PDC deposits serve as a crucial record of current progression, decline, and cessation stages, offering an accessible footprint for researchers. The sedimentary structures found within PDC deposits have been extensively studied, as they can help infer flow, sediment transportation, and deposition processes based on sedimentology principles. These principles however are primarily developed for other natural density currents such as fluvial and turbidity currents. PDCs possess unique characteristics (e.g., a high sediment-to-carrier phase density ratio) that set them apart from other currents. This distinction complicates the interpretation of flow properties from sedimentary structures. As a result, despite years of research, the study of sedimentary structures in PDCs remains an ongoing and active research field.

Branney and Kokelaar (2002) were among the first to provide a systematic classification of PDC deposit lithofacies and to use these to interpret the temporal evolution of currents. This work posited the vertical arrangement of lithofacies for determining unsteady processes (e.g., temporal variation) within the “flow-boundary zone” (Figure 1B). This is the zone in which the deposit forms and is located between the lowermost part of the PDC and the uppermost part of the forming deposit. Unlike older approaches in the interpretation of PDC deposits, Branney and Kokelaar (2002), by means of the flow-boundary zone approach, could reconcile the long-lived debate between endmember high-concentration and low-concentration PDC transport mechanisms; they suggested that whatever the concentration in the PDC, the style of sedimentation and, therefore, deposition is controlled by conditions and processes taking place in the flow-boundary zone. Their systematic classification of lithofacies also included the analysis of lateral variation of lithofacies, which reflected the spatial variation of the flow-boundary zone. Sedimentary structures can be linked to the internal arrangement of clasts resulting in various degrees (i.e., from absence to abundance) of lamination (thickness <1 cm) or stratification (thickness >1 cm). The arrangement of these laminae-strata (e.g., parallel, cross-stratified, ripples and dunes, lenses) are also known as bedforms.

Based on the “flow-boundary zone” concept, Sulpizio et al. (2007) developed a model for reconciling the two models of PDC deposition: en masse (i.e., deposits formed by en masse abrupt freezing of the entire PDC) and aggradation (i.e., deposits formed by the continuous supply of sediment from the flow to the flow-boundary zone). In their model, they assume that PDC deposits originate from stratified currents wherein particle segregation, by differing terminal velocities, can develop a high-concentration zone in the lowermost part of the current (Branney and Kokelaar, 2002). This zone then moves as a succession of high-concentration pulses, in which the interplay amongst shear-rate, rate of deposition, and particle concentration controls the depositional regime (fallout, fluid-escape, granular flow, and traction). Pulse stoppage occurs en-masse when resistive forces overcome the driving forces. The four types of flow-boundary zones are completely intergradational (Branney and Kokelaar, 2002; Burgisser and Bergantz, 2002) and mixed regimes are common (Sulpizio et al., 2007). Using this framework, it is possible to qualitatively characterise the PDC flow condition based on the observed sedimentary structures; for example, faintly stratified deposits with reverse grading can be attributed to multiple pulses depositing in fluid-escape regimes.

Bedforms (e.g., lamination, cross-laminations, ripples, dunes) forming within the flow-boundary zone of a PDC, fluvial current, turbidity current, or aeolian process are the result of the overlying current exceeding the critical shear stress for motion (Bartholdy et al., 2015). One of the long-standing goals of physical volcanology, and sedimentology in general, is to use the sequence of bedforms to interpret the fluid and granular conditions of a current. Douillet (2021) described several types of facies and facies associations commonly found in PDC deposits and the most common qualitative and quantitative interpretation of the flow conditions, with a particular emphasis on the subcritical vs. supercritical flow conditions. If these structures can be attributed to an antidune, it is possible to extrapolate quantitative flow parameters like velocity (Prave, 1990). In addition to the specific case of antidunes, phase diagrams relating ripples, dune wavelength and particle size with dimensionless numbers that describe flow properties (e.g., the Froude number and critical Shields number), are also available (Perillo et al., 2014; Fedele et al., 2016).

Given their use in adding quantification to field observations, further discriminatory and phase diagrams have been produced in recent years. These include using sedimentation and bedload transportation rate relationships to identify the conditions that form massive vs. stratified deposits (Dellino et al., 2020). Experiments have also been used to develop a phase diagram for monodisperse dense granular flows (Smith et al., 2020) relating the backset bedforms (e.g., steep, shallow, or planar) to flow conditions (e.g., Froude number, flow velocity, and thickness). Additionally, by using sedimentological models that relate deposit characteristics to dilute PDC flow properties (Dellino et al., 2008; Dioguardi and Mele, 2018), simple diagrams have been produced in which dilute PDC parameters like dynamic pressure, average particle concentration and sedimentation rate can be estimated by measuring the bedforms’ wavelength and particle median grain size (Dellino et al., 2021b). Going forward, continued collaboration between the field volcanology and numerical modelling community will further support both the validation (Esposti Ongaro et al., 2020a) or ‘ground truthing’ of models and the ability to provide essential quantification of PDC dynamics from field-based observations. Increased sophistication of the experimental and numerical models (e.g., 2D and 3D simulations, polydisperse grain size distributions) that underpin such diagrams will increase their accuracy and extend their use.

Related to sedimentary structure is the deposit fabric, which can be defined as the particle (mutual) orientation/alignment within the deposit. This property had been historically used in the sedimentology of fluvial and turbidity currents to infer flow direction and later applied to interpret entrained-particle long-axis alignment found in pyroclastic deposits (Zrelak et al., 2020 and references therein). Capaccioni and Sarocchi (1996) were among the first to use computer analysis to quantitatively analyse the fabric of particles within ignimbrite deposits and showed how this analysis could give insight into ignimbrite emplacement mechanisms. There is also a method that focuses on analysing the fabric of very fine particles called anisotropy of magnetic susceptibility (AMS). It is used to investigate the preferred orientation of magnetic minerals, such as magnetite, in a rock based on the finding that the maximum axis of magnetic susceptibility corresponds to inferred flow streamlines (Palmer et al., 1999). Using this technique, flow direction has been inferred from large ignimbrites of varying degrees of welding, where the source was unknown (Le Pennec et al., 1998).

PDC deposits vary greatly in area, thickness, and volume and these deposit characteristics have been used to classify eruptions (e.g., Volcanic Explosivity Index and magnitude). Such descriptors allow us to quantify mass partitioning between volcanic processes (e.g., column vs PDCs, PDC vs co-PDC plume) (Walker, 1972; Sparks and Walker, 1977; Druitt, 1998; Ritchie et al., 2002; Cas and Wright, 2012; Scarpati et al., 2014; Bernard et al., 2016; Giordano and Cas, 2021), assess the mobility of the currents and decipher the type of flow involved. Inspired by the work of Heim (1932) on debris and rock avalanches, volcanologists have used simple metrics such as vertical height descent (H) and runout length (L) to assess flow mobility (Hayashi and Self, 1992; Ogburn and Calder, 2017). Similar to non-volcanic granular flows, the H/L ratios of dense PDCs display an inverse relationship with volume that can be attributed to a volume-dependent friction weakening mechanism (Calder et al., 1999; Breard et al., 2018). Although the role of the fluid phase is unclear in debris avalanches (Pudasaini and Miller, 2013) on Earth and other planetary bodies, the volume-dependent friction phenomenology of dense PDCs can be explained by the formation and retention of excess pore pressure (Breard et al., 2018 and references therein).

The H/L ratio has been commonly used to estimate the empirical friction coefficient necessary for describing the Coulomb rheology of dense PDCs (Saucedo et al., 2005; Ogburn and Calder, 2017). Friction is highly variable spatially-and-temporally, despite the practicality of using a constant friction coefficient for modelling purposes (Lube et al., 2019). Using PDC deposit volume V and area A, the ratio A / V 2 / 3 has been used as a proxy of flow mobility, but this metric does not distinguish deposits that result from dense or dilute transport regimes (Calder et al., 1999), however in some cases it can help distinguish sources (e.g., dome and lava flow collapse vs column collapse). Building upon A / V 2 / 3 , Breard et al. (2017) included the role of a dimensionless length scale (Sauter mean diameter/layer thickness), which was shown to distinguish between deposits resulting from dense or dilute currents.

PDC deposits are complicated to interpret due to spatio-temporal changes in the flow-deposit boundary conditions (Branney and Kokelaar, 2002), making it difficult to gain quantitative information about flow dynamics. While at the individual outcrop scale the flow behaviour may be encrypted, at the large-scale, deposit thinning is a proxy for the vertical stratification of the flow, which is sensitive to topographic obstacles (Giordano and Doronzo, 2017). In general, deposit geometry is one of the key metrics that helps us determine the extent of the impact of past PDCs. It is important to note, however, that erosion can significantly alter the observed volume, area, and runout of deposits, thus affecting our estimation of flow mobility, hazards, and risks. Between these parameters, the PDC area and runout of historical flows are generally the easiest to estimate, whereas volume is much more challenging. The calculation of deposit volume is subject to major uncertainties on the deposit thickness (Breard et al., 2018). Paleo-topography understanding, and numerous deposit outcrops are necessary to reduce this uncertainty (Bernard et al., 2014a). Deposits are also susceptible to erosion locally changing deposit thicknesses and can completely remove any evidence of thin deposits. Furthermore, runout and area measurements can be conducted remotely, however volume measurements have typically required field-based observations.

High-resolution digital elevation models (DEMs), provided by either the use of satellite imaging or unmanned aerial vehicles (UAVs, “drones”) equipped with LiDAR technology, have revolutionised the study of PDC deposits from recent volcanic eruptions (Breard et al., 2015; Albino et al., 2020) and have made remote thickness and volume measurements possible. Satellite-based remote sensing allows volcanologists to obtain accurate DEMs (i.e., down to approximately 1 m in horizontal resolution and ∼0.2–0.3 m in vertical resolution), which offer vital topographic data for modelling and characterising PDC deposit distribution, volume, and flow dynamics. UAV-mounted LiDAR sensors provide rapid, high-resolution, and accurate 3D topographic data, enabling the assessment of deposit geometry, even in hazardous or remote areas (James et al., 2020; Granados-Bolaños et al., 2021). Importantly, LiDAR surveys can be conducted swiftly between eruptions, allowing researchers to characterise PDC deposits before erosive events alter the landscape. As a result of the synergistic use of these advanced technologies, more accurate constraints can be placed on the geometry (especially volume and thickness) and emplacement mechanisms of PDC deposits, which in turn enables a more comprehensive assessment of their hazards.

In cases where DEMs prior to eruptions are not available, non-invasive methods such as Georadar, also known as ground-penetrating radar (GPR), provide valuable tools for analysing the thickness of PDC deposits. By transmitting high-frequency electromagnetic waves into the ground and measuring the reflected signals, Georadar enables non-invasive, subsurface imaging of deposit layers, offering insights into their thickness and internal structure with remarkable accuracy (Gase et al., 2017).

Grain size is one of the main indicators of volcanic deposit type and can be used to differentiate PDC from fall deposits. Fall deposits are typically well sorted and mantle topography (Walker, 1971). In comparison, PDC deposits are diverse in nature, both in terms of spatial distribution and grain size (Fisher and Schminke, 1984; Druitt, 1998) due to the myriad of transport and depositional processes that operate within a current, from turbulent suspension to dense granular flow (Sulpizio et al., 2014; Lube et al., 2020). Hybrid deposits also exist, which display characteristics of both fall and flow and are formed due to the simultaneous deposition of particles from the buoyant plume and PDC (Dowey and Williams, 2022). Transition between different transport and depositional processes within a current can be impacted by various scales of topographical obstacles (Branney and Kokelaar, 2002; Doronzo et al., 2010) and by deposition and entrainment of particles from the erodible substrate (Brand et al., 2014; Pollock et al., 2019). Beyond the classification of volcaniclastic deposits, PDC grain size (Figure 2) can be used to differentiate the type of PDC (Walker, 1971). Deposits from dense PDCs, such as block and ash flows, are commonly associated with the gravitational collapse of domes or lava flow fronts, exhibiting complex, multimodal, and poorly sorted grain size distributions (Sparks, 1976; Charbonnier and Gertisser, 2008; Sarocchi et al., 2011; Macorps et al., 2018; Charbonnier et al., 2023). In contrast, deposits associated with dilute PDCs (or surges) commonly have unimodal (in log-scale), better sorted distributions, often with a long fine tail (Walker, 1971; Walker, 1984; Sulpizio et al., 2007; Breard et al., 2015).

A key difference in fall and flow deposit grain size distributions is their spatial variability. While fall deposits show relatively minor changes in grain size locally, the grain size of PDC deposits can vary significantly over short distances (e.g., <<100 m), related to pulsatory activity and flow-substrate interactions (e.g., Richie et al., 2002; Sulpizio et al., 2007; Charbonnier and Gertisser, 2011; Lube et al., 2014). These variations can complicate correlation efforts between exposures across a flow and even at the outcrop scale. Despite local variation, changes in grain size characteristics with distance from source are informative for understanding flow dynamics. The deposits associated with both dense and dilute PDCs generally show a decay in median grain size with distance from source, particularly for dilute PDCs (Figure 1). This relative increase in fines with distance is related to two main mechanisms: 1) fragmentation and attrition of particles, and 2) preferential deposition of coarse particles that cannot be suspended by turbulent eddies in dilute PDCs (Valentine, 1987; Dufek and Manga, 2008; Manga et al., 2011; Kueppers et al., 2012; Brosch et al., 2022; Breard et al., 2023).

Estimating grain size distribution at the outcrop scale is challenging and often requires multiple methods, which include photogrammetry, sieving in the field and the laboratory, and particle laser analysis. Studies typically sample and sieve deposits at the outcrop, commonly using sieves with one or half phi increments { φ = −log₂[d(mm)]}. Measuring the grain size at the coarse and the fine end of a distribution requires specialist approaches. Finer portions are commonly subsampled in the field before undergoing laboratory analysis using, for example, laser grain size analysis. In comparison, the largest particles require individual measurements that can only be conducted in the field. Photographic methods have been developed and employed to estimate the largest clasts (Sarocchi et al., 2011), also providing a means for analysis of inaccessible deposits using UAVs. Grain size analysis may be impossible for indurated and welded deposits, often those associated with particularly large eruptions, such as the Minoan and Campanian Ignimbrite eruptions (Branney and Kokelaar, 2002). The process of welding itself changes the shape and size of clasts; thus, individual clast outlines are not easily identifiable (Roche et al., 2013). This means that grain size information for welded deposits is often lacking or highly uncertain.

Grain size distributions are commonly reduced to representative statistics to enable comparison of information from numerous locations (Walker, 1971; Sparks, 1976; Charbonnier and Gertisser, 2011), with statistics such as median grain size (Md) and sorting coefficient ( σ ) used to describe and compare the grain size characteristics of deposits in the published literature. It is often these parameters that are used as inputs to numerical models simulating flow dynamics and propagation. However, estimation of these parameters is complicated by the complex, often multimodal nature of the distributions and multiple definitions of sorting coefficient (Inman, 1952 versus Folk and Ward, 1957).

Grain size data play a crucial role in designing laboratory experiments for studying PDC behaviour. However, laboratory apparatus size limitations (e.g., channel width) constrain the particle length scales that can be used. In the most simplified cases, analogue materials such as glass beads have been employed due to their ease of use and resistance to abrasion (Roche et al., 2013; Smith et al., 2020; Gueugneau et al., 2022; Penlou et al., 2023). When using natural samples at benchtop scales, the grain size distribution is subsampled to include only fine particles to prevent wall effects and maintain relevant scaling [e.g., pore pressure diffusion timescale, as demonstrated by Girolami et al. (2008)]. Furthermore, restricting grain size narrows the range of gas-particle coupling mechanisms present in a single experiment, which may not accurately represent the complexity of natural PDCs. This limitation prompted the creation of large-scale experiments (Sulpizio et al., 2007; Lube et al., 2015) that allow for the use of nearly complete grain sizes seen in PDC deposits, omitting only the coarse tail of the size distribution. Such large-scale experiments have been instrumental in evaluating how grain size distributions evolve within flows and deposits, ultimately enhancing our understanding of natural PDC deposits (Breard et al., 2016; Brosch et al., 2022).

Grain size information is a critical input for numerical simulation of PDCs (e.g., Esposti Ongaro et al., 2012; Dufek, 2016). Incorporating grain size information into numerical models typically entails either discretizing a grain size distribution into a finite number of classes, representing the most prevalent particles, or inputting statistics such as median and sorting parameters, which is then used to define the proportion of particles in several bins of different sizes (Neri et al., 2002; Esposti Ongaro et al., 2008). Increasing the number of particle size bins simulated significantly raises the computational cost of numerical approaches. One important aspect of numerical model development lies in development of methods to minimize these costs (e.g., de Michieli Vitturi et al., 2015). One such method, already employed when modelling particles in volcanic plumes, is using the method of moments which enables the simulation of a continuous distribution of particles. Implementing this method in PDC models may facilitate the use of more sophisticated grain size data. However, it is essential to recognise that models used in hazard analysis and those simulating flow scale processes overlook complex particle interactions (i.e., four-way coupling, see Section 3.1). Instead, these models modify the particle distribution in a simulated flow by calculating particle deposition using terminal settling laws (Bursik and Woods, 1996; Dellino et al., 2008; Dioguardi et al., 2017; de Michieli Vitturi et al., 2019).

The componentry of pyroclastic deposits is a quantitative parameter describing the proportion of different particle categories defined based on their mineralogy and texture (e.g., vesicularity, crystallinity, morphology). Componentry provides key information that can be used to infer some physical processes occurring during flow propagation. For instance, the process of co-PDC formation by ash elutriation from the PDC body during propagation has been historically identified based on the componentry of PDC deposits, namely, the content of free crystals (Walker, 1972; Sparks and Walker, 1977). Indeed, a crystal enrichment in the matrix of PDC deposits compared to the crystal content of the magma has been observed in several ignimbrite deposits (e.g., Vulsini volcanoes, Italy and Santorini, Greece). This can be explained by a process of density-driven fractionation during particle elutriation, leading to preferential retention of crystals in PDC deposits and escape of glassy, potentially vesicular, particles in the co-PDC plumes.

Componentry is also essential to understand substratum erosion and bulking processes (Bernard et al., 2014b). Componentry allows us to quantify the incorporation of accidental material, to track their origin along the edifice slopes, and hence provides a way to infer the efficiency and timing of substratum erosion. Componentry can also provide insight into particle breaking and comminution during transport, given that different component types have variable susceptibility to fracturing and abrasion (Bernard and Le Pennec, 2016; Hornby et al., 2019; Jones et al., 2022). Componentry is also key for interpreting deposit facies and sedimentological structures, which are controlled by the particle settling behaviour, which in turn depends on the density, and hence componentry, of the grains. For example, Dellino et al. (2008) used componentry analysis to infer the flow properties of past dilute turbulent PDCs; specifically, they based their methodology on observations that the laminated layers in dilute PDC deposits often consist of different components with different densities, grain sizes and shapes. Since the different particle components present in the same laminae are deposited contemporaneously, i.e., by settling at the same terminal velocity, one may assume that aerodynamic equivalence must exist between the different components. From this principle, it is possible to set the equivalence of the terminal velocities of particles of different components, from which their model calculates PDC flow properties like the shear velocity. Finally, componentry is inherently linked to particle density and hence particle settling velocity. This will be discussed in the following sub-section (Section 2.5).

The methods typically used to analyse PDC componentry include component identification and counting of the block/bomb population in the field or using outcrop photographs, and sampling of matrix and separation/counting in the laboratory under the binocular microscope (Bernard and Le Pennec, 2016). The main challenge with any componentry analyses is the determination of the categories of particles (e.g., free crystals, lithics, dense juvenile), which must be based on consistent criteria that do not change with changes in grain size. Because component category determination is dependent on the scientific questions each study is dealing with, comparing componentry datasets across independent studies is often challenging.

Some componentry datasets exist in the literature on specific PDC deposits, such as ignimbrites from the Campanian Ignimbrite eruption (Scarpati et al., 2015), various eruptions in the Azores and Chile (Walker, 1971; Calder et al., 2000), pumice flows from the 3.9 ka BP Somma-Vesuvius eruption (Sulpizio et al., 2010), the 1902 and 1929 Mt Pelée eruption (Fisher and Heiken, 1982; Bourdier et al., 1989), the blast surge and pumice flows from the 18 May 1980 Mount St Helens eruption (Druitt, 1992; Brand et al., 2014), block and ash flows from Merapi (Abdurachman et al., 2000; Charbonnier and Gertisser, 2011; Charbonnier et al., 2013), Soufrière Hills Volcano (Cole et al., 2002, 2014), Colima (Macorps et al., 2018; Saucedo et al., 2019), Santiaguito (Hornby et al., 2019) and Tungurahua (Bernard et al., 2014b; Bernard and Le Pennec, 2016). Yet, studies relating the observed componentry trends to general processes of emplacement are still lacking in the literature.

Going forward, the growing use of automated chemical detection instruments and software, such as QEMSCAN Particle Mineralogical Analysis, based on the scanning electron microscope (Hornby et al., 2019) or raman spectroscopy coupled to morphological imagers (Varga and Roettig, 2018; Thivet et al., 2020) will make the collection of large componentry datasets less time consuming and have the capability to link to other textural properties (e.g., morphology, size) with greater ease. Furthermore, once these large, internally consistent datasets are created, artificial intelligence and machine learning approaches may use these as training datasets to support automated classification. This will enhance the use of componentry as a metric and enhance the number of scientific questions that can be addressed. However, alongside this data increase it would be useful, as a community, to remove some subjectivity and question-dependent component classifications and determine a basic set of classes that, as a minimum, can be robustly compared across different deposits, measured by different laboratory groups. Furthermore, upon creation and archiving of such datasets, transparent community documentation and accessible data storage is essential (Andrews et al., 2022; Wallace et al., 2022).

Particle density is one of the parameters controlling particle terminal settling velocity, where increased particle densities for a given grain size lead to increased settling velocities. Due to this, particle density is extremely important for sedimentation modelling, both during PDC transport and within any associated (co-PDC) plumes (Choux and Druitt, 2002; Dellino et al., 2008; Doronzo et al., 2010; Andrews and Manga, 2012; Dioguardi and Dellino, 2014; Dioguardi et al., 2014, 2017; Dioguardi and Mele, 2015). Additionally, during an eruption, changes to the particle density can increase eruption column density (e.g., increased lithics due to wall rock erosion or increased juvenile density due to reduced vesicularity) and potentially generate PDCs by column collapse (Shea et al., 2011, 2012). Furthermore, particle density is inherently linked to componentry. Lithics and free crystals are typically denser and within a single deposit show less variation in density relative to the juvenile pyroclasts. The density of juvenile components is more complex and varies as a function of dense glass density ρ ₀, the crystal and vesicle volume fractions, ɸ_x and ɸ_v respectively, and the crystal and vesicle size distributions. ρ ₀ is closely related to the chemical composition of the magma where density increases with decreasing silica content (Lesher and Spera, 2015; Iacovino and Till, 2019). ɸ_x, ɸ_v and the crystal and vesicle size distributions can be highly variable and depend on both the magma composition and the magma ascent and fragmentation history. Ultimately, the particle density of juvenile material depends on the inter-relationship between particle size, ɸ_x, ɸ_v and the crystal and vesicle size distributions.

As demonstrated by several studies on fallout deposits, the density of vesicular juvenile particles varies with grain size following a sigmoidal decrease (Barberi et al., 1989; Rosi et al., 1999; Bonadonna and Phillips, 2003; Eychenne and Le Pennec, 2012; Cashman and Rust, 2016). High and low density plateaus are observed at fine and coarse grain sizes, respectively. The high plateau density value corresponds to the Dense Rock Equivalent (DRE) density (i.e., glass and groundmass crystals devoid of bubbles) whereas the low plateau density value indicates the average density of lapilli-sized vesicular particles. The grain size thresholds at which the density plateaus occur depend on ɸ_x, ɸ_v and the crystal and vesicle size distributions. It is generally observed that the high density plateau occurs at a grain size threshold below 500 μm, and the low density plateau at a grain size threshold above 2 mm (Breard et al., 2016; Cashman and Rust, 2016).

A series of well-established methods exist for determining particle density. Typically, these methods include forms of pycnometry–methods to measure volume. With a subsequent measurement of mass, density can be calculated. Other methods include the settling of particles in water (Fisher, 1965) or suspension in heavy liquids (Barberi et al., 1989). Depending on the method and sample used, the exact form of density varies. This is outlined in Table 1.

Despite these well-established methods there are little data on particle density for PDC deposits; most studies with these data are focussed on pyroclastic fall units. However, observations on fall deposits (e.g., sigmoidal distribution) should equally apply. Some previous works on PDC deposits have focussed on particle density variations as a function of grain size (Dellino et al., 2008) and have shown that for some juvenile clasts from Somma- Vesuvius and Campi Flegrei density increases exponentially with decreasing grain size over a narrow range from 0.5 mm to ∼2.5 mm. Other studies have compared particle density variations between directed blast deposits from different volcanoes (Belousov et al., 2007; Bernard et al., 2014a) or have compared fall vs. flow units to elucidate PDC formation mechanisms (Shea et al., 2012).

However, currently studies are often limited to a single grain size. Going forward, aided by the increasing availability and collaborative access to instrumentation, the generation of density distributions will prove useful for more sophisticated modelling of sedimentation and particle segregation within PDCs. There is also a need to add clarification to the terms used to describe density. For example, ‘bulk density’ is frequently used at a range of scales to describe an individual particle, an experimental mixture, and a deposit. Additionally, the numerical value, and thus definition, of particle or envelope density can vary based on methodology. For example, when wrapping particles in a wax film, the extent to which the film is pushed into surface cavities will exert a control on the density calculated. To allow accurate comparison between published datasets, clear and consistent definitions must be sought. Furthermore, robust, and appropriate statistical treatment of density datasets must be performed (Bernard et al., 2015).

The morphology of pyroclasts within PDCs and associated co-PDC plumes exhibits a control on the momentum coupling between the particle and the carrier phase (e.g., gas, or pseudo-gas when very fine particles are fully coupled with the fluid), and thus also controls the momentum dissipation due to the particle-fluid drag, the particles’ trajectory and terminal settling velocity. It is well-established in multiphase flow dynamics that the aerodynamic drag of solid particles depends on their particle Reynolds number, density, and shape (e.g., Ganser, 1993; Dioguardi and Mele, 2018; Bagheri and Bonadonna, 2019). Through its control on particle packing, a particles’ morphology also influences the permeability of both the current and deposits. Furthermore, morphology is frequently used as a diagnostic tool. For example, it can be used to assess the abrasion propensity of pyroclasts, where more angular clasts are more susceptible to mechanical modification, and thus can be used as a proxy for the distance travelled from source (Manga et al., 2011; Brand et al., 2014). Morphology is also extensively used to distinguish between fallout and flow units in the field, where flow units contain more rounded pyroclasts.

There are a range of methods used in the measurement of morphology, of increasing sophistication and use. Simple qualitative visual inspection is a wide-spread field approach with specific clasts quantitatively measured for minor, intermediate and long axis length with tape measures or callipers, depending on the overall pyroclast size. In the laboratory, for pyroclasts of lapilli size or smaller, morphologies based on 2D measurements are typically made. These fall into two categories: projected and cross-sectional. Projected morphology measurement techniques include dynamic image analysis (e.g., Microtrac Camsizer instruments), static image analysis (e.g., Malvern Morphologi), and custom-made camera-light set ups (e.g., Dellino et al., 2005). All these methods measure the particle silhouette. In contrast, cross-section-based measurements involve mounting, impregnating and polishing particles to produce polished grain mounts or thin sections. These are then imaged using a Scanning Electron Microscope (SEM). Lastly, 3D measurements are becoming increasingly common with advances in X-Ray computed tomography (XRCT); however, with current micro XRCT scanners the voxel (i.e., three-dimensional pixel) resolution is not sufficient to accurately document the morphology of (fine) ash-sized particles. The exact resolution is dependent on the individual instrument specification and is expected to improve with continued technological advancement.

Typical or representative values for pyroclast morphology are almost impossible to define. Pyroclast morphology is inherently linked to the primary fragmentation mechanism, which for PDCs is non-unique encompassing a broad range of eruption styles and compositions (Brown and Andrews, 2015; Dufek et al., 2015). Additionally, the pyroclasts are variably modified by further (i.e., secondary) fragmentation processes creating a temporal evolution in morphology (Calder et al., 2000; Manga et al., 2011; Kueppers et al., 2012; Mueller et al., 2015; Jones et al., 2016). This complexity and the lack of representative values hinder the incorporation of particle morphology into numerical models and the scaling of analogue experiments.

Another challenge for the quantification of particle morphology is the huge range of shape descriptors used within the literature. This range makes cross-comparison between different studies and deposits challenging and the frequent use of alternative nomenclature (e.g., roundness vs. circularity vs. form factor) further hinders useful comparisons. The use of shape parameters for juvenile volcanic pyroclasts, associated statistical tests and classifications, and the protocols for data collection have been extensively reviewed and this will not be repeated here (Leibrandt and Le Pennec, 2015; Liu et al., 2015; Dürig et al., 2021; Comida et al., 2022; Ross et al., 2022; Benet et al., 2023). The detailed work of Liu et al. (2015) leads to the recommendation of the following bounded (i.e., scaled from 0 to 1) shape descriptors: solidity, convexity, and axial ratio.

Solidity (SLD) is a measure of the irregularities and roughness on a particle scale (i.e., the morphological roughness) and is expressed as: SLD = A p / A H (1) where A_p is the pyroclast area and A_H is the area of the bounding convex hull. Convexity (CVX) is a measure of the small-scale cavities or protrusions on the particle surface (i.e., the textural roughness) and is expressed as: CVX = P H / P P (2) where P_P is the pyroclast perimeter and P_H is the perimeter of the bounding convex hull. The axial ratio (AxlR) is a measure of particle elongation and is expressed as: AxIR = B / A (3) where B and A are the minor and major axis of the best fit ellipse, respectively. Furthermore, if a single parameter is needed to document the overall particle irregularity, then the form factor (FF) is recommended: FF = 4 π A p / P P 2 (4)

FF measures the deviation of a particle from a circle; however, its sensitivity to both particle elongation and roughness limits its use as a diagnostic tool. A visual representation of these parameters is shown in Figure 3.

Previously, Dellino et al. (2005) recommended the use of the so-called “shape factor” for aerodynamic purposes (e.g., drag calculations): Ψ = ϑ / X (5)

where ϑ is the particle sphericity: ϑ = A sph / A p (6)

In which A_sph is the surface area of the equivalent sphere. A_sph was calculated using the equivalent particle diameter determined by water displacement in Gay-Lussac bottles. Χ is the particle circularity: Χ = P p / P sph (7) where P_sph is the perimeter of the circle equivalent to the maximum projection area.

This shape factor parameter, Ψ has been found to perform well in shape dependent drag laws (even better than 3D shape descriptors, Dioguardi and Mele, 2018) for terminal velocity calculations, which is to be expected since irregular particles tend to settle with the maximum projection area oriented perpendicular to the direction of motion.

As detailed, the quantification of these shape parameters is essential for models of aerodynamic drag which, in turn, are used in PDC simulation tools. This is particularly important for dilute PDCs, in which the particle-fluid interaction dominates. For example, Dioguardi and Mele (2018) showed that, for an overall variation of particle shape factor (Equation 5) of 20% around the measured value of their test case, the dynamic pressure calculated via their simplified dilute PDC model varied by ∼ 65%, while deposition rates and times varied by ∼ 30%.

Despite these advances, challenges remain. For the same particle, the shape parameter value depends on whether cross-sectional or projected images are used. Projected area-based measurements typically exhibit higher values due to the smoothing effect when projecting a 3-dimensional object onto a 2-dimensional plane (Liu et al., 2015). Furthermore, when using projected areas, it has been shown that values of FF, CVX and SLD can be dependent on the data collection method. Differences have been interpreted to stem from the difficulty in keeping the outline of a 3D shape in focus when using optical imaging techniques (Liu et al., 2015). Shape descriptors are also dependent on the grain size class analysed and different studies use different sizes governed by their scientific question, or the sample available, for example. These challenges make comparisons between published results problematic. The tephra fall community has started to define protocols for deposit sampling, data collection and analysis (Ross et al., 2022; Wallace et al., 2022). To support future intercomparison between datasets these protocols should be continually refined and adopted. Going forward, the growing use of XRCT could also be incorporated into such protocols and 3D shape parameter selection. Doing this early as a community may prevent the explosion of terms and methods observed with the 2D shape descriptors. The 3D measurement of particle shape and its use for calculating particle drag (Dioguardi et al., 2017) will be useful as numerical capabilities increase.

PDCs are multiphase flows often composed of two phases: solid and gas. Due to gravity and ambient fluid entrainment, PDCs are density stratified, with a solid concentration that typically decreases upward. As in many other multiphase flows, processes at the microscale (i.e., particle scale) influence those at the mesoscale, which in turn impact macroscale processes. Similarly, the macroscale defines the environment in which the mesoscale features form through instabilities and other cascading processes. Simultaneously, the mesoscales create the environment in which the microscale features of individual particles are embedded. This bidirectional transfer of information up and down the wide range of length scales, from the particle size, interparticle spacing, instability length scales and finally to the scale of the system, makes PDCs extremely challenging to describe mathematically and therefore simplify in numerical models (Lube et al., 2020).

The solid concentration (C) per unit volume (i.e., measurements in volume %) greatly affects the gas-particle coupling regimes in PDCs (Breard et al., 2016). The mass loading (M) is also a dimensionless parameter and is defined as the ratio of particle-to-fluid mass and has been used to assess the coupling regime of multiphase flows (e.g., Capecelatro et al., 2014). Quantitatively it can be expressed as: M = solid density*C/(fluid density*(1-C)).

Very dilute (C<∼10⁻⁵ and M<0.1), particles can be approximated as one-way coupled, because the wake they create in the fluid is smaller than the mean particle separation length (e.g., Elghobashi, 1994). At concentrations of ∼10⁻⁵≤C<∼10⁻⁴ and 0.1≤M<1, particles can modulate the carrier flow field and, through feedback, impact their transport mechanism. This is the two-way coupling regime, where particle ↔ fluid interactions must be accounted for. When C>∼10⁻⁴ and M≥1, interactions between the suspended particles, both in the form of direct particle-particle collisions and fluid-mediated neighbour interactions, become important. This regime of particle-laden flows is traditionally termed four-way coupled, where particle ↔ particle interactions must be accounted for in addition to fluid → particle (forward coupling) and particle → fluid (backward coupling) interactions. Most PDCs, due to their high temperature, will be dominated by 2-way and 4-way coupling, as they become buoyant and transform into a co-PDC plume when concentrations drop below C<∼10⁻⁴ (e.g., Lube et al., 2020).

Concentration and mass loading impacts the settling velocity of particles (Breard et al., 2016; Weit et al., 2018; Penlou et al., 2023), and in turn this impacts the density stratification and partitioning of mass between the basal granular layer (i.e., the bedload) and overriding turbulent suspension (Douillet et al., 2014, 2019; Brosch and Lube, 2020). The concentration of particles in PDCs is expected to be heterogeneous temporally and spatially at any given location due to particle clustering. Clusters mainly form by: 1) turbulence due to preferential sweeping/concentration (in one-way and two-way coupling regimes), as particles with a Stokes number of unity will be swept to eddy margins and accumulate in low vorticity regions. 2) When four-way coupling originates at the microscale (i.e., particle scale) and generates elongated mesoscale clusters of particles that increase the settling velocity of the mixture (Lube et al., 2020). To date, the role of concentration on particle clustering is only crudely captured in 3D PDC models and has yet to be included in 2D models.

When the concentration, C ≳ 0.3, the slip velocity between gas and solid is small, and particle collisions dominate, mesoscale clusters (enhanced settling regime) give place to the granular (collisional and frictional) regime wherein hindered settling can dominate (Chedeville and Roche, 2014). In this granular regime, changes in concentration as the flow responds to changes in the slope/topography (Chédeville and Roche, 2015) or to particle breakage can self-generate elevated pore-fluid pressure because of the pore pressure feedback (Dufek and Manga, 2008; Breard et al., 2023).

The drastic spatial and temporal evolution of the solid concentration make PDCs one of the most challenging multiphase flows to describe on Earth and has led our community to simplify their descriptions as either dense granular flows or dilute turbulent suspensions. The ability to directly image the inertial dynamics of PDCs and observe particle concentration structures is limited, although promising advances have been made in the use of Doppler radar (Voege et al., 2005; Bech and Chau, 2012; Vriend et al., 2013). Nevertheless, these technologies rely on well-timed and perfectly positioned instrumentation and eruption. Going forward, enhanced high-performance computing paired with large-scale laboratory experiments may offer ways to directly image concentration profiles in a systematic way (Esposti Ongaro et al., 2020a).

The permeability of gas-pyroclast mixtures is a key parameter that controls the diffusion timescale of excess pore pressure. Excess pore pressure can build inside dense PDCs due to the pore pressure feedback (Lube et al., 2020). This occurs through a variety of mechanisms involving flow compaction, dilation, and shear. In all these mechanisms the pore pressure is increased within the flow, and this helps to reduce the solid stresses, and consequently strongly contributes to increasing PDC mobility. Increased permeabilities support faster pore pressure diffusion and defluidization of the gas-pyroclast mixture. Permeability is expected to vary by orders of magnitude because of its strong dependence on the grain size distribution and the interrelated voidage/packing fraction (Ergun, 1952; Gidaspow, 1994). Currently, permeability is likely encapsulated within the low effective friction coefficient in depth-averaged PDC models used to reproduce the long runout of past events. Despite the importance of this parameter, permeability measurements of PDCs remain scarce (Bareschino et al., 2007; Druitt et al., 2007; Breard et al., 2019b). This is in part due to physical limitations of having small experimental setups that cannot accommodate the wide grain size distribution transported by flows.

Volcanic eruptions display spectacular evidence of particle charging and strong electric fields, often to the point of producing discharge such as visible lightning. Lightning produces a broad spectrum of electromagnetic signals, and radio waves in particular that can be detected at great distances from the source (100 s–1000 s of km). Charging of volcanic ash is known to be produced by three main processes (Cimarelli et al., 2022): 1) fracto-charging (also known as fractoemission; James et al., 2008) as particles fragment due to rapid decompression or disruptive collisions (Méndez Harper et al., 2021), 2) tribo-charging of ash due to particle-particle interaction or particle-hydrometeor interaction (Méndez Harper and Dufek, 2016) and 3) radioactive charging, for instance as radon decays (Nicoll et al., 2019). Both frictional and comminution processes operate in PDCs (e.g., Dufek and Manga, 2008) and hence particle charging is expected to occur during PDC transport. However, what is less certain is how the higher concentration of particles in PDCs influence the breakdown conditions at discharge. Most research on volcanic lightning has focused on charging in jets and plumes and benefited from a multidisciplinary approach from collaborations across atmospheric sciences, volcanology, and engineering (Cimarelli et al., 2022). However, lightning has also been detected in PDCs (Schultz et al., 2020) and described in early records of witness accounts (Lacroix, 1904). Nonetheless, there is a gap in knowledge regarding the role of particle charging on the dynamics of PDCs (across dense to dilute flow regimes) and whether electric fields, measurements of particle charge, or radio wave measurements could be used to probe the internal properties of PDCs and help their detection/identification, as other mass flows on Earth do not produce significant discharges. Searching PDC deposits for lightning-induced volcanic spherules (Genareau et al., 2015) may provide insight into past events however, separating PDC spherules from those formed in the jet/plume before collapse will be a challenge.

Granular flow rheology plays a crucial role in controlling the transportation and deposition of PDCs and can even influence their initiation (Sulpizio et al., 2014; Lube et al., 2020). However, despite its significance, the granular flow rheology of volcanic materials remains poorly understood as in situ measurements are lacking, and rheometry experiments on volcanic materials are still in their infancy. Similar to other complex granular media, the rheology of volcanic granular flows depends on various properties of the mixture, such as particle shape, density, and grain size distribution. In the past decade, advances in our understanding of PDC dynamics was aided by the development of experiments (Lube et al., 2015; Sulpizio et al., 2016; Smith et al., 2020; Gueugneau et al., 2022; Poppe et al., 2022) and use of tools from soft-matter physics, including the discrete-element method (Cundall and Strack, 1979), which can help us derive constitutive equations to describe granular flow rheology (e.g., μ(I)-rheology; Jop et al., 2006) and its interactions with the substrate (Breard et al., 2020; Breard et al., 2022). Although a bulk rheology that captures some of the complexity at micro- and meso-scales may be sufficient for depth-averaged models, 3D models require inputs such as particle-particle friction, particle-substrate friction, and particle-restitution coefficients (Breard et al., 2019a; Neglia et al., 2022), which are more challenging to measure than simple angle of repose or the H/L ratio.

The textural characterisation of ultra-fine volcanic ash (i.e., particle diameter <10 µm) has direct implications for human and environmental health hazard assessments (Eychenne et al., 2022; Ligot et al., 2022), for the understanding of long-range ash transport (Gouhier et al., 2019; Cashman and Rust, 2020; Eychenne and Engwell, 2022), and for improving satellite ash retrieval methods (Prata et al., 2019). PDCs are significant sources of ultra-fine ash given their high comminution efficiency (Kueppers et al., 2012; Mueller et al., 2015; Bernard and Le Pennec, 2016; Jones et al., 2016; Buckland et al., 2018; Hornby et al., 2020), which are expected to be preferentially partitioned into co-PDC plumes and transported long-distances in the atmosphere, potentially causing widespread impacts. Yet, no study has specifically investigated natural ash from PDCs in this size range. New opportunities for characterising the textural properties of such fine grained material are now emerging, thanks to the recent development of new tools for isolating ultra-fine ash from tephra samples, and the democratisation of high throughput and high spatial resolution analytical instruments, such as scanning and transmission electron microscopes with FEG sources (Eychenne et al., 2022). Characterising the texture of ultra-fine ash produced by PDCs should become a key research avenue in the future.

The surface properties of pyroclasts, in particular the surface area and surface chemistry, play a key role in the eruption dynamics, and in the associated eruption impacts. For instance, the surface area (total surface area, specific surface area, or surface area to volume ratio) exhibits an important control on the gas-particle heat transfer (Stroberg et al., 2010), and therefore affects the buoyancy and cooling of pyroclastic flows and plumes. Surface area also impacts particle drag and hence particle settling velocities (Ganser, 1993), and is used in calculating fragmentation energy budgets (Kolzenburg et al., 2013; Hajimirza et al., 2022). Critically, surface properties are the main control of the physicochemical interaction processes between the pyroclasts and the ambient medium (e.g., air/atmosphere, water bodies, lung lining fluids and lung tissues). Thus, the health and environmental impacts of volcanic pyroclasts are intrinsically related to their surface properties. The surface chemistry determines the available sites, and the surface area available for chemical exchange (e.g., scavenging and leaching) with the gaseous and liquid phases present within volcanic gas-particle mixtures (i.e., plumes, PDCs, co-PDCs) and surrounding atmosphere (Ayris et al., 2013, 2014; Delmelle et al., 2018, 2021). The pyroclasts’ surface properties therefore have a significant control on the fluxing of sulphur and halogen gases into the atmosphere during volcanic eruptions. The scavenging of the surrounding gaseous/liquid species by the pyroclast surfaces leads to chemically loaded particles (e.g., surface sulphate and halide salt formation; Casas et al., 2022) interacting with the environment after deposition. Salts can be readily mobilised into the soils and hydrological system with (positive and negative) implications for surrounding agriculture and water supplies (Ayris and Delmelle, 2012; Stewart et al., 2020). Surface salts are also dissolved in lung lining fluids releasing bio accessible, and potentially toxic, elements in the lungs (Tomašek et al., 2019). For the respiratory health hazard, surface area and chemistry are essential parameters to constrain, as they control the interaction mechanisms between the inhaled particles and the cell membranes, and hence the particles’ bioreactivity and harmful effects (Damby et al., 2013; Stewart et al., 2022).

Surface area measurements of volcanic particles are time consuming and, for small ash-sized particles, typically measured using the Brunauer–Emmett–Teller (BET) method of nitrogen adsorption. Specific surface areas (i.e., normalised per gram) for volcanic ash are typically <2 m² g⁻¹ (Delmelle et al., 2005; Horwell et al., 2007; Ayris and Delmelle, 2012), however larger values can be caused by rougher particle surfaces at the nanometer scale. Surface chemistry can be measured by X-ray photoelectron spectroscopy (XPS) or approached by high-resolution scanning electron microscopy coupled with energy dispersive spectroscopy (EDS) (Delmelle et al., 2007, 2021), while the surface composition in soluble species is typically measured by chemical analyses (e.g., ion chromatography and mass spectrometry) of the particles leachates (Stewart et al., 2020).

Most of the previous work on the surface properties of pyroclasts has focused on particles from fallout deposits. However, surface properties of pyroclasts transported within PDCs and co-PDC plumes are of equal or perhaps greater importance. Indeed, high abrasion rates occur in PDCs, producing abundant surface derived chips with high surface area (Jones and Russell, 2017). Furthermore, PDCs are hot mixtures of particles, volcanic gas, and ambient air, suggesting a high potential for particle-gas chemical exchange via the particles’ surfaces, but these processes have so far barely been studied. Bridging the gaps between the PDC and fallout community on these topics provides a clear way forward.

Distinct from other mass flows and gravity currents, PDCs carry considerable thermal energy, which not only plays a crucial role in their dynamics but also renders them deadly even during brief exposures (<1 min) at high temperatures (>100°C). In addition, unlike (nearly) isothermal currents such as snow avalanches and haboobs, they can generate large thermal plumes (co-PDC plumes) with source areas that can extend over their propagation area. Consequently, understanding the thermal evolution of PDCs is critical for hazard assessment.

The thermal structure of PDCs has yet to be probed in situ. Instead, their thermal signature is acquired through thermal imaging or deposit analysis. Thermal imaging is restricted to the outer opaque ash-cloud layer and can be employed to detect and gain a deeper understanding of the (colder) ambient fluid entrainment (Spampinato et al., 2011; Lube et al., 2020). PDCs that engulf vegetation (such as wood) frequently leave deposits containing charcoal. The charcoal’s reflectance increases with temperature during the charring process, which can help uncover the emplacement temperature of PDC deposits (Scott and Glasspool, 2005). While this method has been applied to only a limited number of historical deposits, laboratory studies demonstrate that charcoal reflectance measurements can accurately reveal the formation temperature from 200°C to 1,100°C (Scott and Glasspool, 2005; Ascough et al., 2010). Thus, charcoal reflectance analysis presents numerous applications in volcanology, including the study of PDC deposition and associated cooling as a function of transport distance (e.g., Pensa et al., 2015). Alternative techniques for uncovering thermal conditions include: 1) using lithic clasts and the natural remanent magnetization (NRM) method (Mandeville et al., 1994; McClelland et al., 2004; Zanella et al., 2015), 2) examining leaves damaged but not burnt by low-temperature PDCs (Efford et al., 2014), 3) oxidation rates (e.g., Tait et al., 1998), 4) calculating the conditions required for deposit welding (e.g., Andrews and Branney, 2011) and 5) quench rind measurements of large juvenile clasts (e.g., Benage et al., 2016).

Using the various aforementioned techniques, we know PDCs emplace deposits at temperatures ranging from <60°C (hydrothermal eruptions) to 850°C (Banks and Hoblitt, 1986; Trolese et al., 2018; Pensa et al., 2019; Brand et al., 2023) and usually display minimal temperature evolution from proximal to distal regions. This, however, does not imply a spatially constant temperature within a current (the deposits record the thermal condition at emplacement). For example, survivor accounts from the 1980 lateral blast from Mt St Helens report being engulfed initially in cold air with mud and ice particles, followed by scorching temperatures after about 10 s, causing severe burns (Lipman and Mullineaux, 1981). Large-scale experiments (Brosch et al., 2022), in which the PDC temperature can substantially vary between the non-depositional flow head (that entrains substantial ambient air) and the flow body (where ambient fluid entrainment is limited due to strong density gradients that prevent mixing), corroborate the Mt St Helens reports. Unfortunately, unless future in situ temperature measurements are obtained using thermocouples immersed in PDCs, present techniques can only offer limited insights into the temporal and spatial evolution of the thermal conditions within currents.

To comprehend the spatiotemporal thermal structure of PDCs, numerical models that solve the energy equation have been developed in 1D (Bursik and Woods, 1996; Shimizu et al., 2019), 2D (de' Michieli Vitturi et al., 2023), and 3D (Esposti Ongaro et al., 2008; Dufek, 2016; Esposti Ongaro et al., 2020b; Hutchison and Dufek, 2021). However, all these models require several key assumptions and approximations. As input parameters, the initial temperatures of both the fluid and particles are required, with the latter potentially being a function of particle size (Moitra et al., 2018). The thermal properties (e.g., specific heat, thermal conductivity) of the particles also need to be established, which may also be a function of particle size and are seldom well-measured. Furthermore, 1D and 2D models must account for ambient fluid entrainment through an empirical entrainment law, such as the one developed by Parker et al. (1987) from turbidity current experiments (which does not consider entrainment in the flow head) but is widely employed in PDC models (Bursik and Woods, 1996; de’ Michieli Vitturi et al., 2023). Finally, these 1D and 2D models do not account for the vertical temperature gradients, as they assume a vertically mixed current, thus potentially underestimating the temperature of the basal flow. Overall, there is a need to understand the thermal properties of volcanic particles as a function of measurable physical properties (e.g., porosity, surface area) to help us understand the partitioning of heat within PDCs.