Tracking Lava Flow Cooling from Space: Implications for Erupted Volume Estimation and Cooling Mechanisms

Abstract

Accurate estimation of erupted lava volumes is essential for understanding volcanic processes, interpreting eruptive cycles, and assessing volcanic hazards. Traditional methods based on Mid-Infrared (MIR) satellite imagery require clear-sky conditions during eruptions and are prone to sensor saturation, limiting data availability. Here, we present an alternative approach based on the post-eruptive Thermal InfraRed (TIR) signal, using the recently proposed VRP_TIR method to quantify radiative energy loss during lava flow cooling. We identify thermally anomalous pixels in VIIRS I5 scenes (11.45 µm, 375 m resolution) using the TIRVolcH algorithm, this allowing the detection of subtle thermal anomalies throughout the cooling phase, and retrieve lava flow area by fitting theoretical cooling curves to observed VRP_TIR time series. Collating a dataset of 191 mafic eruptions that occurred between 2010 and 2025 at (i) Etna and Stromboli (Italy); (ii) Piton de la Fournaise (France); (iii) Bárðarbunga, Fagradalsfjall, and Sundhnúkagígar (Iceland); (iv) Kīlauea and Mauna Loa (United States); (v) Wolf, Fernandina, and Sierra Negra (Ecuador); (vi) Nyamuragira and Nyiragongo (DRC); (vii) Fogo (Cape Verde); and (viii) La Palma (Spain), we derive a new power-law equation describing mafic lava flow thickening as a function of time across five orders of magnitude (from 0.02 Mm³ to 5.5 km³). Finally, from knowledge of areas and episode durations, we estimate erupted volumes. The method is validated against 68 eruptions with known volumes, yielding high agreement (R² = 0.947; ρ = 0.96; MAPE = 28.60%), a negligible bias (MPE = −0.85%), and uncertainties within ±50%. Application to the February-March 2025 Etna eruption further corroborates the robustness of our workflow, from which we estimate a bulk erupted volume of 4.23 ± 2.12 × 10⁶ m³, in close agreement with preliminary estimates from independent data. Beyond volume estimation, we show that VRP_TIR cooling curves follow a consistent decay pattern that aligns with established theoretical thermal models, indicating a stable conductive regime during the cooling stage. This scale-invariant pattern suggests that crustal insulation and heat transfer across a solidifying boundary govern the thermal evolution of cooling basaltic flows.

1. Introduction

Volcanic eruptions, especially at mafic volcanoes, are predominantly characterized by lava effusion. These eruptions can last from hours to years and exhibit highly variable eruption rates [1,2]. Long-term records of magma output rates and volumes are essential for understanding deep volcanic dynamics, deciphering decadal eruptive cycles, and improving the assessment of volcanic hazards [3,4].

Estimating erupted volumes from ground-based observations can be challenging, even at well-monitored volcanoes. Satellite-retrieved thermal data have therefore become a cost-effective and reliable alternative. Mid-InfraRed (MIR)-based Volcanic Radiative Power (VRP_MIR [5]) data have been instrumental in quantifying erupted products, allowing the retrieval of Time-Averaged Discharge Rate (TADR) and, in turn, lava volumes by the end of an eruption, by leveraging the relationship between emitted energy and mass, and their conversion into volume flux [6].

However, accurate volume estimation via MIR-based satellite information mainly relies on acquiring imagery under optimal weather conditions, where the eruptive scene is free from clouds and/or volcanic plumes, and the thermal sources can be clearly distinguished and, in turn, the thermal energy quantified. In volcanic regions, however, as demonstrated by [7], this is seldom the case, and the likelihood of acquiring volcanologically suitable imagery is reduced by up to 90% depending on the geographical setting [8]. Furthermore, during thermally extreme events, sensor saturation may impede the detection of the total thermal energy radiated by the active flow, resulting in an underestimation of VRP_MIR and, by extension, the associated erupted volumes [2,3,4,5,6,7,8,9].

To overcome the unavailability of satellite thermal information (i.e., due to plume obscuration and/or saturation) during paroxysmal episodes at Mount Etna, Ganci and colleagues developed a method to estimate erupted volumes exploiting the cooling curves of the emplaced lava flows [10]. The authors first retrieve the VRP_MIR signal associated with the initial cooling stages of the emplaced flow using the high-temporal, low-spatial resolution SEVIRI sensor aboard the geostationary Meteosat Second Generation (MSG) satellite. Then, solving for the theoretical treatment of the Stefan cooling problem [11] proposed by Harris et al. [12,13], Ganci et al. [10] model the theoretical lava cooling curve, estimating the temperature of the flows’ surface at each time step (once a cooling curve was established). After converting temperature into radiative power per square meter (W/m²) using the Stefan-Boltzmann equation, the curve is multiplied by an area, until the theoretical cooling curve aligns with the observed one. Finally, assuming a range of thicknesses typical for Etnean lava flows, the authors combine the estimated area and assumed thickness to retrieve erupted volumes.

The method proved successful in estimating erupted volumes at Mount Etna, largely overcoming the limitations due to plume obscuration and saturation. However, the approach still relies on (i) the persistence of meteorologically favorable conditions over the eruptive scene in the hours following the emplacement and (ii), a priori knowledge of the lava flow thickness. In particular, the limited (~24 h) time window available for cooling data collection is dictated by the fact that cooling lava surface temperature rapidly drops well below 600 K, thus falling below the MIR-method operational threshold, resulting in a drastic underestimation of the measured VRP_MIR [14,15] as well as the loss of the detectable thermal anomaly in satellite images and/or hotspot detection algorithms.

Wooster and colleagues [16] proposed a satellite-based heat-budget approach to estimate erupted volumes from the 1991–1993 Etna eruption by assessing the total heat released through cooling via radiation, conduction, convection, and vaporization. Although the model is theoretically applicable to any eruption, two major limitations make this method unsuitable for real-life applications: (i) the only parameter that can be accurately estimated from satellite thermal imagery is the heat lost through radiation, whereas the other three terms require continuous external data such as information on the geology of the substratum, wind speed, and precipitation [6]; and (ii) the need to track the full cooling process until equilibrium with the surroundings and underlying materials is reached, a task rarely achievable in practice due to both temporal (the time required for complete cooling can range from years to decades, or even centuries) and instrumental (thermal sensor detection limits) constraints.

Recent work by [8] has highlighted the potential of extending the time window for cooling curve detection by reinvigorating the use of Thermal InfraRed (TIR) channels for monitoring volcanic thermal activity. Aveni et al. [17] further demonstrated that TIR channels must be used to measure Volcanic Radiative Power for targets with temperatures ranging from ≲600 K to near ambient (i.e., VRP_TIR). This temperature range encompasses the rapid cooling phase of lava flows after emplacement until equilibrium is reached over months to years (i.e., ambient temperature).

In this work, we introduce a new approach for estimating erupted volumes from VRP_TIR time series, overcoming limitations due to the unavailability of suitable scenes at the time of eruption, and/or multidecadal and multiparametric data. To achieve this, we first compile a catalog of 191 mafic eruptions that occurred between 2010 and 2025 and propose a new relationship to estimate lava flow thicknesses from knowledge of episode duration and areal coverage of the lava flow (s). Then, we extract the VRP_TIR cooling curves for 68 volcanic eruptions exploiting the high sensitivity of the TIRVolcH algorithm [8], and apply the methodology first outlined by [10] to estimate the area of the cooling lava body from these cooling curves. Combining both thickness and area, we estimate the bulk erupted volumes. Validation of our results against those available in the literature demonstrates the effectiveness of our workflow. Finally, we provide insights into lava flow cooling mechanisms, demonstrating that cooling basaltic flows exhibit a consistent, scale-invariant decay pattern that aligns with established theoretical models [12,13], and discuss possible physical processes driving this behavior.

2. Methods

2.1. Catalog of 2010–2025 Basaltic Eruptions

We compiled a literature-based catalog (Supplementary Material S1) of erupted volumes and durations of mafic eruptions that occurred between 2010 and 2025 (including the 35-year-long eruption of Pu‘u ‘Ō‘ō, Kilauea, that began in 1983). The catalog is made of 191 eruptions at 16 different volcanoes (Figure 1), here summarized by region:

(i)

Italy: 137 eruptions, with 134 from Mount Etna and 3 from Stromboli (2014, 2019, 2024).

(ii)

France (Réunion Island): 27 eruptions from Piton de la Fournaise.

(iii)

Iceland: 11 eruptions, including Bárðarbunga (2014), Fagradalsfjall (Geldingadalir, 2021; Meradalir, 2022; Litli-Hrútur, 2023), and 7 from Sundhnúkagígar (2023–2024).

(iv)

United States (Hawaiian Islands): 4 eruptions, including Pu‘u‘ō‘ō, Kīlauea (1983), Kīlauea (2018), Mauna Loa (2022), and Kīlauea (September 2024).

(v)

Ecuador (Galápagos Islands): 7 eruptions, including Wolf (2015, 2022), Fernandina (2017, 2018, 2020, 2024), and Sierra Negra (2018).

(vi)

Democratic Republic of Congo (DRC): 3 eruptions, from Nyamuragira (2010, 2011–2012) and Nyiragongo (2021).

(vii)

Cape Verde: 1 eruption from Fogo (2014).

(viii)

Spain (Canary Islands): 1 eruption from La Palma (2021).

2.2. Theoretical Framework

2.2.1. Lava Flow Thickening Curve

Flow thicknesses vary widely depending on several parameters, such as lava rheology, emplacement style and morphology, pre-existing topography, etc. Hon et al. [19] first assessed the inflation of pāhoehoe flows as a function of time ($t$), showing that the time-dependent thickening of Hawaiian flows can be approximated by a power law of the form:

$$H=b{t}^a$$

(1)

where $H$ is the thickness, and $a$ and $b$ are the slope and intercept coefficients, respectively. Further studies suggested that the same physical principles, thus the same power-law-governed time-dependent thickening processes, also apply to lava flows and lava fields at different scales (i.e., [20,21]).

Building on the findings of [19,20,21] (and references therein), we assessed whether this relation could be extended to mafic flows worldwide using the catalog summarized in Section 2.1 (Supplementary Material S1). Assessing the time-dependent thickening of 191 mafic lava flows (Figure 2a), these varying in average thicknesses (from ~1 m to ~30 m) and emplacement duration (19 min to 35 years), we find that a power law relationship generally describes the thickening of mafic lava flows and lava fields as a function of time, with a best fit (R² = 0.68, ρ = 0.74, p-values < 0.001) described by

$$H_{\left(m\right)}=b{t}^a=1.6416·t_{\left(hr\right)}^{0.2007}$$

(2)

where thickness ($H$) is given in meters ($m$), and time ($t$) must be entered in hours ($hr$). Considering that these lava flows present different rheological, topographical, and thermal insulation conditions, the fit produces reasonably good results.

In turn, erupted volume ($Vol$; in m³) can be estimated from knowledge of episode duration and areal coverage ($A_{lava}$; in m²) of the lava flow (s), as

$$Vol=A_{lava}1.6416·t_{\left(hr\right)}^{0.2007}$$

(3)

Figure 2b reveals the robust and remarkable agreement between observed and predicted volumes computed via Equation (3), which is statistically corroborated by an R² = 0.99, ρ = 0.96, and p-values < 0.001, with an uncertainty largely comprised within ±50% calculated at a 90% confidence interval, and in agreement with error margins given in the literature.

2.2.2. Lava Flow Cooling Curve

Hon et al. [19] demonstrated that as soon as surface temperature drops below solidification point, a crust forms and begins to cool due to conduction. Starting from this predictable cooling behavior, refs. [12,13] developed a thermal model to estimate surface temperature at each time step by solving for the theoretical treatment of the Stefan cooling problem [11], the latter describing the process of phase change between liquidus and solidus, and the heat transfer mechanisms at the interface boundary (see refs. [6,12,13,22,23], and references therein). With the notion that the heat transfer to the flow’s surface is controlled by the formation and growth of the crust at the interface with a molten core held at a constant fusion temperature ($T_h$, in Kelvin), ref. [12,13] predict the time required ($t_{\left(s\right)}$, in seconds) for a lava surface to cool to a given temperature ($T_{surf}$, in K), following:

$$t_{\left(s\right)}={\left\{\left[\left(\frac{T_h-T_a}{\epsilon \sigma \left(T_{surf}^4-T_a^4\right)+h_c\left(T_{surf}-T_a\right)}-\frac{R_c-R_r}{R_c+R_r}\right)k\right]1000\frac{1}{2\lambda }\right\}}^2\frac{1}{\alpha }$$

(4)

where $T_a$ (in K) is the ambient temperature, $\epsilon$ is the emissivity (adim.), $\sigma$ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W m⁻² K⁻⁴), $h_c$ is the convective heat transfer coefficient (in W m⁻² K⁻¹), $k$ is the thermal conductivity (in W m⁻¹ K⁻¹), $\alpha$ is the thermal diffusivity (in mm² s⁻¹), $R_c$ and $R_r$ (both in W m⁻² K⁻¹) are the thermal resistance terms for convection and radiation, respectively, and can be computed as:

$$R_c=\frac{1}{h_c}$$

(5)

$$R_r=\frac{T_h-T_a}{\epsilon \sigma \left(T_{surf}^4-T_a^4\right)}$$

(6)

and $\lambda$ is a dimensionless scaling value that, according to [22,23], can be determined iteratively by solving a transcendental equation, calculating the right side of Equation (7) until agreement is found:

$$\frac{L_f\sqrt{\pi }}{c_p\left(T_h-T_a\right)}=\frac{e^{-{\lambda }^2}}{\lambda ·erf\left(\lambda \right)}$$

(7)

where $L_f$ is the latent heat of fusion (in J kg⁻¹), $c_p$ is specific heat capacity (in J kg⁻¹ K⁻¹), and $erf$ is the error function (see ref. [6] for full derivation of Equations (4)–(7)).

Equations (4)–(7) now allow plotting $T_{surf}$ as a function of $t$, providing the theoretical cooling curve a lava flow should undergo after emplacement. With $T_{surf}$ known, we can also extract the radiant flux density curve through cooling ($M_{Cooling}$, in W/m²), as:

$$M_{Cooling}=\epsilon \sigma \left(T_{surf}^4-T_a^4\right)$$

(8)

In turn, expanding Equation (7) to include the areal extent of the lava flow ($A_{lava}$, in m²), we can also obtain the total Radiative Power through cooling (${RP}_{Cooling}$, in Watt), following:

$${RP}_{Cooling}=A_{lava}{M}_{Cooling}$$

(9)

2.3. Satellite Data

2.3.1. TIRVolcH

TIRVolcH algorithm [8], processes and elaborates VIIRS I-5 (11.45 μm) nighttime Suomi-NPP and NOAA-20 VIIRS Level 1B radiance products (VNP02IMG and VJ102IMG 6-Min L1B Swath 375m, respectively), freely distributed by NASA’s Level-1 and Atmosphere Archive & Distribution System–Distributed Active Archive Center (LAADS-DAAC). Both platforms are placed in a polar orbit, each providing full coverage of the globe daily since January 2012 [24,25,26]. The algorithm compares the observed VIIRS imagery to a reference set of Brightness Temperatures (BT), which are calculated by averaging over ten years of mostly cloud-free images for each volcano. TIRVolcH first detects extremely anomalous (hot) pixels using fixed thresholds. Then, an iterative process compares the reference BT to the observed scenes. Assuming an approximate linear relationship between these two scenes, the algorithm identifies pixels significantly deviating from this fit using a Euclidean distance-based clustering approach. A set of contextual thresholds is then applied to identify any remaining or undetected subtle thermal anomalies. Hotspot-contaminated pixels are removed from the scene to compute the theoretical background temperature, the latter calculated through bi-cubic interpolation of the surrounding, non-thermally anomalous pixels. The algorithm’s high sensitivity enables the detection of hotspots with pixel-integrated temperatures as low as 0.5 K above the background, up to 25 km from the volcano’s summit, thus providing the opportunity of tracking the long-term (months to years) cooling curve of emplaced lava bodies (see ref. [8] for details).

2.3.2. VRP_TIR

Assessing the relationship between the true radiative power (${RP}_{True}$) emitted per unit surface area and the excess of spectral radiance (${∆L}_{TIR}$, in W m⁻² sr⁻¹ µm⁻¹), namely the radiance of a hotspot-contaminated pixel above that of the background ($L\left(T_{bg}\right)$, in W m⁻² sr⁻¹ µm⁻¹), ref. [17] demonstrated that in the TIR portion of the spectrum and for temperature ≲ 600 K, ${RP}_{True}$ may be approximated as

$${RP}_{True}=\approx A_{pix}·k_{TIR}·{∆L}_{TIR}$$

(10)

where $A_{pix}$ is the pixel area (in m²), and $k_{TIR}$ (µm·sr) is the sensor-specific constant of proportionality linearly relating ${∆L}_{TIR}$ to ${RP}_{True}$. For VIIRS I-5 channel $k_{TIR}$ equals 60.17 µm·sr (see ref. [17] for $k_{TIR}$ derivation). Accordingly, the VRP_TIR (in watts) can be computed as:

$${\mathrm{V}\mathrm{R}\mathrm{P}}_{\mathrm{T}\mathrm{I}\mathrm{R}}=A_{pix}·k_{TIR}·{\sum }_{i=1}^{N_{pix}}(L_{{TIR}_{{hot}_i}}-L_{{TIR}_{bg}})$$

(11)

where $N_{pix}$ is the number of hotspot-contaminated pixels, $L_{{TIR}_{{hot}_i}}$ is the $i$-th hotspot-contaminated pixel-integrated radiance and $L_{{TIR}_{bg}}$ is the spectral radiance of the background pixels. The VRP_TIR has an uncertainty of ±35% [17]. $L_{{TIR}_{hot}}$, $L_{{TIR}_{bg}}$, and $N_{pix}$ are obtained from the thermally anomalous pixels detected by the TIRVolcH algorithm. To ensure VRP_TIR time series were not biased by geometrical unfavorable acquisitions, scenes acquired with zenith angles > 50° were discarded (see [8] for details).

2.3.3. Derivation of Area from Cooling Curves and Parameters Setting

The VRP_TIR here represents the energy radiated from a lava surface during the cooling process, making Equation (2) directly comparable to Equation (8). However, solving Equations (4)–(9) requires knowledge of the parameters described in Section 2.2.2. Many of these parameters necessitate extensive field and laboratory experiments, and detailed information is often scarce for most of the locations examined in this study. To address this limitation, previous studies have relied on parameter values obtained from the literature. These values were typically estimated for specific regions or eruptions, leading to significant variability even within the same location. Parameters such as $h_c$, $k$, $\alpha$, and $c_p$, have been assumed across a broad range, as they were likely selected within plausible limits to best fit observational data. In this work, we set these parameters (see

Table 1. Set of parameters used to run the thermal model of [12,13]. Please note, all parameters were kept constant, except for ambient temperatures ($T_a$), which were derived from VIIRS monthly average ambient brightness temperature [8], and $h_c$ (see text for details).

Variable	Value	Units	Reference
$T_a$	273–285	Kelvin	Variable, based on VIIRS monthly average ambient BT [8].
$T_h$	1423	Kelvin	[29]
$\epsilon$	1	adim.	[30]
$\sigma$	5.6704 × 10−8	W m−2 K−4	[6]
$h_c$	10–120	W m−2 K−1	[6]
$k$	1.5	W m−1 K−1	[31]
$\alpha$	0.5	mm2 s−1	[10]
$L_f$	3.5 × 105	J kg−1	[32]
$c_p$	900	J kg−1 K−1	[33]

) based on the most commonly reported values in the literature, with the exception of $h_c$. This parameter is in fact highly location-dependent and has been found to vary over more than an order of magnitude (~10 to ~120 W m⁻² K⁻¹; e.g., [6,27,28] and references therein). To account for these variations, we let $h_c$ range between 10 and 120 [28], assuming variations in heat released through cooling are primarily due to differences in the thermal properties of the surrounding medium and the thermal and physical boundary conditions encountered in different volcanic settings, which is an appropriate assumption [6]. By holding all other parameters constant and allowing only $h_c$ to vary, this coefficient now incorporates the influence of varying rheological, insulation, and topographic conditions of the emplaced lava flow (s), as well as the geographical and atmospheric conditions of the eruptive regions. Thus, to avoid ambiguity, we rename $h_c$ with $h_c^{*}$, factually introducing a new empirical scaling factor which incorporates the natural variability of the other parameters. An initial calibration is now needed for $h_c^{*}$. To achieve this, we first categorize the dataset introduced in Section 2.1 by volcano groups, based on location. For each eruption where both observed VRP_TIR cooling curves and independent area estimates were available, we determined $h_c^{*}$ by minimizing the RMSE between the observed and theoretical cooling curves. Finally, we computed the average $h_c^{*}$ value for each group to be used in our analysis. For volcanoes that could not be grouped, we used $h_c$ values reported in the literature (see Supplementary Material S1). With $h_c^{*}$ known, we can now recompute Equations (4)–(9), to calculate the $T_{surf}^{*}$ and $M_{Cooling}^{*}$ at each time step. This allows us to retrieve the area of the cooling lava flow (${\mathrm{A}}_{Sat}$; in m²) from the observed VRP_TIR curves, following

$${\mathrm{A}}_{Sat}=\frac{{\mathrm{V}\mathrm{R}\mathrm{P}}_{\mathrm{T}\mathrm{I}\mathrm{R}}}{M_{Cooling}^{*}}$$

(12)

Specifically, following the methodology outlined by [10], we adjust $A_{sat}$ in Equation (9) until the theoretical curve matches the observed one, with the best fit determined by minimizing the RMSE between the two curves, applying the Nelder–Mead algorithm.

3. Results

3.1. Cooling Curves of Bulk Basaltic Flows

Out of 191 lava-flow-producing events, 167 occurred after the availability of VIIRS data in January 2012. After removing paroxysmal sequences at Mt. Etna and events that occurred within two weeks of each other (to avoid contamination from overlapping thermal signatures), we were left with 73 events. From this subset, we successfully identified 69 cooling curves (94.52%) from the TIRVolcH-processed VRP_TIR time series. Figure 3a–j shows a selection of cooling curves obtained from the TIRVolcH-processed VRP_TIR time series for global case studies. These curves exemplify typical cooling patterns observed across the identified events, demonstrating the reliability and consistency of the applied methodology, as well as the effectiveness of VRP_TIR in capturing both the thermal radiation magnitude and the cooling patterns over time.

3.2. Area and Volume Retrieval from VRP_TIR Cooling Curves

To assess the applicability of the area retrieval methodology described in Section 2.3, we compared the results against ground truth data, observing a strong agreement (Figure 4a). This consistency is statistically supported by a coefficient of determination (R²) of 0.991 (p-value < 0.001) and a Spearman′s correlation coefficient ($\rho$) of 0.976 (p-value < 0.001). The Mean Absolute Percentage Error (MAPE) was 19.91%, and the Mean Percentage Error (MPE) of just −0.79%, indicating a negligible bias in the method. The uncertainty associated with the model, calculated at a 90% confidence interval, is less than ±50%.

With both area and duration known, volumes (${Vol}_{sat}$; in m³) can be calculated as

$${Vol}_{Sat}=A_{Sat}1.6416·t_{\left(hr\right)}^{0.2007}$$

(13)

For the 68 eruptions where a cooling curve could be extracted, applications of Equation (13) demonstrate the reliability of the proposed approach, as evidenced by an R² of 0.947 (p-value < 0.001) and ($\rho$) of 0.966 (p-value < 0.001). The estimated volumes exhibited a MAPE of 28.60% and an MPE of −0.85%, again indicating a negligible bias in the method. The uncertainty associated with the model, calculated at a 90% confidence interval, is ±50%, consistent with the uncertainty reported in the literature (Figure 4b).

3.3. Applications to the February-March 2025 Etna Effusive Eruption

On 8 February 2025, an effusive event began on Mount Etna with the opening of a fissure at the base of the Bocca Nuova (BN) crater, at an altitude of approximately 3050 m above sea level. Due to adverse meteorological conditions, this activity was first detected at 17:35 UTC [34]. The first thermal anomaly linked to the onset of eruptive activity was detected by TIRVolcH on 9 February 2025, at 00:54 UTC, approximately seven hours after the beginning of the eruption was confirmed (Figure 5a). The VRP_TIR signal gradually increased, reaching its peak during the early hours of February 19 (Figure 5b), before exhibiting a fluctuating decline throughout the remainder of the month. The last thermal anomaly, detected before persistent cloud cover obstructed further observations, was recorded on 1 March at 01:42 UTC, with weak activity still visible in the upper portion of the lava field (Figure 5c). Adverse meteorological conditions hindered further observations until 4 March, when the dispersal of cloud cover revealed the lava flow was in its cooling phase, as indicated by a significant reduction in VRP_TIR values (Figure 5d). Over the following days, a distinct cooling curve was established, enabling the application and validation of the methodology outlined in this study. We estimated the erupted volumes based solely on thermal satellite imagery. Accordingly, we set the eruption’s start time as 9 February 2025, at 00:54 UTC, and the eruption’s end time as 1 March 2025, at 01:42 UTC, resulting in an eruption duration of approximately 20 days, or 480 h and 48 min. By fitting the cooling curve using the methodology described in Section 2.3.3, we estimated the area of the cooling lava field to be 0.74 × 10⁶ m² and a total erupted volume of 4.23 × 10⁶ m³ (±50%). These results are in close agreement with preliminary estimates from independent data, which reported an area of 0.7 × 10⁶ m² and a volume of 4.5 × 10⁶ m³ (±40%) [35].

4. Discussion

Quantification of magma output rates and eruptive volumes provides insights into the dynamics of the magmatic–volcanic system and facilitates the identification of patterns in decadal eruptive cycles, thereby improving the assessment of volcanic hazards. Satellite-based information has long been the primary source of data to estimate such parameters. Building and expanding on existing methodologies, here we demonstrated how tracking the thermal signature of an emplaced lava flow through its cooling phase allows estimation of erupted volumes. Using a database of ~200 mafic eruptions that occurred between 2010 and 2025, we also found that the time-dependent lava thickening law originally proposed by [19] holds true at the scale of entire lava fields. Notably, the power-law exponent obtained for the whole lava field (0.201; Equation (9)) closely matches that reported by [19] for individual pāhoehoe lobes (0.217), and more generally to the theoretical value for viscous gravity currents (0.25 [20]). The larger scaling coefficient obtained for our dataset (1.642; Equation (9)) compared to that of a single lobe (0.649) by ref. [19] likely reflects the greater initial thickness typical of compound flows. However, it should be noted that these coefficients represent average conditions for around 200 lava flows, which vary in composition, rheological properties, emplacement topographies, and other factors. Therefore, some variation in these coefficients is expected at the local scale.

We demonstrated that this approach enables the estimation of both areas and emplaced volumes independently of meteorological conditions. For instance, during the February–March 2024 Etna eruption, persistent cloud cover hindered direct observation of volcanic activity at the beginning, throughout, and at the end of the effusive phase. Despite this, the extended temporal window over which our method is applicable—ranging from days to years after emplacement, depending on eruption size and local conditions—allowed us to retrieve reliable volume estimates. In situations where TADR-based methods are limited by the total or partial absence of clear-sky observations and/or affected by sensor saturation, our approach provides a valuable complementary or alternative means of volume assessment. Nonetheless, it is important to note that this approach should not be applied to estimate erupted volumes for overlapping lava flows emplaced in close succession (e.g., during paroxysmal sequences at Mt. Etna), as contamination from overlapping thermal signatures may lead to an overestimation of the flow area and, consequently, the erupted volumes.

This work has also provided evidence regarding the characteristic radiative waveform that lava undergoes through cooling (i.e., ref. [36]). In fact, we have shown that regardless of the area, the thickness, and the volume, the initial decay of a cooling lava body closely matches the thermal model first proposed by refs. [12,13]. This evidence indicates that, as soon as the surface temperature drops below the solidification point, the formed crust insulates the inner molten core, and in turn supports the maintenance of consistent heat transfer processes within the cooling flow [32]. In turn, as previously suggested by refs. [6,12,13,22,23], our findings seem to corroborate that as long as there is a molten region within the flow (between the upward and downward growing crusts), the same heat transfer mechanisms at the liquidus-solidus interface boundary apply. Molten core(s) or lens feed the conductive heat transfer dynamics within the crust that transfer the heat to the surface of the flow, where it is then radiated by the surface, and finally quantified in terms of VRP_TIR.

5. Conclusions

In this study, we evaluated the cooling behavior of mafic lava flows by analyzing radiative energy losses at their surface. We quantified the radiative power lost during cooling using the VRP_TIR approach proposed by ref. [17]. To verify the reliability of the TIR method, we compared the VRP_TIR time series, which represent the total radiative energy loss from the cooling lava bodies, with the theoretical cooling curves expected for lava bodies of the same area [10,12,13]. The remarkable agreement between observed and theoretical measurements demonstrates and cross-validates that (i) the VRP_TIR method effectively quantifies thermal energy losses for surfaces ≲ 600 K to near ambient temperatures, and (ii) cooling basaltic lava bodies exhibit a characteristic cooling pattern described by the thermal model of [12,13], a phenomenon that, to our knowledge, has not previously been observed over decadal time scales. Furthermore, our findings highlight that the consistent time dependence observed across scales points to a common relationship in basaltic lava emplacement. This finding supports the possibility of developing models for predicting lava flow evolution across multiple spatial scales. While additional studies are needed to validate these results, we foresee that these observations could have important implications for hazard assessment and lava flow behavior forecasting. Future research should investigate whether the cooling relationships observed in mafic systems are transferable to more silica-rich lava bodies, such as andesitic flows, lava domes, or coulees, and to what extent the proposed coefficients must be adjusted to account for their distinct thermal properties, emplacement dynamics, and rheological behavior. Additionally, this approach may be adapted for planetary volcanology, as anticipated by [37,38], and contribute to improving thermal emplacement and cooling models for extraterrestrial lava bodies (i.e., [39,40,41]). Moreover, this method could complement and expand the growing body of techniques designed to explore analogies between terrestrial and planetary volcanism (i.e., [42,43]). Besides, given the adaptability of the VRP_TIR retrieval method to past, present, and future TIR-equipped sensors, as well as its compatibility with different processing algorithms (e.g., [44]), we believe that the observations presented in this study establish a robust foundation for future research. As high-resolution TIR sensors become operational, this research will also provide the groundwork for more detailed investigations. For instance, upcoming missions like the Global Change Observation Mission-Climate “SHIKISAI” (GCOM-C [45,46]), the Surface Biology and Geology (SBG [47,48]), the Thermal infraRed Imaging Satellite for High-resolution Natural resource Assessment (TRISHNA [49,50,51,52]), and the VULCAIN mission [53], will enable a more nuanced understanding of cooling dynamics, helping to refine and expand upon the insights presented in this work.