas where the dense basal avalanche velocity was at a maximum, the ash-cloud surge was vigorous and spilled out of the valley confines.
Another possibility for comparing flow velocity to ash-cloud surge detachment is to model the dense basal avalanche using a physical flow model and to extract the modelled flow velocities. TITAN2D is a computational model that solves depth-averaged conservation equations for granular flows using a DEM (Patra et al. 2005). TITAN2D can use known flow parameters (volume, collapse location and basal friction angles from H/L measurements) to simulate mapped dense basal avalanches. Although TITAN2D does not model the ash-cloud surge, information about how the dense basal avalanche interacts with topography is useful when considering surge dynamics. Using the model, unknowns such as basal avalanche flow thickness, velocity and centre of mass can be approximated. The simulations closely replicate flow volume, centre line and coverage of mapped flows, and also generally agree with the limited data that are known about basal avalanche thickness and velocity. In the absence of other velocity data, or in addition to sparse data, TITAN2D can provide velocity approximations for the entire length of flow runout. Seven flows were modelled using TITAN2D with appropriate input parameters (Table 10.5). The TITAN2D modelled velocities in Figure 10.13 are the maximum velocities reached during the simulation at each profile, and show the same general trend in velocity evolution as compared with observed velocity estimates for a number of flows, but there also are considerable differences. In proximal regions, TITAN2D velocities are often tens of m s 21 higher than observed velocity estimates ( Fig. 10.13a, b). TITAN2D probably overestimates the proximal flow velocities, but, because of poor visibility, it is assumed that proximal observed velocity estimates underestimate actual flow velocities, especially on the upper flanks of the volcano (Loughlin et al. 2002b). The error estimates in Table 10.4 reflect this, with proximal velocity observations having the largest errors. It is also important to note that the velocities from TITAN2D are maximum velocities reached by any part of the flow during the simulation, whereas estimates from observations are minimum or average flow front velocities. In fact, Simpson (1987) estimated that the flow front travels at only 60% of the maximum speed achieved within the main flow body, which would account for the differences between TITAN2D modelled velocities and observations. Comparing TITAN2D and observed velocities with detached surge areas shows a general positive correlation between velocity and detached surge area (Fig. 10.13), with the highest velocities colocated with the maximum detached surge. Our results show that a line representing 60% of the modelled (maximum) flow velocities correlates well with the estimated flow front velocities. However, TITAN2D does not show all of the variations and peaks in local velocity that observations record because of the differences in measuring maximum flow velocity v. minimum or average flow front local velocities.

Discussion
A number of channel morphology parameters were compared to detached surge areas, including channel slope, width, depth, wetted perimeter, cross-sectional area and sinuosity. Valley width and depth had no consistent correlation with surge detachment, nor did any ratio of width to depth; while slope, wetted perimeter (not discussed as it is related to cross-sectional area, see Fig. 10.2), cross-sectional area and sinuosity all affect surge morphology and detachment. The results here are consistent with the findings of Loughlin et al. (2002b) for the 25 June 1997 event, of Lube et al. (2011) for the June 2006 Merapi BAFs, and of Charbonnier et al. (2013) and Komowoski et al. (2013) for the October-November 2010 Merapi PDCs, but highlight the extent to which these relationships can be generalized.
The data identify three dominant regimes of surge generation for moderate-to large-volume BAFs: (1) a rapid proximal surge expansion and detachment on slopes greater than 108; (2) a medial decline in surge expansion after the peak surge detachment on slopes from 5 to 108; and (3) a more uniform distal surge 'fringe' on slopes less than 58. Breaks in slope have been proposed as a major driving factor in the development and detachment of surges at Merapi, with significant detachment and decoupling occurring as BAFs flow across the break in slope at the foot of the cone, an area composed of cliffs and a slope that rapidly changes from .308 in the proximal 1.5 km to less than 158 from 1.5 to 2 km (Bourdier & Abdurachman 2001;Charbonnier & Gertisser 2008Lube et al. 2011;Jenkins et al. 2013). Valley slopes on Montserrat tend to change more gradually, but, even so, there is a general relationship between slope and surge generation and detachment. An inverse correlation exists between surge detachment and valley cross-sectional area for all moderate-to large-volume BAFs; that is, valley constrictions greatly promote surge detachment. Once a valley constricts below a critical cross-sectional area, surges overspill the channels and inundate large areas. This critical cross-sectional area is, naturally, dependent on the volume (or, more specifically, mass flux) of the BAF; for instance, the critical cross-sectional area is about 1200 m 2 for the 8 January 2010 event and 6800 m 2 for the 25 June 1997 event. In fact, critical cross-sectional area appears to be roughly 1 Â 10 23 of BAF volume. Sustained events, consisting of multiple pulses that progressively infill channels and reduce cross-sectional area, are thus most likely to experience significant surge detachment. For hazard-mapping purposes, one could identify critical channel constrictions for a range of BAF volumes in order to predict where ash-cloud surges are likely to overspill the channels. An example of this type of mapping is shown in Figure 10.14. Critical cross-sectional areas were identified for three flow volumes (1 Â 10 6 , 5 Â 10 6 and 10 Â 10 6 m 3 ), and regions of the Belham Valley where this critical cross-sectional area is exceeded were indicated. This information is useful for indicating where ashcloud surges are likely to detach, and shows that the 'danger area' for surge detachment migrates downstream with larger flows. It is important to note that these examples do not consider flow runout. For example, Figure 10.14c, which maps areas where the critical cross-sectional area is exceeded for a 5 Â 10 6 m 3 volume flow, shows a red zone at the most distal reaches of the Belham Valley. A flow of this size is, however, unlikely to actually reach these areas. Small-volume BAFs show surge detachment only within the first few hundred metres of the flows, which then decreases rapidly, and some minimal surge detachment around valley bends in more distal regions. Valley cross-sectional area plays a minor role in surge detachment for small-volume events where the flows are almost completely contained within the channels.
This negative correlation between valley cross-sectional area and detached surge area makes intuitive sense; surges spill out of narrow or shallow channels and travel laterally, often surmounting steep slopes and gaining elevation. As valleys are progressively in-filled by successive pulses from sustained collapses, the extent of channel overspilling can increase with time through a sustained event. This corresponds with the findings of Loughlin et al. (2002b), which showed that valley constrictions and depositional filling of channels contributed to the ash-cloud detachment during the 25 June 1997 event. However, comparing the elevations traversed by detached surges with valley-bank and longitudinal-stream profiles shows that the surges are far from simply in-filling topography in the proximal and medial zones (regions 1 and 2). High-velocity surges often surmount steep slopes and gain elevation beyond that which would be expected for a surge of uniform thickness infilling topography. This is especially so at areas of peak surge detachment. This is consistent with experiments by Andrews & Manga (2011), which showed that flows were able to surmount obstructions up to 1.5 times the current thickness, and that barriers less than this height serve to enhance air entrainment and buoyancy. In distal areas (region 3), however, the surges appear as narrow fringes that, to a first order, do fill topography. However, even in distal regions, surges do gain elevation and detach more vigorously at valley bends, which is particularly important for assessing the hazard to communities along the distal reaches of the Belham Valley.
In addition, pyroclastic surge detachment does not seem to be merely a function of BAF volume, although volume certainly plays a role. Surge detachment does seem to have a relationship with surge volume (as opposed to total BAF volume), suggesting that processes that drive surge formation (e.g. elutriation, comminution, entrainment) play a significant role in the decoupling Fig. 10.14. Areas in the Belham Valley where critical cross-sectional areas were exceeded (red areas) for three BAF volumes (1 Â 10 6 (a), 5 Â 10 6 (b) and 10 Â 10 6 m 3 (c)). These maps show an example of how the relationship between BAF volume and critical cross-sectional area could be used for mapping areas where surge detachment is likely. of pyroclastic surges. We recognize that other factors such as dome pressurization, explosivity, and particle size and lithology may also influence the generation, but detailed investigations of these aspects are beyond the scope of this work. Observational and modeled pyroclastic flow and surge velocities show a correlation with surge detachment. A relationship exists between experimental flow velocity and comminution of ash from pumice blocks (Cagnoli & Manga 2004;Dufek & Manga 2008). Collisions among highly pressurized clasts can release gas and ash, and promote the fluidization of fine particles (Fujii & Nakada 1999). Areas of inferred topography-induced increases in velocity could result in more numerous or vigorous particle collisions, causing more particles to become fluidized, ultimately enhancing surge generation.
From these data, we propose the following conceptual model for ash-cloud surge development and detachment.
Proximally (region 1), vigorous surge expansion is probably due to a combination of high velocities due to steep slopes, and auto-brecciation processes and explosive expansion of pressurized dome rock during collapse. The surge reaches a maximum detached surge area when the valley constricts below a critical, volume-dependent, capacity. Here, passive overflow processes combine with more active velocity-and constriction-induced increases in interparticle collisions to contribute to the vigorous detachment of the surge. After the surge reaches a maximum detachment, the expansion decreases as the valley slope shallows and the valley broadens in the medial region 2. Building damage and tree blow-down in regions 1 and 2 indicate dynamic pressures .7 kPa (Cole et al. 2002). Distally (region 3), the ash-cloud surge deposits appear as narrow fringes around the dense basal avalanche deposits, indicative of more passive expansion of elutriated fines from the basal avalanche and subsequent lift-off. In this region, the ash-cloud surges expand to fill topography, sometimes spilling out of channels around valley bends. Damage to trees is minimal, indicating dynamic pressure ,3 kPa (Cole et al. 2002).
Small-volume flows exhibit only the characteristics of regions 2 and 3. Some surge detachment occurs in the proximal 0.5-1 km, but this appears to be directly related to collapsing dome rock, as the surge expansion declines rapidly from the start of the deposit. In this regard, the proximal surge detachment for smallvolume flows resembles region 2, as described above. In region 3, there is minimal surge detachment, only around valley bends. Small-volume events simply fill topography.

Concluding remarks
Relatively few available numerical models attempt to simultaneously capture the behaviour of both the dense and dilute parts of lava dome-collapse PDCs (Denlinger 1987;Fujii & Nakada 1999;Burgisser & Bergantz 2002;Doyle et al. 2008). Some simulation tools exist for modelling coupled dense -dilute flows using Lagrangian methods (e.g. Takahashi & Tsujimoto 2000;Todesco et al. 2002;Dartevelle et al. 2004;Valentine et al. 2011), but these models are complex and computationally expensive. Other computational models exist to model the dense basal avalanche (Kelfoun & Druitt 2005;Patra et al. 2005;Kelfoun et al. 2009) or the ash-cloud surge separately (Ishimine 2005). Simpler empirical models have also shown success (e.g. Wadge et al. 1998;Wadge 2000;Widiwijayanti et al. 2008), but have similar limitations for modelling both the coupling of the pyroclastic flows and surges. Using these models for hazard mapping can therefore be problematic, as potential surge inundation limits are typically drawn in as a uniform lateral buffer around the modelled dense basal avalanche (e.g. Ogburn 2008;Widiwijayanti et al. 2008) or estimated with simple models for lateral motion (e.g. Wadge et al. 1998;Wadge 2000;Widiwijayanti et al. 2008). The models for lateral motion assume that a uniform percentage (10%) of the dense basal avalanche is elutriated to form the surge, which seems unlikely given the data presented herein. In distal region 3, where the surge exists as a narrow 'fringe' around the dense basal avalanche and generally fills topography by passive lateral expansion, these methods might be reasonable approximations. In fact, we have shown that a 'vertical buffer', determined by calculating longitudinal-stream profiles parallel to the valley thalweg and whose height is based on BAF volume, captures the detached surge area in region 3 quite well. However, horizontal or vertical buffers and 1D models that assume a uniform surge elutriation percentage would not predict the detached surge areas in the proximal and medial regions 1 and 2, where the surge expands rapidly, spills vigorously from constrictions and surmounts steep topography. Here, the surge is not merely filling topography or passively expanding. Instead, the communition of ash and the release of gas from colliding particles of high pore pressure dome rock leads to the generation of violently expanding turbulent ash-cloud surges with capabilities of reaching high lateral velocities. In this region, surge mobility and potential detachment is enhanced by steep slopes, and valley constrictions within region 1 and, to a decreasing degree, region 2.
Characterizing the effect of topography on BAFs can lead to a better understanding of PDC mobility, and ash-cloud surge generation and detachment mechanisms. The relationships investigated herein have the potential to inform physical flow models and to be directly incorporated into empirical models for delineating surge detachment. Improving our ability to accurately gauge zones potentially at risk from surge inundation remains a key concern; indeed, understanding and forecasting surge detachment continues to represent a point of weakness in volcanic hazard mitigation.
Without the dedication of numerous MVO staff, who originally created and compiled many of the deposit maps, this work would not have been possible. E. S. Calder and S. E. Ogburn were supported by NSF grants 0809543 and 0757367.