Phreatic eruptions at Whakaari Volcano driven by hydrothermal mineralisation and magmatic gas input

Abstract

Phreatic eruptions are a potentially lethal type of volcanic activity that is notoriously difficult to forecast. Understanding the complex processes that make eruptions more likely is a key step towards detecting precursory signals. Here, we employ 3-dimensional numerical models of heat and fluid flow based on field and laboratory data from Whakaari/White Island Volcano in New Zealand to explore the thermal, hydraulic, and geologic conditions that promote phreatic eruptions. Our results show that hydrothermally mineralised low-permeability seals can trap rising steam and magmatic gases until the pressure exceeds the tensile strength of the rock within days to months. Changes in persistent degassing through secondary vents can provide valuable insights into when the main sealed conduit is building to eruption. This study provides new insights into the timescales and mechanisms promoting phreatic eruptions, and a starting point to quantitatively interpret volcanic signals in terms of subsurface activity and eruptive potential.

Phreatic eruptions at Whakaari volcano are influenced by subsurface pressurisation magnitudes and timescales, which are significantly influenced by hydrothermal mineralisation and magmatic gas input rates, according to 3-dimensional numerical modelling of volcanic hydrothermal systems.

Introduction

Phreatic, or gas-driven, eruptions occur when groundwater is heated by contact with hot magma, magmatic gases, or volcanic rock^1–4. The resulting fluid expansion can generate immense pressure that causes violent eruptions, ejecting ballistics and steam without involving new magma. Key factors contributing to these eruptions include the intensity of the heat source, the volume of available fluid, and the characteristics of the overlying rock, such as permeability^2,4. However, phreatic eruptions are typically unpredictable due to their shallow subsurface origins and rapid changes in activity^1,4. Fatalities resulting from the Mount Ontake eruption in Japan in 2014⁵ and the Whakaari/White Island Volcano eruption in New Zealand in 2019⁶ show their sudden and hazardous nature, highlighting the importance of monitoring hydrothermal systems and understanding the underlying physical processes.

One favoured mechanism for initiating phreatic eruptions is pressure build-up due to accumulating and expanding hot gases trapped under a hydrothermal seal^2,4,7. When the pressure exceeds some threshold, depending on the mechanical properties of the seal, the seal ruptures and hot gases escape violently as a phreatic eruption^7–9. Changes in monitoring signals such as seismic activity, ground deformation, and increased degassing and heat flux can indicate subsurface heat and fluid movement potentially associated with pre-eruptive processes^1,3,4,10. However, the process of pressurising trapped gases is not directly observable at the surface, and so numerical simulations are necessary to determine the geological and thermal conditions as well as the timescales under which pressurisation can occur.

Simulating the processes leading to a phreatic eruption requires comprehensive conceptual models of the volcano-hydrothermal system, robust rock property input parameters, and monitoring data for calibration/sense-check. Whakaari volcano meets all of these requirements. Studies of Whakaari have benefited from its historical, relatively easy access for sampling and field campaigns, its publicly available monitoring data¹¹, and long-term concerted efforts by researchers that have resulted in unusually comprehensive conceptual models^6,12. Phreatic eruptions have been the dominant type of eruption at Whakaari since the 1970s, resulting in numerous events with high-resolution monitoring time series that have been analysed extensively^13–16. Crucially for this study, rock properties have been measured at Whakaari and placed in a global context^17–20, providing field-based ranges to inform numerical models and ensure that they are as realistic as possible.

Whakaari is an active stratovolcano located ~50 km offshore in New Zealand’s Bay of Plenty, which has experienced more than 30 phreatic eruptions since 1826^18,21. Between 2012 and 2019, there were four episodes of phreatic activity that culminated in the tragic December 2019 eruption that killed 22 people^21,22. Observations have been limited following the 2019 eruption due to restricted access, but steam explosions and eruptive activity have been detected as well as frequent steam and gas plumes²³.

Prior to the eruptions in 2012, 2013, and 2019, seismic monitoring detected changes in subsurface activity over days to around three months, which were attributed to a combination of increased magmatic gas input and variable hydrothermal sealing^13,14,21,24. A lack of precursors before the 2016 eruption, combined with evidence of hydrothermal mineralisation and a seal in the shallow vent area, suggests that this event was generated by trapped meteoric fluids, without any increased magmatic gas input^19,21.

Phreatic eruptions at Whakaari are fed by a hydrothermal system that is long-lived (>20ka) and dynamic^6,25. Hydrothermal fluids are derived from a mixture of meteoric water, saltwater, magmatic vapour, and solutes dissolved from rocks^12,26. There is compelling evidence that heat and magmatic vapour are rising from magma ponding at 1–2 km depth that is periodically fed by deeper magma at ~4–9 km depth^6,27. Surface expressions of the hydrothermal system include a crater lake, fumaroles, and acid springs that are primarily focussed over ~100 m-long area within the crater floor²⁸. Two major and reasonably persistent surface features, the shallow crater lake above the main vent and a fumarole to the southeast (Fumarole 0), are thought to be fed directly by magmatic gases via permeable conduits that are connected in the subsurface (Fig. 1a)^12,28. Contrasting long- and short-term temperature trends at these features^12,29,30 suggest that, while their conduits are connected at some depth, fluid pathways and flow rates are somewhat independent in the shallow subsurface. Variable hydrothermal alteration is thought to create sealing at the top and along the vertical sides of the conduits^12,19,31,32, reducing the ability of hydrothermal fluids to escape.

Fig. 1. Model of our study area representing Whakaari volcano.

a Rock types comprise host rock (grey), fluid conduit (orange), and top and side seals (brown). The main surface degassing features, the vent and Fumarole 0 (F0), are also labelled. Models explored how overpressure built up below the seal (red star) as a factor of varying seal permeabilities and fluid injection rates from depth. Initial pressure (b) and temperature (c) conditions were calculated from 1 Myr of low-level passive magmatic degassing ^6,25 followed by 200 years of present-day degassing levels ^18,21.

Observations of persistent degassing at Whakaari imply that it has an open conduit and a reasonably constant gas source. For example, SO₂ measurements have typically averaged around 5 kg s⁻¹ over the last 30 years^28,30,33. They increased to ~20 kg s⁻¹ in 2013²⁹ and 2019²⁸, and to 45 kg s⁻¹ approximately 40 min prior to the 2019 eruption¹⁶. Geochemical analysis suggests that degassing at the surface is ~59% water/steam, 28% CO₂, and 10% SO₂ by mass³⁰. Based on measured SO₂ flux, this provides total mass flux estimates of 50 kg s⁻¹ during background activity, 200 kg s⁻¹ when moderately elevated, and up to 500 kg s⁻¹ during pre-eruptive activity.

Volcanic activity and hydrothermal alteration have resulted in highly heterogeneous rocks at Whakaari, with interlayered and variably altered ash tuffs and lavas³¹. Laboratory experiments found a range of porosity from ~0.01 to ~0.7 and permeability from ~10^–19 to ~10^–11 m², depending on the rock type, the presence of fractures, and hydrothermal alteration^19,31. The strength of the rock was also found to be within a wide range, depending on the porosity and the presence of water^17,19,20. At Whakaari and globally, the tensile strength at a porosity of <0.05 could be as high as 28 MPa, but as low as 2 MPa³⁴. However, high-porosity volcanic rocks (i.e.,> 0.3) always have a tensile strength below 5 MPa³⁴. Hydrothermal mineralisation reduces porosity and therefore increases the tensile strength, while dissolution increases porosity and therefore decreases the tensile strength³⁵.

Little is known about the timescales of hydrothermal sealing processes, which may vary from decades down to days^2,4. The precipitation of pore-filling sulphates, clay and sulphur minerals, and silica can be localised or extensive, and occur progressively or rapidly^7,36. This can result in decreased permeability over varying spatial and time scales, which can also be offset by rapid increases in permeability due to fracturing^19,32,37,38. At Whakaari, mineralised zones (alunite, anhydrite) may open/close rapidly, in seconds to hours, due to the low tensile strength of the hydrothermally altered material¹⁹.

For an eruption to occur, steam and magmatic gases accumulate in the subsurface, increasing pressure until the rock fails. This requires that pore fluid pressure exceeds the combination of confining pressure from overlying rocks and fluids, and the rock tensile strength. The difference between pore fluid pressure and confining pressure, termed the overpressure, must therefore exceed the tensile strength of the rock for failure to occur. Laboratory measurements on hydrothermally altered rocks suggest a tensile strength between ~2 and 7 MPa for porosity of around 0.15³⁵. We compare modelled fluid overpressure to a failure overpressure of 5 MPa, given the likely lower porosity and therefore higher tensile strength of the highly altered seals in our models, and that the tensile strength of a rock-mass may be lower than that of a sample measured in the laboratory³⁹.

To simulate the effects of hydrothermal mineralisation on fluid flow and potential eruptive activity, we used the software Waiwera⁴⁰ to model changes in overpressure under different conditions at Whakaari volcano. Permeable zones representing vertical or dipping fluid conduits (1 × 10^–12 m²; orange zones in Fig. 1a) were surrounded by seals of varying permeability (brown zones in Fig. 1a). We assumed that the hydrothermal sealing process was instantaneous because of uncertainties around sealing timescales and the potentially rapid mineralisation at Whakaari¹⁹. Due to the lack of subsurface information, the host rock was assigned a uniform permeability of 1 × 10^–14 m². This value considers the wide range of permeability exposed by laboratory measurements^19,31 as well as the influence of permeability-enhancing fractures³⁷, and is consistent with other volcano-hydrothermal modelling studies^12,41,42. Guided by experimental observations, we decreased the permeability in the top seal and side seals by orders of magnitude^19,32 to explore how the overpressure below the bottom of the seal (where a phreatic eruption is most likely to originate) increases as the permeability of the seal is reduced by hydrothermal mineralisation. We also changed fluid input into the base of the model based on total mass flux estimates from surface measurements^16,28,30,33 to simulate varying levels of magmatic activity at depth. We began these simulations from initial pressure (Fig. 1b), temperature (Fig. 1c), and gas saturation distributions calculated to represent historical hydrothermal activity at Whakaari, with elevated temperatures beneath the crater floor and a gas-filled main conduit as observed in the field⁶. A range of models was then run for a simulated time of three months to represent hydrothermal activity in the lead-up to a potential eruption.

Results and Discussion

The modelling results (Fig. 2) show how overpressure gradually increases from the base of the model (just above the magma reservoir) vertically to the surface, also spreading laterally. Initially, pressure is broadly hydrostatic and uniform with depth (Fig. 1b). As heated fluid rises from below, overpressure builds near the surface (Fig. 2). If the system is open, the shallow overpressure increase is relatively small unless fluid input rates are at the highest level (Fig. 2a; Supplementary Table 1). However, the overpressure begins to build in the shallow subsurface if a seal has formed at the top of the conduit (Fig. 2b). If there is vertical sealing along the sides of the conduits instead of the top, lateral fluid flow is inhibited, and overpressure increases along the conduits at all depths (Fig. 2c). The combination of top and side seals results in the greatest increase in overpressure (Fig. 2d, e). If fluid input is simultaneously increased, the capability limits of the software can be approached and the models terminate after days or months (Fig. 2e; Supplementary Table 1).

Fig. 2. Modelled overpressure under different sealing conditions.

Model results after 3 months of consistent background activity (50 kg s⁻¹; left panels), moderately elevated fluid input (200 kg s⁻¹; centre panels), or high fluid input (500 kg s⁻¹; right panels). The cross-section is along the same NW-SE line as Fig. 1a. a Seal rocks have the same permeability as surrounding rocks: 10^–12 m² at the top of the conduit, 10^–14 m² at the sides. b The seal at the top of vent conduit has a reduced permeability of 10^–17 m². c Seals at the sides of the conduits have a reduced permeability of 10^–17 m². d) Seals at the top and sides of the conduits have permeability reduced by one order of magnitude: 10^–13 m² and 10^–15 m², respectively. e Seals at the top and sides of the conduits have reduced permeability of 10^–17 m². Moderate and high fluid input models ended prematurely with top and side seal permeabilities of 10^–17 m², and results are shown after 15 days.

The numerical modelling results show that overpressure increases with any hydrothermal sealing at the top or along the sides of the conduit (Fig. 2). However, if the sides or top are unsealed, the final overpressure is below 5 MPa with background levels of fluid input (Supplementary Table 1 and Fig. 1), and a phreatic eruption would therefore only occur if the seal or surrounding material was weak. To exceed our threshold overpressure of ~5 MPa, permeability must decrease in both the top and side seals of the conduit, by at least one order of magnitude in one and two orders of magnitude in the other (Fig. 2d). If there is a concurrent increase in fluid input from below, a decrease of one order of magnitude in either top or side seals may be sufficient (Fig. 2b, c) corresponding to partial or spatially inconsistent sealing.

It is often assumed that boiling is an important mechanism leading to phreatic eruptions^1,2,9. However, the shallow hydrothermal system at Whakaari is already hot and largely vapour dominated^12,28. Our results suggest that as hot fluids become trapped and accumulate beneath the seal (Fig. 3a), overpressure increases rapidly for several hours and then more gradually over weeks (Fig. 3b). Fluids stay in vapour phase throughout (Fig. 3c) and boiling is not necessary because the increasing mass of steam raises the pressure, while the resulting higher pressure reduces the steam compressibility. This mechanism is likely applicable at other vapour-dominated hydrothermal systems where gas accumulation beneath a shallow seal occurs. In contrast, in liquid-dominated systems, boiling and phase changes probably play a more critical role in generating overpressure and initiating phreatic eruptions.

Fig. 3. Changes in modelled mass flux, pressure, and vapour saturation over one month.

Model results in a grid block below the seal (red star in Fig. 1) for a representative model: top and side seal permeabilities 10^–15 m² and fluid input 200 kg s⁻¹. a Fluid mass flux upwards through the grid block over one month. b Overpressure. Dashed grey line shows failure overpressure threshold. c Vapour saturation, the proportion of air + steam as a fraction of total fluid.

Timescales of pre-eruptive hydrothermal changes

Timescales of hydrothermal changes before phreatic eruptions have been inferred after the event in many studies globally. Changes in gas emissions, seismicity, and deformation have preceded eruptions by minutes, days, weeks, or months at volcanoes in Chile (Lascar), Costa Rica (Poás, Rincón de la Vieja), Indonesia (Kawah Ijen), Japan (Aso caldera, Hakone, Mt Ontake), and New Zealand (Ruapehu, Tongariro)^5,36,43–46. These timescales are consistent with changes over days to months observed prior to phreatic eruptions at Whakaari^13,14,21,24. Our results indicate that these timescales are a direct result of hydrothermal mineralisation and fluid input rates from depth.

If the system seals completely while flux is elevated, our model results suggest that overpressure can increase to the failure threshold in around nine days, or 21 days if flux is moderately elevated (Fig. 4; Supplementary Table 1). If the sides of the conduits are completely sealed, even a decrease in permeability of one order of magnitude at the top can result in failure overpressure in timeframes of 10 or 28 days (Fig. 4). Similarly, if the top is completely sealed and the permeability of the sides is only reduced by an order of magnitude, it takes 12 days to reach failure overpressure with elevated fluid input, or 27 days if fluid input is moderately elevated (Fig. 4; Supplementary Table 1).

Fig. 4. Time to failure overpressure under different conditions.

Arrows indicate direction of increasing permeability from fully sealed to unsealed (where permeability is the same as surrounding rock). Colours correspond to the volume of fluid input needed for failure overpressure to be reached: never reached (blue), only with highest gas input (green), with high and moderate input (orange), and with any level of gas input (red). In each box, the columns show days to failure overpressure for background (left), moderate (middle), and high (right) levels of fluid input.

As expected, lower rates of fluid input from depth result in slower pressure build-up near the surface. However, if the hydrothermal seals are well developed (i.e. low permeability), failure overpressure can still occur without any increased fluid input from depth over one or two months (Fig. 2e left panel; Fig. 4). If there is a moderate increase in fluid input, most sealing conditions result in failure overpressure within weeks (Fig. 4). With a maximum fluid input rate of 500 kg s^-1, pressurisation timescales are days to weeks depending on the permeabilities of the side and top seals, and months if only the top is sealed (Fig. 4). However, this level of fluid flux is much higher than typically observed^28,30 and is unlikely to be sustained for days to weeks, suggesting that sealing needs to be present at both the top and sides of the conduit for an eruption to occur because of sealing (Fig. 4).

Model assumptions and their implications

Timescales of days to months from our models are consistent with timescales observed prior to eruptions at Whakaari^13,14,21,24. Modelled timescales are indicative only because of limitations and assumptions in our models. There are several assumptions implicit in the modelling software, such as the applicability of modified Darcy’s Law to simulate fluid flow, the discretisation of rock properties into finite elementary volumes, the assumption that rocks are in local thermal equilibrium with fluids, and the absence of reactive fluid flow^40,47. Assumptions are unavoidable given the nature of the modelling and the sparse subsurface information, but could have implications for our results.

A key component of our models is the occurrence and failure of a seal. The seal at Whakaari is comprised of alunite, silica polymorphs, and clay minerals¹⁹. Alunite is thought to be the main binder and can impart strength to the material¹⁹. There is little information about rates of alunite precipitation in volcanic environments, but seal formation at Whakaari is typically thought to be fast¹⁹. We therefore assume that alunite precipitation occurs on a timescale that has minimal effects on the timescales of pressurisation presented in our models. If alunite precipitation was slow, our modelled timescales would underestimate the time required to pressurise the system. Further constraints, for example, from laboratory experiments, would be very welcome.

The seal is assumed to be 100 m-thick at the top of the main conduit, based on geophysical measurements at Whakaari²⁸. However, a seal was not incorporated at the top of the conduit feeding Fumarole 0 because the fumarole has been persistently active even when mass flux rates have dropped at the main conduit⁶. Vertical seals were simulated around the edges of the main conduit and the conduit feeding Fumarole 0 because they are thought to be linked at depth¹². If both conduits were sealed at the top, pressurisation within the edifice would be faster and the time to failure reduced. Thicker or more extensive seals could result in faster pressurisation, and a thinner top seal in slower pressurisation.

For failure to occur, we envisage the tensile failure of an intact seal when pore pressure exceeds confining pressure of overlying gas-saturated rock combined with the tensile strength of the sealing rock⁴⁸. We consider only tensile failure, and do not consider reactivation of any local shear fractures/faults within the seal that could reduce time to eruption. Conversely, progressive tensile failure or brittle shear failure without tensile failure could increase time to eruption⁴⁸. We have assumed a threshold of 5 MPa for tensile strength of the sealing rock, in the middle of the 2–7 MPa range suggested by experiments³⁴. A threshold of 5 MPa results in 43 models reaching failure, compared with 62 for a threshold of 2 MPa and 39 with a threshold of 7 MPa (Supplementary Table 1). Many of the differences are models with background levels of fluid input (Supplementary Table 1). This shows that detailed site-specific rock strength measurements are important, especially when fluid flux is not elevated.

To minimise assumptions, we have used the simplest rock properties in our models. Permeability especially is known to be heterogeneous and anisotropic, which can have strong effects on fluid flow⁴⁷. However, field-scale measurements are notoriously difficult, and laboratory measurements reveal orders-of-magnitude variability and do not account for large fractures that would increase permeability and decrease strength^19,31. To explore the effects of more complex rock properties, we ran additional models with anisotropic permeability or heterogeneous porosity. In the anisotropic permeability cases, permeability in the conduit was reduced by one or two orders of magnitude in the lateral directions, and host-rock permeability was reduced by one or two orders of magnitude in the vertical direction^42,49–51. In these models, time to eruption is less (Fig. 5) and maximum overpressure is greater than equivalent models with isotropic permeability (Supplementary Table 1). This is not unexpected, because modelled permeability across the direction of flow is reduced, enhancing flow up the conduit and therefore overpressure below the seal. Measurements of porosity on rocks thought to represent the seal at Whakaari suggest they could have lower or higher porosity than host rock¹⁹. Higher porosity in the conduit and either lower or higher porosity seal have a much smaller effect on model results than permeability (Fig. 5). Timescales to eruption in all cases are days to months, and eruption occurrence is only different if the system has little to no sealing (Fig. 5, Supplementary Table 1). Therefore, we conclude that results from even our simplest models are representative of the processes and timescales leading to phreatic eruptions. However, using these models for a more detailed study would require detailed rock property estimates from field measurements and experiments, and robust model calibration with field data.

Fig. 5. Time to failure overpressure for different model setups, with moderate fluid input of 200 kg s^-1.

Arrows indicate the direction of increasing permeability from fully sealed to unsealed. Colours correspond to different model scenarios: blue bars show results for the simplest model with isotropic permeability, homogeneous porosity, and initial conditions after 200 years of background activity. Red (k_1) and green (k_2) correspond to models with anisotropic permeability, where permeability is reduced by one or two orders of magnitude, respectively, in the horizontal direction in the conduit and seal, and in the vertical direction in the host rock. Heterogeneous porosity is 0.3 in the conduit, 0.15 in the host rock, and either 0.05 (Φ_low; yellow bars) or 0.3 (Φ_high, purple bars) in the seal. Teal bars (IC 50 yrs) show results for the simplest model, but with initial conditions after 50 years of background activity.

A limitation imposed by the Waiwera software is that rock deformation is not accounted for. If rocks could deform elastically, they could absorb some of the increasing pressure^15,52 and therefore the onset of failure would likely be delayed. Similarly, rock properties are assumed to be constant over time for each model, whereas changes in pressure, temperature, or fluid-rock interactions can affect the petrophysical properties of the rocks through, for example, the opening or closing of fractures²⁰. Resulting porosity and permeability are unlikely to be outside the ranges modelled, but could change within those ranges, therefore changing the time to failure or possibly whether failure occurs.

Hydrothermal fluids at Whakaari are comprised of a mixture of water and magmatic gases^12,26. For simplicity, our models have used steam as the simulated fluid, which is estimated to make up 60% or more of the mixture^6,30. Model temperatures within the conduit (Fig. 1c) are above the critical temperature for gases that dominate magmatic hydrothermal systems: steam has a critical temperature of 374 °C, CO₂ 31 °C, and SO₂ 157 °C³⁰. At the base of the model, pressures exceed 8 MPa when the system is sealed and has increased fluid input (Fig. 2), which is above the critical pressure for CO₂ (7.38 MPa) and SO₂ (7.88 MPa) but not steam (22 MPa). However, the critical pressure is not exceeded in most of the conduit, and all three major fluids would be in a superheated state with comparable fluid properties. We are focused on shallower depths below the seal, and therefore steam is a reasonable first approximation for the combined hydrothermal fluids. If liquid water were present as well as steam, for example, if modelling monitoring data at a fumarole or spring, the significant proportions of CO₂ and SO₂ observed at Whakaari^12,30 would reduce the boiling point of the mixture and so would be important⁵³.

The rate of fluid injection into the base of the model was based on surface measurements^16,28–30. Because the fluid flux rate 1 km below the surface is unknown, we modelled three different scenarios to encompass the range of activity observed at Whakaari. Linking monitoring data^28–30 to these models would help to refine likely rates and provide indications of changes over time that our models do not incorporate.

To explore changes over three months, we have to select reference starting conditions. These were based on low levels of hydrothermal activity followed by an increase to background levels for 200 years. If initial conditions are based on activity modelled at background levels for 50 years, areas around the conduit are cooler and with less extensive vapour phase (Supplementary Fig. 2). The system therefore responds faster if hot fluids enter the conduit at elevated levels, and eruptive overpressures are reached if a top seal with permeability ≤ 10⁻¹⁵ m² traps fluids, even without sealing at the sides (Fig. 5). Under all other conditions, time to failure and final overpressure are comparable to those with the simplest model (Fig. 5, Supplementary Table 1). Initial conditions are unknown and so need to be explored, but our models suggest they only strongly affect results for a small subset of scenarios.

Implications for interpreting monitoring data

Phreatic eruptions are the most unpredictable type of volcanic eruption globally¹⁸. Our new analysis adds to the understanding of phreatic eruptions by showing that the magnitudes and timescales of subsurface pressurisation are highly dependent on permeability-reducing hydrothermal mineralisation and rates of hot fluid input from depth. Because these cannot be measured directly at the surface, our models are an important step towards quantitatively interpreting data that monitor hydrothermal activity. As such, they can also help to inform monitoring networks and field campaigns⁵⁴.

Model results suggest that rapid pressurisation requires temporarily tight permeability and/or increased fluid flux (Fig. 5). Monitoring data can indicate these changes, but are often ambiguous²⁹. For example, decreasing surface gas flux measurements could result from waning magmatic hydrothermal activity or tightening seals, which have opposite implications for the likelihood of a phreatic eruption. However, increasing pressurisation from tightening seals may also be reflected in changing seismicity or deformation, helping to distinguish between these scenarios^21,55. Comparing model outputs to monitoring data can test and refine qualitative interpretations of subsurface activity from these integrated datasets; temperatures and gas fluxes can be modelled directly, while deformation, seismicity, and gravity signals can be calculated from modelled pore pressures^{15,41,42,54,56–58}. As models are modified and refined to better represent these data, they can provide new insights into the location, timing, and other hydrothermal source characteristics of phreatic eruptions. Integrated, quantitative models therefore hold promise for improving universal forecasting, as well as forecasts tailored to individual volcanoes⁵⁹.

Fluid flow models can also provide insights into veiled vent processes by linking them to activity at secondary vents or diffuse degassing zones. These are common features at volcanic hydrothermal systems and can be monitored even when the primary vent is inaccessible^4,60–62. Changes in fumarole activity related to volcanic eruptions have been observed at Poás, Mt Etna (Italy), and Masaya (Nicaragua) volcanoes, and the Kirishima Volcanic Complex (Japan), although the relationship is often complicated by atmospheric and hydrologic effects^63–66. At Whakaari, Fumarole 0 has been intermittently active for at least 15 years, and has experienced temperature increases of 10–50 °C between monthly measurements^12,29. Our models suggest that changes at the top of the sealed conduit are likely too small and too late to indicate an impending eruption, but temperature and mass flux at Fumarole 0 may increase over similar timescales to subsurface pressure build-up (Fig. 6). This study therefore highlights the possibly important role of monitoring temperature, heat and/or gas flux at auxiliary degassing zones when assessing potential eruptive activity. More refined subsurface models can provide a mechanism to quantitatively link fumarolic activity to subsurface pressurisation for eruption forecasting.

Fig. 6. Model of a fully sealed system with background levels of fluid input over three months.

a Modelled overpressure over time just below the seal (subsurface); at the vent; and at Fumarole 0 (F0). The grey dashed line corresponds to failure overpressure. b Cross-section of modelled overpressure after three months. c Modelled temperature over time. d Cross-section of modelled temperature after three months. e Modelled mass flux over three months. f Cross-section of the geological model, showing rock types as in Fig. 1a and model output locations.

Based on a range of simplifying assumptions, model results suggest that hydrothermal mineralisation and magmatic fluid fluxes have a strong control on the occurrence and timing of phreatic eruptions. Our results should encourage the quantitative examination of volcanic monitoring datasets around the world within the context of fluid flow-induced pressurisation in hydrothermal systems.

Methods

Whakaari hydrothermal system model

We created 3D multiphase heat and fluid flow models of Whakaari using Waiwera software. Waiwera is a parallel, open-source simulator designed specifically for hydrothermal fluid flow⁴⁰. It solves time-dependent mass and energy conservation equations within the flow domain, discretised using a finite volume mesh⁴⁰. If multiple mass components are present such as water and air or CO₂, a separate conservation equation is solved for each; in our models, we used energy, water, and air components to simulate the vadose zone above saturated rock. The elevation of the water table was calculated within the models and was around sea level across the model domain.

To create the Waiwera models, we used Leapfrog Energy to create a geological model with three rock types (Fig. 1a). The model encompassed an area of 4.5 km by 4.5 km, extending well beyond the volcanic conduit to minimise boundary effects. The base of the model was 1 km below sea level, just above the inferred shallow magma reservoir. The top surface of the model followed topography with a maximum elevation of 300 m above sea level (Fig. 1). We discretised the geological model and populated the resultant mesh with rock types within Leapfrog Energy. The main high-permeability conduit encompassed an area of 100 m by 100 m with grid dimensions of 25 m × 25 m. Grid block size increased progressively away from the conduit to a maximum of 500 m × 500 m (Supplementary Fig. 3). Grid blocks were 50 m thickness vertically between the base of the model and 300 m below sea level, and 25 m thickness above. In total there were 172,260 grid blocks.

We exported the resulting populated model grid from Leapfrog Energy and set the top surface boundary condition at atmospheric temperature (15 °C). Pressure was set at atmospheric at the top of the subaerial parts of the edifice (101,325 Pa), and hydrostatic where the edifice was under the ocean (Supplementary Fig. 3). Hydrostatic pressure was calculated at the centre of the grid block at the top of each column, given by density of water × gravity × depth of sea water. Whakaari’s crater lake was not included in the model because it is ephemeral, and shallow compared to model resolution⁶. Vertical boundary conditions were no-flow. Heat was injected into the base of all models at 0.1 W m^-2 and rainfall across the top at 1.93 × 10^–6 kg s^–1 m^–2 to represent background conditions typical of Whakaari and the Bay of Plenty area^67,68 (Supplementary Table 2).

Relative permeability and capillary pressure functions can both have large effects on hydrothermal fluid flow, but are typically poorly constrained⁴⁷. Relative permeability, which accounts for reduced mobility of one fluid phase due to the interfering presence of another phase, was represented by the Corey curve in our models. This follows similar modelling of the volcanic hydrothermal system at Campi Flegrei⁴², with irreducible gas and liquid saturations of 0.05 and 0.33, respectively. Capillary pressures, pressure differences between fluid phases, were given by a linear function of liquid saturation above 0.33, and equal to 0.01 MPa for liquid saturation below 0.33. This was consistent with similar studies⁴² and found to be more stable than the van Genuchten function at high temperatures and pressures. We tried all functions available within Waiwera for relative permeability and capillary pressure⁴⁰, but other than model instabilities with the van Genuchten function, we found minimal differences in results. This is likely due to the predominantly single-phase steam in the conduit in the models (Fig. 3).

Modelling hydrothermal activity

We ran three stages of models to reach present-day conditions (Supplementary Fig. 4).

Stage 1 represented long-term, low-level activity over the >20 kyr existence of the hydrothermal system^6,25. The model began from uniform atmospheric temperature and pressure and full air saturation (Supplementary Fig. 4-1). Mass was injected into the base of the conduit area evenly across its 16 grid-blocks at 5 kg s^–1 and 350 °C to represent low-level fluid input from depth as measured and modelled at Whakaari^12,30,69. The model was run for 1 Myr to ensure results were not sensitive to the starting conditions. Resulting temperature, pressure, and vapour (air+steam) saturation distributions were saved (Supplementary Fig. 4-2).

Stage 2 represented increased hydrothermal activity over recent decades. Models were run for 200 years with increased fluid input of 50 kg s^–1 across the base of the conduit at an increased temperature of 700 °C^6,30. Models were also run for 50 years to assess sensitivity of final results to initial conditions as discussed in the main text. Temperature, pressure, and vapour saturation distributions calculated from Stage 1 models were used as initial conditions for Stage 2 models, and resulting temperature, pressure, and vapour saturation distributions were saved (Supplementary Fig. 4-3).

Stage 3 explored the effects of varying fluid input rates and permeabilities on hydrothermal fluid flow in the lead-up to a possible phreatic eruption. Temperature, pressure, and vapour saturation calculated in Stage 2 were used as initial conditions for models in Stage 3. For each simulation, a different combination of top seal permeability, side seal permeability, and gas input rate was used (Supplementary Table 1). Overpressure was calculated for each timestep over three months by subtracting the confining pressure in each grid block from modelled pressure. Confining pressure was calculated by Waiwera at the end of Stage 2 for each grid block, and is ~2 MPa under 100 m of sealing gas-saturated rock (Fig. 1b). The final overpressure in a grid block directly below the seal with coordinates 1969780, 5839060, –112 m was saved (Supplementary Fig. 1 and Table 1). The time when overpressure exceeded 5 MPa in that grid block was also saved as a threshold for rock failure and therefore potential eruption (Supplementary Table 1).

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

S.P.-G. conceived the study, designed the models, analysed the results, created the figures, and wrote and revised the manuscript. M.H. collated rock property data, contributed to study design, contextualised model results, and reviewed and edited the manuscript. A.C. ran the model simulations and reviewed and edited the manuscript.

Peer review

Peer review information

Communications Earth and Environment thanks Samuel Scott and Shaul Hurwitz for their contribution to the peer review of this work. Primary Handling Editors: Domenico M. Doronzo and Alireza Bahadori. A peer review file is available.

Data availability

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

Code availability

The Waiwera modelling code is available on GitHub (https://github.com/waiwera/waiwera). Input files and associated Python scripts are also available on GitHub (https://github.com/s-pearsongrant/Whakaari_Waiwera)⁷⁰.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s43247-025-03057-8.