Many volcanic systems are partially or entirely submerged, implying that vents may open underwater. The effect of submerged vents on probabilistic volcanic hazard assessment (PVHA) for tephra fallout has always been neglected, introducing potentially uncontrolled biases. We present a strategy to quantify the effect of submerged vents on PVHA for tephra fallout, based on a simplified empirical model in which the efficiency of tephra production decreases as a function of the water depth above the eruptive vent. The method is then applied to Campi Flegrei caldera, comparing its results to those of two reference end-member models and their statistical mixing.

Several very hazardous volcanic systems are located very close to seas, oceans or lakes worldwide and their vents can be partially submerged by water. As a consequence, the vent of possible future eruptions for such volcanoes could be both inland or offshore, inferring the need of considering the possible different eruptive behaviour of the submerged opening vents with respect to the subaerial ones. Notorious examples of high-risk volcanoes with potentially submerged vents are, among many others, the Auckland Volcanic Field (New Zealand), Rabaul caldera (Papua New Guinea), Santorini (Greece), and the Campi Flegrei caldera (CFc, Italy).

The high risk associated with volcanic activity at some of these partly
submerged volcanoes motivated many efforts to estimate the hazard posed on
the surrounding high-density populated areas, for different possible
hazardous volcanic outcomes

Tephra fallout hazard assessment is commonly achieved by using different
methodologies ranging from mapping the geological record

The goal of the paper is to explore the sensitivity of PVHA results when
considering the inhibiting effect of the overlying water on subaerial tephra
production, in the case that the vent opens offshore. Such sensitivity is evaluated by
comparing the two PVHAs resulting from the proposed models with the two
end-member PVHAs. We also check the sensitivity of the PVHA results of the
empirically based model against the value of

In order to evaluate such sensitivity, in practice we apply the proposed
models to CFc, a caldera system which is approximately half-submerged, being
formed by two nested calderas originated by two major collapses, the first
related to the Campanian Ignimbrite eruption, which occurred about 39 ka ago

Our PVHAs are based on the Bayesian Event Tree for Volcanic Hazard

As we mentioned above, for the sake of simplicity, here we neglect the
possible enhancement in explosivity due to magma–water interaction

The final results of each PVHA are presented as Bayesian probability maps, showing the probability of exceeding a threshold of 3 kPa of tephra load in the target domain and within a time window of 50 years. We then check the sensitivity of the effect of water in the case of CFc by comparing the PVHA resulting from the presented model with the reference PVHAs and with their statistical mixing.

General event tree scheme for BET_VH after

In this section we describe how the effect of the sea has been quantitatively
taken into account. In order to distinguish a possible different behaviour
between inland and submarine eruptions, we introduce a variability of the
probability in subaerial tephra production as a function of the vent
position. In other words, the probability of tephra production at node 6 (see
Fig.

In this case we do not take into account the presence of
water above the offshore vents; in other words, we rely on the assumption
that both inland and offshore vents have the same capability to produce
subaerial tephra. In general, this corresponds to set a uniform best guess
probability at node 6 (

In this case we assume that if waters are deeper than
10 m, the production of subaerial tephra is totally suppressed. The
cut-depth of 10 m is here assumed as a possible order-of-magnitude
size of uplift precursor to explosive eruptions

inland or in shallow water (i.e. water shallower than
10 m) having a maximum capability of producing subaerial tephra
(

offshore deep water (i.e. water deeper than 10 m)
having a totally null capability of producing subaerial tephra (

This hypothesis consists in assuming that the hazard can be modelled by a statistical mixing of the two opposite end-members described in H1 and H2 hypotheses. In this view, the results obtained from H1 and H2 are statistically combined into H3 by representing the latter with a sample composed by the union of two randomly sampled subsets of values (one subset from H1 and one from H2). The relative numerosity of the two subsets is a proxy of the relative weight assigned to H1 and H2, and might be assigned according to the credibility of the two hypotheses for the considered volcano: for example, depending on the knowledge of the local bathymetry, if the sea is very shallow throughout the submerged part, one might want to assign a higher weight to H1, and vice versa.

This empirical hypothesis is based on the set of
observations on subaqueous eruptions described by

PVHA based on H1, H2, H3 and H4 hypotheses at CFc are shown from top to bottom respectively (CF1, CF2, CF3 and CF4). The middle column panels show the best guess (average) value for the probability of observing a tephra load larger than 3 kPa in 50 years due to CFc magmatic eruptions, according to the PVHA model adopted. Left and right column panels show respectively the corresponding 10th and 90th percentiles.

Percent variation (%) between CF1 and CF2 (top left panel), between CF1 and CF3 (middle left panel) and between CF1 and CF4 (bottom left panel) relative to CF1 (in terms of average probability to overcome a threshold equal to 3 KPa in a time window of 50 years). Similarly, percent variations between CF3 and CF2, and CF4 and CF2 relative to CF2 are given in top and middle right panels, respectively. Bottom right panel shows the percent variation between CF4 and CF3 relative to CF4.

As mentioned above, for our PVHAs at CFc we rely on the model BET_VH

Nodes 1–3 represent the probability of experiencing an
eruption in the time window

Nodes 4 and 5 represent the conditional probability to
experience a specific eruptive scenario – that is, an eruption from a given
vent position (Node 4) and of a given size (Node 5). For the spatial
probability distribution (Node 4) of vent opening we rely on results by

Nodes 6–8 represent the impact due to a specific eruptive
scenario. At Node 6 we assess the probability of tephra production given an
eruption of a given size from a given vent. Such probability is parameterized
according to different possible hypotheses, as explained in
Sect.

By modelling with BET_VH the water effect at CFc under the four different
hypotheses H1, H2, H3 and H4, we obtain four different PVHAs for the target
region, respectively labelled in the following as CF1, CF2, CF3 and CF4. CF3
is the statistical mixing of CF1 and CF2, giving equal weight to the two, as
we have no evidence that one of the two hypotheses H1 and H2 could be more
reliable than the other. In Fig.

As mentioned above, for CF4 we set

The overall feature resulting from a comparison of the four PVHAs is that the
maximum of difference is to the southeast of the submerged part of the
caldera. This is due to a combination of factors very peculiar to CFc: the
submerged part of the caldera has a much lower probability of vent opening

As we have stressed above, the variations found in the hazard assessment
computed in this study making different hypotheses is due to the features of
CFc that are not general for other volcanoes, as for example in the case of
the Auckland Volcanic Field

We have explored the effect of potentially offshore eruptions on the PVHA for tephra fallout, by comparing four different hypotheses for tephra production from submerged vents. The proposed models H3 and H4 seem to be a reasonable way to account for submerged vent locations, at least in our application at CFc. In such application, the differences among the four proposed PVHAs are within the epistemic uncertainty attached to the most commonly used H1 model, and are mostly confined to offshore areas. However, this might be a consequence of two peculiarities of CFc (i.e. the low probability of offshore vent opening and the SE direction of prevalent winds). In addition, such differences might not be negligible in terms of risk mitigation strategies and the effects could be completely different for other volcanoes worldwide. Both H3 and H4 models can, in principle, be applied to any other (partially or totally) submerged volcanic system. However, while for CFc they provide similar results, this might not be generalized to other volcanoes, since their results depend on local features of the considered volcano (i.e. bathymetry, spatial probability of vent opening, prevailing wind field compared to coastline direction, etc). In conclusion, we argue that a comparison with PVHAs based on H3 and H4 assumption might be a simple and computationally cheap strategy to quantify the effect of submerged vents on subaerial tephra production and related hazard.

The proposed contribution neglects possible efficient magma–water interaction at very shallow waters, that should be considered in future works on more comprehensive PVHA for tephra fallout and other phenomena, to further explore the sensitivity of hazards to such effect.

The work has been developed in the framework of “ByMuR”
(