Terrain analysis – computation of lavasheds
The project sites are located on Mauna Loa’s northeast rift zone, where 31% of eruptions
since 1843 have been located (Trusdell, 1995). We can narrow down further the number of
eruptive events that would affect a project site by delineating the "lavashed" of that site. A lavashed
is the region that is uphill from each project site. The lavashed estimates included in this study were
computed using the WATRSHED function in IDRISI for Windows (Eastman, 1997) on 30 m
Digital Elevation Models (DEM) (USGS, 1987). The only input parameters for the operation of the
WATRSHED function are the aspect of the DEM (azimuth of the slope vector) and the "angular
region to either side of the uphill vector over which flow is accepted into an adjacent cell."
Lavasheds are computed from the project site uphill (rather than from the uppermost point
downhill as with other geographic operators), and the angle parameter allows broadening of the
acceptable uphill direction to include directions to either side of directly uphill (plus or minus half
the angular parameter). If the DEM were a perfect representation of the terrain, then we could
characterize a lavashed reliably with a small angular parameter. However, angular parameters of up
to 90-degrees are required to smooth out errors and uncertainties in the DEM.
These errors and uncertainties are also evident by the presence of "holes" in the computed
lavasheds. Lavasheds should have holes only where pits in the terrain occur. We ignore these
holes, but we represent the lavashed with holes as computed in figures in this report.
To illustrate the utility of the concept, example lavasheds were calculated for a hypothetical
project site consisting of the terminal lobe of flow 1 and 1A produced by the 1984 Mauna Loa
eruption (Lockwood and others, 1985). The flow has already been emplaced, but, for the purposes
of this example, we can pretend that it hasn’t and that we are charged with evaluating the
vulnerability of this small area that was covered by the flow. Three different lavasheds were
computed for the same hypothetical project site using three different values of the angular region
parameter. Figure 8 shows the nested lavasheds for values of 60, 75, and 90 degrees. The 60- and
75-degree lavasheds indicate that there are two main topographic paths to the project site, but DEM
uncertainties preclude tracking them fully uphill. Only the 90-degree lavashed is sufficiently
general to permit outlining both paths all the way to Mauna Loa’s summit. The 90-degree lavashed
is the most general and probably includes more area than is useful for our purpose. Our best choice
for the angular parameter is between 75- and 90-degrees, but we will continue to use 90-degree
lavasheds to err on the conservative side.
Map showing the nested 60-, 75-, and 90-degree lavasheds computed for the terminal lobes of the Mauna Loa 1984-1 and 1984-1A flows. For comparison, the 1852, 1855, 1880, 1881, 1942, and 1984 lava flows are also shown. Flow lobes 1984-1 and 1984-1A are referenced in the text. The blank areas within the lavasheds are the "holes" mentioned in the text.
How have recent lava flows traveled compared to the computed example lavasheds? The
outlines of the most recent lava flows in the area (1984, 1942, 1880, 1881, 1855, and 1852) are
also plotted in figure 8. The 1855 and the 1880 flows begin within the 90-degree lavashed and
flow out of it without ever entering the 75-degree lavashed. Neither enters the hypothetical project
site. The 1881 and 1942 flows enter the 75-degree lavashed, and the 1881 flow also enters the 60-
degree lavashed before departing all lavasheds; neither of these flows enters the hypothetical
project site. The 1852 and the 1984-1 flows begin within the 75-degree lavashed, and a portion of
each flow remains within it to finally enter the hypothetical project site. The 1984-1A flow is
essentially a separate flow, starting at the channel breach outside the 75-degree lavashed and
entering the 75-degree and 60-degree lavashed and finally the hypothetical project site. The reason
that the 1984-1A flow must be considered a separate flow is that it is responding to the additional
topography of the previously emplaced 1984-1 flow which changed the way a lavashed would be
computed for the next flow. The DEM we used includes the topographic expression of all flows
except the 1984 flow, because the DEM is based on air photos taken in the 1970s. In other words,
flows earlier than 1984 did not respond to the same topography that was used to compute these
lavasheds; they would have responded to the preflow topography, which we can no longer
characterize.
Experience with lavasheds computed in the above way allows the following generalizations:
Adjacent project sites can have overlapping lavasheds, i.e., lavasheds are not mutually exclusive.
All lava flows that inundate the project site enter from the lavashed. Not all lava flows that begin
within the lavashed will enter the project site. Lava flows that begin within the lavashed, then exit,
do not seem to reenter; the one exception would be breakouts or channel breaches at the edge of
lavasheds like the Mauna Loa 1984-1A flow. Such breakouts should be treated as separate flows
that originate at the breach point. Hanley (1998) formulated similar generalizations in an application
of ARC/Info FLOWDIRECTION and COSTPATH functions for lava flows produced by Pu`u
`O`o. A lavashed is a reasonable means of using terrain to define the area from which lava flows
can enter a project site.
Finally, we can use the nearly identical flow advance rates for the 1942 Finch (1942) and 1984
(Lockwood and others, 1985) flows to estimate probable advance rates for flows in the lavasheds
of the three project sites. Figures 9 and 10 show the
estimated 9-, 24-, 48-, and 72-hour warning lines based on these advance rates for each of the
project sites. Lavashed maps with these warning lines can be used to estimate how much lead time
is available to respond to a flank eruption that begins within the lavashed. For example, using
figure 9 we can estimate that a flow produced by a vent that opened on the 9-hour warning line
could enter the existing prison project site 9 hours later. Maximum warning times can also be
determined from figures 9 and 10. The existing prison project site would have no more than 24
hours warning for a flank eruption that started within its lavashed. Sites B and C could have as
much as 72 hours warning for a flank eruption that started within their respective lavasheds.
Map of the lavashed for the existing prison site showing the 9- and 24-hour warning lines. Note that any eruption beginning within this lavashed would produce a lava flow that could enter the existing prison project site in less than 24 hours. The 1984 lava flows are shown for comparison. The short southern lobes slowed within 15 hours.
Map of the lavashed for future prison Site B and Site C showing the 9-, 24-, 48-, and 72-hour warning lines. The 1984 lava flows are shown for comparison.
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