While global initiatives to directly determine CO2 flux from biogenic sources, i.e., FLUXNET , have advanced our understanding of the surface carbon cycle, estimates of volcanic flux are to a large extent obtained by combining SO2 flux measurements with observed CO2 / SO2 ratios . This approach relies on two separate sets of measurements utilizing a ground-based or space-based remote sensing technique to determine the SO2 concentration of the volcanic plume and a direct sampling or sensing technique to determine the CO2 / SO2 ratio. In almost all cases, these two separate sets of measurements are not made simultaneously and result in intrinsic uncertainties in CO2 flux estimates . CO2 surveys have been performed using satellite-based approaches; for example, performed CO2 flux estimates of Kīlauea volcano in 2018. Their work utilized the Orbiting Carbon Observatory-2 (OCO-2) to measure the CO2 emissions from the 2018 Kīlauea eruption. A measurement of 77.1 ± 41.6 kt d-1 was obtained during the 1 d of observations where conditions enabled the collection of consistent high-quality data. Cloud coverage and aerosol are the major inhibitors for obtaining consistent CO2 data using OCO-2. In addition, the wind direction must be near perpendicular to the satellite's orbit path and the measurements must be made downwind from the plume. The OCO-2 16 d​​​​​​​ repeat cycle currently makes this method impractical for frequent, high-rate CO2 flux measurements from erupting volcanoes, and the only other successful volcanic CO2 emission study was by of Yasur in Vanuatu. Therefore, space-based CO2 instruments require favorable atmospheric conditions and satellite positioning and are not yet feasible for volcano monitoring .

The value of UAS surveys of volcanic emissions was recognized by , who surveyed passively degassing SO2 at Turrialba volcano, Costa Rica, and estimated SO2 flux. Other investigators have used UASs to measure plume SO2 and collect plume trace gases or use miniDOAS (differential optical absorption spectroscopy) systems mounted on an unpiloted aerial vehicle (UAV) to obtain SO2 fluxes . Recently UASs (unpiloted aerial systems) have been used to collect gas samples and measure gas compositions of volcanic plumes from passively degassing volcanoes in remote regions and during the 2023 eruption of Litli Hrútur, Iceland, to obtain information on CO2 degassing and related carbon isotope fractionation

and estimate plume CO2 flux using the parsimonious assumption that plumes are uniform. They use the mean value to estimate the flux, whereas we use our observations in the field that support the hypothesis that plumes can be well modeled by Gaussian distributions. Our work relies on the assumption that a Gaussian model of the plume cross-section results in more accurate estimates of total flux.

surveyed emissions of the Tajogaite eruption in early October 2021. Their survey included SO2 measurements by UAV that were used to infer CO2 concentrations. Our work in late November complements the ​​​​​​​ survey by providing additional information on the evolution of the eruption and using a different CO2 flux estimation method that employs direct CO2 measurements rather than CO2 / SO2 ratios. Our estimates of CO2 flux taken a month later were lower than those of .

The island of La Palma is in Spain's Canary archipelago . The northern sector of the island hosts the oldest subaerial (on-land) volcanism, characterized by repeated large lateral edifice collapses (; ). Volcanism resulted in the formation of Garafía and Taburiente and then moved southward to form Cumbre Vieja volcano, at the southern part of the island. This southern system represents the last stage in the geological evolution of the island of La Palma, as volcanic activity has taken place exclusively on that part of the island for the last 123 kyr . The most recent volcanic eruption of Cumbre Vieja is Tajogaite (2021) , preceded by that of Teneguía in 1971 and San Juan in 1940 . At 14:10 UTC on 19 September 2021 Tajogaite volcano erupted from a vent on the western side of the island of La Palma, in the vicinity of the Llano del Banco eruptive center of the San Juan eruption of 1949 . The eruption was forecast using seismic, geodetic and geochemical techniques by Spanish researchers who alerted the civil protection officials several days before the start of the eruption . The monitoring network of diffuse CO2 emissions on La Palma detected magmatic CO2 several months before the eruption . This monitoring activity took advantage of extensive previous work characterizing diffuse CO2 emissions on La Palma. This work provided key insights into the dynamics of magmatic CO2 degassing on the island . The eruption itself began with an explosive phase that ejected ash to an altitude of 5 km, then transitioned to fire fountains, violent strombolian activity and the production of highly fluid lava flows. Within 24 h of the initial eruption a 3 km long lava flow was evident . The eruption lasted for more than 85 d and built a pyroclastic cone of about 225 m in height. Over the period of the eruption, the volcano showed dynamic and changing activity with new vents frequently opening on the active cone. These vents produced explosive and effusive eruptions of varying intensity . Bulk tephra, matrix glass and glass inclusions have a basanitic–tephritic composition of 43 wt % to 46 wt %.

Since the onset of the 2021 Tajogaite eruption on 19 September, frequent measurements of SO2 emission rates using miniDOAS traverses by car, ship and helicopter have been performed. Using these data a flux of over 5×104 t d-1 of SO2 was estimated . Daily monitoring of SO2 gas emissions occurred before and throughout the eruption using TROPOMI (TROPOspheric Monitoring Instrument) data from the Sentinel-5P satellite (Copernicus SO2 satellite monitoring; Smithsonian Institution's Global Volcanism Program, 2021). The range of measured emissions rates depended upon wind direction and velocity, as well as eruptive style and activity. The measured SO2 flux ranged from 3×104 to 5×104 t d-1 at the beginning of the eruption and had a mean of 104 t d-1 over the duration of the active eruption . These SO2 emission rates are likely different from CO2 but provide the best available proxy for CO2 emissions and are a useful point of comparison for our UAS-based flux estimates in addition to the measurements made by in October 2021, which range from 3.36×104 to 4.19×104 t d-1.

Additional gas monitoring techniques deployed during the eruption included stationary Multi-GAS- (multiple gas analyzer) and FTIR-based plume gas composition measurements as well as carbon isotope analyses of plume CO2 in collaboration with the international volcanic gas community .

The calculated CO2 flux for the five relevant transects with the corresponding wind velocities and directions are shown in Table  for transects across plume A and plume B. The wind velocity measured by UAS drift method was 10.7 m s-1. ERA5 modeled wind velocities yielded results ranging from 10.0 to 12.2 m s-1 with an average of 11.1 m s-1. The wind direction given by the ERA5 model yielded results ranging from 38 to 68°, with an average of 53°. These ranges contribute to the overall uncertainty ϵd.

The CO2 concentrations and δ13C values of plume gas samples are given in Table . Samples collected from the ground at the University of New Mexico (UNM) Multi-GAS site show background CO2 concentrations of 416 to 471 ppm CO2 with δ13C values of -8 ‰ (relative to Vienna Peedee belemnite, VPDB), which is close to that of air. The sample collected by UAS has a CO2 concentration distinctly elevated from air of 671 ppm and a heavier δ13C value of -4.44 ‰.

Samples collected from the ground closer to the vent have even higher CO2 concentrations from 1030 to 4459 ppm with δ13C values from -2.40 ‰ to -1.47 ‰.

The Multi-GAS CO2 / SO2 ratios during the period from 21 to 25 November 2021 range from 5 to 26 and are shown in Table 2. These values are consistent with those reported by and . We use the range of reported SO2 fluxes (mean of 104 t d-1 over the duration of the active eruption; ) in combination with the range of our Multi-GAS CO2 / SO2 ratios to obtain CO2 fluxes ranging from 7.3×104 to 3.6×105 t CO2 d-1 for this period (Table ).

Our UAS-based CO2 emission estimation technique yields CO2 fluxes using direct measurement with a single instrument type. This simplifies the estimation of CO2 flux. However, in situ measurement during an active eruption is challenging. The most serious difficulty we encountered was obtaining complete transects across the plume or plumes. In several of our transects, especially for the more distant plume B, we were not successful in flying the UAS far enough to get to background CO2 on the far side of the plume. Gas plumes change shape and direction on relatively short timescales as the wind shifts. While, ideally, we would like to perform several flights at various altitudes through a plume in order to obtain a complete CO2 concentration map of the plume, this is challenging for wide or distant plumes because of limited UAS flight times and the need to know the plume's location and extent a priori. To address this challenge we assume a Gaussian plume and fit a Gaussian curve to our data. We then rotate the Gaussian fit to obtain a 2D concentration slice which is multiplied with estimated wind velocity to yield the flux. This approach produces the most accurate results if we transect the plume through its widest part. However, identifying the widest part and then transecting the plume before the plume changes will require teams of collaborating UASs. A good fit of the data by the Gaussian model is given by a high R2 value. For instance, transect 2 was fit with a R2 value of 0.93 and accounts for 93 % of the variance in the observed data. The model fit represented by this high R2 value is depicted in Fig. .

Uncertainty is introduced by the assumptions made by the model. We combine the various sources of uncertainly using the RSS method (Eq. ). With just one horizontal transect, we assume the vertical Gaussian standard deviation is identical to the horizontal standard deviation of the plume. The standard deviations of both dimensions are linearly correlated to the flux calculation, meaning that a 20 % error in the vertical standard deviation will affect the flux estimate by 20 %. We estimate that the vertical standard deviation is likely close to the horizontal standard deviation, but the difference is impossible to determine. Additionally, we assume that the horizontal transect samples the plume at the altitude where the plume is widest. If the transect is not through the largest cross-section, the flux calculation may be a lower bound. Wind velocity was measured during one of the transects, but weather is notoriously unpredictable. This represents another source of uncertainty in the model which has a linear effect on the flux measurement. We used our wind estimates during the time of each flux calculation. This variation in wind velocity ϵv is ±11 %, which is calculated from the wind velocity range measured over the experiments (Table ). The range of wind directions is ±15° from Table , which gives an error in the flux estimate based on ϵd=1-cos⁡(angle), thus ±3.40 %. The SBA-5 documentation reports sensor error ϵs of 1 % in the range of CO2 we measured. Finally, background ambient CO2 ϵb adds 1 % to the uncertainty model which we calculated from the uncertainty in ambient CO2 readings. Therefore, our estimated flux uncertainty given by the RSS method is ϵ=±11.61 %.

Our data show that for plume A, transect 6 (Fig. ) represents the widest plume and results in the highest CO2 flux value of 2.23±0.26×104 t d-1, an order of magnitude higher than the other two plume A transects. This transect was flown at the lowest altitude (100 m) of the three, implying that the other two transects only captured the upper parts of the plume. Comparison with CO2 fluxes obtained by combining SO2 fluxes with CO2 / SO2 ratios measured 1 km from the vent gives fluxes ranging from 7.3×104 to 3.6×105 t CO2 d-1 (Table 3). Therefore our highest flux measurement is consistent with the lowest estimate using the combined method. While comparing these two approaches is helpful, our experiment was not designed to make a direct comparison. The discrepancy could be due to a significantly varying CO2 emission rate during eruptions, an overestimate of the SO2 flux or the lack of validity of the 2D Gaussian extrapolation approach. Our estimates are consistent with the October 2021 high emissions presented by , who report fluxes of 3.36×104 to 4.19×104 t CO2 d-1 (389 to 486 kg s-1) for the smaller, non-ashy plume that we measured. More work needs to be performed in the future to better assess sources of discrepancies with new and coordinated measurements at passively degassing and erupting volcanoes. However, even with such discrepancies, it is clear that the Tajogaite eruption in November 2021 produced a CO2 flux up to 2×104 t d-1 or even 5×105 t d-1. Even the 5×105 t d-1 would be only 0.4 % of the daily CO2 emitted by the burning of fossil fuels .

The carbon isotope data obtained from the UAS-captured samples and the samples collected from the ground are generally consistent and show mixing of air-derived CO2 with a deep magmatic source. Figure  shows that all plume samples collected from the ground define a set of mixing lines in δ13C–CO2-1 space, i.e., in a Keeling plot that allows for the extrapolation of the δ13C value of the pure CO2 being emitted from the volcanic vent. The sample collected by UAV lies slightly above this set of mixing lines and extrapolates to somewhat heavier δ13C. The resulting volcanic δ13C values taking into account all samples lies between -1.5 ‰ and +1.5 ‰. Despite these uncertainties, these values overlap with δ13C data obtained from mantle xenoliths in lava erupted at the nearby El Hierro volcano .

Extrapolation of all these data results in a δ13C value of 0.1±1.5 ‰. Notably the carbon isotope values are significantly heavier than those measured in cold CO2-rich gas discharges from springs on La Palma and within the range of values measured in olivines and pyroxenes of xenoliths from the island of El Hierro . These authors suggested that the heavy values of the xenoliths are related to recycling of crustal carbon, likely derived from carbonates into the mantle source of the Canary Islands hot spot. Our data suggest that the magmatic system that is driving the Tajogaite eruption taps into this deep CO2, rather than remobilizing CO2 that feeds the cold degassing springs on the island. report δ13C values measured in olivines, clinopyroxenes and orthopyroxenes from lava flows erupted in 2021. Their data are consistent with our extrapolated heavy δ13C values. For olivines, representing the earliest crystallization phase, their values range from 0 ‰ to 1 ‰. Values are somewhat lighter for orthopyroxenes and clinopyroxenes. Using all data, their estimated mantle endmember is -1.5 ‰. Our data extrapolate to -1.4 ‰ to +1.6 ‰. Given the difference in sample medium, i.e., phenocrysts versus gas plume, the results are remarkably consistent. More work on erupting volcanoes is needed to better constrain the sources of magmatic CO2 emitted during heightened activity of volcanic systems.