Probabilistic tephra hazard maps for the Neapolitan area: Quantitative volcanological study of Campi Flegrei eruptions

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113,, doi:1.129/27jb4954, 28 Probabilistic tephra hazard maps for the Neapolitan area: Quantitative volcanological study of Campi Flegrei eruptions G. Mastrolorenzo, 1 L. Pappalardo, 1 C. Troise, 1 A. Panizza, 1 and G. De Natale 1 Received 26 January 27; revised 7 November 27; accepted 13 March 28; published 16 July 28. [1] Tephra fall is a relevant hazard of Campi Flegrei caldera (Southern Italy), due to the high vulnerability of Naples metropolitan area to such an event. Here, tephra derive from magmatic as well as phreatomagmatic activity. On the basis of both new and literature data on known, past eruptions (Volcanic Explosivity Index (VEI), grain size parameters, velocity at the vent, column heights and erupted mass), and factors controlling tephra dispersion (wind velocity and direction), 2D numerical simulations of fallout dispersion and deposition have been performed for a large number of case events. A bayesian inversion has been applied to retrieve the best values of critical parameters (e.g., vertical mass distribution, diffusion coefficients, velocity at the vent), not directly inferable by volcanological study. Simulations are run in parallel on multiple processors to allow a fully probabilistic analysis, on a very large catalogue preserving the statistical proprieties of past eruptive history. Using simulation results, hazard maps have been computed for different scenarios: upper limit scenario (worst-expected scenario), eruption-range scenario, and whole-eruption scenario. Results indicate that although high hazard characterizes the Campi Flegrei caldera, the territory to the east of the caldera center, including the whole district of Naples, is exposed to high hazard values due to the dominant westerly winds. Consistently with the stratigraphic evidence of nature of past eruptions, our numerical simulations reveal that even in the case of a subplinian eruption (VEI = 3), Naples is exposed to tephra fall thicknesses of some decimeters, thereby exceeding the critical limit for roof collapse. Because of the total number of people living in Campi Flegrei and the city of Naples (ca. two million of inhabitants), the tephra fallout risk related to a plinian eruption of Campi Flegrei largely matches or exceeds the risk related to a similar eruption at Vesuvius. Citation: Mastrolorenzo, G., L. Pappalardo, C. Troise, A. Panizza, and G. De Natale (28), Probabilistic tephra hazard maps for the Neapolitan area: Quantitative volcanological study of Campi Flegrei eruptions, J. Geophys. Res., 113,, doi:1.129/27jb Istituto Nazionale di Geofisica e Vulcanologia, Osservatorio Vesuviano, Naples, Italy. Copyright 28 by the American Geophysical Union /8/27JB4954$9. 1. Introduction [2] Campi Flegrei is high risk volcanic field due to both the explosivity of the eruptions and to the urbanization of the surrounding districts of Naples and Caserta, which together exceed three million of inhabitants. [3] That said, even if tephra fallout production is not the dominant phase of a future event, our study shows it is a major risk component of any Campi Flegrei eruption. Modeling shows that tephra produced from moderate to high Volcanic Explosivity Index (VEI) eruptions in the area may cause critical ash loads on buildings, and generate serious direct and secondary effects on people over a very wide area. [4] Several parameters affect fall-out hazard: vent positions, magma eruption rates, total erupted mass, grain-size parameters, initial velocity, and transport conditions, including atmospheric thermodynamic parameters, wind direction, wind velocity and their relative temporal changes. [5] These parameters may be, in part, retrieved from the study of past eruptions and from time series of present climate data. However, with a wide range of variability of eruptive and/or transport conditions, realistic hazard maps must be based not simply on data retrieved from the volcanic history of the area, but on a complete and reasonable statistical combination of the parameters [Connor et al., 21; Rossano et al., 1998, 24]. Values of key parameters, not directly retrievable, and their variability, may be constrained by tephra deposition patterns from past eruptions [Connor and Connor, 26]. [6] Here we present the first volcanological, probabilistichazard maps for tephra fall events in the Campi Flegrei area, including Naples and all other districts of the Campania region. The maps are based on simulations of large sets of events, with parameters spanning the whole range of possible eruption VEI for Campi Flegrei caldera. Therefore a large amount of stratigraphic and granulometric data have been collected for a set of well-preserved deposits spanning 1of14

2 Figure 1. Digital topographic map of the Campi Flegrei volcanic field including monogenetic volcanoes and volcanic formations.: AS = Astroni tuff ring; AV = Averno tuff ring; BA = Baia tuff ring; BM = Breccia Museo pyroclastic flow formation; FB = Fondi di Baia cinder cone; MI = Miseno tuff ring; MN = Monte Nuovo cinder cone; MP = Montagna spaccata strombolian formation; MS = Monte Spina small scale pyroclastic flow formation; MSA = Monte S. Angelo plinian deposit; NI = Nisida tuff cone; SF = Solfatara tuff ring; SG = Senga spatter cone; MO = Minopoli violent strombolian formation; PP = Pomici Principali Plinian formation; TGN = Neapolitan Yellow Tuff. the entire history of Campi Flegrei. We have developed a suitable inverse technique to invert tephra deposition data for the main unknown parameters of a complete sample of past eruptions at the caldera. The inferred parameters, and their variability, are used in turn, to give more objective constraints to the hazard maps in terms of occurrence of eruption types and transport parameters. 2. Tephra Fall Events in the Volcanic History of Campi Flegrei [7] The 4, year eruptive history of Campi Flegrei volcanic field is marked by a few very large scale explosive eruptions, and tens of intermediate- to small-scale ones (Figure 1). [8] High volume explosive eruptions occurred at 39 and 14.9 ka BP [Deino et al., 1992, 24; De Vivo et al., 21] and formed a 12 km wide caldera structure that strongly controlled the subsequent volcanic evolution of the area [e.g., Rosi and Sbrana, 1987; Orsi et al., 1996; Di Vito et al., 1999 and references therein]. Vents of the 57 known eruptions occurring after the Neapolitan Yellow Tuff (dated at 14.9 ka BP) were scattered within the caldera depression. Since 5 ka ago, the vents have been located within the innermost caldera structure, within a radius of about 3 km around Pozzuoli. [9] Fallout eruptions in the volcanic history of Campi Flegrei range between VEI values of to 5, with erupted masses ranging between 1 8 to 1 13 kg, column heights from 1 to 45 km, magma eruption rates from 1 2 kg/s to 1 8 kg/s, and a wide variability in the total grain-size distribution, fragmentation and dispersion. However, extremely large events are rare given that the VEI is generally lower than 4. [1] In the last 14.9 ka, the intracaldera activity, prevalently hydromagmatic, mainly formed pyroclastic cones, and consisted of interbedded pyroclastic surge and fallout beds. The pure magmatic, strombolian, subplinian and plinian events, which were subordinate, consist of scoria and lapilli beds with dispersion ranging between a few km 2 and some thousands km 2. Small scale strombolian deposits are mostly dispersed within the caldera rim, while the larger deposits spread outside the caldera within a large area, mostly toward the east. [11] Most deposits consist of sequences of alternating lapilli and fine ash beds, resulting from both pyroclastic surges and fall-out sedimentation. Hydromagmatic and magmatic fallout layers generally show bed sequences with different grain size and thickness, thus indicating a pulsating magma eruption rate and/or column height, likely resulting from subordinate magma/water interactions and/or conduit instability [Mastrolorenzo, 1994]. Vesiculation studies [Mastrolorenzo et al., 21] indicate that most eruptions derive from a common rising and decompression mechanism, while magma/water interaction occurs only at shallow depth, after near-complete magma vesiculation. [12] Maximum thickness of the different fall-out deposits range between tens of meters and a few centimeters for the intracaldera pyroclastic successions. In the stratigraphic sequences of the urban area of Naples, east of Campi Flegrei, subplinian and plinian deposits range in thickness from a few decimeters to about a few meters. In particular, recent archeological excavations in Naples have revealed alternation of human settlements and fallout deposits since the Neolithic. Distal outcrops, of centimeter-thick plinian and subplinian deposits, have been recognized at distances even exceeding 6 km east of the caldera rim [e.g., Di Girolamo et al., 1984; Lirer et al., 1987; Rosi and Sbrana, 1987]. Only the basal fallout unit of the exceptionally high magnitude Campanian Ignimbrite is recognizable thousands kilometers away from Campi Flegrei [Rosi et al., 1999; Perrotta and Scarpati, 23]. [13] Fallout deposits range in composition from trachybasalt to trachyte [D Antonio et al., 1999]. Compositions are not correlated with the age of eruption, but mostly with their magnitude and explosivity; in general the strombolian eruptions are less evolved in composition (from trachybasalt to latite), than are to the subplinian and plinian products (mainly trachytic). An exception is the 1538 AD Monte Nuovo eruption that was fed by magmas with chemical and isotopical composition similar to the high magnitude Campanian Ignimbrite event [Pappalardo et al., 1999]. In only a few cases do major compositional variations occur within a single event, as marked by the emission in the last phase of less evolved magma fractions (e.g., Campanian Ignimbrite, Neapolitan Yellow Tuff, Agnano Monte Spina). 3. Field and Laboratory Studies [14] A set of deposits of the best-known fallout eruptions, both purely magmatic and mixed magmatic and hydro- 2of14

3 Table 1. Volcanological Data for the Main Campi Flegrei Fallout Deposits Clast density (g/cm 3 ) Total deposit volume (km3) Mdf sf F (%) D (km 2 ) Mass Eruption Rate, kg/s Max Column Height, km Dispersion Axes Orientation Volcanic Explosivity Index, VEI Volcanological Classification Pyroclastic Formation Age, Ka Campanian ignimbrite a 39 ultraplinian deposits 5 N9-N E >1.6 Neapolitan yellow tuff b 14,9 plinian deposits 5 N E E Pomici Principali c 1,3 plinian deposits 4 N9-N6 2 E Montagna Spaccata strombolian deposits 2 near circular deposit 5 E Agnano Monte Spina d 4,1 plinian deposits 4 N7 27 E Minopoli >1 strombolian deposits 3 N53 8 E Astroni e plinian deposits 3 N9 2 E Averno f subplinian deposits 3 N215 8 E Monte Nuovo g 1538 AD strombolian deposits 2 near circular deposit <3 <E a Rosi et al. [1999]. b Wohletz et al. [1995]. c Lirer et al. [1987]. d De Vita et al. [1999]. e Isaia et al. [24]. f Mastrolorenzo et al. [1994]. g Di Vito et al. [1987]. 3of14 magmatic, representative of different VEI, have been adopted as reference eruptions and studied in detail. Their thickness and grain-size variations (including granulometric distribution, grain shape and clast density) have been determined, in order to constrain input data for computer simulations (Table 1). For each deposit, samples representative of the whole depositional area have been collected and analyzed. Data available in the literature have also been considered [e.g., Mastrolorenzo, 1994; De Gennaro et al., 1999; Mastrolorenzo et al., 21; Piochi et al., 25]. [15] About 15 new granulometric analyses have been made for the reference deposits. Descriptive Inmann statistical parameters have been weighted by the corresponding relative deposit volumes in order to calculate the average grain-size for the deposit; these data are reported in Table 1. [16] Grain shape analyses have also been carried out on clasts, sized from 5 to4f. For each size class, 3 or more grains have been imaged. A digital camera connected to an optical microscope was used for the 1 to5f class, and macro scale photography was used for the 5 to 2f class. Images were processed and analyzed using Adobe Photoshop and NIH Image 1.6 software. Thus areas and perimeters of the grains were measured and their equivalent values computed; the ratio between the measured perimeter of each grain and the computed equivalent perimeter from the measured area assuming a circular shape give an estimate of the grain smoothness (maximum for ratio equal to 1). Results for such a shape factor are reported in Figure 2. [17] Last, clast densities were also measured for the reference eruptions. Sets of 3 clasts for each granulometric class between to 5f were weighted, then coated by a thin film of paraffin wax for determination of average densities using a picnometer. In order to evaluate the standard deviation in clast density within a sample, densities of single clasts in the range 2 to 5f were determined separately. We consider the volume of the paraffin wax film negligible, because its density is about equal to that of water (1 kg/m 3 ). In addition to the direct density measure- Figure 2. Shape parameters for CF pumice clasts. The measured to computed perimeter ratio gives an indication of the roughness of the clast; values close to 1 indicate smooth, near circular sections. Stars indicate the mean value of the whole data.

4 described by the following well-known convection-diffusion-migration equation @V K K ð1þ Figure 3. Measured CF clast density for all the eruptions considered in Table 1. ments, the inferred densities of clasts in the range.5 mm and 1 micron have been calculated by vesicularity analyses made on backscattered electron images of polished thin sections of epoxy impregnated grains, using a Leo-Cambridge 44 scanning electron microscope at the Engineering Faculty of the University of Naples. Results are reported in Figure 3. [18] Table 1 reports all new and literature data for the reference eruptions, including their inferred VEI values. Detailed data relative to smaller deposits (strombolian events with VEI 1) are mostly unavailable due to the scarcity of outcrops; however, in about ten cases, data are inferred on the basis of the few available field and laboratory results and data. [19] Data relative to the range of VEI with their inferred occurrences (Table 1) have thus been adopted to constrain the ranges of eruptive parameters in our simulations. Column heights of the reference eruptions have been calculated on the basis of the largest clast distribution by using the method of Carey and Sparks [1986]. Total deposit volumes have been calculated by the method of Pyle [1989]. 4. Computational Model [2] The computational model consists of three main parts: (1) a physical model that describes convection, diffusion and the settling of volcanic particles, based essentially on the Suzuki [1983] model, with several improvements, (2) a bayesian approach whose aim is to calibrate and validate critical model parameters not directly measurable by volcanological studies, including initial vent velocity, diffusion coefficients and vertical mass distributions within the column ( beta factor by Suzuki [1983]) and (3) computation of probabilistic hazard maps by simulating several events with different values of eruption parameters and differing wind profiles, with specific probabilities based on the statistics of past eruptions. Simulations are run in parallel on a cluster of 64 processors to allow fully probabilistic analyses in reasonable times Physical Model [21] The transport of tephra in the atmosphere, due to the processes of convection, diffusion and settling, may be where Q is the concentration of tephra (kgm 3 ), v (u,v,w) is the wind velocity vector, K x, K y, K z are diffusion coefficients, and V s is the settling velocity. In the hypothesis of low volume concentrations of tephra, v, K i, and V s depend only on (x,y,z,t) but not on Q so the equation is linear. Given an expression for such coefficients and suitable boundary and initial conditions, equation (1) may be numerically solved to give Q = Q (x,y,z,t). The mass distribution of tephra after all particles have settled may then be calculated by the integration of vertical fluxes at the surface, at a time sufficiently longer than the settling time of the smallest particles of interest. However, such an approach is computationally expensive; in order to calculate the 2D distribution of tephra on the ground for a time t F larger than the settling time of the particles with lowest settling velocity, we have to compute a 3D field for all times t < t F. Instead, we can use a simpler model based on the superposition of analytical 2D solutions: according to Suzuki [1983], we neglect vertical diffusion and convection in the atmosphere with respect to horizontal diffusion and convection because the former has a much smaller effect than the latter above the atmospheric boundary layer. We also consider an isotropic horizontal diffusivity (K x =K y = where c has the meaning of mass of accumulated tephra per unit surface (kgm 2 ). The settling term does not explicitly appear in Suzuki s equation, but its effect is implicitly taken into account by considering that in turbulent diffusion of air fall particles the diffusion time is the fall time of particles [Suzuki, 1983]. This equation is only valid for a wind velocity constant with respect to height, so in order to apply it with a z-dependent wind profile we discretize the atmosphere in layers and apply the solution of equation (2) to each layer. [22] Following Bonadonna et al. [25], we use two functional forms for the diffusion coefficient, depending on the fall times (and hence indirectly from the sizes) of the particles involved in the diffusion process. Horizontal diffusion of large particles, actually, characterized by short fall times, is better described by a linear diffusion, in which K = k is constant in time. Diffusion of small particles, on the contrary, characterized by long fall times, is better described by power law diffusion: K = Ct 3/2, with C =.4 m 2 s 5/2. The parameter K is not a turbulent diffusion coefficient but a partly empirical parameter, which takes into account all effects which tend to spread the plume, such as eddy diffusion, gravity flow, and so on. We assume the following ð2þ 4of14

5 initial condition (I.C.) and boundary conditions (B.C.) for equation (2): I:C: cðx; y; Þ ¼Qdðx x ; y y Þ ð3aþ B:C: p lim cðr; tþ ¼ r ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi x 2 þ y 2 r!1 ð3bþ corresponding to the instantaneous release at t = of a mass Q from a vent of coordinates (x, y ), in a doubly infinite domain, with the physical conditions that the concentration of tephra decreases at sufficiently high distances from the source. Then equation (2) has the following analytical solution: c ¼ 5Q 8pCt 5=2 1 5 ðx ut x Þ 2 þðy vt y Þ 2 exp@ A for small particles 8Ct 5=2 c ¼ Q 4pKt 1 ðx ut x Þ 2 þðy vt y Þ 2 exp@ A 4Kt for large particles ðlinear diffusivityþ ð4aþ ð4bþ [23] In order to obtain the distribution of tephra at the ground, we set t equal to the fall time of the particle. To take into account the wind dependence on z, let us divide the height of the atmosphere into layers of height Dz i, each one characterized by constant wind velocity and direction. Particles in the eruption column have different diameters, and arrive at different heights within the eruption column. Particles of grain size f j arriving at height z k in the column (z k H, total column height) fall through layers Dz k = z k z k 1, Dz 1 = z 1 z,(z = ). Each layer is crossed in a time Dt i = Dz i /V s (z i, f j ), where the settling velocity, V s, depends both on the height and the grain size, but not on time since we can assume that atmospheric density and viscosity at heights of kilometers are independent of time considering the timescales of tephra deposition. Over this time, the center of the Gaussian distribution is displaced by Dx i = u(z i )Dt i and Dy i = v(z i )Dt i. So, when the particles reach the ground, the distribution is: 5Q c ¼ 5=2 8pC PK Dt i 2 2! 1 5 x x PK Dx i þ y y PK Dy i exp B 5=2 8C PK A Dt i for small particles ð5aþ Q c ¼ 4pK PK Dt i exp 2 2! 1 x x PK Dx i þ y y PK Dy i 4K PK C Dt A i for large particles ðlinear diffusivityþ ð5bþ [24] This formula is valid for a point source of intensity Q of particles having all the same diameter and falling from the same height. In the eruption column, the tephra mass is distributed along the height of the column with a distribution law f z (z,f), and it has a continuous grain size distribution f f. The contribution from particles in the height interval [z, z + dz] and in the size integral [f,f + df] is given by dq ¼ f z ðz; fþf f ðfþdfdz [25] Summing on all the heights from to H (column height) and from minimum to maximum grain diameters, we get the complete grain size distribution: Z H Z max 5Q c ¼ f z ðz;þf ðþ min 8C Rz dz 5=2 V s ðz;þ þ t s 5 x x Rz uz ðþdz 2! þ y y Rz vz ðþdz 2 1 V s ðz;þ V s ðz;þ exp B 8C Rz dz 5=2 V s ðz;þ þ t A dfdz s for small particles Z H c ¼ Z f max f min exp ð6þ ð7aþ Q f z ðz;þf ðþ 4pK Rz dz V s ðz;þ þ t s x x Rz uz ðþdz 2! þ y y Rz vz ðþdz 2 1 V s ðz;þ V s ðz;þ 4K Rz dz V s ðz;þ þ t C A ddz s for large particles ðlinear diffusivityþ ð7bþ [26] In expressions 7a and 7b, f z and f f are the distribution functions with respect to particle height and to diameter, respectively. To the diffusion time, we added the value t s corresponding to the diffusion of particles inside the eruption column, due to the fact that the eruption column is not really a vertical line, but has a nonzero cross-section. 5of14

6 [27] We use the following expressions for t s : t s =( 5z2 288C )2/5 for small particles the semiempirical expression from Suzuki [1983], and t s =( :32z2 K ) 2/5 for large particles (after Bonadonna et al. [25]) [28] We considered release from an instantaneous point source at time t = and position (x,y ), while in reality an eruption has a defined duration and spatial extension. In order to understand these implications, we describe a continuous eruption as the integral with respect to time of instantaneous emissions of intensity I = dq/dt. This is possible because of Duhamel s principle for parabolic linear PDEs, such as equation (1) and equation (2). If f z and f f are independent of time, and thus also total column height, the maximum and minimum grain size are, all quantities in equation (7) are independent of time, with the only possible exception of I. So we take all parameters except I out of the time integral, and, since the integral of I from to t is equal to Q, we have precisely the same result as that in the case of an instantaneous eruption. Physically, the reason for this is that we have already assumed that transport phenomena in the atmosphere are independent of the initial and final time, depending only on the difference between them, and are also independent of particle concentrations. Thus identical particles released at different times from the same height will remain in the atmosphere for the same time, and tend to fall to the same place. [29] Thus we proved that in order to model a continuous eruption as an instantaneous release, we must assume that f z and f f do not depend on time, i.e., to consider a quasi-steady eruption column. This assumption is valid for Plinian eruptions after the initial explosion [Woods, 1988]. [3] In order to complete the mathematical description of our model, we must then specify the following. [31] 1. Settling velocity. [32] 2. A functional form for grain-size distribution and the vertical mass distributions in the column. [33] 3. The vertical distribution of wind velocity and wind directions with their relative probabilities. [34] We have supposed that particles fall always with their settling velocities, i.e., we neglected transients, which is reasonable due to the extent of the vertical layers into which we divide the atmosphere. The expression for the settling velocity of a particle is a critical point. Suzuki [1983] found an expression which fits well a variety of experimental data: r p gd 2 V s ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p 9mF :32 þ 81m 2 F :64 þ 1:5r a r p gd 3 1:7 F d ¼ a þ b þ c 3 F ¼ b þ c 2a [35] where r p is particle density, r a is air density, a, b, c are the three principal axes with a being the major axis, m is air shear viscosity, F is called shape factor and is equal to 1 for spherical particles, and d is the mean particle diameter. [36] Such an expression works well for low- to moderate- Reynolds numbers: its limit for Re! and F = 1 is the ð8þ well-known Stokes law. However, it fails for higher values, because it predicts a decreasing drag coefficient C D, while experimental evidence for volcanic particles shows that the drag coefficient approaches the value of 1 for high Re [Bonadonna et al., 1998]. We thus chose to compute the Reynolds number Re L which, according to Suzuki s expression, corresponds to a drag coefficient of 1, and use Suzuki s expression for Re Re L, while if Re > Re L we set C D = 1 and, by equating particle weight and aerodynamic drag force, we obtain V s as: sffiffiffiffiffiffiffiffiffiffiffiffi 4r p dg V s ¼ 3r a [37] Air density and viscosity in the atmosphere depend on height, thus particles will fall quickly through the higher atmospheric layers, but will slow down at lower elevations: the phenomenon is less important for the smallest particles which move in the Stokes regime, their settling velocity does not depend on density. We model the dependence of atmospheric thermodynamic properties according to the U.S. Standard Atmosphere of 1976 [U.S. Government Printing Office, 1976]. [38] We assume that the grain size distribution is lognormal, e.g., the distribution in f units is normal (f = log 2 (d) where d is the particle diameter in millimeters):! f f ðfþ ¼ ffiffiffiffiffiffiffiffiffiffi 1 ð p exp f m dþ 2 2ps d 2s 2 d ð9þ ð1þ where m d and s d are respectively the mean and standard deviation. [39] The vertical mass distribution in the column is taken from Connor et al. [21]: 8 bw YðÞexp z ð YðÞ z Þ >< V s ð; fþhð1 ð1 þ YðÞexpð YðÞ ÞÞÞ z H f z ðþ¼ z otherwise >: YðÞ¼ z bwðþ z V s ð; fþ WðÞ¼W z 1 z l H ð11þ where W(z) is the eruption gas velocity at height z and W is the eruption gas velocity at the vent. In this work it always assumed that l =1[Connor et al., 21] since, according to Carey and Sparks [1986], linear variations of W with z are satisfactory approximations for the major part of the column, except near the very top and the bottom. From equation (11) it may be easily shown that the integral of f z over[,h] is 1, and that f z for any z, so it is indeed a distribution. [4] H is a normalization factor which does not change the shape of the function, so there are apparently three parameters b, W, V s (, f) =V in equation (11). However, f z depends only on the product Y() = bw ðþ V = bw V = Y,soit is a one parameter distribution. In practice, W and V are 6of14

7 Figure 4. Comparison between the frequency of wind directions collected at Brindisi (Southern Italy) meteorological station in the period (black symbols), in the height interval 34 km and the observed tephra dispersions of Campanian eruptions in the last 1 ka (white symbols). constrained by the physics of the problem, so we study the dependence of f z on b only. Omitting the simple but tedious calculation, we say that f z has a maximum in [,H] if and only if b 3 = V W. The settling velocity at sea level of big particles is of the order of tens of meters for second, while the eruption velocity is of the order of hundreds of meters for second, so this condition is usually satisfied for all particles when b 3 =.1. The maximum is attained for Z M = H(1- V bw ) and has the value, bw f z ðz M Þ ¼ e V 1 H 1 1 þ bw V exp bw ð12þ V [41] So we note that as b!1z M! H, f z (Z M )!1: since the integral of f z must be 1, this means that larger values of b correspond to more mass being accumulated near the top of the column, and less mass accumulated at lower heights. [42] In order to treat the wind velocity term in equation (1), we have adopted the database of wind velocity and directions measured between and 34 km of elevation from the ground at the Brindisi (Southern Italy) meteorological station, the nearest to Naples (about 2 km) where a good data set at such high altitude is collected. Average values of wind velocities and frequency of occurrence of wind direction have been computed, from the database, in sectors of 1 and for 1 selected heights. Thus probabilities can be assigned, at each elevation, to each direction in steps of 1, and the corresponding wind velocity assigned. As previously shown by Cornell et al. [1983], the average wind directions in the troposphere and stratosphere are almost independent of the height above 5 km, with nearly West prevailing directions in all seasons. In summer, however, there is higher variability, and above 2 km, a nearly East prevailing direction. Figure 4 shows histograms of fallout deposit dispersal axes relative to several tens of past Campi Flegrei eruptions. The good correlation of the observed dispersal axes in past eruptions with the relative frequencies of wind directions is evident Estimations of Transport Parameters Within the Eruption Column [43] Simulations of past eruptions have been carried out by using the parameters reported in Table 1, and by comparing the observed and computed mass accumulations, dispersions and the fragmentation values. Furthermore, an inverse method has been developed to find the values of key unknown parameters giving the best fit to deposits of past eruptions. The mostly unknown parameters of the model are, in principle, the eruption velocity V, the parameter b, and the linear diffusivity coefficient k, as previously described. Inverse methods for the estimation of critical unknown fall-out parameters have been also recently used by Connors and Connors [26]. Several theoretical tests, however, demonstrated that the change of the eruption velocity within very large ranges produces only minor variations in the simulated mass accumulation patterns. Hence the critical parameters, which need to be determined from observed deposits, are just b and k. The inverse method has been implemented by simulating a large number of mass accumulation deposits, sampling the b and k parameters within large ranges of possible values (Table 2), and then choosing the values giving the minimum sum of the squared residuals between the mass accumulations observed Table 2. Parameters Used for the Simulation of the Reference Eruptions a Pyroclastic Formation Campanian Ignimbrite Neapolitan Yellow tuff Pomici Principali Agnano Monte Spina Averno Astroni Monte Nuovo Column height, Km <3 Erupted mass, kg Inizial velocity, m/s Mdf sf Mdf Max Mdf Min Clast density, kg/m Shape factor Vertical distribution parameter Coefficient of diffusion, m 2 /s 1, 1, 1, 1, 1, 1, 1 a Values in italic are the parameters varied to test the sensitivity of the model. 7of14

8 Figure 5. Comparison between isomass maps compiled from field data and obtained by best fit models, for some reference CF eruptions: (a) Averno (37 years BP); (b) Agnano-Monte Spina (41 years BP); (c) Campanian Ignimbrite (39, years BP). 8of14

9 Figure 6. Composite, probability density-distribution of transport parameters b and k, for eruptions with VEI between 1 and 4. in real deposits and those calculated by simulation at the same points. The unknown value of the threshold fall-time has been determined by trial and error, by performing several inversion runs with varying values, and then choosing the one producing the best fit. A further improvement to the inversion program has been the inclusion of mean grain-sizes, as determined at each observation point in actual deposits, as data. In such a framework, the best values of b and k have been chosen to give the best fit to both the accumulation mass deposits and to the mean grain sizes at each observation point. In this case, a normalization factor, inversely proportional to the average error of each type of data, has been used to handle the different units of grain sizes with respect to the deposit thickness. The normalization factor has been determined empirically in order to obtain roughly the same order of magnitude for misfits of different data. [44] Figure 5 shows three examples of comparisons between the observed mass accumulation distribution and the computed ones, on the basis of the respective best fit models. [45] Results of the inversions relative to all the reference eruptions indicate that the best values of b and k are mostly clustered in a narrow range and are practically uncorrelated with VEI. In order to have a complete, statistically meaningful overview of the results obtained from all the inversions of fall-out distributions, we used a Bayesian approach to compute the probabilities of occurrence of b and k values. Bayes theorem states that: Pðm=d Pðd=mÞ Þ ¼ P ðmþr M Pðd=mÞdm ð13þ [46] In which P(m/d) is the probability on the model parameters we wish to compute (in this case m =(b,k)), P (m) is the a priori probability on the parameters (in this case, a constant over the considered, parameter space) and P(d/m) is the probability of each model given the observed data d. We assume, for the probability P(d/m), a Gaussian function of the kind: Pðd=mÞ / e 1 2s 2kd OðmÞk ð14þ where the exponent is the sum of square residuals between observed and simulated data (in our case deposit heights and average granulometries). The simulated data are represented in terms of the nonlinear operator O, which acts on the model m. We must assume a value for the data variance s 2 ; we use, as common in these cases, the a posteriori variance at the best fitting point [Menke, 1984]. Once the probability density function for each considered eruption (which is taken as representative of all the eruptions of the same VEI) is computed, the total probability is obtained by multiplying all the density functions obtained for the different VEI, each one weighted by the probability of occurrence of that VEI. Weighted probabilities have been computed from the past eruptive history as given in Table 3, by computing the relative frequency of each kind of eruption (the number of eruptions in the given category divided by total number of eruptions in the catalogue). Hence we obtain the final probability density distribution on the b and k parameter values as shown in Figure 6. In Figure 6, data from the 9of14

10 Table 3. Matrix of Input Parameters and Their Relative Probability VEI VEI 1 VEI 2 VEI 3 VEI 4 VEI 5 Probability Column height, km Erupted mass, kg Initial velocity, m/s Mdf (probability) 4, 3, 1 4, 3, 1 3, 2, 1 2, 1, 2, 1, 2, 1, (.25,.5,.25) (.25,.5,.25) (.25,.5,.25) (.2,.4,.4) (.2,.4,.4) (.2,.4,.4) Mdf min Mdf max sf 1,.5 1,.5 1,.5 1,.5 1,.5 1,.5 b k Campanian Ignimbrite eruption have been excluded, because they presented a significantly different value of b (b =.5 and more), with respect to all other eruption VEI s. An eruption like the Campanian Ignimbrite, occupying the larger end of the eruption volume spectrum, is however very rare. [47] From these analyses, we infer that optimum b values are very clustered between.8 and.2, while k ranges between 2 3 m 2 /s, thus suggesting common eruption column regimes irrespective of the eruption magnitude, except for perhaps very large (Campanian Ignimbrite) eruptions. This result helps to constrain the variability of transport parameters within a narrow range, thus increasing the significance of the simulated tephra dispersion over the whole VEI range. These values of diffusivity, rather large for atmosphere although similar to many other results from different volcanic areas, possibly reflect also the wind variability Campi Flegrei Volcanic Hazard Maps [48] The hazard map computation has been facilitated using a probabilistic approach to simulate a large, mostly complete set of eruptions, whose relative distribution in energy classes (VEI) best matches those observed in the intrinsically incomplete set of past eruptions. The incompleteness of the historical catalog comes from two main sources: the first, is the sparse sampling of the eruption spectrum, which gives us, in any case, the general statistical distribution of eruptions in each class of VEI; the second is the sparse, spatial sampling of eruption vents, from which we can infer some information about their statistical distribution. At Campi Flegrei caldera, for instance, vents have opened seemingly everywhere, in the last 1, years but largely, within a radius of about 3 km from the caldera center. Larger distance vents are both more rare and more ancient. [49] In order to compute hazard maps, a geographic grid, 1 km in longitude, by 1 km in latitude, has been used. Thirty vents have been regularly spaced on two concentric sectors of circles with radii of, respectively, 3 and 5 km distance from the city of Pozzuoli, with the level of probability decreasing with distance away from the town. A 7% (of total opening) vent probability has been attributed to the area within the innermost part of the caldera according to the actual distributions of recent monogenetic volcanoes, and corresponds well to the area involved in recent unrest episodes [Dvorak and Berrino, 1991; Dvorak and Mastrolorenzo, 1991; Gaeta et al., 1998]. [5] Input parameters for the simulations consist of six distinct matrices corresponding to VEI to 5, each one including the range of values for total erupted mass, column height, and grain size data inferred from the Campi Flegrei reference eruptions (Table 3), and the values of the critical parameters calculated from the inverse approaches. Different probabilities have been assigned to the different VEIs according to their relative frequency of occurrence in the volcanological history of Campi Flegrei (see Table 3) retrieved from the very detailed record available for Campi Flegrei. For the ranges indicated, random sampling, with uniform probability, has been carried out, except for the fixed parameters, and for Mdf which has been sampled at three different values for each VEI. The combination of different parameters gives a total of ca. 1 6 simulations. [51] For hazard assessment, three different eruptive scenarios have been considered: (1) an upper limit scenario relative to the worst-case event (VEI 5); this is useful to determine the upper limit value of tephra fall accumulation; (2) an eruption range scenario (VEI 1 4) which excludes the upper-limit highest risk but very rare events, as well as the lowest VEI events that are frequent but are associated to very low risk; this represents the most useful scenario expected over a medium-short time interval; (3) and whole-range eruption scenarios (VEI 5) which include all the possible VEI events (a long-lasting activity scenario). [52] For the three case scenarios, hazard maps relative to the critical load for less resistant roof collapse of 2 kg/m 2 [Cherubini et al., 21; Spence et al., 25] have been built by a selective (partial or total) sampling of the matrix reported in Table 3. [53] Figures 7a 7c shows hazard maps that report the yearly probability to exceed the critical load for each point for the reference scenarios (a is for upper limit scenario (1), b for eruption range scenario (2), c for whole range scenario (3). Besides the yearly probability, whose absolute value depends from the frequency of eruptions in the area, what is much more important for civil defense purposes is the conditional probability in case of eruption, i.e., the probability of load exceedence once we know that an eruption is going to occur. Figures 8a 8c shows conditional probability hazard maps for respective scenarios 1 to 3, that report the probability to exceed the critical load (2 kg/m 2 )for each location, in case of eruption occurrence with a given VEI. [54] Conditional probability hazard maps have been also built for the eruption range scenario, for mass loading exceeding respectively 7 kg/m 2, 4 kg/m 2 and 1 kg/m 2 Figures 9a and 9c; these values correspond, 1 of 14

11 we also produced separately a summer time hazard map (Figure 1b). 5. Discussion and Conclusion [57] Our probabilistic approach provides the first complete, statistically accurate description of expected tephra dispersion from the wide variety of possible explosive events at Campi Flegrei, which will affect the Neapolitan area and its surroundings. [58] The work initiated by first obtaining complete descriptions of a variety of past eruptions by Bayesian inversions of fall-dispersal patterns and granulometric data. Inversion results helped calculate the main transport parameters within the eruption columns, which cannot be directly inferred from field data. Our results for the parameter b, which describes the vertical distribution of product sizes within the column (equation (1)); indicates that it is effec- Figure 7. Yearly, probability hazard maps computed for the minimum load for the building roof collapse of 2 kg/ m 2 run for (a) an upper limit scenario (VEI 5), (b) an eruption range scenario (VEI 1 4), (c) the whole range eruption scenario (VEI 5). respectively, to total roof collapse of dwellings, 4% of roofs collapsing and severe damage to agriculture, respectively according to Cherubini et al. [21]. Nevertheless, due to the prevalence of concrete and reinforced roofs in the area, these values should be considered mainly as qualitative indicators of the various levels of damage. [55] In order to take into account the possible occurrence of magma/water interactions during column-generating eruptions and the consequent magma fragmentation, an additional hazard map with very fine grain-sizes (Md F = +2, typical of Campi Flegrei phreatomagmatic deposits), has been considered (Figure 1a) for the eruption range scenario. [56] Since the summertime vertical wind directions is anomalous if compared with other seasons according to our data and consistently with Cornell et al. [1983], Figure 8. Conditional, probability hazard maps relative to the minimum load for building roof collapse of 2 kg/m 2, run for (a) an upper limit scenario (VEI 5), (b) an eruption range scenario (VEI 1 4), (c) the whole-range eruption scenario (VEI 5). 11 of 14

12 Bonadonna et al., 22], except for Bonadonna et al. [25] who found very low values of linear diffusivity, around 1 m 2 /s. High values of diffusivity k, including our ones, are possibly affected by large wind variability. Values of b are difficult to compare, because of the large variability generally found, depending on the studied area [Suzuki, 1983; Connor et al., 21; Bonadonna et al., 22]. Once the main parameters of the individual eruptions at Campi Flegrei have been estimated, probabilistic hazard maps may be computed, giving the first accurate, statistically rigorous maps of tephra fall-out hazard from explosive eruptions in this area. [59] Our results indicate that, due to the yearly winddirection variability, all sites within Campi Flegrei caldera are potentially exposed to tephra fallout. However, the prevalence of westerly winds causes the areas east of the volcanic field to be most exposed to higher tephra loads, and thus in greatest relative potential danger. [6] Using our probabilistic approach we have built hazard maps giving the probability of loading exceeding values of 2 kg/m 2 (critical loading for roof collapse of structures, i.e., collapses start in less resistant structures), 4 kg/m 2 (4% of roofs collapsing) and 7 kg/m 2 (complete roof collapse). In addition, we have computed hazard maps for loading of 1 kg/m 2, which has been Figure 9. Eruption-range scenario, conditional-probability hazard maps for: (a) mass loading exceeding 7 kg/m 2 (roof collapse for all buildings), (b) 4 kg/m 2 (roof collapse for 4% of buildings) and (c) 1 kg/m 2 (damage to vegetation). tively independent from the considered eruptions at Campi Flegrei, spanning a narrow range.8 < b <.1. The remaining inverted parameter, k, represents the lateral diffusion of larger-size clasts in the column, and it is largely independent from the analyzed eruptions, lying in the range 2 < k < 3 m 2 /s. The parameter k describes the linear diffusion of larger eruption products; the transition at which the nonlinear diffusion of finer products occurs, has also been constrained, by the inversion of field data, to fall times of about 3 s. We have thus a very complete description of the parameters characterizing eruptive columns at Campi Flegrei caldera, and also important indications that the main transport parameters are rather constant, which helps to further constrain the range of parameter variability applicable to the probabilistic estimation of hazard maps. Inferred values of k are in good agreement with values generally found in the literature [e.g., Hurst and Turner, 1999; Figure 1. (a) Eruption range scenario conditional probability hazard maps computed for a deposit threshold of 2 kg/m 2 in the case of a hydromagmatic eruption and (b) yearly, probability hazard maps computed for the minimum load for the roof collapse of 2 kg/m 2, run for summer months. 12 of 14

13 demonstrated to cause heavy damage to agricultural activity, one of the primary economic resources of the greater Naples area. [61] In the case of small- and intermediate-sized eruptions (VEI not exceeding 3) with relatively low eruption column heights, highly variable low tropospheric winds prevail, causing the tephra to be potentially dispersed in all directions with near-homogeneous probability. However, in these cases the critical tephra load and the associated volcanic hazard are confined within a few kilometers of the vents and inside the caldera boundary. Since fallout hazard contourlines are nearly circular for such low eruption columns, and the vent opening could occur potentially every where within the volcanic field, very high fallout hazard characterize the inner caldera area for all considered scenarios. [62] Outside the caldera, the hazard level strictly depends on the details of the considered scenario. In the case of the eruption range scenarios, which is most useful for civil defense, significant (.25 event/a) hazard for critical tephra load characterizes a wide sector from the northeast to the southeast and within a range of about 1 km from the caldera center, which include the western part of Naples. The area north of Campi Flegrei is exposed to moderate hazard levels. The sectors west and south of the caldera are exposed to low hazards but are also less important in terms of risk because they are mostly occupied by the sea. [63] In the case of the whole- range and upper-limit scenarios, an area up to 6 km from the caldera is potentially exposed to critical load. In the whole-range scenario the yearly hazard for the area northeast to southeast of the caldera between ca. 1 and 6 km, show respectively, between about.5 events/a to.1 events/a potentially affecting the districts of Napoli, Caserta, Avellino and Salerno. In the upper-limit scenario, the yearly probability for critical loading (2 kg/m 2 ) hazard maps is.15 events/a within 3 km of the vent, and decreases up to.1 event/a at distances of 6 km. A significant, conditional probability level of 1% of the critical load characterizes the area within the first 1 km in the case of small to moderate eruptions, and within 3 km for the eruption range scenario. [64] Extreme accumulations of 7 kg/m 2 (total buildingroof collapse) may potentially be produced everywhere inside the caldera for all reference scenarios, and may occur up to 3 km from the vent in the whole range scenario. [65] The load of 1 kg/m 2, which causes severe damage to agriculture, may be potentially produced within a range of 1 km from the vent in the case of the eruption range scenario, and within a range of ca. 1 km in the cases of small scale eruptions from VEI 1 to 3. [66] Additional hazard conditions are produced in the case of magma/water interactions due to the expected abundance of fine ash production. In these cases, a wider dispersion of ash causes the critical tephra load to be limited closed to vent (within ca 1 km) but the 1 kg/m 2 load limits to be spread over a wider area. [67] Importantly, because inferences on the possible magnitudes of future eruptions, and the relationship between eruption precursors and eruption size are largely unknown, forecast of future eruptions should be based only on the statistical occurrences of the different VEI. This implies that all eruptions considered in the probabilistic approach are realistic, albeit with different levels of probability, for any time. However, due to the strict dependence of hazard evaluation on the considered scenario, practical applications of hazard levels for risk assessment and mitigation are mostly a matter of government policy. [68] The probabilistic method developed here to compute tephra hazard maps represents the most complete formulation we know of to compute volcanic hazards from fall-out products. It makes the best use (in a statistical sense) of the intrinsically, incomplete information coming from past eruptions, to give projections of future hazards coming from a complete range of simulations that preserve the main statistical features of actual eruptions at Campi Flegrei. As such is of crucial importance for civil defense purposes in this extreme-risk area, but could also be easily implemented at any volcanic area in which some information exists on the eruptive history, and/or can be inferred from the study of fallout deposits. [69] A further improvement of the method, besides building the completeness of the probabilistic approach, would be to refine the description of plume dynamics and proximal fallout, for instance, using fully 3D models. In this case, however, simulation of fall-out from each eruption could be significantly time-consuming even on large parallel computers, while the improvement would be significant only in the near-field [Bursik et al., 1992] where the largest source of uncertainty is generally given (as at Campi Flegrei) by the large variability of low level winds. [7] Acknowledgments. We gratefully acknowledge J. Martì, C. Bonadonna and an anonymous reviewer for helping to greatly improve the clarity of the paper. References Bonadonna, C., G. G. J. Ernst, and R. S. J. Sparks (1998), Thickness variations and volume estimates of tephra fall deposits: The importance of particle Reynolds number, J. Volcanol. Geotherm. Res., 81(3 4), Bonadonna, C., G. Macedonio, and R. S. J. Sparks (22), Numerical modeling of tephra fall-out associated with dome collapses and vulcanian explosions: Application to hazard assessment on Montserrat, Geol. Soc. London Mem., 21, Bonadonna, C., C. B. Connor, B. F. Houghton, L. Connor, M. Byrne, A. Laing, and T. K. Hincks (25), Probabilistic modeling tephra dispersal: Hazard assessment of a multiphase rhyolitic eruption at Tarawera, New Zealand, J. Geophys. Res., 11, B323, doi:1.129/23jb2896. Bursik, M. I., R. S. J. Sparks, J. S. Gilbert, and S. N. Carey (1992), Sedimentation of tephra by volcanic plumes. Part I: Theory and its comparison with a study of the Fogo A Plinian deposit, Sao Miguel (Azores), Bull. Volcanol., 54, Carey, S., and R. S. J. Sparks (1986), Quantitative models of the fallout and dispersal of tephra from volcanic eruption columns, Bull. Volcanol., 48, Cherubini, A., S. M. Petrazzuoli, and S. Zuccaro (21), Vulnerabilità sismica dell area Vesuviana, p. 19, CNR-Gruppo Nazionale per la Difesa dai Terremoti, Roma, ISBN Cornell, W., S. Carey, and H. Sigurdsson (1983), Computer simulation of transport and deposition of the Campanian Y-5 ash, J. Volcanol. Geotherm. Res., 17, Connor, L. J., and C. B. Connor (26), Inversion is the key to dispersion: Understanding eruption dynamics by inverting tephra fallout, in Statistics in Volcanology, edited by H. M. Mader et al., p. 296, Geol. Soc., London. Connor, B. C., B. E. Hill, B. Winfrey, N. M. Franklin, and P. C. La Femina (21), Estimation of volcanic hazards from tephra fallout, Nat. Hazards, 2, D Antonio, M., L. Civetta, G. Orsi, L. Pappalardo, M. Piochi, A. Carandente, S. de Vita, M. Di Vito, and R. Isaia (1999), The present state of the magmatic system of the Campi Flegrei caldera based on a reconstruction of its behavior in the past 12 ka, J. Volcanol. Geotherm. Res., 91, of 14