Introduction
Mauna Loa’s most recent eruption began in its summit caldera
at 0130 on March 25, 1984. In the next several hours, the eruption migrated into the southwest and
northeast rift zones up to 10 km from the summit. At 1641, a new eruptive fissure opened 19 km
from the summit and only 15 km from the Kulani medium-security correctional facility. By
daybreak the following day, four flows had moved up to 9 km east and northeast (Lockwood and
others, 1985); prison officials were placed on alert. By mid-morning, the flows moving eastward
toward the prison had slowed, and officials decided against evacuation. The prison remained on
"stand-by alert" for a few days, but the flows that had posed the most direct threat had stagnated by
March 28, while the bulk of erupted lava continued to flow to the northeast away from the prison
and toward Hilo (Hawaii Tribune-Herald, 1984). The eruption ended on April 15, 1984
(Lockwood and others, 1985), sparing both Kulani prison and Hilo. Only portions of a secondary
road and power poles that supplied electricity to a meteorological observatory, and several
communications relay stations, were destroyed (Hawaii Tribune-Herald, 1984).
The State of Hawai`i proposes to locate a new, approximately 2,300-bed medium-
security correctional facility in the same general area as the existing approximately 100-bed
medium-security correctional facility (Wilson, Okamoto & Associates, Inc., 1998). The
events of the 1984 eruption demonstrate the reality of lava flow hazards in this area and underscore
the importance of hazard awareness for future construction projects, such as a new prison.
Lava flow hazards for the Big Island have been estimated qualitatively, based on coverage
rates (Mullineaux and others, 1987; Heliker, 1990; Wright and others, 1992), and quantitatively,
based on probabilistic arguments for specific areas (Kauahikaua and others, 1995a and 1995b).
The qualitative hazard maps are excellent for quickly judging relatively safe and unsafe areas
island-wide, but their generalized nature and purposely vague boundaries make them difficult to
use for evaluating hazards at specific project sites. On the other hand, probabilistic estimates of
hazard can be computed for any project site, such as a prison, a hotel, or a geothermal development
(e.g., Kauahikaua and others, 1995a), so long as the required input information is available.
Our probabilistic estimates must be computed for specific project sites and require GIS digital
maps and dates of individual lava flows and volcanologic structures in the area of interest. We use
the best available geologic data for the general area, which includes the project sites and
surrounding areas and is collectively referred to as the study area, to evaluate lava flow hazards
specific to each project site. The three project sites are labeled "Existing," "Site B," and "Site C"
(Wilson, Okamoto & Associates, Inc., 1998, written communication) in figure 1 within the
boundary
of the study area.
Specifically, the hazard we investigated is inundation by lava, defined as the entrance of an
active lava flow into the boundaries of a project site. No distinction is made as to whether the lava
flow enters from outside the project site or whether it is generated from a vent within the project
site. Probabilities are calculated for at least one incident of lava inundation within arbitrary periods
of 50 and 100 years. Probabilities for other periods may be calculated easily with the Poisson
equation given in a later section. Probabilities are computed from estimates of recurrence interval or
its reciprocal, event frequency.
Site-specific Recurrence
The probability of any event can be estimated from a time series of those events (e.g.,
Davis, 1986). Therefore the probability of lava inundation of a project site in the future can be
based on a time series of lava inundation of that project site in the past. Specifically, we wish to
estimate the average recurrence interval for lava flows reaching the project site. The average
recurrence interval is the reciprocal of the average flow frequency. The most direct way to estimate
either quantity is to excavate the site, date all flows found, and compute the average time interval
between flows. The flows beneath the site are obviously the result of any eruption that could
possibly produce a lava flow capable of reaching the site across any topographic obstacles now or
in the past. One may think of the excavation findings as the result of the most realistic lava flow
simulation experiment imaginable for this specific project site. Excavation is, of course, not
practical, so we must search for the best alternative.
a) Geologic map (J.P. Lockwood and F.A. Trusdell, unpublished mapping)
of the area surrounding the three project sites shown in figure 1. The lava flows are color-coded
into 1,000-year intervals and represent ages from 14 years to 14,000 years before present. b)
Legend for the geologic map.
The most comparable data set can be obtained by detailed geologic mapping of the surface
of the study area. Such a geologic map is shown in figure 2 (J.P. Lockwood and F.A. Trusdell,
unpublished geologic mapping). The map portrays the contacts of 49 lava flow units within the
study area, 19 of which have been dated by radiocarbon methods or observed. Ages for the
remaining 30 units are estimated from stratigraphic relations. Based on all data regardless of
quality, the average recurrence interval for lava flows found on the surface within the study area is
about 260 years (3.8 flows per thousand years [table 1]). For the 19 dated flows (oldest is 10,400
years) composing 37% of the total number of mapped flows, the average recurrence interval is
about 200 years (10,400 yrs * 0.37/19).
Table 1. Lava Flow Frequencies and other parameters for each project
site.
|
|
|
|
|
|
|
|
|
cumulative |
|
|
|
|
|
|
|
|
|
fractional |
|
interval, yrs |
study area |
existing |
existing+ |
Site B |
Site B+ |
Site C |
Site C+ |
cover |
|
0-1000 |
11 |
4 |
6 |
1 |
1 |
1 |
1 |
0.196 |
|
1000-2000 |
4 |
2 |
2 |
0 |
0 |
1 |
1 |
0.423 |
|
2000-3000 |
2 |
2 |
2 |
1 |
1 |
0 |
0 |
0.437 |
|
3000-4000 |
4 |
3 |
3 |
0 |
0 |
0 |
0 |
0.533 |
|
4000-5000 |
2 |
1 |
1 |
0 |
0 |
0 |
0 |
0.631 |
|
5000-6000 |
6 |
1 |
4 |
1 |
1 |
0 |
0 |
0.832 |
|
6000-7000 |
5 |
1 |
4 |
0 |
0 |
0 |
0 |
0.852 |
|
7000-8000 |
5 |
1 |
1 |
0 |
0 |
0 |
0 |
0.906 |
|
8000-9000 |
3 |
0 |
3 |
0 |
0 |
0 |
0 |
0.934 |
|
9000-10,000 |
2 |
1 |
2 |
1 |
2 |
1 |
1 |
0.988 |
|
10,000-11,000 |
3 |
1 |
1 |
0 |
0 |
0 |
0 |
0.995 |
|
11,000-12,000 |
1 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
|
>12,000 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
Ave. /1000 yrs |
3.8 |
1.3 |
2.3 |
0.31 |
0.46 |
0.23 |
0.23 |
|
|
STDev /1000 yrs |
1.9 |
0.89 |
1.3 |
0.43 |
0.57 |
0.36 |
0.36 |
|
|
TOTAL |
49 |
17 |
30 |
4 |
6 |
3 |
3 |
|
|
Area, sq. km |
552.85 |
29.36 |
345.22 |
2.492 |
34.95 |
0.5968 |
15.6 |
|
Number of flows within 1,000-year intervals for each of the project sites
considered. Data are derived from J.P. Lockwood and F.A. Trusdell (unpublished
mapping).
Specific recurrence-interval estimates for the three project sites can be estimated in a
similar manner. First, all map units within each project site were selected and tabulated. In order to
compensate for flows that are completely buried beneath a project site, all map units directly
downslope from that site were also selected; the result is three expanded project sites (referred to
here as the downslope adjustment; Kauahikaua and others, 1995a). Average recurrence
intervals and areas are tabulated in table 1 (headings followed by "+" are the expanded project
sites); the average number of flows per thousand years is plotted versus area in figure 3.
Number of flows per thousand years is proportional to the area of the project
sites listed in Table 1.
The square symbols in figure 3 represent the three expanded project sites and the entire study
area. The diamond symbols represent the three actual project sites, with the flow numbers obtained
from the corresponding expanded sites. The number of flows exposed on the surface per thousand
years shows a direct proportionality to the area over which they are exposed - approximately 0.64
flows per thousand years per 100 sq. km. The proportionality must be due to the random
distribution of lava flow plan dimensions (width or length) in this region.
We are, however, more interested in the flow frequency for all flows not only exposed at the
surface, but also buried beneath each project site for probability computations. The flow frequency
for the expanded sites (as determined by the downslope adjustment) also shows a direct
proportionality to project site area - 7.07 flows per thousand years per 100 sq. km. We again have
the intuitive result that lava flow frequency (including exposed and buried flows) is approximately
proportional to project site area, with the implication of random distribution of lava flow plan
dimensions.
In the preceding analysis, we introduced the concept of downslope adjustment as one
method of compensating for the under representation at the ground surface of older map units that
are progressively covered by younger units. However, there is a problem with this method. For
example, the surface of Mauna Loa is being covered at an approximately exponential rate of 40% in
the first thousand years (Lipman, 1980; Lockwood and Lipman, 1987; Trusdell, 1995; see
Kauahikaua and others, 1995b, for a discussion of exponential coverage rates). At this rate, more
than 99% of Mauna Loa’s surface older than 10,000 years is covered, and we can no longer get an
accurate idea of the number of flows emplaced before that time. The picture gets increasingly foggy
even after 1,000 years. We need a more general method than downslope adjustment to modify the
frequency distribution of flows now at the surface for the number of flows that are completely
buried by younger flows and no longer visible.
Plot showing the number of exposed flows equal to, or older than, a
specified age versus the
fractional coverage by younger flows. The linearity of these data suggest that we can use coverage
rate to estimate the number of flows covered during each thousand year period. A histogram of
adjusted flow frequencies is also plotted in figure 5.
We can compute the coverage rate
specifically for these flows within the study area. Figure 4 plots the cumulative fractional coverage
at the beginning of each 1,000-year period (from (figure 3) produced per unit
time, then the number of older flows not covered by younger flows
should be inversely proportional to the cumulative fractional coverage of the younger flows. This
is similar to saying that you see fewer unpainted tiles as you paint over a tiled floor; the number of
unpainted tiles is inversely proportional to the area of paint applied. A straight line (y = -43.765x +
49.348) fits the data well in figure 4, consistent with our hypothesis but not proving it. The
number of flows exposed beneath younger ones is estimated by 49.348 – 43.765 * [cumulative fractional coverage] so the total number of buried flows
can be estimated in turn as 43.765 * [cumulative fractional
coverage]. Using this relation to estimate the number of unseen flows within each time interval, the
adjusted estimate for the entire study area is 7.4 flows per thousand years, nearly twice the
unadjusted estimate of 3.8 flows per thousand years (table 1). Figure 5 shows
histograms of the
exposed and adjusted flow frequencies in 1,000-year groupings. The adjustment (here termed the
burial adjustment) is not perfect and may be better within the first 10,000 years than for the
more distant past.
Histogram of observed and burial-adjusted flow ages found within study
area, 1,000-year intervals.
We derived the burial adjustment for the entire study area and have already shown that
flow frequency (both exposed and buried [figure 3]) is proportional to area considered. Thus we
feel confident that we can apply this general factor to subareas, such as the three project sites. That
is, the estimated frequency of lava flows, including buried flows, is 1.95 times (7.4/3.8) the
frequency of unburied flows now exposed at the surface in the study area. Using the burial
adjustment, we get an estimate of 2.5 flows per thousand years for the existing project site, 0.6
flows per thousand years for Site B project site, and 0.45 flows per thousand years for Site C
project site. Normalized by area, the adjusted estimate is 7.3 flows per thousand years per 100 sq.
km (R2=1.0). This compares well with the 7.07 flows per thousand years per 100
sq. km. (R2=0.998) obtained by the downslope adjustment.
A third method of flow frequency adjustment for the effect of under-representation by
burial is to use only data from the most recent and best known period (here referred to as the
recency adjustment; Kauahikaua and others, 1995a). Older periods are acknowledged as
under-represented and therefore not included in any computation. The most recent period is
recognized as the best known and least likely to be under-represented. For the present study, this
would result in an estimated flow frequency of 11 per thousand years for the study area (based on
the 0-1000 year row in table 1). The area-normalized flow frequency is 10.8 flows per thousand
years per 100 sq. km (R2=0.997) using project site entries in the 0-1000 year
interval row of table 1.
We could also use the statistic of three flank eruptions since 1832 on the
northeast rift zone near the project sites to estimate an equivalent flow frequency of 18 flows per
thousand years. Kauahikaua and others (1995a) recognized that this simple method of adjustment
generally yields the largest flow frequency estimate of any method, because every histogram of
lava flow age distributions is shaped like the one labeled "observed" in figure 5. The number of
flows exposed at the surface is generally highest in the most recent past and decreases backward in
time.
This method also relies on a presumption that the most recent past is most representative of
Mauna Loa’s eruptive behavior in the near future. Discomfort with this method stems from its
reliance on only a small part of the available data. How can we differentiate between a volcano
whose eruptive frequency is changing with time and a volcano whose eruptive frequency is
random and has had a recent period of more frequent activity? Even with a complete data set, the
distinction may be difficult (Ho, 1996). The problem is compounded in our case by the increasing
incompleteness of the data set further into the past. The dates on a lava flow sequence drilled
through near Hilo form the only data set complete enough over several tens of thousands of years
to assess the constancy of Mauna Loa’s eruption rate. Beeson and others (1996) show that the rate
at which lava flows overran the drill site in the last 86,000 years was fairly constant at about one
flow per 4,000 years. While this is not definitive, it is the only indication available. It does not
support a pattern of increasingly frequent eruptions for Mauna Loa; we believe, therefore, that the
recency adjustment will underestimate recurrence intervals and should not be used if there are better
options available.
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