Introduction

Hawaiian-style fire fountains represent the weakest type of volcanic explosive activity, having a Volcanic Explosivity Index of between zero and one (Newhall and Self, 1982). However, they are common explosive events at basaltic systems (e.g., Behncke et al. 2006) and, although typically short lived, can feed extensive, fast-moving lava flows at high discharge rates (e.g., Wolfe et al. 1988). As such, they present a frequent hazard both in terms of the airborne tephra rising above the fountain and inundation of property by a high-discharge-rate flow fed by lava falling back to the ground around the fountain. Understanding the rate at which fountain-fed lava flows are fed, as well as the flux variation in time, is, thus, important in terms of understanding not only the dynamics of the system feeding the eruption but also the hazard posed by the associated lava flows (e.g., Calvari and Pinkerton, 2002). Because fountaining events can wax and wane over time scales of minutes (e.g., Richter et al. 1970; Wolfe et al. 1988; Behncke et al. 2006; Bonaccorso et al. 2011), any such flux time series need a similar temporal resolution. To date, studies on lava discharge rate time series for a short duration and high-intensity fountain-fed lava flows have been lacking. The total lava volumes erupted during individual fountaining events have been used, with the duration of emission, to provide the mean output rate for the entire event, as well as during the fountaining events at Kilauea's Pu'u 'O'o (Wolfe et al. 1988), Kilauea Iki (Richter et al. 1970) and Etna's SE Crater (Behncke et al. 2006). However, these data sets provide no information regarding the time-varying nature of the lava discharge during the event. Although ground-based cameras have been used to document fountaining (e.g., Behncke et al. 2006), the ground-based view lacks a synoptic perspective, and lava flows issuing on the camera's blind side will be missed.

We here demonstrate the ability of the data collected from the perspective of a geostationary satellite platform to document and track lava flows that are active during short-lived fountaining events. These data have the advantage of providing a synoptic view every 15 min, a capability that has meant that they have long been used to track rapidly evolving ash plumes (e.g., Holasek and Self, 1995; Holasek et al. 1996), including those associated with fire fountains (e.g., Aloisi et al. 2002; Bertrand et al. 2003), and to detail short-lived effusive events developing over time scales of less than an hour (e.g., Harris et al. 1997a; Harris and Thornber, 1999). We here explore two methods to extract and track time-averaged discharge rates (TADR) for a complex lava flow field resulting from a fountain-fed event at Etna using geostationary satellite (Spinning Enhanced Visible and InfraRed Imager, or SEVIRI) data. First, we attempt to estimate the TADR using the well-established method of Harris et al. (1997b). Then, we present an alternative method, based on an analysis of the cooling curve subsequent to the lava flow emplacement, to estimate the mean output rate using posteruptive data.

Data and methods

Time series from MSG-SEVIRI

For many years, thermal infrared (TIR) (3–12 μm) data from sensors flown on polar-orbiting satellites have been shown capable of providing data suitable for tracking an effusive volcanic activity. While time series from Landsat's Thematic Mapper (TM) have an optimal temporal resolution of 16 days, sensors such as the Advanced Very High Resolution Radiometer (AVHRR) and the Moderate Resolution Imaging Spectrometer (MODIS) have nominal temporal resolutions of between 6 and 24 h. TM-, MODIS-, and AVHRR-derived time series have thus proved capable of tracking effusive events that evolve on timescales of days to months (e.g., Oppenheimer et al. 1993; Harris et al. 1997b). However, sensors flown on geostationary platforms have the advantage of a 5- to 30-min repeat period, allowing generation of time series for effusive events with a nominal temporal resolution of 15 min (e.g., Harris et al. 1997a). The Imager launched on GOES-8 in April 1994 was the first geostationary sensor to have the crucial midinfrared (3.9 μm) capability necessary to detect an effusive activity in a 4-km pixel. GOES has a footprint that extends over the Pacific as well as North, Central, and South America, allowing an effusive activity across these regions to be tracked (Harris et al. 2002). In August 2002, the SEVIRI sensor was launched on the first of the Meteosat Second Generation (MSG) satellites, extending a high-temporal-resolution midinfrared capability to the volcanoes of Africa and Europe. SEVIRI operates at a very high temporal resolution of up to one image every 5 min, with a pixel size of up to 1 km in 12 channels ranging from the visible to the TIR. For the purposes of this study, the data collected in the IR3.9 (3.48–4.36 μm) and IR12 (11.00–13.00 μm) channels are the most useful. These data have a pixel size of 3 km and are collected at typical frequencies of one image every 15 min.

The data are available to us via direct reception at the Observatoire de Physique du Globe de Clermont-Ferrand (OPGC, Clermont Ferrand, France) and are processed, on reception, to track volcanic activities in near-real time as part of the HotVolc Observing System (Labazuy et al. 2011). Here, we use all MSG-SEVIRI images available for Etna over a 24-h period (a total of 96 images), spanning the 12–13 January 2011 eruption. On all images, the lava flow activity was apparent as a positive thermal anomaly in the midinfrared (IR-3.9 μm) only. Due to the large pixel size, the relatively small lava field extent, and the low sensitivity of the TIR to subpixel hot spots, the effusive activity was not detected using the IR-12-μm channel.

Conversion to TADR

To convert heat flux (Q tot) to TADR using the satellite thermal data, we applied the well-established conversion of Harris et al. (1997b). The conversion to TADR reduces to an empirical relation, whereby (Wright et al. 2001):

$$ {\text{TADR}} = mA/c $$
(1)

in which A is the area of active lava flow derived from the satellite image, and m and c are coefficients defining a linear relation between TADR and A. These coefficients need to be set on a case-by-case basis (Harris and Baloga, 2009), and those set for lava flows at Etna by Harris et al. (2010) are those applied by us here (also see Table 1 in Supplementary Material). As explained in Harris and Baloga (2009), solution is given for a range of coefficients, which take into account the maximum and minimum bounds on the range of uncertainty in all input parameters. A solution now requires estimation of the active lava area (A) using the satellite TIR data. This involves application of a simple two-component mixture model to estimate the active lava area within the pixel, A i . This approach has commonly been applied to TIR (TIR: 10–12 μm). However, because we have anomalous radiance in the MIR only, we have to use pixel-integrated radiances in this waveband (R MIR) to calculate A i following the equation below (Harris et al. 2007):

$$ {A_i} = \frac{{{R_{{MIR}}} - {L_{{MIR}}}\left( {{T_a}} \right)}}{{{L_{{MIR}}}\left( {{T_c}} \right) - {L_{{MIR}}}\left( {{T_a}} \right)}}{A_{{pix}}} $$
(2)

in which L MIR(T a) and L MIR(T c) are the radiances for the lava component of the pixel, which is radiating at temperature T c, and of the ambient surfaces surrounding the flow at T a. A pix is the pixel area, and summing A i for all pixels within the anomaly gives the total area at T c, that is, the area of active lava flow. Because we have no anomaly in the TIR, following Wright and Flynn (2004), we use the MIR radiance equivalent for the TIR pixel-integrated temperature to approximate L MIR(T a) for surfaces within the MIR pixel. Now, the solution of Eq. 2 requires assumption of T c. Given the fact that we cannot fix a single temperature to characterize the lava surface temperature (T c), we use a range of possible T c values to obtain a range of probable lava areas, within which the actual area likely lies. Following the methodology, as calibrated for the 1-km AVHRR data collected in the TIR for Etna by Harris et al. (2010), we use a T c range of 100°C to 600°C. Inputting the two areas that these two temperature assumptions yield, along with the appropriate T c, into Eq. 1 yields a range of TADR, which, in the test case of Harris et al. (2010), was centred on the actual value.

All pixel-integrated radiances inputted into Eq. 2 need to be corrected for atmospheric, reflection, and emissivity effects. This involves estimating and removing the contributions due to atmospheric upwelling (R u) and surface reflection (R R) from the at-sensor radiance (R*), as well as dividing by emissivity (ε) and atmospheric transmissivity (τ):

$$ R = \frac{{R^* - {R_u} - {R_R}}}{{\varepsilon \tau }} $$
(3)

We estimated the atmospheric parameters for an altitude of 2,500 m using a (winter) US standard atmosphere in the MODerate resolution atmospheric TRANsmission (MODTRAN) model (http://modtran.org/). The altitude was set as typical for the main section of the flow field as centered in a 3-km pixel, and the model was that which performed best during in situ ground testing performed in 1994 by Harris (1996). Emissivity was set to that of Etna's lava (0.97—this being the average emissivity calculated for each of the two SEVIRI wavebands considered here using reflectance spectra for an Etna ′a′a clast). This was used to calculate reflection as a function of hour, for the given day (12–13 January) and at Etna's latitude following Iqbal (1983).

Ground-based Doppler radar monitoring of Etna

Since July 2009, a 23.5-cm wavelength pulsed Doppler radar (VOLDORAD 2B) has been operational at Etna. This instrument is described by Donnadieu et al. (2005) and is located on Etna's southern flank. From this location, the radar sounds a conical beam 9°-wide pointing N342°E and looking at an upward angle of 14°. Data are acquired at 0.23 s−1 in 11 successive volumes. Each volume is 150 m deep, so that the field of view is a 1.65-km-deep sector above the summit craters (Donnadieu et al. 2009). Because the pit crater from which the 12–13 January fountain was erupted was slightly to the East of the beam, the radar could not record a weak Strombolian activity preceding the explosive paroxysm on January 12. However, it clearly detected the fountain-fed ash plume associated with the main fountaining phase between 2140 and 2340 hours. This was mostly located in two sampling volumes at distances of 3,135 and 3,285 m, making the fountain no more than 300 m wide.

Results

The eruption began during the afternoon of 11 January 2011 (Calvari et al. 2011) and was initially characterized by a weak explosive activity confined to a pit crater on the E flank of Etna's Southeast Crater. Neither the satellite nor the Doppler radar data were able to detect this activity, with the thermal energy radiated being too small to be detected by MSG-SEVIRI and the Strombolian explosions being too weak to reach the radar beam. The activity remained at low levels until 12 January at 2020 hours UTC (2120 local time—all times from herein are UTC), when lava began to overflow from the lower rim of the pit crater (Calvari et al. 2011). The first hot spot was recorded in SEVIRI's 3.9-μm channel at 2000 hours (Fig. 1a). The SEVIRI-recorded increase in hot-spot intensity actually preceded the overflow by 20 min and probably resulted from the lava beginning to pond inside the pit prior to overflow. This is consistent with the increasing glow observed above the pit between 2000 and 2020 hours. By 2020 hours, the pit had filled to a point level with the lowest point on the rim, and overflow began (Calvari et al. 2011). The waxing limb of the 3.9-μm radiance plot is thus associated with the onset of effusive activity. Around 2130 hours, the overflow began to be accompanied by a stronger explosive activity, peaking between 2200 and 2300 hours when fire fountaining up to 800 m in height was recorded (Calvari et al. 2011).

Fig. 1
figure 1

Time series of MSG-SEVIRI 3.9- and 12-μm spectral radiance during Etna's 12–13 January 2011 episode. The bottom plot shows the power backscattered by the fountain-fed ash plume recorded by the ground-based Doppler radar (VOLDORAD 2B) in the 3,135-m range gate, during the same time period

Full size image

The Doppler radar detected the onset of the fountaining phase as an increase in echo power that began at 2140 hours (Fig. 1c). The radar signal fluctuated for about 1.3 h at a level between 10 and 20 dB, reaching maximum values of 30 dB between 2220 and 2230 hours. However, the peak radar signal was accompanied by anomalously low radiances in MSG-SEVIRI's 12-μm channel, which showed a strong decrease in 12-μm radiance beginning around 2140 hours (Fig. 1b). At the same time, the hot-spot signal in the 3.9-μm channel vanished (Fig. 1a). The coincidence of the trends recorded in the radar, 12- and 3.9-μm data, suggest a common origin. This can be explained by the intense fountaining that produced a large tephra plume responsible for the strong radar signal: the high, cold plume top explain low temperatures and, hence, low radiances in the 12-μm band; the same plume obscured the hot spot associated with the active lavas.

When the radar power began to decline, after 2300 hours, the 12-μm radiance began to increase once more, and the 3.9-μm hot spot began to become visible again (Fig. 1). This is consistent with waning activity and clearance of the plume to reveal the hot spot associated with the active lavas. The ash plume had, in effect, placed a false hiatus in the 3.9-μm effusion record. By 2300 hours, the 3.9-μm radiance had recovered to such an extent that the emitted radiance was sufficiently intense to saturate the 3.9-μm channel. Saturation continued to be recorded until 0030 hours, explaining the flat top to our 3.9-μm time series (Fig. 1a). The change between saturated and unsaturated data in the 3.9-μm band occurred between 0030 and 0045 hours. Termination of saturation in 3.9-μm data has previously been shown to correlate with the termination of effusion (Aries et al. 2001), so we assume that this point marked the end of effusion. This assumption is confirmed by thermal camera-based observations that show termination of the main effusive phase around 0055 hours, although flow fronts continued to move due to passive drainage of channels until 0600 hours on 13 January (Calvari et al. 2011). After this point, we record a cooling curve as the flow stagnated and cooled (Fig. 1a). This cooling curve can be traced until 1100 hours when it became obliterated by the ambient signal.

In Fig. 2, we plot the TADR calculated every 15 min using the MIR method (3.9 μm) from the MSG-SEVIRI data. In doing so, we can distinguish three different phases: (1) the lava effusion phase (~2000–0100 hours), (2) the lava cooling phase (~0100–1100 hours), and (3) the ambient phase (~1100–1600 hours). The lava cooling phase is characterized by a trend of steadily waning TADR after 0100 hours. However, these are “false” TADR because they relate to heat fluxes from stagnant, cooling flows that are no longer supplied. Thus, from 0100 hours onward, TADR is actually around zero, even though the heat loss (estimated for the cooling, but still hot flow field) can still be used to generate a false TADR.

Our range of assumed temperatures used to estimate the active flow area (and, hence, also TADR) yields a very large range of TADR when the conversion method is applied to the MIR. To better constrain the range of TADR estimates, we used the TIR (10–12 μm) data from the AVHRR and MODIS sensors. The pixel size of these sensors is 1 km so that anomalies in the TIR are usually available. However, only four images per day are nominally acquired. Unfortunately, no useable AVHRR images were available: the pass of 0119 hours (13 January) revealed an anomaly, but the core was cold, making the image difficult to use. The next pass was at 1114 hours but was badly smeared due to Etna's location at the scan edge. The first good image was recorded at 1254 hours and showed a weak thermal anomaly in band 4 (10.3–11.3 μm), but by this time, no anomaly was detectable by SEVIRI. Two MODIS images could be used. The first one was acquired at 2105 hours and gave TADR in the range of 8–11 m3/s. The second occurred just after the end of lava flow emplacement, at 0120 hours, and gave false TADR in the range 20–45 m3/s. As a comparison, we found our MSG-SEVIRI MIR data yielded TADRs of 6–75 and 10–105 m3/s at 2105 and 01:20 hours, respectively. This comparison allows us to narrow down the likely envelope for the SEVIRI-estimated TADRs during the actual period of effusion, where a best fit with the MODIS data is obtained with a lava crust temperature (T c) of 350°C and an m/c value of 6.9 × 10−5 in our MIR model. We thus use this as the most likely SEVIRI-derived TADR curve, as plotted in Fig. 2. Now, the total volume of lava erupted during the main lava emission phase (2000–0100 hours) can be obtained from integrating syn-eruptive TADRs through time, which yielded 0.2 × 106 m3. However, this value will be a minimum bound because it does not use TADRs lost to ash obscuration (between 2100 and 2315 hours when discharge likely peaked) and during the period of pixel saturation (between 2315 and 0030 hours when a cap—maximum recordable value—is placed on the TADR).

Fig. 2
figure 2

TADR time series during Etna's 12–13 January 2011 episode generated using MSG-SEVIRI and MODIS data. Black lines represent the plots for the 100°C and 600°C temperature assumptions, and the red lines show the best-fit curve between the MSG-SEVIRI 3.9-μm and MODIS data (best fit is obtained using a temperature assumption of 350°C)

Full size image
Fig. 3
figure 3

MSG-SEVIRI-derived TADR plot for the period of fountain-fed effusion. We can see that the recorded lava volume (blue area) is very small when compared with the total lava volume emitted (dashed area), as retrieved using the cooling curve data

Full size image

Cooling curve method

We next used the cooling curve acquired between 0100 and 1100 hours to estimate the total volume erupted during the emission phase (2000–0100 hours). To do this, we integrated the total heat flux (Q tot) through time during the cooling phase to estimate the total power released (E th) during the 10-h-long period of recorded cooling:

$$ {E_{\text{th}}} = \sum\limits_t {{Q_{\text{tot}}}\Delta t} $$
(4)

where Δt is the time step between two points of acquisition, here equal to 15 min, and Q tot is the average of that acquired at the beginning and end of the period (i.e., we apply trapezium rule). This gave a total power value of 4.6 × 1011 J. The lava volume that needs to be cooled to generate this power can now be calculated using:

$$ {\text{Total\_volume}} = \frac{{{E_{\text{th}}}}}{{\rho \left( {{C_{\text{p}}}\Delta T + L\Delta \varphi } \right)}} $$
(5)

in which ρ is the bulk lava density, C p is the lava-specific heat capacity, ΔT is the cooling interval, L is the latent heat of crystallization, and Δϕ is the volume fraction of crystals grown in cooling through ΔT. Using the values given for Etna by Harris et al. (2010), Eq. 5 yields a total lava volume of 1.2 × 106 m3 and compares with a field estimated value of 0.8–2.5 × 106 m3 (expressed as DRE using ~22% vesicles; Calvari et al. 2011). Dividing by the period of main effusion gives a mean output rate for the entire 5-h-long event of 67 m3 s−1. By comparison, we show that the total lava volume estimated previously from the standard syn-effusion TADR method (0.2 × 106 m3) is underestimated by a factor of 6. Given an actual total volume of 1.2 × 106 m3, this allows us to say that a volume of 1 × 106 m3 is missing from the syn-eruptive TADR estimate due to plume obscuration and saturation. If we distribute this across the 3.5-h-long period (2100–0030 hours) of obscured and saturated data, that is, the period of peak emission, we have a TADR for this period of ~80 m3 s−1 (Fig. 3).

Conclusions

Given the short duration of the 12–13 January 2011 fire fountain event at Etna, SEVIRI data recorded every 15 min proved to be the only option capable for rapidly producing a volumetric time series for lava discharge. This is revealed by the fact that although 96 images were available from SEVIRI during the 24-h event, only 2 were available from MODIS and 1 from AVHRR, which turned out not to be useable. The SEVIRI time series shows a short waxing phase between 2000 and 2130 hours when TADRs climbed to 15 m3 s−1. The ensuing period of peak effusion lasted until 0030 hours and was obscured by the tephra plume, but (using the subsequent cooling curve) can be estimated to have had a TADR of at least 80 m3 s−1. Thereafter, effusion ceased and flows began to cool, as apparent from termination of saturation and establishment of a cooling curve.

On all images, the lava flow activity was apparent as a positive thermal anomaly in the MIR only. Indeed, due to the large pixel size and the relatively small lava field extent, the lava flow activity was not detected using TIR channels. Therefore, we needed to use the MIR channels, which is not usual (the less sensitive TIR is normally used). As a consequence, the high sensitivity of the MIR led to a very wide envelope of TADR extractions, as well as false TADRs during the posteffusive phase when flows were still hot (and detectable) but no longer fed. To better constrain our data in the MIR, we used (1) data points from higher-spatial-resolution sensors operating in the TIR (10–12 μm), such as MODIS and AVHRR, to obtain narrower TADR bounds within SEVIRI time series and (2) the cooling curve to obtain a total erupted lava volume. This allowed us to narrow down the envelope of likely TADR derived from SEVIRI's MIR data, yielding total lava volumes of about 1.2 × 106 m3, in good agreement with ground-based measurements, and indicated peak discharge rates of at least 80 m3 s−1.