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Dynamics of large effusive eruptions driven by caldera collapse


The largest effusive basaltic eruptions are associated with caldera collapse and are manifest through quasi-periodic ground displacements and moderate-size earthquakes1,2,3, but the mechanism that governs their dynamics remains unclear. Here we provide a physical model that explains these processes, which accounts for both the quasi-periodic stick–slip collapse of the caldera roof and the long-term eruptive behaviour of the volcano. We show that it is the caldera collapse itself that sustains large effusive eruptions, and that triggering caldera collapse requires topography-generated pressures. The model is consistent with data from the 2018 Kīlauea eruption and allows us to estimate the properties of the plumbing system of the volcano. The results reveal that two reservoirs were active during the eruption, and place constraints on their connectivity. According to the model, the Kīlauea eruption stopped after slightly more than 60 per cent of its potential caldera collapse events, possibly owing to the presence of the second reservoir. Finally, we show that this physical framework is generally applicable to the largest instrumented caldera collapse eruptions of the past fifty years.

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Fig. 1: Geodetic signature of caldera collapse.
Fig. 2: Model set-up and main features of the two regimes.
Fig. 3: Comparison between data, best-fit model and posterior prediction uncertainty.
Fig. 4: Time between collapses for Piton de la Fournaise, Miyakejima, Fernandina and Kīlauea.

Data availability

Tilt data are available in ref. 5 and Sentinel SAR data are available at data are provided with this paper.

Code availability

The codes used in this work are available through Zenodo at


  1. 1.

    Kumagai, H. et al. Very-long-period seismic signals and caldera formation at Miyake island, Japan. Science 293, 687–690 (2001).

    ADS  CAS  Article  Google Scholar 

  2. 2.

    Michon, L., Massin, F., Famin, V., Ferrazzini, V. & Roult, G. Basaltic calderas: collapse dynamics, edifice deformation, and variations of magma withdrawal. J. Geophys. Res. Solid Earth 116, B03209 (2011).

    ADS  Article  Google Scholar 

  3. 3.

    Neal, C. et al. The 2018 rift eruption and summit collapse of Kīlauea volcano. Science 363, 367–374 (2019).

    ADS  CAS  Article  Google Scholar 

  4. 4.

    Lipman, P. W. C. Encyclopedia of Volcanoes 643–662 (Academic, 2000).

  5. 5.

    Johanson, I. & Miklius, A. Tiltmeter data from Kīlauea Volcano, Hawaiʻi, spanning the 2018 eruption and earthquake sequence. US Geological Survey Data Release (US Geological Survey, 2019).

  6. 6.

    Lundgren, P. R., Bagnardi, M. & Dietterich, H. Topographic changes during the 2018 Kīlauea eruption from single-pass airborne InSAR. Geophys. Res. Lett. 46, 9554–9562 (2019).

    ADS  Article  Google Scholar 

  7. 7.

    Fontaine, F. R., Roult, G., Michon, L., Barruol, G. & Muro, A. D. The 2007 eruptions and caldera collapse of the Piton de la Fournaise volcano (la Réunion island) from tilt analysis at a single very broadband seismic station. Geophys. Res. Lett. 41, 2803–2811 (2014).

    ADS  Article  Google Scholar 

  8. 8.

    Ukawa, M., Fujita, E., Yamamoto, E., Okada, Y. & Kikuchi, M. The 2000 Miyakejima eruption: crustal deformation and earthquakes observed by the NIED Miyakejima observation network. Earth Planets Space 52, xix–xxvi (2000).

    Article  Google Scholar 

  9. 9.

    Liu, Y.-K., Ruch, J., Vasyura-Bathke, H. & Jonsson, S. Influence of ring faulting in localizing surface deformation at subsiding calderas. Earth Planet. Sci. Lett. 526, 115784 (2019).

    CAS  Article  Google Scholar 

  10. 10.

    Gudmundsson, M. T. et al. Gradual caldera collapse at Bárdarbunga volcano, Iceland, regulated by lateral magma outflow. Science 353, aaf8988 (2016).

    Article  Google Scholar 

  11. 11.

    Ripepe, M. et al. Volcano seismicity and ground deformation unveil the gravity-driven magma discharge dynamics of a volcanic eruption. Nat. Commun. 6, 6998 (2015).

    ADS  CAS  Article  Google Scholar 

  12. 12.

    Fialko, Y. A. & Rubin, A. M. What controls the along-strike slopes of volcanic rift zones? J. Geophys. Res. Solid Earth 104, 20007–20020 (1999).

    Article  Google Scholar 

  13. 13.

    Pinel, V. & Jaupart, C. Magma storage and horizontal dyke injection beneath a volcanic edifice. Earth Planet. Sci. Lett. 221, 245–262 (2004).

    ADS  CAS  Article  Google Scholar 

  14. 14.

    Andronov, A. A., Vitt, A. A. & Khaikin, S. E. Theory of Oscillators: Adiwes International Series in Physics Vol. 4 (Elsevier, 2013).

  15. 15.

    Anderson, K. R. et al. Magma reservoir failure and the onset of caldera collapse at Kīlauea volcano in 2018. Science 366, eaaz1822 (2019).

    CAS  Article  Google Scholar 

  16. 16.

    Poland, M. P. et al. in Characteristics of Hawaiian Volcanoes Vol. 1801, 179–234 (US Geological Survey, 2014).

  17. 17.

    Salvatier, J., Wiecki, T. V. & Fonnesbeck, C. Probabilistic programming in Python using PyMC3. PeerJ Comput. Sci. 2, e55 (2016).

    Article  Google Scholar 

  18. 18.

    Patrick, M. et al. Cyclic lava effusion during the 2018 eruption of Kīlauea volcano. Science 366, eaay9070 (2019).

    CAS  Article  Google Scholar 

  19. 19.

    Wu, S.-M., Lin, F.-C., Farrell, J., Shiro, B., Karlstrom, L., Okubo, P., and Koper, K. Spatiotemporal seismic structure variations associated with the 2018 Kīlauea eruption based on temporary dense geophone arrays. Geophys. Res. Lett. 47, e2019GL086668 2019.

    ADS  Google Scholar 

  20. 20.

    Costa, A., Melnik, O. & Sparks, R. Controls of conduit geometry and wallrock elasticity on lava dome eruptions. Earth Planet. Sci. Lett. 260, 137–151 (2007).

    ADS  CAS  Article  Google Scholar 

  21. 21.

    Epp, D., Decker, R. W. & Okamura, A. T. Relation of summit deformation to east rift zone eruptions on Kīlauea Volcano, Hawaiʻi. Geophys. Res. Lett. 10, 493–496 (1983).

    ADS  Article  Google Scholar 

  22. 22.

    Iverson, R. M. et al. Dynamics of seismogenic volcanic extrusion at Mount St Helens in 2004–05. Nature 444, 439–443 (2006).

    ADS  CAS  Article  Google Scholar 

  23. 23.

    Roche, O. & Druitt, T. H. Onset of caldera collapse during ignimbrite eruptions. Earth Planet. Sci. Lett. 191, 191–202 (2001).

    ADS  CAS  Article  Google Scholar 

  24. 24.

    Chen, C. W. & Zebker, H. A. Network approaches to two-dimensional phase unwrapping: intractability and two new algorithms. J. Opt. Soc. Am. A 17, 401–414 (2000).

    ADS  CAS  Article  Google Scholar 

  25. 25.

    Agram, P. et al. New radar interferometric time series analysis toolbox released. Eos 94, 69–70 (2013).

    ADS  Article  Google Scholar 

  26. 26.

    Lohman, R. B. & Simons, M. Some thoughts on the use of InSAR data to constrain models of surface deformation: noise structure and data downsampling. Geochem. Geophys. Geosyst. 6, Q01007 (2005).

    ADS  Article  Google Scholar 

  27. 27.

    Mogi, K. Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them. Bull. Earthq. Res. Inst. 36, 99–134 (1958).

    Google Scholar 

  28. 28.

    Baker, S. & Amelung, F. Top-down inflation and deflation at the summit of Kīlauea volcano, Hawai’i observed with InSAR. J. Geophys. Res. Solid Earth 117, B12406 (2012).

    ADS  Google Scholar 

  29. 29.

    Segall, P., Anderson, K. R., Pulvirenti, P., Wang, T. and Johanson I. Caldera collapse geometry revealed by near-field GPS displacements at Kīlauea Volcano in 2018. Geophys. Res. Lett. 47, e2020GL088867 (2020).

    ADS  Article  Google Scholar 

  30. 30.

    Dietterich, H. R. et al. Lava effusion rate evolution and erupted volume during the 2018 Kīlauea lower East Rift Zone eruption. Bull. Volcanol. 83, 25 (2021);

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We acknowledge I. Johanson and the Hawaiian Volcano Observatory for providing tiltmeters and GPS stations data. A.R. acknowledges support from the NASA Postdoctoral Program and the Universities Space Research Association, through a NASA-ASI (Italian Space Agency) agreement. We are grateful to M. Patrick and E. Rivalta for their constructive reviews, which helped to improve the clarity and completeness of the manuscript. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (grant 281945.

Author information




A.R. developed the theory and performed the inversions. P.L. processed InSAR data and provided support with critical discussions of the results. Both authors contributed to the manuscript writing.

Corresponding author

Correspondence to Alberto Roman.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Matthew Patrick and Eleonora Rivalta for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Time between collapses for Piton de la Fournaise, Miyakejima, Fernandina2 and Kīlauea.

The solid lined corresponding to the best fit of equation (7). The time between collapses has been scaled by the value of equation (34) when n = 0. The collapse number has been scaled by Nmax. PdF, Piton de la Fournaise. Source data

Extended Data Fig. 2 Tilt data.

a, North–south component of tilt recorded at UWD. This average signal was obtained by stacking 24-h periods of 19 collapses between 3 July and the end of the eruption. The shaded area corresponds to 2 s.d. of the stacking. The best fit of the function Aexp(ξ1t) + Bexp(ξ2t) − C is shown. The corresponding time constants ξ1 and ξ2 are 1.5 h and 8 d, respectively. b, Projection of the tilt of SDH along the radial direction to HLM (blue) and to SCR (green). Source data

Extended Data Fig. 3 Sketch of the two-chamber model.

For clarity, only the additional parameters relevant to the two-chamber model are indicated. Parameters such as the geometrical properties or the position of the piston, which are the same for the one-chamber model, are not indicated (see Fig. 2). The properties of the shallow reservoir are marked with subscript s, whereas those of the deeper chamber with subscript d. For Kīlauea the shallow reservoir corresponds to the HLM source and the deep one corresponds to the SCR source. The properties of the conduit feeding the eruption are noted with subscript e, and those of the conduit connecting the two chambers with subscript c.

Extended Data Fig. 4 InSAR data.

a, b, Linear LOS velocity maps (left) and time series (right) for a point (cross on the maps) in the area of maximum subsidence (green dots, blue curve) and the radial UWD tiltmeter (triangle on the maps) time series (black line) for Sentinel-1 descending track 87 (a) and ascending track 124 (b). Grey shading represents the time interval used in the InSAR source modelling. Source data

Extended Data Fig. 5 Subsampled InSAR dataset and inversion results.

Top, data, model and residuals for Sentinel-1 ascending (right) and descending (left) geometries. Bottom, PDFs of the source locations. The horizontal origin is set at the GNSS CRIM station. Source data

Extended Data Fig. 6 Predicted volumes.

Caldera and lava volume (DRE) as a function of collapse number. The relation between the two is given by equation (9). The orange dots correspond to the case in which only VHLM is used to calculate Ψ, whereas for the yellow dots we use VHLM + VSCR. The blue dot indicates the value of the final caldera volume as measured by GLISTIN-A, which is used as an inversion constraint, and the red dot indicates the current estimate of the total erupted volume, which was not included in the inversion dataset. Error bars (2 s.d.) correspond to the uncertainty in the prediction for the VHLM + VSCR case. Error bars for all other predictions are smaller than the marker size. Source data

Extended Data Fig. 7 PDFs of the parameters of the Kīlauea plumbing system.

VHLM, the volume of the HLM reservoir, corresponds to VS in Extended Data Fig. 3. VSCR, the volume of the SCR reservoir, corresponds to Vd in Extended Data Fig. 3. For all the other parameters, see Fig. 2 and Extended Data Fig. 3. Source data

Extended Data Table 1 Parameters used in the calculations shown in Fig. 2
Extended Data Table 2 Parameters of the model kept fixed during inversion

Supplementary information

Supplementary Video 1

This video shows the variation of tilt measured by three stations during the collapse of the Kīlauea caldera. On the top the orange line indicates instantaneous tilt direction, whereas at the bottom the NS component of UWD and SDH station is shown. The locations of the two sources HLM and SCR inferred from InSAR are indicated by the red dots.

Supplementary Video 2

This video illustrates the characteristics of a model in which two reservoirs are connected in series. Instantaneous tilt direction and reservoirs locations are shown in map by the orange lines and the black dot respectively. The caldera is collapsing on the ‘northern’ reservoir, whereas the ‘southern’ reservoir is feeding the eruption. The color-scale indicates vertical elastic displacement, whereas the anelastic displacement due to slip of the piston block is not shown to avoid color saturation. On the bottom the temporal evolution of the tilt for the two stations is shown. The parameters used in this example are given in the Methods “Two reservoirs model” section.

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Roman, A., Lundgren, P. Dynamics of large effusive eruptions driven by caldera collapse. Nature 592, 392–396 (2021).

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