at which magma exited the reservoir are im-
portant to the timing of caldera collapse and
the dynamics of summit draining and its
relation with processes in the ERZ ( 19 , 21 ).
We computedV
¼ 1 : 3 106 T 0 :1m^3 =day
ðe15 m^3 =sÞusing estimated model param-
eters together with a numerical model for
the elastic compressibility of the magma
reservoir ( 8 ). This estimate is tightly con-
strained by the geodetic data. Combined with
our posterior distribution forp
,wefoundthat
each pascal of pressure reduction in the res-
ervoir reduced its volume by ~1 m^3 (dV/dp=
1.0 ± 0.1 m^3 /Pa). Because of the rigidity of
the host rock, the reservoir itself was con-
tracting at only ~0.03% per day while its
internal centroid pressure was decreasing at
~3% per day. At shallower depths in the reser-
voir,therelativepressurechangeratewould
have been even greater.
Because magma is compressible, the rate at
which the reservoir contracted was likely not
equal to the rate of magma withdrawal.
Using our distribution forV
and independent
constraint on compressibility ( 8 ), we esti-
mated a net magma outflow rateqfrom the
Halema‘uma‘u reservoir of 2.3 million to
5.4 million m^3 /day (27 to 62 m^3 /s) at 68%
credible bounds. This rate exceeds the av-
erage supply to Kīlauea from the mantle byan order of magnitude ( 37 , 46 , 47 ) and thus
should approximate the total rate of flow to
the ERZ from the contracting reservoir. Add-
ing another ~5 to 10 m^3 /s from the draining
lava lake and its feeder conduit ( 8 )yieldsa
combined outflow rate of ~35 to 70 m^3 /s from
the lava lake and Halema‘uma‘u reservoir.
This is much higher than the time-averaged
eruption rate from 3 to 18 May (7 m^3 /s) ( 48 ),
indicating that summit magma was enter-
ing the rift without erupting in order to feed
deflation of the middle ERZ and growth of
the LERZ intrusion. By June, after the onset
of collapse events, LERZ eruption rates had
increased by at least an order of magnitude
( 7 ), and the time-averaged rate of caldera col-
lapse was ~two to five times larger than our
estimated magma outflow rate. These obser-
vations strongly suggest a large increase in
magma withdrawal rate from the summit in
association with caldera collapse.Reservoir failure thresholds
Placing bounds on the thresholds at which
magma reservoirs begin to fail is important for
determining the collapse hazard of an ongoing
eruption ( 49 ), interpreting the geological rec-
ord, and understanding the mechanical pro-
cesses that lead to caldera collapse. Reservoir
failure is triggered by stresses imparted to the
host rock by changes in internal pressure.
Kīlauea’s lava lake provided a window into
changing magma system pressure but dis-
appeared from view ~1 week before the first
collapse event. However, by assuming that
pressure continued to decrease at ratep
between the end of the modeled time period
(14 May) and the first collapse (16 May), as
suggested to first order by geodetic data, we
estimated a pressure change at failureDpf=
−17.2 ± 1.1 MPa ( 8 ).
We also used tilt data as a direct empirical
proxy for pressure change, using the scaling
relationship established while the lava lake
was active (at UWD, 0.078 ± 0.006 MPa per
microradian of radial tilt). This approach
does not rely on any model except for the
magmastatic relationship used to establish
the scaling ratio, nor does it require an as-
sumption of constant rates, but it can be
affected by ground deformation caused by
processes other than reservoir pressure change.
We used this approach to estimate pressure
changes after 16 May under the assumption
that ground tilt during collapse events was
caused entirely by changes in reservoir pressure
[this likely overestimates pressure changes
somewhat owing to faulting processes ( 50 )].
With this approach, we obtained pressure
changes of ~17.8 and ~25.0 MPa immedi-
ately before the first collapse event on 16 May
(similar to the model-based results) and the
first broad-scale collapse on 29 May, respec-
tively (Fig. 7 and fig. S10) ( 8 ). These estimatesAndersonet al.,Science 366 , eaaz1822 (2019) 6 December 2019 5of10
Fig. 4. Temporal evolution of summit deflation.(A) Radial ground tilt at UWD over the full eruption.
Positive tilt is consistent with reservoir inflation (pressurization) and negative tilt with deflation. Collapses
appear as small sawteeth from 16 to 26 May (nearly invisible at this scale) and as much larger sawteeth
during broad-scale collapse (29 May and after). Time series were corrected for certain tectonic offsets.
(B) GPS, tilt, lava lake surface height, and vent area time series indicating summit deflation from late
April to early June 2018. Stations UWD (tilt) and UWEV (GPS) are approximately colocated (see Fig. 2 for
station locations). Lava lake points with boxes were derived from structure-from-motion photogrammetry and
are more uncertain. Vent area was inferred from satellite radar (ascending mode in green and descending
mode in black) amplitude images as shown in (C); numbers on the time series correspond to these
images. Time spans of modeled InSAR data are shown as horizontal bars and denoted with“-a”for ascending
mode and“-d”for descending mode. The gray horizontal bar indicates the time span shown in Fig. 3.
CSK, COSMO-SkyMed. (C) CSK radar amplitude images showing enlargement of the summit vent. Brighter
pixels indicate higher radar reflectivity, so the vent appears black.
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