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Simulations and parameterisation of shallow volcanic plumes of Piton de la Fournaise, La Réunion Island using Méso-NH version 4-9-3
S. G. Sivia1,2, F. Gheusi1, C. Mari1, and A. Di Muro3
1 Laboratoire d'Aérologie (LA), University of Toulouse and CNRS, UMR5560, Toulouse, France 2Laboratoire de l'Atmosphère et Cyclones (LACy), Université de La Réunion, CNRS, Météo-France, UMR 8105, Saint-Denis de La Réunion, France
3Laboratoire de Géologie des Systèmes Volcaniques, IPGP, CNRS, UMR 7154, Paris, France Received: 18 September 2014 - Accepted: 29 October 2014 - Published: 26 November 2014 Correspondence to: F. Gheusi (francois.gheusi@aero.obs-mip.fr) Published by Copernicus Publications on behalf of the European Geosciences Union.
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Abstract
In mesoscale models (resolution ~ 1 km) used for regional dispersion of pollution plumes, the heat sources, the induced atmospheric convective motions and the volcanic emissions of gases and aerosols are all sub-grid scale processes (mostly true for effusive eruptions) which need to be parameterized. We propose a modified formulation of the EDMF scheme (Eddy Diffusivity-Mass Flux) proposed by Pergaud et al. (2009) which is based on a single updraft. It is used to represent volcano induced up-drafts tested for a case study of January 2010 summit eruption of Piton de la Fournaise (PdF) volcano. The validation of this modified formulation using large eddy simulation (LES) focuses on the ability of the model to transport tracer concentrations up to 1-2 km in the lower troposphere as is the case of majority of PdF eruptions. The modelled volcanic plume agrees well with the SO2 (sulphur dioxide) tracer concentrations found with LES and a sensitivity test performed for the modified formulation of the EDMF scheme emphasizes the sensitivity of the parameterisation to entrainment at the plume base.
1 Introduction
A critical factor in successfully monitoring and forecasting volcanic ash and gases dispersion is the height reached by eruption clouds, which is affected by environmental factors, such as wind shear and atmospheric vertical stability (Glaze and Baloga, 1996; Graf et al., 1999; Bursik, 2001; Tupper et al., 2009). The term "volcanic plume" refers to both the vertical buoyant column of gas/ash above the eruptive vent, and the following horizontal transport of pollutants at the regional scale by the wind flow. The convective scale corresponds to the unstable region where intense but localised sensible and latent heat fluxes released by pyroclasts, gases and lava near eruptive vents generate convection which transports energy and pollutants to high altitudes through buoyant plumes. Throughout the course of this convection mixing of the plume with the atmosphere takes place at different levels of altitude through entrainment and
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detrainment. This process allows for the distribution of pollutants over a certain vertical range.
Piton de la Fournaise (PdF) is one of the world's most active volcanoes (Lenat and Bachelery, 1987) with an average of one eruption every eight months in the last fifty years (Peltier et al., 2009). Most of the studies undertaken for deep volcanic injection have been applied to stratospheric injections, which are mostly performed by large explosive volcanoes (comprehensive review by Robock, 2000). However, much less is known about the environmental and atmospheric impacts and fates of volcanic plumes injected into the troposphere (Mather et al., 2003; Delmelle et al., 2002). PdF can create a major source of tropospheric air pollution as was the case during the eruption of April 2007 (Tulet and Villeneuve, 2011). The air-quality standard for ecosystem and human health protection was exceeded for sulphur dioxide (SO2) at several inhabited locations in the south-west and north-west part of the island (opposite from the location of the eruption) (Viane et al., 2009; Bhugwant et al., 2009; Lesouef et al., 2011).
Simulations of atmospheric plumes from intense heat source points have been performed using Meso-NH (Lafore et al., 1998) model to represent the impact of forest fires on the dynamic and chemistry of the atmosphere. A study by Strada et al. (2012) simulated forest fire plumes at 1 km resolution which showed good agreement with observations where high sensitivity to the atmospheric stability was observed. Simulations of the eruption column dynamics, chemistry dispersal in the proximal environment and the volcanic cloud tracking at regional scale rely on similar numerical and conceptual approaches as the ones used for the study of the forest fire plumes. In kilometric resolution models used for air quality purposes (simulation or forecasts), the localised heat source is diluted in the model grid and hence no convection is explicitly generated.
Several types of atmospheric movements are sub-grid processes, and they are incorporated into atmospheric models through appropriate parameterisation schemes. In order to determine the evolution of volcanic plumes in the atmosphere, numerical models need to consider two different scales:
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1. an implicit/convective scale corresponding to the convective plume above the erupting volcano, whose processes are sub-grid even at fine resolutions (> 500 m), and
2. an explicit/dispersion scale that corresponds to the dispersion of the volcanic plume in the atmosphere.
In mesoscale models (resolution ~ 1 km) used for regional dispersion of pollution plumes, the heat sources, the induced atmospheric convective motions and the volcanic emissions of gases and aerosols are all sub-grid scale processes which need to be parameterized.
In this article we briefly describe an existing sub-grid shallow convection scheme by Pergaud et al. (2009) usually used in the atmospheric model Meso-NH for weather simulations. This scheme is adapted in Sects. 2.2.2 and 2.2.3 such that the size and intensity of the ground heat source provided by the eruption is initialised for modelling the sub-grid updraft. This parameterisation is tested on a 1 dimensional (1-D) single column model (SCM) with a 1 km resolution for an eruption observed at PdF in January 2010. The choice of 1 km resolution for SCM simulations is because it is the target resolution of future forecast models running over Reunion Island. Simultaneously, a three dimensional (3-D) Large Eddy Simulation (LES) is performed (10 m resolution) using the same size and intensity of the eruption as prescribed for the adapted convection scheme. Finally the results of the vertical mass and tracer concentration budgets obtained from SCM are validated against the LES results.
2 Materials and methods
2.1 Description of the January 2010 summit eruption of Piton de la Fournaise
An eruption took place on 2 January 2010 around 10:20 UTC at the summit of Piton de la Fournaise (PdF) located at 2632ma.s.l. as detected by the monitoring data obtained
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by the Volcanic Observatory of Piton de la Fournaise (OVPF) (Roult et al., 2012). At 10:27 UTC a small and diluted gas plume was first visible and a vertical plume rapidly formed above the crater at 10:57 UTC. Up to 7 lava fountains erupted together from the same number of vents along a fracture on the west Dolomieu crater wall (length of fracture about 60 m) and the highest lava fountain of about 30 m was emitted by the largest vent located in the middle of the fracture. Lava flows were alimented by magma flowing from the vents (Fig. 1) but also from hot fountain products that were remobilized after falling down to the ground. According to Roult et al. (2012) the eruption emitted 1.2 x 106m3 of lava in about 9.6 days; mass flow rate decreased exponentially after the beginning of the eruption and the fountaining and gas plumes described here only occurred till 4 January 2010, whereafter mostly effusive lava flows were observed.
The vertical plume above the crater (Fig. 1; right) is relatively steady implying low winds and a level of neutral buoyancy is reached at approximately 1300 m above the fountain top (from observation). For the development of a parametrisation this case study is the least complex compared to other eruptions of PdF since 2000. There is a well-developed vertical gas column which is less impacted by the horizontal winds and the topography of the area.
2.2 Description of the volcanic plume parameterisation
It is well understood that a volcanic eruption plume enters into an atmosphere that has a pre-existing stratification, in terms of temperature, moisture content and wind (Bjornsson et al., 2011; Petersen et al., 2012). There are three dynamically distinct regions related to volcanic plumes (Sparks, 1986),
1. the gas thrust region, where the dynamics is dominated by the exit velocity at the vent and the flow near the vent is driven upward by its initial kinetic momentum,
2. buoyancy driven convective region which covers most of the height of the plume,
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3. umbrella cloud region where vertical motion is small and the plume disperses horizontally due to wind impacts.
For the purpose of modelling volcanic clouds using Meso-NH, we are predominately interested in the convective region of the volcanic cloud. The current updraft model used in Meso-NH defined by Pergaud et al. (2009), Sect. 2.2.1, is not adapted to volcanic clouds. In this section we propose an adaptation of the updraft scheme (Sects. 2.2.2 and 2.2.3) which is applied to volcanic plumes and consists mainly in a modification of the updraft initialization at ground level (zgrd) using values inspired from terrain observations.
2.2.1 Sub-grid cloud parameterisation as per Pergaud et al. (2009)
The basic idea of EDMF (Eddy Diffusivity Mass Flux) approach is to represent vertical transport of matter and energy that occur at the sub-grid scale in numerical simulations of convective boundary layer (CBL) with resolutions of ~ 1 km or coarser. At such resolutions vertical motions usually dominate the vertical sub-grid transport due to
1. turbulent eddies
2. convective updrafts and compensating downdrafts.
Turbulent transport is commonly parameterised with the Eddy Diffusivity (ED) method, corresponding fluxes being written in the form of -K^dzZ where -K^ is a diffusion coefficient and 0 the average of any model variable 0 (e.g. temperature, tracer etc.) over the local grid cell (Holton, 2004).
A grid box can contain multiple convective updrafts, for simplicity a single updraft is considered carrying the properties of the ensemble of updrafts. This is known as the Mass-Flux (MF) approach. The fraction of the total area of a grid box that is covered by the updraft is known as the fractional updraft area (au). The corresponding net vertical
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flux for 0 over the grid cell takes the form of Mr(0u - 0), where, Mu is the updraft mass
flux, 0 is the mean value and 0u is the updraft value of the variable 0.
Both ED and MF approaches have been combined in a single eddy diffusivity/mass flux (EDMF) parameterisation such that nonlocal sub-grid transport due to strong up-drafts is taken into account by MF, while the remaining transport is taken into account by ED (Siebesma and Teixeira, 2000; Hourdin, 2002; Soares et al., 2004; Siebesma et al., 2007; Pergaud et al., 2009; Witek et al., 2011). In our approach for volcanic induced convection we only modify the MF scheme (Sect. 2.2.2).
The two key parameters determining the mass flux profile are entrainment (s) and detrainment (S) expressed as fractions of the updraft mass flux (Mu) per unit height. This simply leads to the following steady state mass flux continuity equation:
(s - ô)MU
The mass-flux evolves along the vertical at a rate given by the difference between s and S rates. The definition of entrainment/detrainment rates is the crucial point in EDMF parameterisation as it is at this level that the physical coupling between turbulent mixing and mass flux is performed.
In Pergaud et al. (2009) the mass-flux profile depends on the vertical velocity of the updraft (wu), whose vertical evolution is affected in turn by a buoyancy force (Bu) and a drag term where the entrainment of environmental air, namely lateral mixing, is accounted for:
wu^z = aBu - bsW|j
The updraft buoyancy acceleration is evaluated related to the difference of virtual potential temperature (9v) between the updraft and its environment, in the absence of phase change in water: Bu = g(duv - 0v)/dv; parameters a and b are set to one (Simpson and Wiggert, 1969). Independent solutions of Eqs. (1) and (2) permit to calculate
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the vertical variation of the updraft fractional area
that is used to diagnose the cloud fraction, hence to define the sub-grid condensation scheme in the EDMF framework.
2.2.2 Modified EDMF - Updraft Initialisation
Firstly, in the current EDMF parameterisation wu is initialised at the ground level (zgrd) using Turbulent Kinetic Energy (TKE) (e) as; w2(zgrd) = 3e(zgrd) which is bound to local meteorology. However, this computation is not applicable to volcanic plumes as vertical velocity in this case does not depend on the atmosphere, through the TKE. During volcanic eruptions, a mixture of gases, magma fragments, crystals and eroded rocks is injected into the atmosphere at high velocity, pressure and temperature. The diverse and unpredictable variability of eruptive styles depends mostly on the complex rheology of magma and the nonlinear processes leading to the fragmentation of the viscous melt into a mixture of gases and particles (Gonnermann and Manga, 2007). Nonetheless, the explosive character of a magmatic eruption like that of January 2010 is associated with the rapid decompression and the consequent abrupt expansion of gases in the magma (Parfitt and Wilson, 2008). In order to simplify, we consider the vertical velocity of the updraft wu(zgrd) as the vertical velocity of the lava fountain (a variable that is mostly known from observation). The input data mentioned in this section (used for updraft initialisation) and the following sections are listed in Table 3.
Secondly, the updraft fraction area is simply initialised as the ratio of the fissure surface (SFis/SCM) by the model cell surface (SMNH).
au(zgrd)
Fis/SCM SMNH
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Now, as wu(zgrd) and au(zgrd) are both known and are independent of one another, using a similar principle as in Pergaud et al. (2009), the mass-flux at the ground can be calculated such that,
^u(zgrd) - Pmix(zgrd) x au(zgrd)
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where, the density of the updraft (approximated by a mixture of the two main gases _
at PdF; H2O and SO2) pmix(zgrd) = T f7(Zg)c') . P(zgrd) is the pressure at ground level, _
y /u(zgrd)'mix ^
Tu(zgrd) is the temperature of the updraft at ground level and rmix represents the spe-
cific gas constant of the mixture. rmix = R(Mf8- + MpM, where, R is the universal gas i
constant, MH-O is the molar mass of water vapour and MSO- is the molar mass of SO2. In magmas like those erupted in 2010 the gas melange is dominated by water vapour, i.e. about 80% of the melange (Di Muro et al., 2014), the remaining 20% is that of SO2
— 1 HO
(i.e. qu = 0.8 and [SO2] = 0.2 kg kg ). This gives a so- ratio of 4, which is the ratio expected by simple closed system degassing of PdF shallow magmas. This values is at the lower end of the range actually measured by OVPF geochemical network (Allard et al., 2011). Hence, Eq. (5) uses pmix rather than using density of dry/ambient air (in the standard formulation from Pergaud et al., 2009, Eq. 3).
2.2.3 Modified EDMF - Lateral mass exchange
Entrainment of ambient air through turbulent mixing plays a central role in the dynamics of eruption plumes, primarily because the plume density is controlled by the mixing ratio between ejected gas/material and ambient air (Suzuki and Koyaguchi, 2013). Furthermore the amount of air entrained controls the heights of eruption columns (Suzuki and Koyaguchi, 2010). In the current EDMF (Sect. 2.2.1), the mass flux entrainment of the updraft s at the ground level is a constant value of 0.02 m-1 whereas 5 is zero.
In this sub-section we present the modifications to the input method of s and 5 such that for some height above the ground (40 m), a desired mass of ambient air
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may be entrained into the updraft and conversely, a desired mass of the updraft may be expelled. Above this height e and 5 are both calculated as defined by Pergaud et al. (2009) and the coexistence of entrainment/detrainment both continue to feed the vertical evolution of Mu.
The importance of adjusting the ground level e and 5 will become more apparent in Sect. 3 of results. However, due to the importance of this concept of entrainment and its associated effects on a volcanic column, the modifications are presented below. Figure 2 assembles all modifications made to EDMF model along with the input variables (marked in red) used at ground level.
Let Menv represent the mass flux of environmental air that enters the updraft between levels zgrd and zgrd + Az. Hence updraft mass flux at (zgrd + Az) is simply defined as
Mu (zgrd + Az) = Mu (zgrd) + Menv. (6)
If a = M Az) represents a fraction of environmental air in the melange at z = zgrd + Az then by rearranging Eq. (6),
Mu(zgrd)
= 1 - a.
Mu (zgrd +Az)
If e and 5 are constants between zgrd and (zgrd + Az) then by integrating Eq. (1) (Eq. (8) from Pergaud et al., 2009), between zgrd and (zgrd +Az), Eq. (7) can be rewritten
-(e-ô)Az
Mu(zgrd) Mu (zgrd +Az) " '
Finally using Eqs. (7) and (8)
1 - a = e-(£-ô)Az& £- ô = -
ln(1 - a) Az '
For a desired fraction a of ambient air entrained in the volcanic gas column the entrainment and detrainment rates can be such that Eq. (9) is respected.
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2.3 Simulation set-up and configuration
For our chosen case study three sets of simulations were run as depicted in Fig. 3.
1. Section 2.3.2 describes the 3-D spin-up simulation which is used to generate background atmospheric profiles.
2. Section 2.3.3 details the Large Eddy Simulation (LES) considered as the reference.
3. Section 2.3.4 outlines the 1-D single column model (SCM) simulation using the amended EDMF scheme as defined in Sect. 2.2.
Due to the computational efficiency of a 1-D model and the ability to isolate a column of atmosphere for study, SCM is an ideal environment in which to develop and test parameterisations (Randall et al., 1996). Observations relating to the case study are used to evaluate the LES simulations which are further used to validate the SCM results. This methodology has been used by the Global Energy and Water Cycle Experiment Cloud System Study (GCSS) (Browning, 1993) and EDMF scheme used to parameterise shallow convection (Pergaud et al., 2009). As outlined by Pergaud et al. (2009), both Siebesma et al. (2003) and Brown et al. (2002) have shown that LES are robust for representing shallow cumulus convection.
2.3.1 Common features to all simulations
Méso-NH model (version MNH-4-9-3) is used in this study, which is a mesoscale non-hydrostatic atmospheric model enabling it to simulate convective motion and flow over sharp topography. This model has been jointly developed by Laboratoire d'Aérologie (UMR 5560 UPS/CNRS) and Centre National de Recherches Météorologiques - Groupe d'études de l'Atmosphère Météorologique, CNRM-GAME (UMR 3589 CNRS/Météo-France) and is designed to simulate atmospheric circulations from small scale (type - LES) to synoptic scale phenomena (Lafore et al., 1998). All
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Meso-NH related documentations and articles along with various model versions are available at http://mesonh.aero.obs-mip.fr.
Different sets of parameterisations have been introduced for cloud microphysics (Co-hard and Pinty, 2000), turbulence (Bougeault and Lacarrere, 1989) and convection (Bechtold et al., 2001). The shallow convection in Meso-NH is parameterised according to Pergaud et al. (2009) while for the purposes of this study the deep convection option was deactivated. The ISBA (Interactions Soil-Biosphere-Atmosphere scheme) (Noilhan and Mafhaf, 1996) is the scheme used for land surfaces in order to param-eterise exchanges between the atmosphere and the ground providing surface matter and energy fluxes to the atmosphere. The turbulent scheme implemented in Meso-NH is a full 3-D scheme that has been developed by Cuxart et al. (2000) with regards to both LES and mesoscale simulations. Kessler warm microphysical scheme (Kessler, 1969) was activated during the simulation. Meso-NH can be used for idealised as well as real case studies and for the purpose of this article we focus on idealised case studies. For all simulations performed a vertical grid composed of 72 levels in the Gal-Chen and Sommerville (1975) coordinate is used, with a vertical mesh stretched from 40 m at the ground to 600 m at the model top.
2.3.2 3-D spin-up simulation to generate background profiles
A three dimensional (3-D) spin-up simulation is performed to generate the background profiles which are used for SCM and LES. Two, two-way grid-nested domains with horizontal mesh sizes of 4 and 1 km are used (Fig. 3a). Both domains have 100 points in x and y. The initial state for the simulation, as well as the boundary conditions updated every six hours for the outermost model, are provided by analyses from the French Operations forecasting system for Indian Ocean, ALADIN-Reunion (9.6 km resolution; Montroty at al., 2008). The simulation starts 1 January 2010 at 00:00 UTC and ends 2 January 2010 at 18:00 UTC using a time step of 1 and 0.25 s for the 4 and 1 km resolution models respectively.
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Figure 4 shows the vertical profiles of temperature (°C), potential temperature (K) and water vapour mixing ratio (gkg-1) as simulated by the spin-up period for the local area of interest (location of the PdF volcano). The ambient atmosphere is dry with water vapour concentration just under 8 g kg-1 at the ground and decreasing with altitude. The tropopause is found at about 16 km above ground level (a.g.l. hereafter, where the ground level corresponds to about 2.6 kma.s.l. - not shown) which corresponds well to tropical climates and the 0 °C isotherm is located at 2.7 km a.g.l.
The vertical structure of trade winds over Réunion Island was investigated by Lesouef (2010) and Lesouef et al. (2011). The trade wind inversion located at about 4kma.s.l. (Taupin et al., 1999) is described as a consequence of the descending branch of the Hadley cell circulation (Lesouef et al., 2011) where easterly winds prevail in the lower levels while westerly winds prevail in upper levels. It coincides with a temperature inversion, or atleast a layer of enhanced vertical static stability. This is found in Fig. 4 (middle) at about 2 km a.g.l. (4.6 kma.s.l.) as an increased gradient of potential temperature. This stable layer can behave as a barrier for development of clouds (Hastenrath, 1991) and plumes generated through our simulations.
2.3.3 LES simulations
An LES model has such a high resolution that it can resolve not only convective motions but also the largest eddies (responsible for the majority of the turbulent transport). This section describes the initialisation of the LES simulation considered as reference used to validate the EDMF parameterisation for volcano induced convection.
The mass and heat fluxes values are prescribed for 1 LES cell (i.e. SFis/LES = 100 m ; Fig. 3c) with a correction factor (labelled Corr) of 1.2 such that the input fluxes are coherent with that of the SCM model, where SFis/SCM = 120 m2.
LES is initialised such that, for Fv representing the vapour mass flux (kg m s ), Fj = Pmix x ^u x Qu x Corr (10)
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where pmix is the density of the H2O and SO2 mixture in the updraft, where, pmix = S
P (Zgrd) Tu(zgrd)xrm
and wu is the vertical velocity of the updraft. Let Fs represent the sensible
heat flux (Wm 2), then
Tu x Cp, mix x Pmix x ^u x Corr
where Cp mix is the specific heat capacity of the mixture (containing H2O and SO2) such
that, Cp mix = 4rmix and 7u is the temperature of the updraft. Finally, let FSO2 represent
—2 — 1
the SO2 mass flux (kg m s ), then
Fso2 = Pmix x ^u x [SO2] x Corr, (12)
where [SO2] is the mixing ratio of SO2 in the volcanic updraft. SFis/LES the surface
size of the LES grid cell of 100 m and corrected by Corr = 1.2. Table 1 shows the configuration of the LES model.
To be noted that the wind profiles as obtained from the spin-up period have been stabilised i.e. u = 0.1 ms-1 and v = 0ms-1 in LES (and for consistency also in SCM, Sect. 2.3.4). The reason for opting such a strategy is simply because a LES run with the wind fields extracted from the spin-up simulation shows a tilt in the volcanic plume (not shown) above the crater which is clearly not the case as observed in Fig. 1, implying that the wind fields do not appear to be realistic. The average wind speed (10 m above the caldera rim of Bellecombe) provided by Météo France is of 2.3 ± 1.5 ms-1 for the period 2-11 January. Due to the short simulation duration, radiative processes are neglected (i.e. the downward radiative flux is put to zero) and orography of the region is not taken into account, depicting a flat domain for simplifying the model (as also done for SCM model detailed in Sect. 2.3.4).
2.3.4 SCM simulation
Table 2 shows the configuration of SCM model. The volcanic updraft is simulated only in a single central grid cell of size 1 km x 1 km, however the total number of grid cells
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used are 3 x 3 (Fig. 3b). This is simply to allow for the use of open lateral boundary conditions, and hence avoid matter and energy to accumulate in the model. As for the LES (Sect. 2.3.3) the wind profiles obtained from the spin-up period and used as background conditions have been stabilised. The LES simulation is compared to central SCM grid cell of 1 km x 1 km as sketched in Fig. 3.
The adapted EDMF model in Sect. 2.2.2 is used to run this simulation and the variables used to initialise the model are detailed in Table 3 for both SCM and LES, along with their respective formulae (where necessary) and values. As mentioned earlier, since the gas melange in the eruption column consists of 80 % of H2O and 20 % of SO2, the SCM model is simply initialised with qu = 0.8 kg kg-1 and [SO2] = 0.2 kg kg-1 in the updraft at ground level. As for the LES, due to the short simulation duration radiative processes are neglected.
3 Results and analysis
In this section results obtained from the 1-D SCM and 3-D LES of the case study are presented and analysed.
3.1 Need of specific heat source to generate deep plumes
A first most obvious question is whether we need to parameterise volcanic updraft? Figure 5 shows results from 4 simulations; Fig. 5a and b shows simulation results for LES model without and with volcanic heat sources respectively, whereas Fig. 5c and d show results from the 1-D SCM model without and with volcanic heat source respectively. Results for Fig. 5b follow the initialisation of volcanic heat source as outlined in Sect. 2.3.3 above and results from Fig. 5d follow the initialisation of volcanic heat source as outlined in Sect. 2.2.2. All four simulations have been initialised with a passive SO2 tracer as outlined in Table 3 and used as a tracer pollutant injected into the atmosphere. The vertical profiles of SO2 tracer depicted are horizontally averaged over
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the 1 km x 1 km domain for LES simulations (Fig. 5a and c), whereas, for the SCM they are the outputs of the central 1 km x 1 km grid (Fig. 5b and d) as depicted in Fig. 3.
In simulations with no volcanic heat source, SO2 tracer is simply diffused to a few o
hundreds of meters above the ground and majority of the tracer remains at low altitude (Fig. 5a and c). Results from the reference LES simulation (Fig. 5b) shows an uplift of tracer to higher altitudes, with maximum concentration levelled off at around 1.2-1.4 km and a vertical distribution up to 3.75 km above the ground. Similarly, the SCM simulation with modified EDMF (M.EDMF) results (Fig. 5d) also shows tracer lifted to much higher altitudes with majority of the concentration levelled at around 7.25 km. The overall tracer concentrations are vertically distributed between 4 and 11 km above the ground. It is clear that without modifications to EDMF and without initialising LES simulation with volcanic heat sources, the two models are not capable to transport tracer concentrations to higher altitudes.
Although at this stage both Fig. 5b and d show a successful transport of tracer to higher altitudes, it is evident that in terms of maximum detrainment height of the tracer (1.4 and 7.25 km respectively) and its vertical profile, the M.EDMF results are not comparable to that of the LES (the reference simulation); plume generated by M.EDMF is too deep. Hereafter, the height at which there is a maximum detrainment of the tracer will be referred to as the "maximum injection height".
3.2 Influence of entrainment/detrainment at the base of the updraft
It is well known that both entrainment and detrainment have an impact on the updraft development because they affect buoyancy (Woods, 1988; Glaze et al., 1997; Graf et al., 1999; Kaminski et al., 2005; Carazzo et al., 2008) at all updraft levels.
Figure 6 shows the updraft temperature profile for the plume generated in Fig. 5d (left) and the temperature of the plume taken through Infrared (IR) imagery for the PdF eruption of October 2010 (right, as no IR imagery is available for January 2010). The IR imagery shows a temperature of approximately ranging between 55-60°C (labelled Pnt1 on Fig. 6, right and the temperature labelled Z2Mx is the average temperature of
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the box labelled Z2) for the buoyant region of the plume which is comparable to the upper bound of the first model level, at Az = 40ma.g.l. The comparison is very crude and qualitative but at least, it shows that the updraft temperature at the base of our simulated plume of Fig. 5d is not in a correct range of temperatures and consequently the plume is too buoyant and too deep, as not enough fresh ambient air is entrained in the plume base. To correct this discrepancy there is a need to modify the entrainment and detrainment rates at the base of M.EDMF model (as described in Sect. 2.2.3).
The sensitivity of our model to various percentages of ambient air entrained into the updraft at one Az above the ground is shown in Fig. 7.
Here, briefly the labels 1E, 2E and 3E used in Fig. 7 are explained. Using Eq. (9) where, s - 5 = - ln(A-a), for a given value of a (percentage of ambient air entrained into
the volcanic gas column), let s(a) = - ln(A-a). Therefore, we define 1E to correspond to s = s(a) and 5 = 0, 2E to correspond to s = 2s(a) and 5 = s(a), and finally 3E corresponds to s = 3s(a) and 5 = 2s(a).
The M.EDMF model is very sensitive to entrainment and detrainment rates (Fig. 7). Entraining low percentages of ambient air into the updraft aids the plume to reach higher altitudes and conversely higher percentages of entrainment leads to a lower heights. This is due to the dilution of the updrafts which decreases the density of the plume as the ambient atmosphere is much drier (Fig. 4) and cooler with respect to the hotter plume. This also dilutes the water vapour contained within the plume hence affecting the release of latent heat within the plume. From Fig. 7 it is clear that to decrease the injection height of M.EDMF plume (Fig. 5d) such that it is comparable to the LES result (Fig. 5b), an infinite range of possibilities exist for modifications of entrainment/detrainment at the first model level, e.g. modifications related to 1E, 2E and 3E etc.
Figure 8 shows the simulation results for SO2 tracer whereby the a values are tuned in M.EDMF (Sect. 2.2.3) such that the injection height matches the LES results for each of the 1E, 2E and 3E cases.
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Although the injection height for three cases in Fig. 8 are comparable to that of LES, the tracer concentrations are more diluted as the magnitude of entrainment and detrainment is increased (Fig. 8b and c compared to Fig. 8a). The most fitted SO2 concentration with LES (from the three cases explored) is that obtained in Fig. 8a for a = 0.834 and an e/б distribution of type 1E (i.e. no detrainment; б = 0) after 90min of simulation time. The vertical distribution of the tracer is also satisfactory with that obtained from LES, although M.EDMF does overestimate the concentrations at altitudes below 1 km and above 1.6 km. Globally, the results obtained are satisfactory and through this sub-grid parameterisation the SO2 tracer has been injected correctly into higher altitudes.
SO2 concentrations have served to adjust the parameterisation parameters (a, e and б) with the best tuning (a = 0.834, case 1E) which is used from now on.
Figure 9a shows the maximum detrainment observed at about 1-1.4 km a.g.l. which coincides with the maximum detrainment of the tracer at the same level Fig. 8a. The entrainment and detrainment both reach zero at around 6 km a.g.l. indicating the maximum height of the updraft and once again SCM tracer concentrations reach zero at this height (Fig. 8a). Note also that detrainment is weak below 0.75 km.
Figure 9b also shows the anomalies of water vapour mixing ratio (qu) for LES and M.EDMF model, i.e. qu(t90) - qu(t0), where t0 and t90 is simulation time of 0min and 90 min respectively. Although at near ground level the M.EDMF shows lower water vapour concentration at t90 than the LES model (due to the modification in entrainment at ground level), in higher altitudes (> 0.5 km) the two models are in fairly good agreement.
4 Conclusions
In order to represent deep convective injections of volcanic emissions into the low to mid troposphere in case of effusive eruptions, the EDMF parameterisation by Pergaud et al. (2009) has been adapted. The adapted EDMF scheme takes into account the
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intense and localised input of sensible and latent heat near eruptive vent and induces a sub-grid convective plume.
We have shown the need to input specific heat source in order to generate deep plumes using the Méso-NH model by adapting the EDMF scheme. LES simulation were also initialised using water vapour mass flux, sensible heat flux and SO2 mass flux for the same area as for the M.EDMF model. In absence of appropriate terrain observations, the LES simulation (considered as a reference) was used to validate the EDMF parameterisation for volcano induced convection (i.e. M.EDMF model). LES and M.EDMF model have both been successful in generating deep plumes and hence transporting SO2 tracer to higher altitudes. We have further demonstrated the need to modify the existing lateral mass exchanges a few tens of meters above the localised heat source in SCM model as without this modification the plumes generated are too deep because of overestimated temperatures few tens of meters above the ground. The sensitivity of our model to lateral mass exchanges at 40 m above the ground (first model level above the ground) have been presented while further aiding us to tune our model (for SO2 tracer concentrations) such that SCM results are coherent with the results obtained from LES.
Entrainment of ambient air in a volcanic plume is largely known to be one of the key parameters affecting it's buoyancy. Since the first experiments by Morton et al. (1956), extensive research (modelling studies or laboratory experiments) has been deployed to constrain this sensitive parameter (e.g. Wright, 1984; Hunt and Kaye, 2001; Kaminski et al., 2005; Carazzo et al., 2008). Although, great advancements have been made by differentiating between the different regimes; volcanic jets, strong plumes and collapsing columns, it is clear from the comprehensive review found in Tate (2002) and Matulka et al. (2014) that this is still an area of open research. For our case SO2 concentrations have served to adjust the parameterisation parameters (a, e and 5) with the best tuning and furthermore impact of the volcanic plume on the humidity profile by further comparing LES and SCM results, showing a good agreement. The best fit was
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obtained with a large fraction of fresh air incorporated into the plume (a = 83.4%) and no detrainment.
Although this parameterisation has been used in an idealised and controlled set-up for one particular case study (January 2010 summit eruption) further work needs to be undertaken whereby, the parameterisation needs to be tested for different eruptions (i.e. changes in volcanic heat sources, idealised and real case simulations). Furthermore, the tuning of entrainment and detrainment needs to be further investigated such that it too is tested for different eruptions cases and ideally a single tuning factor which may be applied to various eruption cases.
Code availability
Meso-NH model documentation and the model itself is available from the website mesonh.aero.obs-mip.fr. A licence is required to acquire the model version 4-9-3 with the supporting documentation available from the website. The specific routines needed for the purpose of this research paper will then be made available in order to reproduce the results. The licence can be acquired by contacting the Meso-NH team's scientific coordinator, Jean-Pierre Chaboureau (jean-pierre.chaboureau@aero.obs-mip.fr), whereas the specific routines will be supplied by the corresponding author F. Gheusi (francois.gheusi@aero.obs-mip.fr).
Acknowledgements. We greatly acknowledge Observatoire Volcaniques de Piton de la Fournaise - OVPF for providing the pictures of the January 2010 summit eruption along with information relating to the eruption itself. We also thank the Méso-NH assistance team for continuous support and C. Barthe and Meteo-France for kindly providing us with ALADIN-REUNION atmospheric files. This work was performed using HPC resources from GENCI-IDRIS (Grantx2014010005) and CALMIP (Grant P12171). We wish to acknowledge the use of the NCAR Command Language (NCL, Boulder, Colorado) version 6.0.0 software for analysis and graphics in this paper. And finally, we thank the Observatoire des Milieux Naturels et des Changements globaux (OMNCG) and Observatoires des Sciences de l'Univers (OSU), Réunion along with the MoPAV project of the LEFE - CHAT program by INSU - CNRS (Institut
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National des Sciences de l'Univers of Centre National de la Recherche Scientifique) for their financial support and interest in this project.
References
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Table 1. LES model configuration.
Configuration LES
àx, Ay (m) 10
At (s) 0.01
No. of points in x x y 100 x 100
Total run (min) 90
Start time (UTC) 10:50
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Modelling of January 2010 Fournaise summit eruption using Méso-NH
S. G. Sivia et al.
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Table 2. SCM model configuration.
Configuration SCM
àx, Ay (m) 1000
A t (s) 1
No. of points in x x y 3x3
Total run (min) 90
Start time (UTC) 10:50
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Modelling of January 2010 Fournaise summit eruption using Méso-NH
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Table 3. Variables and values used for LES and SCM models.
Variable Notation Model Formula Value Units Data type
Updraft H2O mixing ratio Qu SCM/LES n/a 0.8 kg kg-1 Input
Updraft SO2 mixing ratio [SO2] SCM/LES n/a 0.2 kg kg-1 Input
H2O by SO2 ratio H2O sO2 SCM/LES Qu [SO2] 4 n/a n/a
Updraft vertical velocity ^u SCM/LES n/a 24 m s-1 Input
Updraft temperature at ^u(zgrd) SCM/LES n/a 1320 K Input
ground
Pressure at ground P (Zgrd) SCM/LES n/a 78695 Pa Input
Universal gas constant R SCM/LES n/a 8.314 Jmol-1 K-1 Constant
Molar mass of H2O MH2O SCM/LES n/a 0.018 kg mol-1 Constant
Molar mass of SO2 MSO2 SCM/LES n/a 0.064 kg mol-1 Constant
Specific gas constant of the ^mix SCM/LES R( 0.8 + 0.2 ) * MH O MSO ' 395.49 Jkg-1 K-1 n/a
mixture (H2O and SO2) '"H2O '"SO2
Density of the mixture at Pmix(zgrd) SCM/LES P (Zgrd) 0.15 kg m-3 n/a
Tu (zgrd ) x 'mix
ground m2
Area of the fissure SFis/SCM SCM n/a 120 Input
Area of Meso-NH cell SMNH SCM Ax x Ay 1 x 106 m2 Input
Updraft area ^u SCM SFis/SCM SMNH 1.2 x 10-4 n/a Input
Ratio of ambient air a SCM n/a 0.834 n/a Input
entrained
Area of the fissure SFis/LES LES n/a 100 m2 Input
Correction factor Corr LES SFis/SCM SFis/LES 4^mix 1.2 n/a n/a
Specific gas constant of the C ^ p, mix LES 1581.96 Jkg-1 K-1 n/a
mixture
H2O mass flux Fv LES Pmix x ^u x Qu x Corr 3.456 kg m-2 s-1 Input
Sensible heat flux Fs LES Tu x Cp, mix x Pmix x wu x Corr 9 x 106 Wm-2 Input
SO2 mass flux F3O2 LES Pmix x W x [SO2] x Corr 0.864 kg m-2 s-1 Input
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Modelling of January 2010 Fournaise summit eruption using Meso-NH
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Figure 1. January 2010 summit eruption of Piton de la Fournaise: the 60 m long fissure on the cliff of Dolomieu summit crater emits lava flows towards the bottom of the caldera. The < 30 m high fountains (left) are the source of the ca. 1 km high vertical plume (right) of gas and vapour. Transport and sedimentation of solid particles are mostly confined to the lowest portion (< 100 m) of the plume. Pictures provided by the Piton de la Fournaise Volcanological Observatory (OVPF/IPGP).
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Modelling of January 2010 Fournaise summit eruption using Méso-NH
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Figure 2. Figure displaying the input data the mass flux at ground level (zgrd) and the mass flux at level zgrd + Az after the incorporation of environmental air mass. The input variables of the model are highlighted in red.
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Modelling of January 2010 Fournaise summit eruption using Meso-NH
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Figure 3. The interconnection in terms of the simulation domain between the three sets of simulations performed, namely; Spin-up, SCM and LES. The one cell corresponding to the fissure is tagged for LES.
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Modelling of January 2010 Fournaise summit eruption using Meso-NH
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Temperature (C)
Potential Temperature (K)
Water Vapour concentration fg/kg)
Figure 4. Meteorological profiles from the spin-up model (1 km resolution) at the location of the January 2010 summit eruption on 2 January 2010 at 10:50 UTC. Vertical profiles of temperature (°C), potential temperature (K) and water vapour mixing ratio at the grid scale (g kg-1). Altitude displayed is above ground level (a.g.l.), i.e. 2600ma.s.l.
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Modelling of January 2010 Fournaise summit eruption using Meso-NH
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(a) LES without Volcanic heat source
(b) LES with volcanic heat source
0.0e-1 2.09-1 4.09-1 6.09-1 8.09-1
S02 concentration (g/kg) (c) Pergaud et al.,(2009) EDMF
2.0e-1 4.0e-1 6.0e-1 S02 concentration (g/kg)
-1-1-1-r
0.09-1 0.49-1 0.89-1 1.29-1 1.69-1 2.09-1 2.4o-1
S02 concentration (g/kg) (d) Modified EDMF (M.EDMF)
0.0e-1 0.4e-1 0.8e-1 1.2e-1 1.6e-1 2.0e-1 2.4e-1 S02 concentration (g/kg)
Figure 5. Horizontally averaged SO2 tracer concentrations (gkg 1) over 100 x 100 points for (a) i
and (b); SO2 concentrations (gkg-1) in the central grid cell of the SCM simulations for (c) and (d). All simulations were inputted with the same SO2 concentration at the first model level. Red - 30 min, blue - 60 min, green - 90 min after model initialisation.
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Modelling of January 2010 Fournaise summit eruption using Meso-NH
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Figure 6. Updraft temperature (°C) of Fig. 5d at 90 min (left). Temperature (°C) of October 2010 eruption of PdF through infrared imagery provided by OVPF. The point at 55-59 °C indicated in the figure is at about 20 m above the crater rim.
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Modelling of January 2010 Fournaise summit eruption using Meso-NH
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Figure 7. Sensitivity of maximum injection height of tracer to various percentages of ambient air entrained into the buoyant plume in the first model level (Az = 40ma.g.l.). Red dashed line shows the maximum injection height obtained from Fig. 5d and dashed black line shows the maximum injection height as obtained from Fig. 5b. Legends "IE, 2E and 3E" refer to experiments performed whereby the entrainment and detrainment rates are modified in the first model level (see Sects. 2.2.3 and 3.2 for details).
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Modelling of January 2010 Fournaise summit eruption using Meso-NH
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(a) Alpha = 0.834 at 1E
(b) Alpha = 0.59 at 2E
(c) Alpha = 0.448 at 3E
0.0e-1 0 4©-1 0.88-1 1.28-1 1.68-1 2.08-1 2.48-1 S02 tracer concentrations (g/kg)
0.08-1 0.48-1 0.88-1 1.28-1 1.68-1 2.08-1 2.48-1 S02 tracer concentrations (g/kg)
Figure 8. SO2 tracer concentrations (gkg-1) and maximum injection height (kma.g.l.) for certain values of a used and s/S distribution (1E, 2E, 3E) in the first model level (Az = 40 m) at 90 min. LES (solid lines) and M.EDMF (dashed lines).
0.08-1 0.48-1 0.88-1 1.28-1 1.68-1 2.08-1 2.48-1 S02 tracer concentrations (g/kg)
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Modelling of January 2010 Fournaise summit eruption using Meso-NH
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-|—I—I—I—I-1—r
-9.0e-6 -6.0e-6 -3.0e-6 0.0e-6 3.0e-6 6.0e-6
(a) Updraft Entr (+) and Detr (-) rates (1/s)
-2.0 -1.0 0.0 1.0 2.0 (b) Water vapour mixing ratio anomaly (g/kg)
Figure 9. (a) Updraft entrainment (positive values) and detrainment (negative values) rates displayed from the M.EDMF model at 90 min of simulation time (simulation run using a = 0.834
at 1E). (b) Water vapour mixing ratio (qu) anomaly (gkg 1) i.e. qu (t90) - qu (t0), where t0 and t90 is simulation time at 0 and 90 min respectively. LES (solid line) and M.EDMF (dashed lines).
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Modelling of January 2010 Fournaise summit eruption using Meso-NH
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