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# A multi-decadal view of the heat and mass budget of a volcano in unrest: La
Soufrière de Guadeloupe (French West Indies)

David E. Jessop  Séverine Moune  Roberto Moretti  Dominique Gibert  Jean-
Christophe Komorowski  Vincent Robert  Michael J. Heap  Alexis Bosson  Magali
Bonifacie  Sébastien Deroussi  Céline Dessert  Marina Rosas-Carbajal  Arnaud
Lemarchand  Arnaud Burtin

(Received: date / Accepted: date)

###### Abstract

Particularly in the presence of a hydrothermal system, many volcanoes output
large quantities of heat through the transport of water from deep within the
edifice to the surface. Thus, heat flux is a prime tool for evaluating
volcanic activity and unrest. We review the volcanic unrest at La Soufrière de
Guadeloupe (French West Indies) using an airborne thermal camera survey, and
in-situ measurements of temperature and flow rate through temperature probes,
Pitot-tube and MultiGAS measurements. We deduce mass and heat fluxes for the
fumarolic, ground and thermal spring outputs and follow these over a period
spanning 2000–2020. Our results are compared with published data and we
performed a retrospective analysis of the temporal variations in heat flux
over this period using the literature data.

We find that the heat emitted by the volcano is $36.5\pm
7.9\text{\,}\mathrm{MW}\text{/}$, of which the fumarolic heat flux is dominant
at $28.3\pm 6.8\text{\,}\mathrm{MW}\text{/}$. Given a total heated area of
$26\,780$ ${\mathrm{m}}^{2}\text{/}$, this equates to a heat flux density of
$627\pm 94.\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$, which is amongst the
highest established for worldwide volcanoes with hydrothermal systems,
particularly for dome volcanoes. A major change at La Soufrière de Guadeloupe,
however, is the development of a widespread region of ground heating at the
summit where heat output has increased from $0.2\pm
0.1\text{\,}\mathrm{MW}\text{/}$ in 2010 to $5.7\pm
0.9\text{\,}\mathrm{MW}\text{/}$ in 2020. This change is concurrent with
accelerating unrest at the volcano, and the emergence of two new high-flux
fumaroles in recent years. Our findings highlight the importance of continued
and enhanced surveillance and research strategies at La Soufrière de
Guadeloupe, the results of which can be used to better understand hydrothermal
volcanism the world over.

Orcid IDs:
David E. Jessop: 0000-0003-2382-219X
Séverine Moune: 0000-0002-8485-0154
Roberto Moretti: 0000-0003-2031-5192
Jean-Christophe Komorowski: 0000-0002-6874-786X
Vincent Robert: 0000-0002-9016-7167
Michael J. Heap: 0000-0002-4748-735X
Magali Bonifacie:0000-0002-4797-043X
Marina Rosas-Carbajal: 0000-0002-5393-0389

## Introduction

Hydrothermal systems in active island-arc andesitic volcanoes are produced by
the interaction of hot magmatic fluids, essentially gaseous water, CO2, H2S
and/or SO2 and HCl, produced by magma degassing at depth with marine or
meteoric water at shallower depths and the host-rock (Sigurdsson et al., 2015;
Hedenquist and Lowenstern, 1994). Cooling through interaction with water
(dissolution and/or absorption into deep ground waters and mixing with
meteoric and sea-water) and the host-rock causes chemical species to be
reduced (Giggenbach, 1975; Moretti and Stefansson, 2020). Hence, the
geochemical profile of fluids discharged at the surface of a hydrothermal
system is typically different to that at depth. Hydrothermal systems can
undergo sudden and catastrophic changes in behaviour. Two events in recent
years, in particular, have highlighted the importance of understanding all
aspects of hydrothermal volcanoes and their hazardous behaviour: the September
2014 Ontake (Japan) and December 2019 Whakaari (White Island, New Zealand)
eruptions, both of which resulted in the tragic loss of human life.

The boiling of geothermal liquids liberates a fraction of the dissolved gases,
which fractionate into the vapour phase that ascends to the surface through
steam-dominated fumaroles. Partial condensation of these vapours into ground
waters may generate steam-heated waters likely to disperse laterally where
they can further mix with external waters and discharge as thermal springs
(Hedenquist and Lowenstern, 1994; Sigurdsson et al., 2015). Therefore,
significant amounts of heat are emitted as the super-heated steam, generated
by these interactions, rises towards the surface through networks of cracks,
fissures and more porous rock within the edifice. The super-heated steam
either condenses near the surface or escapes to the atmosphere through
fumaroles (Chiodini et al., 2001; Fischer and Chiodini, 2015; Stimac et al.,
2015). Heat emission can occur in several forms. First, where resistance to
flow is low (high permeability subsurface) the steam may reach the surface
without condensing and, second, where resistance to flow is high (low
permeability subsurface) the steam may condense near the surface. In the first
scenario, the fumarolic output is high and significant amounts of heat and
mass are transferred to the environment. In the second scenario, fumarolic
output is correspondingly lower and heat is brought to the surface by forced
convection and liberated to the environment by radiation and conduction
(Harris, 2013; Gaudin et al., 2016). This leads to thermal anomalies (ground
heating) and small, low-flux fumaroles typically distributed over quite large
areas (cf. Aubert et al., 1984; Aubert, 1999; Harris and Stevenson, 1997;
Harris and Maciejewski, 2000, for example). In many cases, ground heating far
exceeds the fumarolic output in terms of energy transfer (Matsushima et al.,
2003; Mannini et al., 2019). Due to the high heat capacity of water, direct
fumarolic degassing and diffuse small fumarole/soil degassing are generally
the two major components of heat loss at hydrothermal volcanic systems
(Aubert, 1999; Chiodini et al., 2001). The final component of heat transfer in
hydrothermal volcanic systems is through a network of thermal springs which
typically appear along the flanks or base of the system, taking advantage of
structural discontinuities. These springs discharge water, initially heated by
volcanic gases, that has either condensed deep within the edifice or nearer
the surface when it has come into contact with the water table (Fischer and
Chiodini, 2015; Stimac et al., 2015).

Whilst the relative importance of the different heat loss mechanisms will vary
from volcano to volcano and may vary in time at a given site, volcanic heat
flow in general is indicative of (e.g. Hardee, 1982; Lardy and Tabbagh, 1999;
Harris et al., 2009): 1\. The state and position of the magma body; 2\. The
porosity/permeability of the edifice or dome; 3\. The extent of infiltration
of external water into the system. As such, spatio-temporal variations in heat
flow are of particular importance for both monitoring and fundamental research
and allow us to greatly constrain numerical models of the magmatic and
plumbing systems (Di Renzo et al., 2016).

Hydrothermal systems play a fundamental role in providing and enhancing the
physico-chemical conditions that promote rock alteration, as well as the
pressurisation of hydrothermal fluids. These processes act as strong forcing
and triggering agents on the dynamics of volcanic activity by mechanically
weakening edifice-forming volcanic rock (Pola et al., 2012; Wyering et al.,
2014; Heap et al., 2015; Mordensky et al., 2019) and, therefore, promoting
recurrent partial flank collapses (López and Williams, 1993; de Vries et al.,
2000; Reid et al., 2001; Reid, 2004; John et al., 2008), as observed at La
Soufrière de Guadeloupe (Komorowski et al., 2005; Rosas-Carbajal et al.,
2016). Escalating pressurisation of hydrothermal systems, as a result of
permeability loss due to hydrothermal alteration, can also lead to explosive
activity (Heap et al., 2019) that can reach paroxysmal levels with non-
magmatic laterally-directed turbulent pyroclastic density currents or blasts
(e.g. Bandaisan, Japan, in 1889). Hydrothermal alteration has also been
observed to reduce the thermal conductivity and thermal diffusivity of
andesite for a given porosity (Heap et al., 2020). Finally, the hydrothermal
system is a strong modulator of geophysical and geochemical signals of
magmatic unrest and can generate a plethora of non-magmatic unrest signals
that render monitoring, as well as their interpretation and forecasting, very
challenging (Pouget et al., 2015).

In this paper which spans the past 20 years with particular emphasis on the
2010–2020 period, we concentrate on the use of thermal measurements to infer
the state of unrest of a major hydrothermal volcanic system, that of La
Soufrière de Guadeloupe (Lesser Antilles). We present the first study for this
volcano that fully integrates measurements of all the heat sources over such a
long period of time. La Soufrière de Guadeloupe is a good target for such a
study due to the wealth of geochemical, geological and geophysical data
acquired on the volcano. As such, it is often considered a natural laboratory
representative of andesitic hydrothermal systems.

## Context

La Soufrière de Guadeloupe
($16.0446\text{\,}\mathrm{\SIUnitSymbolDegree}\text{/}$ N,
-$61.6642\text{\,}\mathrm{\SIUnitSymbolDegree}\text{/}$ E, alt.
$1467\text{\,}\mathrm{m}\text{/}$, hereby referred to as La Soufrière) is an
andesitic dome volcano situated in the south of the Basse-Terre island of
Guadeloupe (French West Indies), which is part of the Lesser Antilles volcanic
arc and is the most recent edifice of the Grande Découverte complex (445 ka).
La Soufrière is amongst the most active and potentially deadly of the
volcanoes in the Lesser Antilles Arc (Komorowski et al., 2005). Hydrothermal
activity is sustained by gas and heat transfer from a 6–7 km deep andesitic
magma reservoir to shallower aquifers (Pichavant et al., 2018). Owing to an
extensive hydrothermal system, La Soufrière has undergone a series of six
phreatic and hydrothermal explosive eruptions since the last major magmatic
eruption in 1530 C.E. (Komorowski et al., 2005). The most recent, and probably
most famous, eruption was in 1976–77 (Feuillard et al., 1983; Hincks et al.,
2014).

The present edifice dates back at least 9150 years (Komorowski et al., 2005;
Legendre, 2012), during which time several major magmatic eruptions have
occurred, the latter in around 1530 C.E., when the current dome was emplaced
(Komorowski et al., 2005; Boudon et al., 2008). Since this last magmatic
event, there have been a number of phreatic and/or hydrothermal explosive
eruptions. The last eruption occurred in 1976–77, following which the volcano
became essentially dormant until 1992 when seismic activity and steam
emissions from summit fumaroles recommenced (OVSG-IPGP
1999-2001111http://www.ipgp.fr/fr/ovsg/bulletins-mensuels-de-lovsg; Zlotnicki
et al., 1992; Komorowski et al., 2001, 2005). Summit degassing has gradually
increased concomitantly with other observables (seismic, gas flux and
concentration, ground and fumarole temperatures, deformation, emissions of
chlorine-rich acid gases), over the past $\sim 30$ years. This has included
the appearance of two new high-flux fumaroles (Napoléon Nord and Napoléon Est,
labelled NAPN and NPE on Fig. 1; OVSG-IPGP 2014-2016; Komorowski et al., 2005;
Villemant et al., 2014; Moretti et al., 2020a), extensive zones of substantial
surface heating and scalding of vegetation. Several fumarolic sites on the
flanks characterised by a low state of activity since 1976, gradually
vanished. At the summit, Tarissan (TAS), Cratère Sud (CS), la Fente du Nord,
Gouffre 56 (G56) and the Lacroix fumaroles had all become inactive by 1984
(Komorowski et al., 2005; Boichu et al., 2011; Feuillard, 2011; Ruzié et al.,
2013).

An increase in activity in 2018 raised speculation that the volcano is in a
state of growing unrest and is likely to undergo another eruptive episode in
the near future (Moretti et al., 2020a). Until 2014, ground thermal anomalies
and accompanying soil degassing had likely been limited to the areas directly
surrounding the major fumaroles, as well as the Faille de la Ty/Ravine
Claire/Matylis structure (Fig. 1; OVSG-IPGP 2014-2020; Komorowski et al.,
2005; Lesparre et al., 2012; Brothelande et al., 2014). In recent years,
however, a number of thermal anomalies and altered zones have been observed
such as at the Zone Fumerolienne Napoléon Nord (ZFNN) at the summit, delimited
by NAPN, Cratère Dupuy (DUP) and TAS, adjoining the Breislack fault (BLK) and
in the upper Matylis ravine (Fig. 1, OVSG-IPGP 2014-2020 and this work).
Increasing fluxes and acidification of the water and gas rising up within the
volcano has led to significant alteration and weakening of the edifice,
leaving it vulnerable to flank collapse during even moderate seismic activity
or extreme rainfall (Komorowski et al., 2005; Rosas-Carbajal et al., 2016).

The summit vents are located near major fractures and fault zones, i.e. zones
of high vertical permeability (see Fig. 1 and Zlotnicki et al., 1992;
Komorowski et al., 2005). These are likely to have acted as a magma ascent
route for the dome (Brombach et al., 2000). The deepest part of these
fractures act as a zone of preferential input of magmatic gases into the
hydrothermal aquifer, and its shallowest part behaves as a zone of
preferential discharge for the hydrothermal aquifer (Brombach et al., 2000).
The horse-shoe shaped scar of recurrent partial edifice collapses over at
least the last 3000 years, including the major Amic Crater (1370 BCE) and the
1530 CE events, forms a listric clay-rich low-permeability south-sloping
surface. This allows preferential outflow of heated ground waters through a
number of thermal springs (Brombach et al., 2000; Villemant et al., 2005;
Ruzié et al., 2013; Villemant et al., 2014). Here, fluids are heated within
the hydrothermal system and then partially cooled by mixing with meteoric
water before escaping to the environment.

## Materials and methods

Aerial thermal surveys were carried out in 2010 and 2019, MultiGAS and Pitot-
tube measurements have been carried out monthly since 2017 and the thermal
springs have been sampled monthly since 2000. Our measurements are effectively
contemporaneous even though sampling times differ between different methods
and sites. We calculated errors on our estimations using standard error
propagation formulae (Ku, 1966; Gibbings, 1986). Examples of how to apply
these formulae and a table of relative standard errors for all the parameters
used in this study can be found in the Supplementary Material.

### Ground thermal anomaly flux

We used airborne thermal imagery to measure the extent and distribution of
thermal anomalies over the entire volcano using an InfraTec VarioCam HD
thermal camera (8–$14\text{\,}\mathrm{\SIUnitSymbolMicro m}\text{/}$) with
$640\times 480$ pixel resolution. A 15 mm focal length lens ($56.1\times
43.6$$\mathrm{\SIUnitSymbolDegree}\text{/}$ FOV), gave an instantaneous field
of view (IFOV) of $1.65\text{\,}\mathrm{mrad}\text{/}$. The distinguishable
temperature difference between neighbouring pixels, $\mathrm{NE}\Delta T$, was
$0.5\text{\,}\mathrm{K}\text{/}$. We used an Isotech Calisto calibration oven
with black-body source to calculate the drift of the camera’s temperature
measurements and applied this to our thermal images.

The airborne thermal survey was conducted on 22 November 2019 with helicopter
support provided by the local Civil Protection Service and in pre-dawn
conditions (05:40–06:05 local time, sunrise was at 06:14 local time). Ground
heating due to incoming solar radiation was hence minimised. GPS locations
were recorded at $1\text{\,}\mathrm{Hz}\text{/}$ using a Garmin 64st . Images
were acquired through the open door of the helicopter from heights of about
50–300 m . The sky was cloudless with only a very light wind from the North
(cf. the predominant trade winds, les Alizées, blow from the East). Little
rain had fallen in the week prior to the survey, so the ground surface was
dry.

We georeferenced and orthorectified our thermal images using a DEM calculated
from Institut Geographique National (IGN) aerial photography, processed using
MicMac (Rupnik et al., 2017) and IGN orthophotos (Fig. 2). Georeferencing of
the thermal images was performed in QGIS using a thin-plate spline transform
when the images were taken obliquely, or a Helmert transform for vertically-
oriented images. Pixel to physical distance conversions were computed as per
Bombrun et al. (2018).

A schematic of the various fluxes seen by the camera is shown in Fig. 3. The
effective brightness temperature is a function of the incoming fluxes which
are functions of the temperature of the objects in the field of view through
the Stefan-Boltzmann law . The brightness temperature is also affected by
reflection of incoming radiation (e.g. $L_{\mathrm{sol}}$ and
$L_{\mathrm{atm}}$ in Fig. 3). Thus the true temperature of the ground can be
expressed as

$T=\left(\dfrac{T_{\mathrm{cam}}^{4}-T_{\mathrm{atm}}^{4}-(1-\tau)T_{g}^{4}}{\epsilon\tau}\right)^{1/4},$
(1)

where $T_{\mathrm{cam}}$ is the brightness temperature seen by the camera,
$T_{\mathrm{atm}}$ is the brightness temperature of the upper atmosphere,
$T_{g}$ is the temperature of gases between the object and camera, $\tau$ is
the transmissivity of an atmospheric and volcanogenic gas mixture between
camera and the ground and $\epsilon$ is the emissivity of the ground (Fig. 3).

We converted at-camera (brightness) temperature to absolute temperature by
applying Eq. 1. Fumarole plumes and areas outside the region of interest were
masked. We calculated $\tau$ using a radiative transfer model, with the
surface-camera distance given by the georeferenced images and GPS location of
the camera (Kochanov et al., 2016; Berk and Hawes, 2017). We took the surface
emissivity to be constant for all the heated areas with $\epsilon=0.95$ in
line with that found for other studies on andesitic systems (Sekioka and
Yuhara, 1974; Gaudin et al., 2016).

We note that not all of the steam condenses before reaching the surface.
Condensed liquids drain away to be discharged elsewhere in the system (i.e.
through thermal springs, in which case the heat transported is accounted for
in the thermal springs heat budget) and any residual heat transferred to the
ground, where it is accounted for in the soil heat budget. Hence we do not
consider heat transported by condensed water here (cf. Gaudin et al., 2015).
Our heat balance is thus (Sekioka and Yuhara, 1974; Matsushima et al., 2003;
Harris, 2013; Mannini et al., 2019)

$\displaystyle Q_{\mathrm{soil}}$
$\displaystyle=Q_{\mathrm{soil,rad}}+Q_{\mathrm{soil,conv}}$ (2)
$\displaystyle Q_{\mathrm{soil,rad}}$
$\displaystyle=A_{\mathrm{heated}}\epsilon_{\mathrm{soil}}\sigma\left(T^{4}-T^{4}_{\mathrm{amb}}\right)$
(3) $\displaystyle Q_{\mathrm{soil,conv}}$
$\displaystyle=A_{\mathrm{heated}}h_{c}\left(T-T_{\mathrm{amb}}\right)$ (4)

where $Q_{\mathrm{soil}}$ is the soil heat flux and subscripts $\mathrm{rad}$
and $\mathrm{conv}$ refer to radiative and conductive components of
$Q_{\mathrm{soil}}$, respectively, $T$ is the ground temperature,
$T_{\mathrm{atm}}$ is the ambient temperature and $A_{\mathrm{heated}}$ is the
heated area, $\epsilon_{\mathrm{soil}}$ is the soil emissivity. The heat
transfer coefficient, $h_{c}$, depends on several factors, particularly the
local wind speed, $w$. We use the Schlichting-Neri model (Neri, 1998; Gaudin
et al., 2013)

$h_{c}=1500w(z)\left(1.89+1.62\log(z/z_{0})\right)^{-2.5},$ (5)

where $z$ is the height above the surface and $z_{0}$ is a measure of the
surface roughness. Eq. 5 has been shown to produce results that are consistent
with the surface heat balance at La Soufrière (Gaudin et al., 2013), such that
the heat conducted to the surface equals $Q_{\mathrm{soil}}$. We note that the
surfaces on the volcano where heat transfer occurs consist typically of
centimetric blocks and thus we take $z_{0}=$ $0.01\text{\,}\mathrm{m}\text{/}$
as our roughness scale. We determined $w$ from measurements at the Sanner
weather station (cf. Piton Sanner in Fig. 1) at the time of thermal image
acquisition. The anemometer at Sanner is approximately
$2\text{\,}\mathrm{m}\text{/}$ above ground level, so we take $z=$
$2\text{\,}\mathrm{m}\text{/}$ in our calculations. For wind speeds between
5–$10\text{\,}\mathrm{m}\text{/}\mathrm{s}$, as seen on the 22 November, we
find $h_{c}$ between 21.1 and
$42.3\text{\,}\mathrm{W}\text{/}\text{(}{\mathrm{m}}^{2}\text{\,}\mathrm{K}\text{)}$.
Considering error propagation, we estimate a relative standard error of about
10% on the radiative and convective flux measurements, and thus about 15% for
the total flux.

### Fumarole heat and mass fluxes

#### In-plume fumarole steam flux via MultiGAS traverses

The OVSG222Observatoire Volcanologique et Simologique de la Guadeloupe
MultiGAS consists of an IR spectrometer for CO2 determination and electro-
chemical sensors for SO2, H2S and H2. The atmospheric pressure is determined
with the sensor installed on the CO2 spectrometer card. The MultiGAS also
includes an externally-fitted relative humidity (RH) sensor (Galltec, range:
0–100% RH, accuracy: $\pm 2$%) and temperature sensor (range:
-30–70$\mathrm{\SIUnitSymbolCelsius}\text{/}$, resolution:
$0.01\text{\,}\mathrm{\SIUnitSymbolCelsius}\text{/}$), to determine water
vapour concentration (Moussallam et al., 2017). H2O determination with these
external sensors reduced the risk of underestimating the measured water/gas
ratios due to steam condensation in the inlet. An onboard GPS receiver tracked
the location of the instrument at $1\text{\,}\mathrm{Hz}\text{/}$. Data were
visualised on an external tablet in real time. More detailed information about
the OVSG MultiGAS, its design and performance characteristics can be found in
Tamburello et al. (2019) and Moretti et al. (2020a, b).

Fumarolic gas fluxes were determined for the three main vents that generate
plumes (CS, TAS and G56, Figure 1) following Allard et al. (2014) and
Tamburello et al. (2019). The horizontal and vertical distributions of gas
species in the plume cross-sections were measured a few meters downwind from
the vents during orthogonal traverses on foot. Gas concentrations were
measured at two different heights (typically 0.9 and
$2\text{\,}\mathrm{m}\text{/}$) as the volcanic gas plumes are generally
flattened to the ground by strong trade winds
(2–$14\text{\,}\mathrm{m}\text{/}\mathrm{s}$) and have a maximum height of ca.
3–$4\text{\,}\mathrm{m}\text{/}$ above the ground at each measuring site with
a maximum gas density centred at between $\sim 1.5$ and
$2\text{\,}\mathrm{m}\text{/}$ above the ground (our visual observations;
Gaudin et al., 2016; Tamburello et al., 2019). For each site, we interpolated
the concentration measurements using a 2D spline function and then integrated
over the plume cross section to obtain integrated concentration amounts (ICAs)
using RatioCalc (Tamburello, 2015). The CO2 fluxes are derived by multiplying
the CO2 concentration integrated over the plume cross section with the wind
speed measured during the gas survey with a hand-held anemometer. We use CO2
as the volcanic marker as, due to its more conservative behaviour compared to
H2S and due to the faster response of the IR CO2 sensor compared to the
electro-chemical H2S sensor, this way the MultiGAS is able to detect rapid
concentration changes during plume transects. This avoids flux
underestimations and leads to more accurate gas flux measurements (Tamburello
et al., 2019). Due to the high atmospheric background for H2O and CO2, our
walking profiles start and end in pure atmospheric background in order to
characterise and then subtract the ambient air composition from our recorded
data. Steam fluxes, $\dot{m}$, are derived from the CO2 flux by multiplying it
by the weight ratio of H2O/CO2. Steam flux estimates were possible only when
water was successfully determined via the external RH sensor. It is important
to note that some temporal variability of steam fluxes could be due to: i)
different ambient humidity and weather condition at the summit between field
measurements; ii) occasional partial steam condensation on the external
sensors. Indeed, particularly for tropical volcanoes such as La Soufrière,
water vapour in the plume rapidly condenses upon contact with the atmosphere.
However, this condensed water is not taken into account by the MultiGAS
measurements. It has been shown that, in such tropical conditions, properly
accounting for the condensed water adds approximately 35% to the steam flux
estimations (Gaudin et al., 2016), an increase which we consider in our
analysis. Lastly, wind speed is the main source of error in quantifying
volcanic gas fluxes, leading to typical standard errors on steam flux
estimation of about 40%.

#### At-vent fumarole fluxes via Pitot-tube measurements

Measurements of the steam exit speed at the vent of several fumaroles were
made using a Pitot-tube instrument based around Freescale MPX2200AP and
MPX2010DP temperature compensated pressure sensors that measured the dynamic
pressure in the moving stream and ambient (stagnation) pressure. Pressure
readings were taken at $3.75\text{\,}\mathrm{Hz}\text{/}$ and the median of 10
measurements was recorded by an Arduino Due. Uncertainty in the pressure
readings was $3.1\text{\,}\mathrm{Pa}\text{/}$, meaning that the minimum
detectable speed was about $5\text{\,}\mathrm{m}\text{/}\mathrm{s}$. From
these values, the speed of a moving stream of gas, $u$, of density $\rho$ was
calculated as (Massey and Ward-Smith, 1998)

$u=\sqrt{\dfrac{2\Delta p}{\rho}}$ (6)

where $\Delta p=p_{0}-p$ is the dynamic pressure, $p_{0}$ is the stagnation
pressure and $p$ is the free-stream pressure. Vent temperatures were
simultaneously measured using a PT1000 resistance temperature sensor with an
instrumental error of $\pm$$1\text{\,}\mathrm{K}\text{/}$. These measurements,
along with the pressure readings, were used to calculate the steam density,
$\rho(p,T)$, using numerical codes based on IAPWS thermodynamic calculations
(Wagner and Pruß, 1993, 2002). Measurements were taken repeatedly at different
points across the vent in order to build up an idea of the velocity
distribution. Typically 7 measurements were taken and the median velocity from
these measurements was used in the calculations that follow.

From vent speed, we deduce the mass flux from the fumaroles which, as water
vapour contributes up to 98% of the total mass (Allard et al., 2014;
Tamburello et al., 2019; Moretti et al., 2020a, OVSG-IPGP bulletins
2017-2020;), is equivalent to the steam flux,

$\dot{m}=\rho\bar{u}A\approx\rho_{\mathrm{steam}}(T)\bar{u}A$ (7)

where $\bar{u}$ is the mean vent speed (equivalent in this case to median vent
speed), $A$ is the area of the vent. Whereas in Moretti et al. (2020a), vent
area was estimated by eye by the Pitot-tube operator, here we calculate $A$ by
analysing thermal images. We repeatedly took thermal images looking straight
into the vents throughout the period when Pitot-tube measurements were made,
from which we manually traced around the vent perimeter and, using the on-
camera laser distance measurements, then converted to physical area (i.e. in
${\mathrm{m}}^{2}\text{/}$) via a pixel-to-physical length conversion as per
Bombrun et al. (2018). We estimated the relative standard error on mass flux
measurements to be 10%.

### Heat flux estimations

The heat released through fumarolic activity is essentially due to cooling and
condensation of the volcanic steam. Fumarole heat flux can generally be
decomposed into two contributing factors: radiation by the heated vent
surface, $Q_{\mathrm{rad}}$, and the specific and latent heat carried by the
gas phase, $Q_{\mathrm{gas}}$, so that
$Q_{\mathrm{fumarole}}=Q_{\mathrm{rad}}+Q_{\mathrm{gas}}$ (Harris, 2013;
Gaudin et al., 2016). Heat lost to the surroundings through the walls of the
fumarole pipes is not considered as part of this heat budget, but are
accounted for through the geothermal heating of the surrounding ground
(Stevenson, 1993; Mannini et al., 2019), as shown in the previous section.
Following Harris (2013); Allard et al. (2014); Gaudin et al. (2016) we write
these as

$\displaystyle Q_{\mathrm{rad}}$
$\displaystyle=A\epsilon\sigma\left(T^{4}-T^{4}_{\mathrm{amb}}\right)$ (8)
$\displaystyle Q_{\mathrm{gas}}$
$\displaystyle=\dot{m}\left(c_{p,v}(T)\left(T-T_{\mathrm{boil}}\right)+L(T)+c_{p,l}\left(T_{\mathrm{boil}}-T_{\mathrm{amb}}\right)\right)$
(9)

where $\epsilon$ is the ground emissivity, $\sigma$ is the Stefan-Boltzmann
constant, $c_{p}$ is the specific heat capacity , $L\approx$
$2260\text{\,}\mathrm{kJ}\text{/}\text{(}\mathrm{kg}\text{\,}\mathrm{K}\text{)}$
the latent heat of condensation, $T$ is the temperature of the steam,
$T_{\mathrm{boil}}$ $\approx$
$96.7\text{\,}\mathrm{\SIUnitSymbolCelsius}\text{/}$ is the boiling
temperature of water at the dome altitude and $T_{\mathrm{amb}}\approx$
$17\text{\,}\mathrm{\SIUnitSymbolCelsius}\text{/}$ is the ambient temperature
at the summit. The subscripts $v$ and $l$ refer to the vapour and liquid
states of water, respectively, with $c_{p,v}\approx$
$2.015\text{\,}\mathrm{kJ}\text{/}\text{(}\mathrm{kg}\text{\,}\mathrm{K}\text{)}$
and $c_{p,l}\approx$
$4.200\text{\,}\mathrm{kJ}\text{/}\text{(}\mathrm{kg}\text{\,}\mathrm{K}\text{)}$
for summit temperatures and pressures. During the survey period, $T$ ranged
from 96.9 and $108.6\text{\,}\mathrm{\SIUnitSymbolCelsius}\text{/}$ for CS and
has been measured in the water lake at TAS to be approximately
$97.5\text{\,}\mathrm{\SIUnitSymbolCelsius}\text{/}$ (OVSG-IPGP 2016-2020).
Since the G56 vent is in a c. $30\text{\,}\mathrm{m}\text{/}$ deep cavity
within the volcano, requiring specialised equipment to access, it is
impractical to measure it directly. Thus we estimate that the temperature at
the G56 vent is at the boiling temperature of water. We note that $c_{p}$ and
$L$ are functions of $p$ and $T$ and were solved for using similar numerical
routines as for density. $T_{\mathrm{boil}}$ is a function of pressure only
and is also deduced from the IAPWS formulations (Wagner and Pruß, 1993, 2002).

Given the instrumental and measurement errors summarised in the text above,
and using error propagation techniques (see Gibbings, 1986, for example), we
estimated the standard errors on the flux estimation using the Pitot-tube and
MultiGAS instruments. In the case of the Pitot-tube instrument, the standard
error in estimating $Q_{\mathrm{fumarole}}$ is dominated by the mass flux and
radiative flux terms and, overall, is around 10%. The standard error for our
estimates based on MultiGAS measurements is dominated by the uncertainty in
the mass flux measurements alone and so is about 40%.

### Thermal Springs

The nine thermal springs situated around the base of the current dome have
been monitored regularly by the OVSG since 1978 by manually measuring
temperature and flow rate. The majority of sites have been visited on a 1–3
month basis to take manual temperature readings as well as physico-chemical
parameters such as pH and conductivity, and to take samples for future
chemical analysis (Villemant et al., 2005, 2014). During these outings, and
when it was possible, volumetric flow rate, $\dot{V}$, was deduced from the
time taken to fill a container of known volume. This process was repeated 6–10
times and we report here the mean value of these measurements. From this, we
calculate the mass flow rate, $\dot{m}_{\mathrm{spring}}=\rho\dot{V}$, which
then allows us to calculate the heat flux as the sum of specific, evaporative
and radiative heats,

$Q_{\mathrm{spring}}=Q_{\mathrm{spec}}+Q_{\mathrm{evap}}+Q_{\mathrm{rad}}\approx
Q_{\mathrm{spec}}=\dot{m}c_{p,l}(T)(T-T_{\mathrm{amb}}).$ (10)

We drop evapotransport, $Q_{\mathrm{evap}}$, and radiative heat losses,
$Q_{\mathrm{rad}}$, in Eq. (10) as these contribute negligibly to the heat
budget. The relative standard error on these measurements is about 5%.

## Results

### Ground heat flux

We show our results from the analysis of the thermal images (Fig. 2) in Table
1. For each site with detected thermal activity (summit, lower Ravine Matylis,
Ravine Claire and FTY), we have determined radiative and convective fluxes as
well as the flux density, $q_{i}=Q_{i}/A$. As large fluxes can be observed by
low intensity emissions over a large area, we also calculate the total heat
flux density, $q=(Q_{\mathrm{rad}}+Q_{\mathrm{conv}})/A_{heated}$, as a metric
for comparing intensity between sites (Table 1) with a relative standard error
of about 6%. At the summit we found the radiative flux to be
$0.74\text{\,}\mathrm{MW}\text{/}$ and the convective flux to be
$4.94\text{\,}\mathrm{MW}\text{/}$, with $h_{c}=$ $41.6\pm
2.3\text{\,}\mathrm{W}\text{/}\text{(}{\mathrm{m}}^{2}\text{\,}\mathrm{K}\text{)}$
(Eq. 5) and $A_{\mathrm{heated}}=$ $14\,070$ ${\mathrm{m}}^{2}\text{/}$ (areas
were calculated by counting the number of heated pixels, e.g. Fig. 2). These
values were by far the largest in magnitude of all the sites, and larger than
the total heat fluxes for the other sites combined. This finding is supported
by the heat flux density, which is considerably greater than any other site.

We calculated $h_{c}=$ $37.8\pm
2.3\text{\,}\mathrm{W}\text{/}\text{(}{\mathrm{m}}^{2}\text{\,}\mathrm{K}\text{)}$
for wind speeds during acquisition of the images of the flank sites, which was
used in the calculations for all sites. Owing to a relatively large emitting
surface of $8010$ ${\mathrm{m}}^{2}\text{/}$, the heat flux at Ravine Claire
(RC) is second to the summit with radiative and convective fluxes of
$0.13\text{\,}\mathrm{MW}\text{/}$ and $0.75\text{\,}\mathrm{MW}\text{/}$
(Table 1), respectively. In the lower Matylis ravine, a strong thermal anomaly
leads to high flux densities (42 and
$238\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$ for radiation and convection,
respectively), although a low heated area
($1630\text{\,}{\mathrm{m}}^{2}\text{/}$) keeps the overall fluxes low. We
identified two sites along FTY (FTY0 and FTY1 in Figs. 1 and 2) which have
similar results for flux density and had a total flux of
$0.58\text{\,}\mathrm{MW}\text{/}$ and a mean flux density of $227$
$\mathrm{W}\text{/}{\mathrm{m}}^{2}$. We note that all these sites (Matylis,
RC, FTY) are linked to the Ty N-SE and Galion N-S faults that cut the dome
(Komorowski et al., 2005; Rosas-Carbajal et al., 2016).

### Fumarole heat and mass flux

The mass and heat fluxes are shown in Fig. 4 a) and b), respectively. Steam
fluxes estimated from MultiGAS traverses show that, using CO2 as a marker, the
min/mean/max values are: 0.35/0.52/0.86, 0.15/0.30/0.47 and
0.29/0.44/$0.67\text{\,}\mathrm{kg}\text{/}\mathrm{s}$ for CS, G56 and TAS,
respectively. Heat flux estimates based on these data give 0.93/1.36/2.28,
0.40/0.79/1.25 and 0.78/1.12/$1.79\text{\,}\mathrm{MW}\text{/}$ for CS, G56
and TAS, respectively. Considering the relative standard error of 40%, we find
that the MultiGAS fluxes have remained stable since regular estimates began in
mid 2018, subsequent to the M4.1 earthquake.

The temporal variations in fumarole steam flux calculated by the Pitot-tube
for the three vents at CS are also shown in Fig. 4a. These data indicate that
the fluxes can show a large degree of variation in short time periods which is
especially true during periods of accelerated unrest such as from March–May
2018 (Moretti et al., 2020a). We find steam fluxes to have min/mean/max values
of 0.01/0.12/$0.31\text{\,}\mathrm{kg}\text{/}\mathrm{s}$ at CSC,
0.22/0.70/$1.50\text{\,}\mathrm{kg}\text{/}\mathrm{s}$ at CSN and
0.82/2.71/$3.85\text{\,}\mathrm{kg}\text{/}\mathrm{s}$ at CSS (Fig. 4a), which
equate to heat fluxes of 0.03/0.29/$0.75\text{\,}\mathrm{MW}\text{/}$ for CSC
vent, 0.53/1.69/$3.64\text{\,}\mathrm{MW}\text{/}$ for CSN vent, and
1.99/6.56/$9.31\text{\,}\mathrm{MW}\text{/}$ for CSS vent (Fig. 4b). Fluxes
were also measured at NAPN and we found mean mass and heat fluxes of
$0.03\text{\,}\mathrm{kg}\text{/}\mathrm{s}$ and
$0.07\text{\,}\mathrm{MW}\text{/}$ with very little variation over time,
including during the 2018 unrest. The contribution of NAPN to the total heat
and mass budget is thus negligible. We note that, due to an improved method
for estimating vent area based on head-on thermal images compared to visual
estimation during measurements (see Methods), the vent heat fluxes presented
here are quantitatively lower than reported in Moretti et al. (2020a),
although the qualitative temporal variation is the same. The Pitot-tube data
show that vent fluxes at CS were strongly affected by and decreased during the
2018 unrest phase, but have since settled to around
$4\text{\,}\mathrm{kg}\text{/}\mathrm{s}$ and $10\text{\,}\mathrm{MW}\text{/}$
for mass and heat flux, respectively. Fig. 4b) shows, although the
coefficients for heat capacity and latent heat vary with temperature, the same
trends as per Fig. 4a), indicating that the heat flux depended much more
strongly on the variations in mass flux than temperature changes during this
period.

At CS, we have overlap in the Pitot-tube and MultiGAS instrument data that
allows us to compare the data collected by these instruments from closely
spaced outings. For example, in terms of steam flux the Pitot-tube data from
15 June 2020 show that CSC+CSN+CSS emitted around $4.6\pm
0.5\text{\,}\mathrm{kg}\text{/}\mathrm{s}$. The flux estimated from MultiGAS
measurements at CS on 22 May 2020 were $0.7\pm
0.3\text{\,}\mathrm{kg}\text{/}\mathrm{s}$. These MultiGAS estimates are
almost an order of magnitude times lower than those from the Pitot-tube, and
Fig. 4 indicates that this is systematically the case. Whilst we have
attempted to correct for the quantity of condensed vapour that is undetectable
by the MultiGAS, additional errors in this calculation are likely to be
primarily responsible for the difference between these two values, although
they agree to within an order of magnitude and appear to show qualitatively
the same temporal variations.

### Thermal springs heat and mass fluxes

In Fig. 5, we present the mass flow rate and temperature measured over the
period between 2000 and 2020 (a subset of the entire data set, see Villemant
et al., 2005, Fig. 5a and b), as well as the heat flux calculated from this
via Eq. (10) (Fig. 5c). Whilst the flow rate and temperature measurements have
continued until the present day, there are gaps in the mass and heat flux data
during 2014–2016 due to instrument failures. The GA, Tarade spring (TA), Bains
Jaunes (BJ) and Pas du Roy (PR) springs are amongst the most accessible and
this is reflected in both the abundance and persistence of the measurements in
the OVSG database. They are also the most representative of acid-sulphate
thermal springs linked to La Soufrière’s hydrothermal activity. This record
does not reflect the absolute total mass/thermal output of the thermal springs
as i) other sites are known but are far less accessible or impractical to
measure and ii) some sites may not yet have been discovered. However,
particularly as GA and TA have the largest known flow rates, it is likely that
these calculations are nonetheless representative of the total budget for the
thermal springs. We fitted linear trends to the data for TA, GA and PR, and
extrapolated where necessary to project the values to the current date.

Overall, we see that both mass flow rate and water temperature have slowly and
steadily increased over time in an approximately linear fashion. For example,
the flow rate at TA increased from around
$1.1\text{\,}\mathrm{kg}\text{/}\mathrm{s}$ in 2010 to
$2.1\text{\,}\mathrm{kg}\text{/}\mathrm{s}$ at present whilst its temperature
rose from 309 to $318\text{\,}\mathrm{K}\text{/}$ . Only the TA and PR sites
have data that cover the whole data range and manual measurements stopped at
GA in 2014. Historically, GA dominates the heat budget for the thermal
springs, and has almost double the output of TA. Summing over these three
sites, we find that the total heat flux from the thermal springs is around
$0.57\text{\,}\mathrm{MW}\text{/}$ (including the extrapolated trend for GA).

## Discussion

### Comparison of steam and heat flux estimation methods

#### Fumarole flux

Our measurements (Fig. 6) show that the plume mass and heat fluxes have not
undergone extensive evolution since August 2005. With this in mind, we must
consider that the fumarole plume heat and mass flux estimates of Gaudin et al.
(2016) to be excessively high. In their discussion, the order of magnitude
discrepancy with the estimations from MultiGAS traverses (Allard et al., 2014)
was mostly attributed to the MultiGAS studies not accounting for condensed
water vapour. However, we note several key assumptions in Gaudin et al. (2016)
that may have led to systematic errors in their estimations:

  * •

Plume thickness grows linearly with distance from the vent , $x$, and not
$x^{2/3}$. This latter scaling is for the height of the plume axis from the
ground (Slawson and Csanady, 1967), so that their mass flux integral
overestimated the plume area.

  * •

The plume section was assumed to be axisymmetric though this is generally not
true: wind-blown plumes from smoke stacks, cooling towers and in laboratory
experiments have been shown to be more broad (horizontally) than thick
(vertically, Contini and Robins, 2001). Thus, transmissivity calculated
looking horizontally through a plume would have been lower than was actually
the case, leading to an overestimation of plume temperature. Consequently the
plume density and thus the mass flow rate should be lower than the given
estimations.

  * •

The vapour carrying capacity of the plume was assumed to be equal to that of
the atmosphere. However, as plume temperatures are higher than atmospheric and
more water vapour can therefore be carried without condensing, this
relationship does not hold.

Overall, this suggests that a more realistic plume flux for 2010 would be more
in line with the MultiGAS (taking into account condensed vapour) and Pitot-
tube measurements, that is a steam flux of
$5.3\text{\,}\mathrm{kg}\text{/}\mathrm{s}$ for CS. Thus taking the Pitot-tube
measurement at CS as the ground truth, we found a scaling factor for the
MultiGAS measurements. Using this to scale the MultiGAS flux for TAS gives
$6.2\text{\,}\mathrm{kg}\text{/}\mathrm{s}$. Likewise, we find heat fluxes of
$13.0\text{\,}\mathrm{M}\mathrm{W}$ for CS and
$15.2\text{\,}\mathrm{MW}\text{/}$ for TAS (see Table 2) for the 2010 study.

Moreover, despite some assumptions, our results show that MultiGAS traverses
and Pitot-tube measurements provide qualitatively coherent vent flux
estimations yet quantifying the steam flux using MultiGAS is a challenge,
particularly in a tropical atmosphere with 100% RH. To overcome this
shortcoming, we take the H2O/CO2 ratio determined from Giggenbach bottle
sampling (OVSG-IPGP 2017-2020; Moretti et al., 2020b) and multiply this by the
CO2 flux estimated from the MultiGAS data. As this ratio is measured at the
vent, it is not subject to a loss of matter due to condensation contrary to
measurements within the plume. The resulting fluxes at CS resemble much more
closely the Pitot-tube-derived fluxes (see “Reworked CS MG data” in Fig. 4).
This correlation starkly indicates the difficulties in accounting for
condensed volcanogenic vapour in the MultiGAS steam-flux estimations.
Nevertheless, in a monitoring context, either or both methods could be applied
in various volcanoes worldwide to estimate their mass and heat fluxes.

#### Ground flux

Although we have used the same model for $h_{c}$ as Gaudin et al. (2016), we
obtain slightly different values simply due to differing weather conditions
(compare $h_{c}=$ $41.6\pm 2.3$ and $37.8\pm
2.3\text{\,}\mathrm{W}\text{/}\text{(}{\mathrm{m}}^{2}\text{\,}\mathrm{K}\text{)}$
for the summit and flanks, respectively, with $h_{c}=$ $30.5\pm
0.3\text{\,}\mathrm{W}\text{/}\text{(}{\mathrm{m}}^{2}\text{\,}\mathrm{K}\text{)}$
as derived from data in Table 2 of Gaudin et al., 2013). Thus, similarity
between the results of our study and those of Gaudin et al. (2013) at the same
site would be suggestive of a decrease in temperature at that site. A good
comparison can be made at the FTY sites. We note in particular that the mean
total heat flux density for FTY0 + FTY1 sites combined, $228\pm
14.\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$, is in strong agreement with
the heat flux density calculated from temperature gradient measurements of
$265\pm 45.\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$ (Gaudin et al., 2013),
which suggests that, on average, temperatures have not decreased (the ambient
temperature during the 2010 survey and ours was approximately
$17\text{\,}\mathrm{\SIUnitSymbolCelsius}\text{/}$ in both cases). It is
somewhat unclear precisely where Gaudin et al. (2016) defined the boundary of
FTY and, indeed, their Fig. 1 suggests that this might extend into what we
define as Ravine Claire, so judging the evolution of the extent of this site
is difficult. However, taking uncertainties into account, the present-day
total flux for FTY0+FTY1+RC of $1.46\pm 0.23\text{\,}\mathrm{MW}\text{/}$ is
not too dissimilar to the $1.0\pm 0.2\text{\,}\mathrm{MW}\text{/}$ reported in
2010.

Given the angular resolution of the thermal camera and camera-to-ground
distances of 50–$300\text{\,}\mathrm{m}\text{/}$, this equates to a pixel
length of between 0.08 and $0.5\text{\,}\mathrm{m}\text{/}$. As fumaroles are
often of smaller dimension than the resolution length-scale, especially when
recording from greater distances, their temperature is integrated over the
pixel area along with the cooler surroundings and so pixels that cover
thermally non-homogeneous ground will display temperatures lower than the true
temperature of the hotter object. Harris et al. (2009) demonstrated that, at a
distance of 100 m, the pixel-integrated temperature of a $6\times 13$ cm
($78\text{\,}{\mathrm{cm}}^{2}\text{/}$) fumarole in a
$169\text{\,}{\mathrm{cm}}^{2}\text{/}$ pixel was lower than the actual
temperature by $40\text{\,}\mathrm{\SIUnitSymbolCelsius}\text{/}$. Taking this
into account, we must consider that the fluxes that we calculate are minimum
estimates, emphasising the importance of the ground heat flux for La
Soufrière.

### Total heat budget

As noted by Gaudin et al. (2016), some heat loss may be undetectable by the
methods described in this work, due to either vegetation cover (e.g. on the
flanks) or temperature changes that are below the instrument resolution (cf.
summit in the region of CS). As per their work, we note that the “background”
heat conducted through the system, as deduced from borehole measurements and
extrapolated to the scale of the dome adds only an additional
$0.013\text{\,}\mathrm{MW}\text{/}$. Furthermore, we note that some heat will
be transported by gases other than steam, notably CO2 in the plume and, in
particular, CO2 soil degassing which is a widely-used proxy for heat flux (cf.
Chiodini et al., 1998; Bloomberg et al., 2014; Harvey et al., 2015). A
detailed study is beyond the scope of this present work but we may make
progress under the following assumptions:

  1. 1.

Passive CO2 degassing occurs in the same areas and to the same extent as the
ground thermal anomalies.

  2. 2.

The ground heat flux, $Q_{\mathrm{soil}}$, calculated above equals the
underground convection of steam, $\dot{m}_{H2O}c_{p,H2O}(T-T_{\mathrm{amb}})$.

  3. 3.

The CO2/H2O ratio in areas of soil degassing is the same as in the fumaroles
(Chiodini et al., 2001).

Under assumption (2), $\dot{m}_{H2O}=$
$135.5\text{\,}\mathrm{kg}\text{/}\mathrm{s}$ based on a typical anomaly
temperature of $80\text{\,}\mathrm{\SIUnitSymbolCelsius}\text{/}$ and ambient
temperature of $15\text{\,}\mathrm{\SIUnitSymbolCelsius}\text{/}$. Based on a
H2O/CO2 ratio of 43.5 (OVSG-IPGP, 2020), this gives $\dot{m}_{CO2}=$
$3.2\text{\,}\mathrm{kg}\text{/}\mathrm{s}$ and thus
$Q_{\mathrm{CO2}}=\dot{m}_{\mathrm{CO2}}\,c_{\mathrm{p,CO2}}(T-T_{\mathrm{amb}})=$
$0.19\text{\,}\mathrm{MW}\text{/}$.

Clearly, although comparable to the contributions of certain thermal springs,
heat transport by CO2 does not add significantly to the total budget.
Nevertheless, due to the accelerating spread of the altered zones and the fact
that the area over which CO2 degassing occurs may be far greater than that
involved in degassing of water vapour (cf. Chiodini et al., 2005), the OVSG
has begun to carry out joint surveys of soil temperature profiling and CO2
flux (via the accumulation chamber technique, Chiodini et al., 1998) in order
to further constrain ground heat losses and we will return to this issue in a
forthcoming paper.

Summing the fumarole ($28.3\pm 6.8\text{\,}\mathrm{MW}\text{/}$, 77.5%),
ground ($7.6\pm 1.1\text{\,}\mathrm{MW}\text{/}$, 20.8%) and the thermal
springs fluxes ($0.56\text{\,}\mathrm{MW}\text{/}$ 1.5%), we obtain a total
heat output of $36.5\pm 7.9\text{\,}\mathrm{MW}\text{/}$ (see Table 2).

### Temporal evolution

La Soufrière has undergone a significant evolution of its activity during
2010–2020 as described and analysed in detail by Moretti et al. (2020a) and
OVSG-IPGP (2014-2020). This can be summarised as follows:

  1. 1.

The appearance of new fumarolic vents and the reactivation of pre-existing
fumaroles with local high-velocity degassing.

  2. 2.

Vegetation die-off near-to and far-from active vents (see Supplementary
Material Fig. 1).

  3. 3.

The enlargement of a major extensive area of heated ground on the summit areas
that progresses towards the North from the Fracture Napoléon (see below and
Supplementary Material Fig. 2).

  4. 4.

More frequent and stronger seismic events including felt events (M4.1, April
2018).

  5. 5.

An acceleration in the opening rate of several summit fractures.

  6. 6.

The appearance of new mineralised water springs at the base of the volcano as
a result of the rapid cooling of hydrothermal fluids.

Undoubtedly the greatest phenomenological change at the summit of La Soufrière
is indeed the appearance and spread of the ground thermal anomaly in the ZFNN
region. For example, the heated area at the summit has gone from an estimated
$610\text{\,}{\mathrm{m}}^{2}\text{/}$ in 2010 (Gaudin et al., 2016) to
$14\,070\text{\,}{\mathrm{m}}^{2}\text{/}$ for the present study. Indeed,
whereas Gaudin et al. (2016) identified thermal anomalies along the Napoléon
fracture and in the craters containing the CS fumaroles, they calculated that
the associated heat losses were $0.01\text{\,}\mathrm{MW}\text{/}$ by
radiation and $0.2\text{\,}\mathrm{MW}\text{/}$ by forced convection. The
present-day radiative and convective fluxes of $0.74\pm 0.07$ and $4.94\pm
0.49\text{\,}\mathrm{MW}\text{/}$ have increased by an order of magnitude
between 2010 and 2020, which is in large part due to this increase in heated
area and also, to a lesser degree, because of increased temperatures. The
total heat flux density presently estimated at $403\pm
26.\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$ is greater than the 2010
estimate of $326.3\pm 68.5\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$, and
thus suggests an increase in thermal intensity at the summit, though these
values are within the bounds of measurement uncertainty.

Apart from the pulse of unrest around March–April 2018, the fumarolic fluxes
have not changed considerably since early 2018 (Fig. 4), and the thermal
spring fluxes have increased only slightly (Fig. 5) over the past 20 years. To
gain a greater perspective of the overall temporal evolution of plume fluxes
over a similar period, we plot in Fig. 6 our data along with the steam and
heat fluxes taken from Allard et al. (2014), Gaudin et al. (2016) and
Tamburello et al. (2019). This figure shows that our current data are, given
the natural variability of these fluxes, consistent with the previous MultiGAS
measurements of Allard et al. (2014) and Tamburello et al. (2019). They are
far more consistent with the Pitot-tube measurement for the CSN + CSC vents
cited in Gaudin et al. (2016) than the fluxes that they derived from analysis
of thermal images (compare their value of $5.3\pm
1.6\text{\,}\mathrm{kg}\text{/}\mathrm{s}$ to the contemporary sum for CSN +
CSC of around $1.4\pm 0.3\text{\,}\mathrm{kg}\text{/}\mathrm{s}$, Fig. 4a).

Three major swarms of VT earthquakes occurred from 1 February to 28 April
2018, with the third swarm initiated by the off-volcanic axis M4.1 earthquake
which struck at 00:32 UTC on 28 April and was widely felt throughout
Guadeloupe. In particular, as reported in Moretti et al. (2020a), a short-
lived increase in plume flux occurred concurrently with temperature increases
before the earthquakes, but both observables had returned to background levels
before the M4.1 event on 27 April 2018. Hence, our Pitot-tube flux results
illustrate the importance of these flux estimations for close monitoring of
volcanic activity.

Our results combined with published data indicate that plume flux has
decreased overall since these records began. Thus, given a lack of increased
VT seismicity or other signs of sudden evolution in 2010, and in the light of
the errors discussed above, it seems that the values reported in Gaudin et al.
(2016) are anomalous. In order to provide a better comparison with the present
study, we attempt to re-estimate the 2010 plume fluxes given the available
data from this period (Allard et al., 2014; Gaudin et al., 2016). We suppose
that, despite possible overestimation, the ratio of CS/TAS fluxes was
correctly established in 2010 and that the relative standard error will remain
unchanged. Thus scaling with the 2005 Pitot-tube data, for 2010 we find steam
fluxes of $5.3\pm 1.1\text{\,}\mathrm{kg}\text{/}\mathrm{s}$ for CS and
$6.2\pm 2.2\text{\,}\mathrm{kg}\text{/}\mathrm{s}$ for TAS, and heat fluxes of
$13.0\pm 2.6\text{\,}\mathrm{MW}\text{/}$ for CS and $15.2\pm
5.4\text{\,}\mathrm{MW}\text{/}$ for TAS (Table 2).

We recalculate the thermal spring fluxes for 2010 based on an interpolation of
the thermal springs time series the date of the aerial survey (see Fig. 5).
These new values for the thermal springs fluxes are, in general, not
appreciably different to the present values, except for TA which we find to be
about half the reported value for 2010. Additionally, this process does allow
us to calculate fluxes for PR, absent in the 2010 survey. Consequently, we
find that the total heat flux in 2010 was likely to have been around
$30\text{\,}\mathrm{MW}\text{/}$ of which the fumarolic contribution was
approximately $28\text{\,}\mathrm{MW}\text{/}$, or 95% of this total (see
Table 2). This compares to the estimate of 98% by Gaudin et al. (2016).

The starkest change in the past decade is an increase in ground heat flux by
greater than an order of magnitude (see Table 2), reflecting the appearance of
the strong and widespread thermal anomaly in the ZFNN area in particular.
Indeed, the ground heat flux has increased from $1.2\pm
0.3\text{\,}\mathrm{MW}\text{/}$ of a total budget of $29.8\pm
8.3\text{\,}\mathrm{MW}\text{/}$ (4%) to $7.6\pm
1.1\text{\,}\mathrm{MW}\text{/}$ of $36.5\pm 7.9\text{\,}\mathrm{MW}\text{/}$
(21%). Nevertheless, in terms of heat flux density across the entire edifice,
the present-day mean value of $403\pm
24.\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$ is slightly higher than the
$337.1\pm 196.6\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$ estimated in 2010.
Using the reworked values from Gaudin et al. (2016), fumarole heat flux has
decreased at CS and TAS, decreasing from a total of $28.2\pm
8.0\text{\,}\mathrm{MW}\text{/}$ to $17.8\pm 4.5\text{\,}\mathrm{MW}\text{/}$
(see Table 2 and Fig. 6). However, if we also include G56, our reanalysis
shows that the overall change in output is insignificant and, along with the
appearance of NAPN and NPE fumaroles (which contribute negligibly to the total
budget), highlights a spreading of fumarole output over the dome. Heat
transport at the thermal spring sites has increased from 0.4 to
$0.6\text{\,}\mathrm{MW}\text{/}$. Taken together, these findings are
suggestive of the edifice becoming more fractured and porous over time,
allowing some of the hydrothermal fluids to escape via different pathways. The
increase in porosity and fracturing may be a result of rock dissolution and
weakening (e.g. Pola et al., 2012; Wyering et al., 2014; Heap et al., 2015;
Mordensky et al., 2019) as a result of hydrothermal alteration, mainly by
acid-sulphate fluids (Salaün et al., 2011). An increase in porosity and
fractures is coherent with the increased opening rate of fractures as well as
the GNSS radial horizontal displacements of 3–10 mm/year (Moretti et al.,
2020a) and is corroborated by the appearance of mineralised deposits at the
base of the dome in the upper northern branch of the Matylis river and in the
Breislack area (Fig. 1b).

Given recent unrest events, these results are coherent with recent
petrological analysis of the volcano’s last major magmatic eruption which
place a shallow magma reservoir at 5–$8\text{\,}\mathrm{km}\text{/}$ depth
(Pichavant et al., 2018). Furthermore, the interpretation of the geochemistry
of emitted fluids (Villemant et al., 2014; Moretti et al., 2020a, b) infers a
contribution of deep magmatic gases that trigger periodic transitory heating
and pressurisation of the deep hydrothermal system near the critical point of
water at 2–$3\text{\,}\mathrm{km}\text{/}$ below the summit. Despite a lack of
further evidence for the ascent of magma to very shallow depths, it is
important to keep in mind from a hazard perspective, that larger, more
frequent, or more intense transitory pulses of hot magmatic gases could exceed
the buffering capacity of the hydrothermal system bringing the overall system
to critical conditions compatible with phreatic/hydrothermal eruptive unrest.
Consequently we must expect that the extent and magnitude of thermal anomalies
and diffuse degassing on La Soufrière will continue to increase over time and,
indeed, this is evident in aerial images (cf. Figs. A.1 and A.3, supplementary
material).

### Comparison with other hydrothermal systems

La Soufrière’s total heat budget is on par with other major hydrothermal
system volcanoes. For example, the heat output at Vulcano (Italy) was
estimated at 10–$12\text{\,}\mathrm{MW}\text{/}$ from combining ground based
radiometer and ASTER measurements (Mannini et al., 2019). At Whakaari, heat
output estimated using crater floor soil CO2 degassing as a proxy was found to
be $20.0\pm 2.5\text{\,}\mathrm{MW}\text{/}$ (Bloomberg et al., 2014). Our
value is somewhat smaller than Nisyros (Greece), Ischia or Campi Flegrei (both
Italy) which release in the range of 40–$100\text{\,}\mathrm{MW}\text{/}$
(Chiodini et al., 2005). However, as noted by Harvey et al. (2015), whilst
total heat budget is helpful for following the temporal evolution of an
individual volcano, a more useful metric for comparing between systems is the
heat flux density as, in many of these cases, the major component of heat flux
is through diffuse soil heating so larger systems naturally tend to emit more
heat. The mean ground heat flux density (combining radiative and convective
fluxes) for the entire La Soufrière complex is $406\pm
24.\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$ (Table 1) which, if we
consider the total heat budget over the total heated area of
$26\,280\text{\,}{\mathrm{m}}^{2}\text{/}$, the mean flux density of the
currently active part of the La Soufrière complex climbs to $1366\pm
82.\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$ (Tables 1 and 2). Based on the
data compiled in Harvey et al. (2015) from heat flux density calculated from
CO2 flux, this ranks La Soufrière amongst the world’s most powerful heat
producing volcanoes, well above Whakaari (205 W/m2), Vulcano
($140\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$, Mannini et al., 2019),
Campi Flegrei ($118\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$) and Nisyros
($19\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$), and roughly on par with
Ischia ($764\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$). Similar to La
Soufrière, Vulcano, Whakaari and Ischia are also dome volcanoes and the larger
heat flux densities here may indicate optimal steam transport to the surface
along high-permeable pathways associated with dome emplacement: Ischia, in
particular, has a fumarolic H2O/CO2 ratio similar to that at la Soufrière,
(H2O/CO2=147 in 2001, Chiodini et al., 2005). This, due to the very extensive
hydrothermal system at La Soufrière, indicates the dominance of heat and mass
transport by water vapour generated through the interaction of hot magmatic
fluids and the water table. Taken together, especially with respect to the
recent evolution at the summit, these findings indicate the importance of
ground heating and thermal anomalies as a precursor for unrest of volcanic
sites such as La Soufrière which may be far more relevant than at caldera-type
sites (e.g. Campi Flegrei or Nisyros) where CO2 degassing is far more
pervasive and heat loss through the ground is dominant.

## Conclusions

La Soufrière is an andesitic stratovolcano in the lesser Antilles arc with an
extensive hydrothermal system that has undergone six phreatic/hydrothermal
eruptions since 1635 C.E. Here, we have concentrated on using thermal
measurements to highlight the changes to the system over the past two decades
which cover most of the current unrest since its onset in 1992. Direct
measurements were made of the temperature and mass flux at the key fumarolic
emission sites and at numerous thermal springs linked to the hydrothermal
activity of La Soufrière. The ground temperature at sites showing extensive
thermal anomalies was determined from airborne thermal imagery. From these and
ancillary measurements for ambient conditions, we have deduced heat and mass
fluxes as well as heat flux densities. We have compared and discussed our
measurements in light of historic data available in the literature. Based on a
reinterpretation of previously published data, we deduce that fumarolic output
has proportionally decreased from 95% of the total heat budget in 2010 to 78%
currently, whereas ground heating has increased from 4% in 2010 to 21%
currently. The present-day convective and radiative heat fluxes in the summit
area of 4.94 and $0.74\text{\,}\mathrm{MW}\text{/}$, respectively, have
increased by an order of magnitude in the past decade which is largely due to
an increase in heated area and also, to a lesser degree, because of increased
temperatures. The total heat flux density presently estimated at $403\pm
24.\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$ is greater than the 2010
estimate of $326\pm 69.\text{\,}\mathrm{W}\text{/}{\mathrm{m}}^{2}$, and thus
suggests an increase in thermal intensity at the summit, though these values
are within the bounds of measurement uncertainty. These changes are explained
partly by a spreading in fumarolic sites over the dome during the past decade
but also, and more importantly, that ground thermal anomalies on the summit
have propagated significantly in recent years. Fractures on the dome along
with steady horizontal radial displacements of 3–10 mm/year have been observed
over the same period. The thermal spring activity has changed little in 20
years although several of the thermal springs closest to the dome (GA, TA, BJ,
PR) have shown since 2000 a steady linear increase of their temperature and
heat flux rate.

We find that, in terms of heat flux density (heat loss per unit area), La
Soufrière is amongst the most intense emitters of heat for volcanoes
worldwide, and that its ranking has dramatically increased in recent years.
With recent unrest events in mind, plus petrological evidence and geochemical
analysis of magmatic fluids, we must consider that conditions with the
potential to lead to phreatic/hydrothermal events currently exist at La
Soufrière. Hence, La Soufrière remains the subject of continued and enhanced
surveillance and research strategies to better understand the origin of unrest
and track its dynamic evolution.

## Acknowledgements

The authors thank: the Assistant Editor, M. R. James and two anonymous authors
for their constructive comments and suggestions; the OVSG-IPGP team for
logistical support and help with data collection, Pierre Agrinier, and
especially Gilbert Hammouya and Olivier Crispi for data collection before
2013; Pascal Allemand and IGN for DEMs and orthophotos; the Préfecture de
Guadeloupe and the pilots of the Dragon 971 helicopter base in Guadeloupe
(Sécurité Civile, Ministère de l’Intérieur) for providing helicopter support;
the Parc National de Guadeloupe for assistance and authorisation of research
and monitoring on La Soufrière; IPGP, INSU-CNRS through the Service National
d’Observation en Volcanologie (SNOV), and the Ministère pour la Transition
Écologique et Solidaire (MTES) for financial support. This work has been
supported by the ANR DOMOSCAN, ANR DIAPHANE, the AO-IPGP 2018 project “Depth
to surface propagation of fluid-related anomalies at La Soufrière de
Guadeloupe volcano (FWI): timing and implications for volcanic unrest”
(coord.: R. Moretti), and the European Union’s through EUROVOLC (project No
731070). This study contributes to the IdEx Université de Paris
ANR-18-IDEX-0001, is IPGP contribution number 4164 and is LabEx ClerVolc
contribution number 426. MJH acknowledges funding via the INSU-CNRS project
“Assessing the role of hydrothermal alteration on volcanic hazards”.

## Author Contributions

DEJ collected and analysed the field data, prepared the figures and wrote the
manuscript. SM, RM, DG, JCK and VR also collected and analysed field data. All
authors contributed in the writing and discussion of the manuscript, and
consented to its submission.

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Figure 1: a) Topography of La Soufrière region showing the sites (thermal
springs and fumaroles) reported here. b) zoom of the summit area. Site codes
are: Cratère Sud Centre (CSC), Cratère Sud Nord (CSN), Cratère Sud Sud (CSS),
Gouffre 56 (G56), Tarissan (TAS), Napoléon Est (NPE), Napoléon Nord (NAPN);
Carbet-Echelle (CE), Galion (GA), Tarade (TA), Pas du Roy (PR), Bains Jaunes
(BJ) and Ravine Marchand (RM3). The base DEM, hill shading and contours were
calculated from an aerial LiDAR survey at 5 m resolution. Road, footpath and
waterway information were obtained via the French Government’s open data
platform ( https://www.data.gouv.fr/, accessed 2020-04-16). Geological
information is as presented in Lesparre et al. (2012); Brothelande et al.
(2014); Moretti et al. (2020a) and references therein.

Figure 2: a) Georeferenced thermal images of La Soufrière and surroundings
taken from the helicopter on 22 November 2019 between 05:40 and 06:05 local
time b) zoom showing the summit thermal anomalies. The base map is the 2017
IGN aerial orthophoto (BDOrtho). The thermal images are shown in greyscale
where white and black denote hot and cold, respectively. Figure 3: Conceptual
model of the heat flux measured by a thermal camera, $L_{b}$ viewing and
displayed as the “brightness” temperature, $T_{b}$. The incoming heat fluxes
(left) from solar radiation, $L_{\text{sol}}$, and from the atmosphere,
$L_{\text{atm}}$, are reflected from the surface in proportion to the surface
albedo, $\alpha$, and $1-\epsilon$, respectively, where $\epsilon$ is the
emissivity of the surface. For a long-wave infrared sensor such as the thermal
camera used here, $\alpha\approx 1-\epsilon$. The emitted radiation of the
surface, $L$ (which depends on surface temperature, $T$, though the Planck
function, $P$), is added to these reflected fluxes which arrive at the camera
having been transmitted through a mixture of atmospheric and volcanogenic
gases at temperature, $T_{g}$, and having transmissivity, $\tau$. Figure 4:
Time series of the summit fumarole fluxes since the last quarter of 2017 as
estimated from pitot tube and multigas data. Steam fluxes are shown in a) and
heat fluxes in b). Vertical grey bars indicate the record of VT earthquakes
with magnitude $>\mathrm{M}2.0$ (including felt VTs), which are limited to a
sequence in early 2018. To aid interpretation of the pitot tube data, we used
a linear smoothing function to produce the dashed curves. The MultiGAS data
shown (filled symbols) incorporate the 35% increase in steam flux due to
condensation of vapour within the plume. The reworked MultiGAS data correspond
to the CO2 flux multiplied by the H2O/CO2 ratio determined from Giggenbach
bottle analyses. Figure 5: Mass flow rate, water temperature and heat flux for
the thermal springs monitored by the OVSG for the period from 2000-2020. See
text for site codes. The colour code for each site is identical between plots
and dashed lines show linear trends for the GA, TA and PR sites.  Figure 6:
Long term temporal evolution of the fumarole fluxes from 2005-present. In
addition to the present dataset, we also plot Pitot-tube data from March-May
2018 (Moretti et al., 2020a) and 2005, along with thermal camera data 2010
(both Gaudin et al. (2016), MultiGAS data from 2006, 2012 (Allard et al.,
2014), and reworked data from 2016-2017 (Tamburello et al., 2019). The arrow
labelled “True fluxes?” indicates our reworking of the 2010 thermal camera
data. Grey shading indicates the period covered by the present dataset, as
shown in Fig. 4. Table 1: comparison of radiative and convective fluxes, and
heat flux density for the ground-heated sites around La Soufrière from 2019
aerial imagery. In the right-hand column, mean values are given for the flux
densities, and total values for all other quantities.

Summit Matylis (lower) Ravine Claire FTY0 FTY1 Total/Mean∗ Rad. flux density,
$q_{\mathrm{rad}}$/[W/m2] 52 76 50 71 62 54.59 Conv. flux density,
$q_{\mathrm{conv}}$/[W/m2] 350 455 310 432 383 351.16 Total heat flux
density/[W/m2] 403 531 360 504 446 405.75 Radiative flux,
$Q_{\mathrm{rad}}$/[MW] 0.74 0.12 0.40 0.10 0.07 1.43 Convective flux,
$Q_{\mathrm{conv}}$/[MW] 4.94 0.74 2.49 0.63 0.42 9.23 Total
($Q_{\mathrm{rad}}+Q_{\mathrm{conv}}$)/[MW] 5.67 0.87 2.89 0.74 0.49 10.66
Heated area/[m2] 14070 1630 8010 1460 1100 26270

Table 2: Comparison of the mass and heat flux estimates in 2010 (Gaudin et
al., 2016) and for 2020 (present study). Values in parentheses are reworked
fluxes which, for 2010, are based on the likely evolution of fumarole fluxes
(see Fig. 6) and the thermal springs data (Fig. 5) and for the present-day
fumarole estimates are the MultiGAS traverse results scaled to the Pitot-tube
measurements. Dashes indicate that no data was acquired at that site.
*Encompasses RC and Matylis.

Flux Year Fumaroles Ground thermal anomaly Hot springs Total CS G56 TAS Total
Summit FTY Flanks∗ Total GA PR TA Total Mass [kg/s] 2010 $19.5\pm 4.0$ -
$22.8\pm 8.1$ $42.3\pm 12.1$ - - - - 2.5 - 1.5 4.5 $46.8\pm 12.1$ ($5.3\pm
1.1$) ($6.2\pm 2.2$) ($11.5\pm 3.3$) (2.51) (0.44) (1.61) (4.56) ($16.06\pm
3.3$) 2020 $4.9\pm 0.5$ ($2.1\pm 0.8$) ($2.8\pm 1.1$) ($9.8\pm 2.5$) - - - -
3.35 0.44 1.61 5.40 ($15.2\pm 2.5$) Heat [MW] 2010 $48.0\pm 9.8$ - $56.1\pm
19.9$ $104.1\pm 20.7$ $0.2\pm 0.1$ $1.0\pm 0.2$ - $1.2\pm 0.3$ 0.3 - 0.2 0.5
$105.8\pm 21.0$ ($13.0\pm 2.6$) ($15.2\pm 5.4$) ($28.2\pm 8.0$) (0.25) (0.02)
(0.12) (0.39) ($29.8\pm 8.3$) 2020 $15.3\pm 1.5$ ($5.5\pm 2.2$) ($7.5\pm 3.0$)
($28.3\pm 6.8$) $5.7\pm 0.9$ $0.6\pm 0.1$ $1.3\pm 0.2$ $7.6\pm 1.1$ 0.36 0.01
0.19 0.56 ($36.5\pm 7.9$)