Study Site—Spirit Lake and the Sediment Blockage

Spirit Lake occupies the upper parts of two valleys. The west arm is the smaller of the two arms (fig. 1). It has a more irregular topography and a greater area lower than 1,015 m elevation (NAVD 88). Hummocky debris avalanche deposits are present near Bear Cove north of the west arm (Evarts and Ashley, 1993; Glicken, 1996) and presumably underlie the entire western lake. At current typical operating levels, the west arm is about 36 m deep at its deepest point. In 1974, the west arm was at least 37 m deep (120-ft contour in Bortleson and others, 1976). Before the May 1980 eruption, the outlet of Spirit Lake was on the southwest side of the west arm adjacent to Harrys Ridge. The east arm is fed by several unnamed tributaries and is about three times larger than the west arm. At current typical operating levels, the east arm is about 36 m deep at its deepest point. In 1974, the east arm was at least 55 m deep (180 ft in Bortleson and others, 1976; Gawel and others, 2018).

The May 18,1980 debris avalanche left a massive deposit south of Harrys Ridge at the western edge of Spirit Lake (figs. 1 and 2), blocking the outlet and raising the lake basin elevation by ~60 m (Glicken, 1996). Glicken and others (1989) estimated the blockage to be about 1,465 m wide (east-west) by 1,950 m long (north-south), consisting primarily of a heterogeneous assortment of fractured rock, gravel, and sands ranging in thickness from about 60–150 m along its crest (Glicken, 1996). It is overlain by layers of pyroclastic deposits of variable thickness, which are highly erodible (Grant and others, 2017; Major and others, 2020). The toe of the blockage lies about 23 m (1,027 m elevation [NGVD29]) below the current average lake level (Grant and others, 2017). Post-eruption field surveys and dam stability analysis (for example, Youd and others, 1981) suggested that lake-level rise and erosive piping through the pyroclastic deposit layer presented the most likely mode of debris-dam failure. Incision through the loose pyroclastic layer could lead to further downcutting of the underlying debris-avalanche deposit, potentially leading to catastrophic outbreak flooding. This prompted efforts to identify the elevation of the boundary between the debris-avalanche and more erodible overlying pyroclastic deposits (USACE, 1983). The lowest identified points of this boundary were assumed to be critical or threshold values for the maximum lake-surface elevation above which the risk of dam failure was deemed too risky. Glicken and others (1989) identified two such low points lying underneath the crest of the dam—referred to as critical point north (CPN) and critical point south (CPS) at elevations 1,071 m and 1,069 m respectively (fig. 2). Based on mitigation for potential future hydrologic or volcanic events, 1,055 m was determined to be the maximum safe operating level for the lake elevation (USACE, 1983).

At current typical operating conditions, the lake has a water-surface elevation of about 1,050 m and a volume of about 230 million m³ (Mm³). At a theoretical maximum water-surface elevation of 1,070 m, the Spirit Lake volume of 468 Mm³ is about double the volume when the lake level is 1,050 m. At water levels below about 1,027 m, the arms of Spirit Lake become separate bodies of water, both of which have low points of about 1,014 m. The resulting eastern sub-lake is about three times larger than the west sub-lake and has a volume of 27 Mm³ compared to a volume of about 9 Mm³ for the resulting western sub-lake. The western sub-lake has a volume of about 4 percent of the current lake and 2 percent that of the theoretical maximum lake. The eastern sub-lake has a volume of about 11 percent of the current lake and 6 percent that of the theoretical maximum lake. The shortest distance from the crest of the debris dam to the western sub-lake margin is less than 1 km and is 2–2.5 km to the eastern sub-lake margin.

Models and Software

We simulated clear-water outbreak floods lacking erosive entrainment (or volume adjustments to account for sediment) using the software GeoClaw (George, 2008, 2011; Berger and others, 2011). GeoClaw solves the shallow-water equations, a commonly employed depth-averaged mathematical model used for water wave propagation (for example, George, 2008 LeVeque and others, 2011) and large-scale overland flooding (for example, George, 2011; Denlinger and others, 2021). GeoClaw has algorithms tailored for accurately resolving dam-break outflow conditions and inundation fronts over complex topography (George, 2008, 2011).

To model entrainment and its rheological effects, we used the depth-averaged two-phase granular-fluid model, D-Claw (George and Iverson, 2014; Iverson and George, 2014). D-Claw was originally developed for modeling variably dense granular landslides and large-scale debris flows for which high solid-volume fractions (greater than roughly 40–50 percent) and pore-fluid pressure coevolve in a tightly coupled manner. This feedback process controls the local dynamic, effective basal-shear resistance, and thereby dramatically influences flow mobility (see Iverson, 1997; Iverson and George, 2014). D-Claw’s model equations reduce to the shallow-water equations if solid grains are absent and therefore it can be used for surface flow problems that feature the interaction of water with granular sediment, and a spectrum of granular concentrations ranging from clear-water flows to dense debris flows (see for example, George and others 2017, 2019, 2022; Barnhart and others, 2021; Kafle and others, 2024).

Base Topography and Bathymetry Digital Elevation Model

A digital elevation model (DEM) of the model domain was assembled from various sources (George and Cannon, 2025). Topography data for valley bottoms of the Cowlitz and Toutle River systems is mostly based on surveys from 2007 to 2012 acquired to support USGS, USACE, and other studies (USACE, 2010; Mosbrucker 2014, 2015). DEMs derived from USGS data (see George and Cannon [2025] for more information) and various other surveys acquired from 2002 to 2012 were obtained from the Washington Department of Natural Resources (WA DNR) lidar portal (WA DNR, 2025; https://lidarportal.dnr.wa.gov). The source datasets were obtained as DEMs, re-projected to Universal Transverse Mercator zone 10 north and North American Datum of 1983, and mosaicked to form a single DEM covering the study area. The DEM was merged with a bathymetric DEM derived from surveys carried out in August 2009 and July 2010 (Gawel and others, 2018).

Channel-Cut Construction

We modified our DEM to contain elevations of hypothetical outlet channels through the Spirit Lake blockage. The hypothetical channels were assembled along thalweg lines drawn to extend from local minima in Spirit Lake through the critical points of Glicken and others (1989) to an elevation lower than the bed of Spirit Lake in the North Fork Toutle River valley (fig. 3; table 1). The channels were assumed to have approximately parabolic cross-sectional profiles. We constructed two channels that we refer to as the “north” and “south” channels. The channels run east-west, bisecting a ~100-m-thick heterogeneous assortment of sediment and volcanic deposits overlying the pre-1980 topography. The channels extend eastward into Spirit Lake bathymetry to varying extents (fig. 3).

The north channel-cut scenario is a 200-m-wide cut through the north end of the blockage and passing through the CPN of Glicken and others (1989). The channel thalweg descends linearly from an elevation of 1,015 m in the west arm of Spirit Lake (the west arm has about 14,800 m² of lakebed lower than 1,015 m) to about 1,000 m (996 m) in the North Fork Toutle River downstream of the debris blockage. The alignment of the north channel roughly follows the “Truman Channel” (Major and others, 2020; fig. 2), which was mostly incised by water pumped from Spirit Lake by USACE in the early 1980s. This leads to a maximum channel depth about 60 m below the crest of the blockage. In constructing the channel depth, we assumed that pre-eruptive topography was non-erodible. Note that the channel thalweg passes just a few meters above debris-submerged bedrock extensions of north-south trending Harrys Ridge and an unnamed ridge to the west (fig. 3).

The south channel-cut scenario follows a thalweg that descends linearly from an elevation of ~1,014 m in the bed of Spirit Lake to 996 m at its confluence with North Fork Toutle River, passing through the CPS of Glicken and others (1989; fig. 3). The north and south channel cuts are nearly co-located at Spirit Lake’s current typical shoreline (~1,050 m elevation), and they terminate in similar locations on the North Fork Toutle River. However, the south channel cut takes a more circuitous path through the debris dam, heading southward through the CPS and turning northward toward its confluence with the North Fork Toutle River. This endows the south channel with a deeper cut through the debris dam while remaining above pre-eruptive topography. Additionally, the upstream end of the south channel cut extends several kilometers into lake bathymetry, bisecting the submerged divide between the west and east arms of Spirit Lake. The extension was constructed with the goal of providing lake drainage from the east arm of Spirit Lake for establishing a reasonable upper bound on outflow volume—it was not based on a physical assessment of probable lake-bed erosion.

Erodible Bed Sediment

D-Claw requires a predetermined specification of the spatially varying thickness of available erodible bed-sediment as a raster dataset, which we developed for the upper North Fork Toutle River from the downstream terminus of our channel cuts to immediately upstream of the SRS (fig. 4). The approximation was made by subtracting a DEM derived from 1950s maps (Cannon, 2023) from the modern DEM, which in our area of erodible sediment was derived from 2009 and 2012 lidar surveys. This resulted in an erodible layer up to ~195-m-thick with a total volume of 1.7 billion m³. Note that this represents available erodible material in a wide swath, not just the erodible sediment in the Toutle River channel or the actual volume of eroded sediment in simulations. Both upstream and downstream of this segment, the bed was considered non-erodible (fig. 1). The debris-dam failure and breach-growth process were not modeled directly; that process was implied by the specified channel cuts. The bed surfaces of the hypothetical outlet channel cuts were assumed to have stabilized following breach growth and erosion and lacked remaining erodible material. We avoided adding an approximation of channel-eroded solid volume from the hypothetical channel cuts to our outflow discharge, as doing so in a simple fashion could violate energetic constraints (refer to the “Entrainment Mechanism” section ). However, the volume of that neglected sediment is small, roughly10 percent of the total eroded sediment in the upper Toutle River (see the “Results” section). We assumed that the river below the SRS would contribute negligible net entrainment rates compared to the segment above the SRS, based on topographic gradients and erodible sediment data.

Entrainment Mechanism

In depth-averaged models of entrainment, the incorporation of material into the overriding flow is typically assumed to occur at the basal interface between moving material and static erodible sediment (as opposed to longitudinal mobilization of material or collapse and failure en masse, see McGuire and others, 2017). Numerically, at each timestep and for each computational grid cell where entrainment occurs, a total mass per unit area is added of ρ_b Δh (where ρ_b is the density of saturated granular material in the erodible bed and Δh is the thickness of mobilized material or equivalently the reduction in the height of the bed surface) and a solid volume m_b Δh (where m_b is the solid-volume fraction of the erodible bed material, table 2). This process exchanges momentum between the overriding flow and the mobilized bed material without contributing directly to net flow momentum (equivalent to discharge or mass-flux). The addition of mass therefore decreases the local flow velocity upon entrainment while the mass-flux is unchanged. However, the process transfers potential energy from the static bed to the flow, which can be subsequently harnessed into downslope flow momentum (discharge or mass-flux). This can lead to apparent momentum growth at the flow front (see, for example, Iverson and others, 2011); however, the added contribution of entrained material to the cumulative discharge of the entire flow body is limited by the initial potential energy of that material minus its contribution to flow resistance and energy dissipation.

The physical processes described above are implied by basic physical conservation laws of mass, momentum, and energy. However, the entrainment rate (the amount of material Δh that is mobilized over a timestep in a grid cell) is not rigorously described by physical models and is poorly constrained by available data (see for example Iverson and Ouyang, 2015; Conroy and George, 2022; Lee and others, 2022; Könz and others, 2024). We follow a traditional empiricism (see, for example, Lee and others, 2022) of using an affine function for the entrainment rate that depends on approximations of the bed-shear stresses, critical mobilization or threshold stresses, and uncertain, or calibrated parameters. In D-Claw, the bed-shear stress is approximated as the sum of the effective basal coulomb friction, an effective fluid viscosity, and a Manning resistance formula (see the “Model Scenarios and Initation” section, Iverson and George, 2014; George and Iverson, 2014). Because of the wide range of flow regimes, solid concentrations, and uncertainty and (or) variability in the bed characteristics (for example, saturation levels) of the modeling described herein, we used a very simple model with a single tunable proportionality constant (C_e=01) relating the bed-shear stresses to the entrainment rate, which provided the best fit for large-scale experimental data of entrainment of loose saturated material at the USGS debris-flow flume (Iverson and others, 2011). It is worth noting that highly energetic outburst floods and debris flows can mobilize considerably more material than what would be predicted by more common fluvial sediment transport models or runoff models that use grain-by-grain mobilization and suspension or bed-load transport (see, for example, Iverson and others, 2011; McGuire and others, 2017, Roelofs and others, 2022, 2023).

Deposition in our modeling occurs en masse through flow halting: grain by grain deposition through vertical particle settling is neglected. Inclusion of this latter effect would presumably have little effect near high-energy flow fronts but may lead to larger deposits in the late downstream stages of the floods. However, the validity of extending depositional settling models developed for fluvial and coastal systems to highly energetic and concentrated debris flows is largely untested (see, for example, Cheng, 1997; Iverson and others, 2011).

We tested several alternative entrainment schemes in D-Claw; however, different schemes produce nearly equivalent results given adjustments of unconstrained tunable parameters. Therefore, we present results for one scheme and one entrainment-rate parameter value and focus on the effects of the entrained material on flow dynamics rather than presenting a broad comparison of entrainment models and rates. An exploration of lower entrainment rate coefficents, C_e, than used for the results presented produced results intermediate between the erosive and clear-water floods. Higher entrainment rates than those presented produced less mobile flows overall due to substantially enhanced friction in the lower gradient valleys.

Model Scenarios and Initiation

Our simulations are initiated with Spirit Lake filled to a specified water level bounded planimetrically by the lake-surface intersection with current (non-eroded) topography, which predicates lake volumes that precede dam breaching and outflow (fig. 5). Because our simulations begin with preexisting channel cuts, dam-break initial conditions occur at the outlet upon model initiation. We neglected flood initiation mechanics for which outflow, breach growth, and entrainment of dam material co-evolve in a complex sequence. These inherently stochastic processes can be modeled with D-Claw (for example, George and others, 2019); however, results are sensitively dependent on material parameters that characterize the subsurface geology for which well-constrained modeling inputs are lacking. Assessing the variability of results within the range of uncertainty is beyond the scope of this study.

We modeled multiple sets of clear-water and erosive floods with identical outflow conditions, providing baseline comparisons regarding the effects of downstream entrainment on hazard extent. Variable lake levels and channel cuts are intended to help characterize the sensitivity of downstream variability to outflow conditions. The volumes of material removed to produce our channel-cut DEMs (the volume of material that would be lying above the hypothetical channel-cut bed if we left our base DEM unaltered ) are 12.9 Mm³ and 25.0 Mm³ for the north and south channel cuts, respectively. For comparison, the volumes of actual eroded sediment in our simulations varied but were less than 300 Mm³ (see the “Results” section), about 10 times the volume removed from the channel cuts.

We carried out simulations for two lake levels: 1,070 m and 1,050.4 m, corresponding to total lake volumes of 468 Mm³ and 234 Mm³, respectively. The higher lake level is based on the assessment of Glicken and others (1989) for the maximum lake level above which breaching becomes more likely. The lower lake level corresponds to the lake surface in recent lidar, and we use it for our lower bound on lake volume in the event of a catastrophic failure.

Simulations for both lake levels, through the north and south channel cuts, with and without erosion, result in a total of eight simulations described in this report (table 1). The simulations are denoted with abbreviations for the channel (NC or SC), lake level (1070 or 1050), and erosive or clear water (ER or CW) (for example, NC-1070-ER, SC-1050-CW, and so forth).

Our simulations were computed on a 78 km (east-west) by 40 km (north-south) domain, encompassing Spirit Lake, the Toutle River valley, and the Cowlitz River valley extending ~10 km to the north of the Toutle River mouth and ~10 km to the southwest of the Cowlitz River mouth at the Columbia River. To optimize computational efficiency and accuracy with respect to numerical grid resolution, available DEM resolution, or regions of particular interest, the GeoClaw and D-Claw software packages employ adaptive mesh refinement (AMR) schemes (Berger and Oliger, 1984) designed for free-surface flows over topography (Berger and others, 2011; George, 2011; LeVeque and others, 2011). AMR provides patches of variable resolution grids that evolve with the advancing flow path and flow dynamics. Spirit Lake, the outlet, and flow in the channel cuts were resolved at a grid resolution of 4 m. Flows downstream of the channel cuts were resolved at a grid resolution of 10 m and simulated for up to 24 hours from the debris-dam-break initiation. Optimal temporal resolution (time step sizes) is variable and based on numerical accuracy and stability constraints.

For the D-Claw erosive flows, model input parameters characterizing the erodible and entrained material are constrained only to the degree possible based on available data for granular sediment samples used in controlled experiments (for example, Iverson and others, 2010) and shown in table 2. Refining these parameters based on samples of actual sediment deposits in the North Fork Toutle River would require further study. For a description of these parameters and their effect on simulation results, see George and Iverson (2014), Iverson and George (2016), and George and others (2022).

Dam-Break Initiation, Outflow Discharge, and Spirit Lake Drainage

Simulations began (defined as time [t] =0 seconds [s]) with the release of water as dam-break initial conditions located at the lake boundary and channel-cut intersections (fig. 5). The erosive and clear-water simulations are identical (aside from small numerical discrepancies due to different software implementations) upstream of the erodible sediment (fig. 4) that lies below the hypothetical channel cuts, yielding four pairs of outflow scenarios (table 1). Channelized flow quickly advances through the pre-computed breach cuts and into North Fork Toutle River. Outflow discharge for the four scenarios was computed along a transect across the Spirit Lake outlet (labeled Γ_SLO, figs. 6 and 7). For all outflow scenarios, peak discharges at the outlet are reached within 3 minutes, and lake drainage continues for ~12 hours. The south channel cut scenarios lead to more complete lake drainage by providing a lake-floor bathymetric channel from Spirit Lake’s east arm (fig. 3). The remaining lake levels after 12 hours of drainage are shown in figure 8. Discharge and total volume of outflow for the four scenarios are shown in table 3.

Comparison of Flows in the Upper North Fork Toutle River Overlying Erodible Sediment

Erodible bed material was considered only between the channel cuts and the SRS (fig. 4). In this reach of the North Fork Toutle River, the erosive flows simulated with D-Claw mobilize and entrain bed material, increasing the total flow volume (defined as the summed volume of any material [water or sediment] displaced from its initial location). The influence of sediment entrainment on flow dynamics is observable immediately as floodwaters encounter the erodible bed material. Flow variables for the eight scenarios are compared at a set of cross-channel transects located progressively downstream (figs. 9–11, table 4). Below the upstream boundary of erodible sediment (Γ_NFT), the peak and cumulative discharges are reduced by the entry of flood waters into thick, erodible, material. This presumably occurs because the mobilization of frictionally resistive material acts as an energy sink before entrained material gains momentum downslope. Farther downstream, at Γ_ElkRock and below (fig. 9), this pattern is reversed as the peak and early discharge rates of the erosive flows are elevated substantially from that of the non-erosive flows in the leading rush (less than [<] 1 hour) (fig. 10 and 11). Note also that the peak discharges for the erosive flows increase progressively downstream, while those for the clear-water flows decrease. This pattern occurs from the accumulation of mobilized mass and accompanying potential energy that is released downslope, leading to a larger and more energetic flow front. At later times (greater than [>] 1 hour), as the overall discharge rates of both the clear-water and erosive floods begin to wane, the discharges of the erosive flows fall below that of the clear-water floods (figs. 10, 11). We attribute this to the presence of resistive and slowly moving sediment-laden flows.

The erosive flows achieve larger maximum flow depths along the upper North Fork Toutle River; however, note that inundation extent (affected area) is only marginally increased with bulking (fig. 12). This pattern is intuitive if one considers the combination of the larger volume flow fronts and erosion of the channel (the depth of bed scour and remaining erodible material are shown in figure 13); a flow composition of resistive granular material does not spread laterally as easily as clear water.

In summary, active entrainment of material affects the flow discharge in complex and variable ways depending on time and location. The competing effects of momentum growth upon the release of potential energy with that of increased shear resistance from the presence of solids lead to faster and more energetic flow fronts followed by slower and less energetic trailing flows subject to higher frictional resistance. The pore-fluid pressure response to the mobilization of solid-grains may accentuate the enhanced mobility of the flow fronts due to high fluid pressure followed by more resistive trailing flows with low pressure (see Iverson and George, 2014). Note that although the erosive flows lead to the displacement of more volume overall (bulking), this does not imply that more volume is ultimately transported long distances downstream or beyond the SRS—more material (sediment and water) is also left behind in resistive deposits (fig. 10; see the “Discussion and Summary” section). Conversely, clear water ultimately drains thoroughly (fig. 10).

Comparison of Flows Downstream of the Sediment Retention Structure (SRS)

Downstream of the SRS, erodible bed sediment is absent in the model simulations—topography is considered non-erodible in this region (refer to figs. 14 and 15 for map views and transect locations); however, the erosive flows continue as debris flows carrying sediment entrained from upstream.

At the most upstream transect in this reach (Γ_Toutle), flows maintain characteristics observed at locations in the active zone of entrainment above the SRS—the erosive flows have a substantially larger and faster leading phase followed by a more rapid drawdown in discharge later, compared to the clear-water flows (figs. 16, 17). However, in contrast to the zone of active entrainment upstream (above the SRS), the peak discharges in the leading phase of the erosive flows decrease monotonically downstream, dropping faster than their non-erosive counterparts (table 5). This leads to greater similarity between the discharge curves of the erosive and non-erosive flows with distance downstream from the lower segment of the Toutle River (fig. 14) to the lower Cowlitz River (fig. 15). This likely occurs because the volumes of the granular-fluid flows are no longer bolstered with the addition of sediment, but they retain the resistive granular material from upstream. Although arriving considerably earlier because of their high speeds achieved upstream, the erosive flows more closely resemble their non-erosive counterparts the farther they are observed downstream from the reach where material is entrained (figs. 16, 17; table 5). Note that at the farthest downstream transect, Γ_Cowlitz, the peak discharges of the clear-water floods exceed that of their erosive counterparts (table 5), which deliver more material that ultimately inundates more of the low-lying areas adjacent to the Columbia River (fig. 17). This pattern is consistent with the fact that the mobile flow volume of the debris flows diminishes because stalled resistive material remains upstream.

Erosive-Flow Composition and the Development of Debris Flows

In this section we look more closely at the erosive-flow composition resulting from incorporation of granular sediment and focus on comparisons of just two scenarios: the NC–1070–ER erosive flow and the NC–1070–CW clear-water flood.

As flood waters begin to entrain large amounts of debris below the channel cuts, their solid-volume fraction increases accordingly. This occurs progressively downstream; fractions increase moving downstream at a given time, and fractions at a given location increase at later times (figs. 18A–D, 19). However, most erosion occurs in the first 2 hours (figs. 18E–H, 20). The increasing solid-volume fractions at later times may occur because the lake outflow discharge diminishes substantially yet erosion and deposition persist. Substantially more erosion is observed in the narrower, steeper, section near the channel outflow (Γ_NFT, fig. 20A and fig. 21A), compared to the flatter river valley above the sediment retention structure (Γ_SRS^U_, fig. 20B and fig. 21C). In the first few hours (t<2h) flows range from 20–30 percent solids nearer to the upstream extent of the erodible material to about 50–60 percent near the SRS, indicating that the sediment-laden floodwaters transition to debris flows as they accumulate eroded material. At later times (6–12 hours) slowly moving or stationary material with >60 percent solid content remains above the SRS.

As sediment is entrained, it contributes to momentum growth at the flow-front leading to increasing peak discharges progressively downstream (time series of the total and constituent [solid versus fluid] discharges are depicted in fig. 21). Cumulative discharges or total volume throughput (fig. 21A–D) indicate that a substantial volume of both water and sediment remains upstream above the sediment retention structure.

Downstream of the reach where entrainment occurs (below the SRS), the sediment-rich flows can be characterized as variably dense debris flows (~50–60 percent solids). Solid concentration maps at selected times on the Toutle and Cowlitz Rivers are shown in figures 22 and 23, respectively. Time series of the total and constituent (solid and fluid) discharges and time series of solid-volume fractions at transect locations along the Toutle and Cowlitz Rivers are compared in figures 24 and 25, respectively. The fraction of solid material increases slightly at later times—a pattern observed upstream in the upper North Fork Toutle River. The slightly denser and more resistive material appears near the edges of the flow, apparently shouldered aside by more dilute and mobile material nearer the channel thalweg (figs. 22, 23).

Comparison of Arrival Times, Inundation Extents, and Volumes

A noteworthy distinction between the erosive and non-erosive simulations are the faster flow-front speeds and shorter arrival times of the erosive flows (observed in time-series plots and depicted as map-view arrival-time contours in figs. 26, 27). We attribute this difference to the larger volume and higher energy leading phase of the erosive flows due to bulking and attendant momentum growth. Larger flows travel faster—a simple rough estimate for flow-front speeds of a shallow gravity-driven mass flow is given by

where However, a variety of factors determine the actual front-speed. Note that the final inundation extent of the erosive flow (NC–1070–ER) is only slightly larger than the clear-water flood (NC–1070–CW) in the upper North Fork Toutle River (fig. 26), and smaller farther downstream in the lower Cowlitz River, particularly near the Columbia River (fig. 27). As described in section “Comparison of Flows Downstream of the Sediment Retention Structure (SRS),” these results are likely due to the resistive composition of the debris-flow material and the fact that the mobile volume of the erosive flows diminishes as resistive material deposits (stalls) upstream of their distal extent whereas clear-water continues to flow freely, as can be ascertained by cumulative discharge curves.

Several volumetric calculations for the NC–1070–ER and NC–1070–CW scenarios are shown for comparison in figure 28 and table 6. The mobile volumes for the two scenarios are determined by summing the total flow-volume elements with non-zero velocity on the entire domain. The erosive flow volume exceeds that of the clear-water flood as material is entrained, reaching a maximum of 624 Mm³ within 1 hour before subsequently declining substantially, dropping below that of the clear-water flood after about 4 hours. Note that the total volume of mobilized material (lake plus total entrained volume—material that has been mobilized over all time) exceeds the total mobile volume at any given time (fig. 28, table 6) because of flow deposition (stalled flow). After ~4 hours, the clear-water flood comprises a larger volume of flowing material—water which encounters considerably less resistance.