Alison Ming
email: a.ming@damtp.cam.ac.uk

V Holly

L Winton

James Keeble

Mohit Nathan L Abraham

C Dalvi

Paul Griffiths

Nicolas Caillon

Anna E Jones

Robert Mulvaney

Joël Savarino

Mohit C Dalvi

Markus M Frey

Xin Yang

Stratospheric ozone changes from explosive tropical volcanoes: Modelling and ice core constraints

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The ozone layer protects life on Earth from ultraviolet (UV) radiation. Explosive tropical volcanic eruptions can inject volcanic gases into the stratosphere which can disrupt the complex stratospheric chemistry and lead to substantial changes in total column ozone [START_REF] Solomon | Stratospheric ozone depletion: A review of concepts and history[END_REF]Robock & Oppenheimer, 2003, for a comprehensive review).

Over the last 1000 years, a number of explosive tropical volcanoes have injected copious volumes of sulphur dioxide (SO 2 ) and hydrochloric acid (HCl) into the stratosphere.

Injection of sulphur dioxide into the stratosphere from an explosive volcanic eruption increases the number of sulphate aerosol particles, providing a larger surface area for heterogeneous reaction to take place on. The impact of this change in stratospheric aerosol loading on ozone is dependent on the stratospheric chlorine loading (e.g., [START_REF] Timmreck | Modeling the climatic effects of large explosive volcanic eruptions[END_REF].

In a low chlorine atmosphere, N 2 O 5 reacts with water vapour on the surfaces of these volcanic aerosols to form HNO 3 , effectively sequestering reactive NO x species into a longlived reservoir and limiting the availability of NO x radicals to take part in catalytic reactions which deplete stratospheric ozone [START_REF] Crutzen | The influence of nitrogen oxides on the atmospheric ozone content[END_REF][START_REF] Johnston | Reduction of stratospheric ozone by nitrogen oxide catalysts from supersonic transport exhaust[END_REF]. However, in a high chlorine atmosphere, while the heterogeneous reaction of N 2 O 5 on aerosol sur-faces has the same effect, halogenated reservoir species also undergo heterogeneous reactions, liberating reactive ClO x and BrO x species from long-lived reservoirs (e.g., [START_REF] Solomon | Stratospheric ozone depletion: A review of concepts and history[END_REF]. As a result, a large sulphur dioxide injection is expected to cause polar ozone loss when the chlorine loading of the stratosphere is high (e.g. [START_REF] Tie | The response of stratospheric ozone to volcanic eruptions: Sensitivity to atmospheric chlorine loading[END_REF], while in a low chlorine environment, such as a pre-industrial atmosphere or a future atmosphere where the chlorine loading of the stratosphere has declined, it is widely accepted that an injection of sulphate from an explosive tropical volcanic eruption will lead to ozone gain over polar regions (Langematz et al., 2018, and references therein). To understand the future atmospheric impact of volcanic eruptions, studying historic eruptions is a useful analog.

Estimates of the amount of sulphur dioxide emitted into the stratosphere from eruptions over the past 1000 years are highly variable. For example, sulfate mass concentration records from ice core data give the following estimates for recent tropical eruptions:

∼ 10 to 20 Tg SO 2 from Mount Pinatubo in 1991 [START_REF] Timmreck | The interactive stratospheric aerosol model intercomparison project (isa-mip): motivation and experimen-tal design[END_REF], ∼ 60 Tg SO 2 from Mount Tambora in 1815 [START_REF] Zanchettin | The model intercomparison project on the climatic response to volcanic forcing (volmip): experimental design and forcing input data for cmip6[END_REF] and ∼ 100 to 140 Tg SO 2 from the Samalas 1257 series of eruptions (1257, 8.4 • S, 116.5 • E) [START_REF] Toohey | Volcanic stratospheric sulfur injections and aerosol optical depth from 500 bce to 1900 ce[END_REF]. Samalas is the largest eruption over the last 1000 years and part of a series of 4 large eruptions occurring over a period of about 26 years. Some types of explosive volcanoes also emit chlorine and other halogen compounds.

Volcanic stratospheric chlorine emissions are important for ozone destruction reactions [START_REF] Kutterolf | Combined bromine and chlorine release from large explosive volcanic eruptions: A threat to stratospheric ozone?[END_REF] but are less well constrained, since the highly soluble HCl is scavenged by processes in the volcanic plume [START_REF] Halmer | The annual volcanic gas input into the atmosphere, in particular into the stratosphere: a global data set for the past 100 years[END_REF]. In the stratosphere, HCl is the dominant chlorine reservoir species and a source of reactive halogen such as chlorine monoxide, ClO, that destroys ozone. A sophisticated plume model [START_REF] Textor | Injection of gases into the stratosphere by explosive volcanic eruptions[END_REF] suggest that 10% to 20% of the HCl emitted would enter the stratosphere and recent satellite observations have detected HCl injection into the stratosphere from explosive volcanoes [START_REF] Theys | First satellite detection of volcanic oclo after the eruption of puyehue-cordòn caulle[END_REF]. Geo-chemical evidence by [START_REF] Vidal | The 1257 samalas eruption (lombok, indonesia): the single greatest stratospheric gas release of the common era[END_REF] suggests that the Samalas eruption could have injected as much as ∼ 230 Tg HCl into the atmosphere. In contrast, observations during the 1991 Pinatubo eruption show that the efficiency of the scavenging is highly dependent on atmospheric conditions with barely detectable increases in stratospheric HCl following the eruption [START_REF] Wallace | The effect of the pinatubo cloud on hydrogen chloride and hydrogen fluoride[END_REF]. Volcanic HCl emissions and the fraction of HCl mass entering the stratosphere are hence highly variable as these depend on the geochemistry of the eruption and the efficiency of the scavenging processes respectively. The type and location of the eruption also play a role.

The impact of an explosive eruption on stratospheric ozone also depends on dynamical processes. Variability arising from the El Niño-Southern Oscillation (ENSO), the quasi-biennial oscillation (QBO) and the variability in the Brewer-Dobson circulation are able to affect the ozone response following the eruption (Lehner et al., 2016;[START_REF] Telford | Reassessment of causes of ozone column variability following the eruption of mount pinatubo using a nudged ccm[END_REF]. In addition, the radiative heating from the aerosol injection and associated changes to the planetary wave flux from the troposphere are able to alter the stratospheric circulation and hence the transport of aerosols and trace gases [START_REF] Poberaj | Missing stratospheric ozone decrease at southern hemisphere middle latitudes after mt. pinatubo: A dynamical perspective[END_REF].

Since the precise time of the year of the historic eruption is often not known, these factors have to be taken into account in the model simulations [START_REF] Stevenson | Role of eruption season in reconciling model and proxy responses to tropical volcanism[END_REF].

Ground-based observations of total column ozone (TCO) commenced in the 1920s and captured the severe decline in the ozone layer resulting from anthropogenic production of long-lived ozone destroying-halocarbons e.g., Harris et al. (2015, and references therein). However, beyond the relatively short instrumental period, records of total column ozone are non-existent and thus paleo-reconstructions are required to understand how natural phenomena, such as volcanic eruptions, can impact the variability of total column ozone.

Recent research has focused on novel Antarctic ice core proxies of surface UV radiation, which can provide constraints on past ozone variability as changes in total column ozone affect the surface UV over Antarctica. The UV proxy is based on the stable isotopic composition of nitrate (δ 15 N(NO -

3 )) at low accumulation sites in Antarctica [START_REF] Frey | Photolysis imprint in the nitrate stable isotope signal in snow and atmosphere of east antarctica and implications for reactive nitrogen cycling[END_REF]. Theory, laboratory and field experiments have shown that nitrate (NO - 3 ) loss from snow and associated isotopic enrichment of δ 15 N(NO - 3 )in the NO - 3 fraction remaining in the snow is driven by UV photolysis [START_REF] Shi | Isotope fractionation of nitrate during volatilization in snow: A field investigation in antarctica[END_REF][START_REF] Berhanu | Laboratory study of nitrate photolysis in antarctic snow. ii. isotopic effects and wavelength dependence[END_REF][START_REF] Berhanu | Isotopic effects of nitrate photochemistry in snow: a field study at dome c, antarctica[END_REF][START_REF] Frey | Photolysis imprint in the nitrate stable isotope signal in snow and atmosphere of east antarctica and implications for reactive nitrogen cycling[END_REF]. The presence of the heavier isotope of nitrogen in NO - 3 leads to an increase in reduced mass which causes a red shift in the vibrational frequencies and a reduction in zero point energy. The UV absorption peak of the heavier isotope is then narrower and blue shifted resulting in a difference in isotopic fractionation.

Further details of this process can be found in [START_REF] Frey | Photolysis imprint in the nitrate stable isotope signal in snow and atmosphere of east antarctica and implications for reactive nitrogen cycling[END_REF]. The photolytically-induced fractionation of the δ 15 N(NO - 3 ) signal is eventually archived in firn and ice. This depends on a number of site-specific factors aside from the UV irradiance including the snow physical properties and the amount and timing of snow accumulation [START_REF] Erbland | Air-snow transfer of nitrate on the east antarctic plateau; part 2: An isotopic model for the interpretation of deep ice-core records[END_REF][START_REF] Erbland | Air-snow transfer of nitrate on the east antarctic plateau; part 1: Isotopic evidence for a photolytically driven dynamic equilibrium in summer[END_REF][START_REF] Noro | Evaluation of the new ukca climatecomposition model -part 2: The troposphere[END_REF][START_REF] Shi | Distinguishing summertime atmospheric production of nitrate across the east antarctic ice sheet[END_REF]. The largest enrichment of δ 15 N(NO - 3 ) is observed at low accumulation sites on the East Antarctic Plateau, where near surface snow is exposed for more than one summer season to incoming UV radiation [START_REF] Erbland | Air-snow transfer of nitrate on the east antarctic plateau; part 1: Isotopic evidence for a photolytically driven dynamic equilibrium in summer[END_REF][START_REF] Shi | Distinguishing summertime atmospheric production of nitrate across the east antarctic ice sheet[END_REF]. forth referred to as the DML site following the terminology in Winton et al. (2019). The DML region experiences low annual accumulation rates (< 10 g cm -2 yr -1 ) but ice cores from the area still record seasonal, centennial and millennial scale variability in glaciochemistry [START_REF] Göktas | A glacio-chemical characterization of the new epica deep-drilling site on amundsenisen, dronning maud land, antarctica[END_REF][START_REF] Oerter | Accumulation rates in dronning maud land, antarctica, as revealed by dielectric-profiling measurements of shallow firn cores[END_REF]Sommer et al., 2000), as well as highlyresolved tropical volcanic eruptions [START_REF] Hofstede | Firn accumulation records for the past 1000 years on the basis of dielectric profiling of six cores from dronning maud land, antarctica[END_REF][START_REF] Severi | Synchronisation of the edml and edc ice cores for the last 52 kyr by volcanic signature matching[END_REF]. This site offers useful potential to investigate the impact of volcanic eruptions on TCO, surface UV radiation and its imprint in the δ 15 N(NO - 3 ) ice core signature.

The aim of this study is to combine modelling studies with ice core evidence to understand the impact on the total column ozone of explosive tropical volcanic eruptions in a low chlorine stratosphere. The first part of this study will explore the sensitivity of ozone over Antarctica to different volcanic emission scenarios using a state-of-the-art chemistryclimate model (UM-UKCA) with additional key heterogeneous and photolysis reactions.

The second part of the study examines the δ 15 N(NO - 3 ) signal for the tropical volcanic eruption, Samalas. Section 2 described the methods used in this paper. We provide a brief overview of the UM-UKCA chemistry-climate model and the additional key heterogeneous and photolysis reactions that were added to improved the representation of stratospheric ozone. A Pinatubo eruption test case is used to validate the response to a present day volcanic eruption. We also provide a brief description of the ice core data and the isotopic analysis. In Section 3.1, we use the model to investigate the response of stratospheric ozone to various volcanic emission scenarios in a pre-industrial atmosphere. The isotopic constraints offered on past ozone change from the ice core evidence are presented in Section 3.2. Finally, Section 4 combines the model results and ice core analysis to discuss the implications for past and future ozone changes from explosive tropical volcanoes.

2 Data and methods

Model description, changes

We make use of the coupled chemistry-climate model which consists of the United Kingdom Chemistry and Aerosol (UKCA) module together with the UK Met Office Unified Model (UM) [START_REF] Walters | The met office unified model global atmosphere 7.0/7.1 and jules global land 7.0 configurations[END_REF][START_REF] Morgenstern | Evaluation of the new ukca climatecomposition model; part 1: The stratosphere[END_REF]O'Connor et al., 2014).

The model is free running and with prescribed sea ice and sea surface temperatures. The original configuration is similar to the Atmospheric Model Intercomparison Project (AMIP) simulation of UK Earth system model (UKESM) submission to the Coupled Model Intercomparison Project Phase 6 (CMIP6) [START_REF] Eyring | Overview of the coupled model intercomparison project phase 6 (cmip6) experimental design and organization[END_REF]. The resolution is 1.875 • longitude by 1.25 • latitude with 85 vertical levels extending from the surface to 85 km.

The UKCA module is run with the combined stratosphere and troposphere chemistry (CheST) option at version 10.9. The model has an internally generated QBO and the dynamics of the stratosphere is well represented [START_REF] Osprey | Stratospheric variability in twentieth-century cmip5 simulations of the met office climate model: High top versus low top[END_REF]. The model includes the aerosol scheme, GLOMAP-mode, to simulate the direct and indirect radiative effects [START_REF] Mann | Description and evaluation of glomap-mode: a modal global aerosol microphysics model for the ukca composition-climate model[END_REF]. Aerosol optical properties are computed online as the particle size distributions evolve due to micro-physical processes.

Stratospheric ozone concentrations are determined by sets of photo-chemical reactions first described by [START_REF] Chapman | A theory of upper-atmospheric ozone[END_REF] plus ozone destroying catalytic cycles involving chlorine, nitrogen, hydrogen and bromine radical species [START_REF] Solomon | Stratospheric ozone depletion: A review of concepts and history[END_REF]. The photolysis reactions in the model make use of rates calculated from a combination of the FAST-JX scheme [START_REF] Wild | Fast-j: Accurate simulation of in-and below-cloud photolysis in tropospheric chemical models[END_REF][START_REF] Bian | Fast-j2: Accurate simulation of stratospheric photolysis in global chemical models[END_REF][START_REF] Neu | Global atmospheric chemistry: Integrating over fractional cloud cover[END_REF] and look-up tables. FAST-JX wavelengths range from 177 to 850 nm over 18 bins and calculates scattering for all bands [START_REF] Telford | Implementation of the fast-jx photolysis scheme (v6.4) into the ukca component of the metum chemistryclimate model (v7.3)[END_REF]. Above about 60 km, a look-up table of photolysis rates [START_REF] Lary | Diffuse radiation, twilight, and photochemistry. I, II[END_REF][START_REF] Morgenstern | Evaluation of the new ukca climatecomposition model; part 1: The stratosphere[END_REF]) is used when wavelengths below 177 nm become important. Heterogeneous reactions are also important for determining stratospheric ozone concentrations in the presence of polar stratospheric clouds in the polar lower stratosphere or in the presence of sulphate aerosol following explosive volcanic eruptions. Ozone depleting radicals are produced by the photolysis of the products formed from halogen containing compounds reacting on the surface of stratospheric aerosol such as polar stratospheric clouds. These species include hydrochloric acid (HCl), chlorine nitrate (ClONO 2 ), hydrogen bromide (HBr) and bromine nitrate (BrONO 2 ).

Three types of aerosol are considered by the model: ice, nitric acid trihydrate and sulfate aerosol. Above a temperature of about 195 K, reactions occur on liquid sulfate aerosol, around 195 K to 188 K, the model forms nitric acid trihydrate particles and below about 188 K, ice particles form.

We add 8 new heterogeneous reactions to the model involving chlorine and bromine species in a similar way to [START_REF] Dennison | Improvements to stratospheric chemistry scheme in the um-ukca (v10.7) model: solar cycle and heterogeneous reactions[END_REF], following the previous work by [START_REF] Yang | How sensitive is the recovery of stratospheric ozone to changes in concentrations of very short-lived bromocarbons?[END_REF], with the main difference being the explicit treatment of the reactions of 4 additional chemical species: Cl 2 , Br 2 , ClNO 2 and BrNO 2 . These species are also photolysed to produce Cl and Br radicals. Reaction rates depend on the probability of a gas molecule colliding irreversibly with the surface of the aerosol and this is given by an uptake coefficient. We update the calculation of the uptake coefficients using the same scheme as [START_REF] Dennison | Improvements to stratospheric chemistry scheme in the um-ukca (v10.7) model: solar cycle and heterogeneous reactions[END_REF] with the differences listed in Table A1 in the Appendix. [START_REF] Klobas | Ozone depletion following future volcanic eruptions[END_REF] show that stratospheric bromine from natural, very shortlived biogenic compounds is critically important in determining the sign of the ozone change from eruptions when stratospheric chlorine levels are low. Stratospheric bromine is about 100 times more efficient at removing ozone in the high latitudes than chlorine. [START_REF] Yang | How sensitive is the recovery of stratospheric ozone to changes in concentrations of very short-lived bromocarbons?[END_REF] showed that a 5 pptv increase in Br y from very short-lived substances (VSLS) (a doubling of the emissions in a present day experiment) resulted in an ozone decrease in the Southern Hemisphere lowermost stratosphere of about 10 DU. This suggest interhalogen reactions are likely to be important for Pinatubo sized eruptions in a low background chlorine environment (as shown by [START_REF] Klobas | Ozone depletion following future volcanic eruptions[END_REF]) but we expect the ozone response to be largely dominated by chlorine for larger Samalas sized eruptions where the background chlorine loading approaches present-day values. Hence, we explicitly add the emissions of five very short-lived bromocarbon species (CH 3 Br, CH 2 BrCl, CH 2 Br 2 , CHBr 2 Cl, CHBrCl 2 ). These represent estimates of pre-industrial natural emissions of the species [START_REF] Yang | How sensitive is the recovery of stratospheric ozone to changes in concentrations of very short-lived bromocarbons?[END_REF] and are modified from [START_REF] Warwick | Global modeling of biogenic bromocarbons[END_REF]. For large injections of chlorine, the ozone response will still be dominated by chlorine rather than the details of the interhalogen reactions. Further details of the model setup are described in Appendix A.

Model validation

The .com/data/total-column-ozone). The ozone hole minimum in the satellite data reaches about 185 DU although this happens earlier in September. The modified model still under predicts the summer ozone values which take longer to recover compared to observations. This could be due to the vortex breakup being delayed and is a known issue in a number of comprehensive chemistry climate model [START_REF] Eyring | Multi-model assessment of stratospheric ozone return dates and ozone recovery in ccmval-2 models[END_REF][START_REF] Butchart | Multimodel climate and variability of the stratosphere[END_REF][START_REF] Mclandress | Is missing orographic gravity wave drag near 60s the cause of the stratospheric zonal wind biases in chemistryclimate models[END_REF]. Overall, our changes to the chemistry scheme lead to an ozone distribution that is very similar to [START_REF] Dennison | Improvements to stratospheric chemistry scheme in the um-ukca (v10.7) model: solar cycle and heterogeneous reactions[END_REF].

To assess the model response to a volcanic perturbation in the present atmosphere we run an experiment that simulates the eruption of Mount Pinatubo. The model is first spun up using CMIP6 present day forcings, including changing trends in trace gases. We

Ice core analysis

The first high-resolution record of δ 15 N(NO - 3 ) was obtained for the last 1. [START_REF] Göktas | A glacio-chemical characterization of the new epica deep-drilling site on amundsenisen, dronning maud land, antarctica[END_REF][START_REF] Weller | Year-round chemical aerosol records in continental antarctica obtained by automatic samplings[END_REF][START_REF] Weller | Seasonal variability of crustal and marine trace elements in the aerosol at neumayer station, antarctica[END_REF] constrained by well-dated volcanic horizons (further details can be found in Table B1). An age uncertainty of ±3 years is estimated at the base of the ice core. High-resolution sampling for δ 15 N(NO - 3 ) analysis was carried out i) across volcanic horizons with a sample resolution of 5 to 30 cm, and ii) in 10 cm resolution baseline samples 1 m either side of the volcanic peak. A total of 119 discrete measurements of δ 15 N(NO - 3 ) are reported here. Discrete δ 15 N(NO - 3 ) samples were preconcentrated and analysed using the denitrifier method following [START_REF] Frey | Photolysis imprint in the nitrate stable isotope signal in snow and atmosphere of east antarctica and implications for reactive nitrogen cycling[END_REF] and [START_REF] Morin | Comprehensive isotopic composition of atmospheric nitrate in the atlantic ocean boundary layer from 65 • s to 79 • n[END_REF]. The nitrogen isotopic ratio was referenced against N 2 -Air [START_REF] Mariotti | Atmospheric nitrogen is a reliable standard for natural 15N abundance measurements[END_REF]. We report 15 N/ 14 N of NO - 3 (δ 15 N(NO - 3 )) as δ-values:

δ 15 N(NO - 3 ) = R sample R standard -1
where R is the elemental isotopic ratio in the sample and standard respectively. The overall accuracy of the method for δ 15 N(NO - 3 ) is 3 per mil.

3 Results

Volcanic perturbations in model

Using the CMIP6 pre-industrial forcings, a year 1850 control run is produced. The (c)), substantial changes in total column ozone are seen for 1.5 years following the eruption. These two cases (high SO 2 and no HCl case, high SO 2 and low HCl) are qualitatively similar suggesting that transport effects still dominate when the amount of HCl is low in a pre-industrial atmosphere and the volcanic chlorine injection is not sufficient to make a significant change to the background stratospheric chlorine loading. The primary impact of a large injection of SO 2 is to locally decrease TCO in the tropics and increase TCO at high latitudes, via the mechanisms described below. Since chemical, dynamical and radiative processes are coupled in the model, it is difficult to quantify the contribution from individual processes but the results suggest that the main driver of the ozone changes is dynamical in the year following the eruption. The SO 2 aerosol leads to both longwave and shortwave heating in the lower stratosphere [START_REF] Robock | Volcanic eruptions and climate[END_REF] resulting in a change in the meridional circulation as shown in Figure 3(a). The increased upwelling brings more ozone-poor tropospheric air into the lower stratosphere leading to lower total column ozone. In contrast, the decreases in upwelling outside the initial SO 2 cloud results in an increase in ozone in the regions polewards of the SO 2 cloud in both hemispheres. Compared to the changes in transport, the changes to the partitioning between radicals and reservoir species for ClO x , HO x and NO x appear to be a second order effect (not shown). The warming in the lower stratosphere results in a warming of the cold point region. This region controls the freeze-drying of water vapour entering the lower stratosphere and warmer temperatures will result in a moistening of the stratosphere and subsequent changes to HO x chemistry. Changes in SO 2 aerosol also change the partitioning between NO y and N 2 O 5 in the polar regions which can result in ozone changes but these have not been quantified in this study.

In contrast, when a substantial amount of HCl together with SO 2 is injected into the stratosphere (high SO 2 and high HCl case, Figure 2 [START_REF] Brenna | Global ozone depletion and increase of UV radiation caused by pre-industrial tropical volcanic eruptions[END_REF] show that the average ozone decreases by more than 120 DU over the polar cap and observe a similar ozone increase over Antarctica in the year after that eruption which is followed by a series of four years with large spring-time ozone depletion. The duration of the response to a volcanic eruption is controlled by stratospheric dynamics and the material that is injected in the lower stratosphere is transported to the troposphere and removed within 2 to 5 years.

In summary, in a pre-industrial atmosphere with low chlorine levels in the stratosphere, we do not detect a significant ozone response to a Pinatubo strength eruption in the model. A large explosive volcano, of similar magnitude to Samalas with no or low HCl produces an increase in total column ozone over Antarctica. The change is shortlived (∼ 2 years) and primarily driven by transport changes. In contrast, if a volcanic injection of HCl (2 Tg in our experiments) is able to raise stratospheric chlorine concentrations closer to present day levels, ozone depleting chemical reactions will occur to produce Antarctic ozone depletion in spring as long as sufficient HCl is present. The stratospheric lifetime of chlorine is determined by the age of air and the strength of the stratospheric circulation. When the chlorine reaches the troposphere, it is washed out, giving a lifetime of about 5 years for HCl entering in the shallow branch of the Brewer-Dobson circulation. The increase in surface UV, resulting from ozone depletion, will affect the δ 15 N(NO - 3 ) ratio in the snow pack. The timing of the change in surface UV could lag, by a number of years, behind that of the volcanic sulphate signal in ice cores, since sulphate arrives via tropospheric and stratospheric transport whilst the UV signal is dependent on stratospheric ozone depletion. An additional difficulty is that the timing of the arrival of the signal depends on the season of the eruption; a quantity that is unknown for most volcanoes over the past 1000 years.

Ice core results

We expect a tropical volcanic eruption to lead to a sulphate signal in the ice record.

The previous modelling studies show that high SO 2 and high HCl eruptions can cause a decrease in TCO which would increase the UV dose reaching the surface at the ice core site. As a result, stronger photolysis would enhance NO - 3 loss, redistribution and recycling from snowpack, decreasing the NO - 3 mass concentration and enriching the δ 15 N(NO - 3 ) signature. 2002)), where sulphate originated from the 1257 series of eruptions, was transported via the stratosphere to Antarctica [START_REF] Baroni | Anomalous sulfur isotope compositions of volcanic sulfate over the last millennium in antarctic ice cores[END_REF]. Nitrate mass concentrations in the ice core decrease coincident with the four large volcanic eruptions (Figure 4(c)). This observation has been reported for other volcanic eruptions in Antarctic and Greenland ice cores, and is thought to occur from the displacement of NO - 3 away from the highly acidic (sulphuric acid) volcanic layers [START_REF] Wolff | Nitrate in polar ice[END_REF][START_REF] Laj | Modified hno3 seasonality in volcanic layers of a polar ice core: Snow-pack effect or photochemical perturbation[END_REF][START_REF] Legrand | Origins and variations of nitrate in south polar precipitation[END_REF]. This post-depositional process, unrelated to photolysis, leads to the anti-correlation between the sulfate peaks and NO - 3 during the volcanic eruptions. Based on other records of NO - 3 in Antarctica [START_REF] Pasteris | Acidity decline in antarctic ice cores during the little ice age linked to changes in atmospheric nitrate and sea salt concentrations[END_REF], we expect the NO - 3 mass concentration to be correlated to the accumulation rate outside of the volcanic eruptions. We do not see this positive correlation in the background variability in the ISOL-ICE ice core (Figure 4(c) and (e); R 2 = 0.04, p < 10 -3 with data from five years either side of the volcanic eruptions is not used). The δ 15 N(NO - 3 )

is weakly anti-correlated to the accumulation rate as would be expected from spatial transects across Antarctica (Figure 4(d) and (e); R 2 = 0.2, p < 10 -4 again with five years either side of the volcanic eruptions removed.) [START_REF] Erbland | Air-snow transfer of nitrate on the east antarctic plateau; part 2: An isotopic model for the interpretation of deep ice-core records[END_REF][START_REF] Erbland | Air-snow transfer of nitrate on the east antarctic plateau; part 1: Isotopic evidence for a photolytically driven dynamic equilibrium in summer[END_REF][START_REF] Noro | Evaluation of the new ukca climatecomposition model -part 2: The troposphere[END_REF][START_REF] Shi | Distinguishing summertime atmospheric production of nitrate across the east antarctic ice sheet[END_REF], and sensitivity tests of variable accumulation rate on the δ 15 N(NO - 3 ) signal at the DML site (Winton et al., 2019).

The accumulation rate is variable at the DML site (2.5 to 11 cm yr -1 water equivalent) [START_REF] Oerter | Accumulation rates in dronning maud land, antarctica, as revealed by dielectric-profiling measurements of shallow firn cores[END_REF]Sommer et al., 2000) and there is no trend over the last 1000 years. We speculate that changes in the accumulation rate will lead to changes in e-folding depth over time which can account for part of the variability of the δ 15 N(NO - 3 ) signal (Winton et al., 2019), with a smaller contribution from extreme precipitation events [START_REF] Turner | The dominant role of extreme precipitation events in antarctic snowfall variability[END_REF]. The e-folding depth of the local snowpack depends on snow physical properties and contributes to the δ 15 N(NO - 3 ) signal eventually preserved in local firn and ice (Winton et al., 2019). Unfortunately, the variability of e-folding depth in the past is not known and may be a source of additional noise in the δ 15 N(NO - 3 ) signal. We see no enrichment of the δ 15 N(NO - 3 ) signal above the background variability 455 during the four volcanic eruptions Figure 4(d). We speculate on possible reasons for thus 456 lack of enrichment after the 1257 series. Firstly, the δ 15 N(NO - 3 ) UV proxy is not sensitive enough to record TCO and concurrent surface UV changes lasting only a few years. (Winton et al., 2019) assessed the sensitivity of the δ 15 N(NO - 3 ) UV proxy to changes in total column ozone using the TRANSITS model [START_REF] Erbland | Air-snow transfer of nitrate on the east antarctic plateau; part 2: An isotopic model for the interpretation of deep ice-core records[END_REF]. We expect that a decrease in the total column ozone of 100 DU, estimated for a large eruption on the magnitude of Samalas (assuming an eruption in September), would result in a 25 per mil increase in δ 15 N(NO - 3 ) at DML. However, this is below the inter-annual δ 15 N(NO - 3 ) variability of 30 to 90 per mil at DML (over the period 1227 to 1350 AD), and thus the development of a volcanic induced-large ozone depletion in spring is unlikely to be observed above the natural background δ 15 N(NO - 3 ) variability. Note that the inter-annual variability of δ 15 N(NO - 3 ) is larger than the seasonal variability of about ±25 per mil of δ 15 N(NO - 3 ) seen at the bottom of the snow pits in Winton et al. (2019). Despite DML having a relatively low snow accumulation rate, the sensitivity of the δ 15 N(NO - 3 ) UV

proxy is low at this site. Secondly, although we observe a significant decrease in the NO - 3 concentration during the volcanic eruptions, we cannot rule out the possibility that the lower NO - 3 concentrations are due to migration of NO - 3 in acidic layers. Lastly, the impact of acidic volcanic layers on the δ 15 N(NO - 3 ) has yet to be quantified.

Discussion and conclusions

The aim of this paper is to understand the impact on the total column ozone of explosive tropical volcanic eruptions in a low chlorine stratosphere and to search for evidence of these changes in the ice core record over the last 1000 years. We made use of the UM-UKCA chemistry-climate model, with improved heterogeneous reactions and emissions, to model the evolution of ozone after different injections scenarios of SO 2 and HCl representing possible past volcanic eruptions. We then compare the model results to the δ 15 N(NO - 3 ) isotopic ratio from the recently obtained ISOL-ICE ice core. Winton et al. (2019) and earlier work [START_REF] Berhanu | Isotopic effects of nitrate photochemistry in snow: a field study at dome c, antarctica[END_REF][START_REF] Erbland | Air-snow transfer of nitrate on the east antarctic plateau; part 2: An isotopic model for the interpretation of deep ice-core records[END_REF] suggest that it may be possible to use δ 15 N(NO - 3 ) as a UV proxy for Antarctic ozone changes, after accounting for accumulation rate changes. A decrease in ozone leads to increased surface UV which increases the fractionation of δ 15 N(NO - 3 ) in the photolytically active region of the snowpack. The resulting δ 15 N(NO - 3 ) isotopic signal, which integrates the UV signal seen over several years, is then buried. We analyse the δ 15 N(NO - 3 ) ice core signature around the period of the Samalas eruption to reconstruct past UV changes.

The model experiments show that a "Pinatubo-like" eruption (low SO 2 , 10 Tg + low HCl, 0.02 Tg) in a pre-industrial atmosphere does not produce a significant response in ozone over Antarctica (Figure 2 The model experiments suggest that if a tropical volcano emits a substantial amount of SO 2 and HCl (high SO 2 , 100 Tg + high HCl, 2 Tg), prolonged ozone depletion, lasting more than four years, will occur over Antarctica. We choose to focus on the ice core record around the Samalas eruption (part of the 1257 series of four volcanoes) since ice core and geochemical evidence suggests that this volcano was the largest in the past 1000 years in terms of SO 2 and HCl emissions although there is significant uncertainty in the amount of HCl that was able to reach the stratosphere from this eruption [START_REF] Halmer | The annual volcanic gas input into the atmosphere, in particular into the stratosphere: a global data set for the past 100 years[END_REF]. The 1257 series of volcanoes that includes Samalas consists of four eruptions that occur at intervals of 10, 8 and 8 years. If all four eruptions caused ozone depletion, we expect to see a prolonged period of increase in δ 15 N(NO - 3 ) in the ice core.

Spatial transects across Antarctica (Noro et al., 2018, and references therein), supported by air snow-photochemistry modelling (TRANSITS) (Winton et al., 2019;[START_REF] Erbland | Air-snow transfer of nitrate on the east antarctic plateau; part 2: An isotopic model for the interpretation of deep ice-core records[END_REF] show a strong non linear dependence of δ 15 N(NO - 3 ) on snow accumulation rate which is not seen in the ice record (60-70 m depth). Deeper ice core records in Greenland have observed a dependence of δ 15 N(NO - 3 ) and accumulation rate on glacialinterglacial transition timescales [START_REF] Freyer | First results of 15n/14n ratios in nitrate from alpine and polar ice cores[END_REF]. However, in this paper, we present the highest resolution record in ice cores and do not observe a clear relationship on centennial timescales. Our record of the isotopic ratio of δ 15 N(NO - 3 ) in the ice core around the 1257 series eruptions shows that using δ 15 N(NO - 3 ) as a proxy for ozone changes is inconclusive. Winton et al. (2019) show that for 100 DU change in total column ozone (Figure 2(d)), we expect to see a change of about 25 per mil in δ 15 N(NO - 3 ). This is below the level of inter-annual variability in δ 15 N(NO - 3 ) seen in the ice core of about 60

to 90 per mil. The maximum uncertainty in our samples is less than ±3 per mil over this time period. Note that the snow pack also integrates UV changes over a couple of years and smooths out seasonal variability. For a δ 15 N(NO - 3 ) signal to have been detected at the DML site from the 1257 eruptions, we suggest that it would require a prolonged period (several years) of near complete ozone destruction, for instance, during the series of seven stratospheric volcanic eruptions that occurred over a deglaciation ∼ 17.7 ka [START_REF] Mcconnell | Synchronous volcanic eruptions and abrupt climate change ˜17.7 ka plausibly linked by stratospheric ozone depletion[END_REF]. With the additional caveat that the timing and magnitude of ozone changes depends on the season of the eruption, the climate model results suggest that this would require more than 2 Tg HCl to have been injected into the stratosphere. Since we do not see a δ 15 N(NO - 3 ) signal of this magnitude in the ice core, this provides a constraint on the magnitude of past ozone changes caused by the 1257 eruptions.

In summary, we have evaluated the impact of various explosive tropical volcanic emission scenarios on stratospheric ozone changes in a pre-industrial atmosphere and found that the sign of the ozone change over the polar regions depends on the amount of HCl injected by the eruption. δ 15 N(NO - 3 ) can theoretically be used as a proxy for UV and thus has the potential to indicate changes in past TCO. Changes in δ 15 N(NO - 3 ) could be positive or negative (indicating either increases or decreased in TCO) depending on the type of volcanic eruption and they are unlikely to be synchronous with sulphate peaks because of different transport pathways and the different timings of the ozone changes.

Using a novel high resolution δ 15 N(NO - 3 ) ice core record, we are unable to detect a signal from the largest volcanic eruption (1257 series) in the past 1000 years as there is a large inter-annual variability in the δ 15 N(NO - 3 ) record. We recommend that future studies of this nature should first understand why the δ 15 N(NO - 3 ) record has a large variability at DML site. A site with lower variability than 25 per mil in δ 15 N(NO - 3 ) could be considered although increasing the sensitivity of the UV proxy by choosing a site with lower annual accumulation comes at the expense of reduced time resolution making it less likely to resolve volcanic eruptions.

Appendix A Model improvements A1 Heterogeneous and photolysis reactions f denotes uptake coefficients calculated using the method in [START_REF] Shi | Kinetic model for reaction of clono2 with h2o and hcl and hocl with hcl in sulfuric acid solutions[END_REF].

Table A1. New heterogeneous reactions added to the UKCA module together with the uptake coefficients.

to calculate the values of the uptake coefficients that are not constant and are denoted by f in Table A1.

A2 Bromocarbon emissions

The emission flux datasets of the five very short lived bromocarbon species (CH 3 Br, CH 2 BrCl, CH 2 Br 2 , CHBr 2 Cl, CHBrCl 2 ) are explicitly included as emission files. These are similar to the ones used in [START_REF] Yang | How sensitive is the recovery of stratospheric ozone to changes in concentrations of very short-lived bromocarbons?[END_REF], which are based on the original work (scenario 5) of [START_REF] Warwick | Global modeling of biogenic bromocarbons[END_REF], except for the emissions of CH 2 Br 2 . The emissions of CH 2 Br 2 were scaled to give a total emission of 57Gg yr -1 , corresponding to 50% of the original flux and in better agreement with [START_REF] Liang | Finding the missing stratospheric br y : a global modeling study of chbr 3 and ch 2 br 2[END_REF] and [START_REF] Ordóñez | Bromine and iodine chemistry in a global chemistry-climate model: description and evaluation of very short-lived oceanic sources[END_REF].

The combined effect of the bromocarbons is to provide ∼ 5pptv of inorganic bromine to the stratosphere [START_REF] Yang | How sensitive is the recovery of stratospheric ozone to changes in concentrations of very short-lived bromocarbons?[END_REF]

  Winton et al. (2019) carried out a comprehensive field and modelling study of the air-snow transfer of NO - 3 at the low snowfall accumulation site at Kohnnen Station in Dronning Maud Land (DML), East Antarctica as part of the ISOL-ICE (ISotopic constraints of past Ozone Layer in polar ICE) project. At the DML site, NO - 3 is recycled three times before it is archived in the snowpack below a depth of 15 cm and within 0.75 years. Sensitivity analysis with a 1D air-snow model, TRANSITS (TRansfer of Atmospheric Nitrate Stable Isotopes To the Snow) (Erbland et al., 2015), of δ 15 N(NO - 3 ) at DML showed that the dominant factors controlling the archived δ 15 N(NO - 3 ) signature are the snow accumulation rate and e-folding depth of the surface snowpack for incident UV, with a smaller role from changes in the snowfall timing and TCO. The Winton et al. (2019) study sets the framework for the interpretation of a δ 15 N(NO - 3 ) record from the new ISOL-ICE ice core drilled in January 2017 at Kohnen Station in Dronning Maud Land, hence-

  changes to the stratospheric chemistry are tested by running the model for 30 years in a year 2000 time slice experiment using CMIP6 prescribed trace gases and sea surface temperature forcings. The model is mostly able to reproduce the observed total column ozone and the results are similar to those found by Dennison et al. (2019) in which a more thorough discussion of the changes can be found. The improved match with observed TCO resulting from our model updates is shown in Figure 1(a). The spring ozone hole over Antarctica is deeper than the original model with total column ozone values reaching about 175 DU (65 to 90 • S average) in October compared to about 200 DU in the original model. These values are closer to those in the ozone values from the satellite ozone dataset from the National Institute of Water and Atmospheric Research -Bodeker Scientific (NIWA-BS) satellite dataset (version 3.4; see http://www.bodekerscientific

  then initialize four ensemble runs using the climate state taken from four different years of the spun up model state. The runs use the CMIP6 trace gas forcings from 1979 to 1994 with the eruption happening in 1991. Although the exact climate state at the time of the Pinatubo eruption is known from observations, the four ensemble runs are done so as to span over the variability arising from the QBO and ENSO. This allows the Pinatubo run to be compared to the pre-industrial volcanic runs in Section 3.1. The timing of historical volcanic eruptions is not well constrained and we do not know the phases of the QBO and ENSO in which the eruptions occurred. The ensemble is designed to average over this variability. We simulate the Pinatubo eruption as an emission of 10 Tg SO 2 and 0.02 Tg HCl on 1 June 1991 into the stratosphere as a single vertical plume between 19 and 24 km altitude (the neutral buoyancy height of the plume) at 15.1 • N and 120.2 • E.[START_REF] Mills | Global volcanic aerosol properties derived from emissions, 19902014, using cesm1(waccm)[END_REF] discuss the justification for various choices of modelling parameters for Pinatubo. The aim of this experiment is not to reproduce the observations after the Pinatubo eruption exactly but to check that, with the additional chemical reactions and emissions, our model is still able to simulate the broad pattern of the ozone response after a current day explosive volcano.

Figure 1 (Figure 1 .

 11 Figure 1(b) shows change in total column ozone from the Pinatubo eruption in the NIWA-Bodeker dataset as the difference between a 1991 to 1994 average and a clima-

  3 kyr from the 120 m ISOL-ICE ice core. The core was drilled in the clean air sector at Kohnen Station, DML on the high-elevation East Antarctic Plateau (2892 m above sea-level; 74.9961 • S, 0.094717 • E) in January 2017. A full description of the methods for the ISOL-ICE ice core can be found in Winton et al. (2019) and only a brief summary is given here. The core was analysed for i) continuous flow analysis (CFA) of nitrate (NO - 3 ), sodium (Na) and magnesium (Mg) mass concentrations and electrolytic meltwater conductivity at the British Antarctic Survey (BAS), Cambridge, and ii) discrete sections for the δ 15 N(NO - 3 ) composition at the Institute of Environmental Geosciences (IGE), University of Grenoble. Here we report the dated section of the ice core from 1227 to 1350 AD (69.8 to 79.4 m) covering the Samalas eruption in 1257. Dating was achieved by annual layer counting of measured concentrations of Na and Mg following previous studies at DML

  control run is 60 years long excluding 10 years of spin up which are discarded. The effect from explosive volcanoes on the stratosphere is investigated by running a series of four volcanic perturbation runs spun off from four different years of the control run to represent the variability arising from different ENSO and QBO states in a similar way to the Pinatubo case study in Section 2.2. The volcanic emissions are prescribed in a similar way to the Pinatubo eruption on 1 September of the first year of the run. Since historical volcanic eruptions are variable and HCl emissions are less well constrained, we develop a matrix of simulations that span the uncertainty in emissions. The six sets of experiments have one of low SO 2 (10 Tg) or high SO 2 (100 Tg) paired with no HCl, low HCl (0.02 Tg) and high HCl (2 Tg). Changes are plotted as the difference between the average of the four perturbation runs and a climatology derived from the control run.

Figure 2

 2 Figure 2 shows the change in total column ozone in the (a) low SO 2 + low HCl, (b) high SO 2 + no HCl, (c) high SO 2 + low HCl and (d) high SO 2 + high HCl cases.The low SO 2 + no HCl case and high SO 2 + no HCl cases are found to be qualitatively similar to two further experiments (not shown): the low SO 2 + low HCl and high SO 2 + low HCl cases, respectively. This is expected since the stratospheric chlorine loading is low (< 0.4 ppbv of HCl over the polar region averaged between 65 to 90 • S), as it is in a pre-industrial atmosphere. We do not observe large depletion of ozone depletion events by chlorine radicals during spring to form ozone holes.The low SO 2 + low HCl case in Figure2(a) represents the ozone response to a Pinatubolike explosive volcano in a pre-industrial atmosphere. It shows that the changes in TCO are small and dominated by internal variability in most regions. This should be contrasted with the Pinatubo case study shown previously in Figure1(c) where an eruption of an equivalent magnitude was able to cause significant ozone changes, including an ozone depletion of about 20 DU in the year following the eruption over Antarctica. In contrast, under scenarios of low or no HCl but when the SO 2 emitted is high(Figures 2(b) and

Figure 2 .

 2 Figure 2. Change in total column ozone (DU) for the pre-industrial volcanic perturbation experiments. The plots show the difference between the average of four ensemble members and a single climatology drawn from a 60 year run. The emission scenarios shown are (a) low SO2, low HCl case (b) high SO2, no HCl (c) high SO2, low HCl and (d) high SO2, high HCl. The red triangle denotes the location of the injection. Note the different colour scales.

  (d)), large, chemical ozone depletion occurs over the polar regions during spring time in the year two to four following the eruption. The initial, low latitude, response still appears to be dynamical but when the injected chlorine reaches polar regions (Figure 3(b)), catalytic destruction of ozone occurs in the polar vortex during spring. The mixing ratio of HCl reaches values of up to 4 ppbv and 1.3 ppbv at 20 km over the North and South poles respectively. These values are comparable to the present day (year 2000) values of the equivalent effective stratospheric chlorine of ∼ 3 ppbv. The high SO 2 and high HCl scenario is the one experiment where we observed prolonged ozone destruction occurring over a number of years over Antarctica with a maximum decrease in total column ozone of ∼ 90 DU in spring of the second year after the eruption. Over the North pole, stratospheric ozone is nearly completely removed in the spring for at least four years following the eruption. The results are sensitive to the date, location and height of the injection in the tropics. A discussion of the sensitivity of eruption source parameters on volcanic radiative forcing can be found in Marshall et al. (2019). In our experiment, the lower branch of the Brewer-Dobson circulation is stronger in the Northern Hemisphere in September and hence the injected chlorine is primarily advected to the North pole in the months following the eruption. It takes about 1.5 years for chlorine to be transported to the South pole. Our results are comparable to the experiments by Brenna et al. (2019) who impose a Central American explosive volcano in a chemistry climate model (CESM1) in which the effect of sulphuric acid aerosols are imposed as a modified El Chichòn surface area density forcing equivalent to 30 Mt SO 2 . The results from their experiment with 2.93 Mt Cl, 9.5 Mt Br at 14 • N, 89 • W with an injection height of 29.7 hPa on January 1 (their Figure 3(c)) are qualitative similar to our results in Figure 2(d).

Figure 3 .

 3 Figure 3. (a) Change in the mean residual vertical velocity averaged over one year after the eruption and 4 ensemble members for the high SO2 and no HCl case from the control run to show dynamical changes. The red triangles represent the location and vertical extent of the volcanic eruption. (b) Change in HCl volume mixing ratio (ppbv) at 20 km for the high SO2 and high HCl case from the control run to show chemical changes.

Figure 4 .

 4 Figure 4. 1227 to 1350 AD section of the ISOL-ICE ice core data from DML, Antarctica. Age is plotted along the bottom and the corresponding ice depth along the top. The vertical grey region marks the dates around the 1257 series of volcanoes. (a) Sulphate mass concentrations. (b) Electrolytic melt water conductivity. (c) Nitrate mass concentration (d) Isotopic ratio of 15 N/14N of NO - 3 (δ 15 N(NO - 3 )) given as δ-values. (e) Snow accumulation rate in (cm yr -1 water equivalent (w.e)). Note that the various quantities are available at different time resolutions depending on the analysis method used.

  (c)) whilst the high SO 2 (100 Tg) volcanoes (with no or low HCl) both produce increases in ozone over Antarctica that are short-lived, lasting about 1.5 years (Figure 2(b) and (c)). The pattern of ozone changes for the latter are primarily caused by transport changes arising from changes to the Brewer-Dobson circulation (Figure 3(a)). In contrast, when the amounts of SO 2 and HCl emitted are both high (high SO 2 , 100 Tg + high HCl, 2 Tg) and the HCl loading over the polar regions becomes comparable to present day stratospheric values, our model results show significant ozone depletion over both poles (Figure 2(d)) for at least four years following the eruption. Note that the chemical reactions that destroy ozone are only able to occur when HCl in the stratosphere reaches the polar regions and hence the timing of the springtime ozone depletion depends strongly on the date of the eruption. Since we model the eruption as occurring on 1 September, we find that it takes about 1 year for the injected HCl from the volcano to reach Antarctica (Figure 3(b)). Before the HCl reaches Antarctica, the increase in ozone over the Southern Hemisphere is caused by the same dynamical changes as in the low HCl model experiments.

Table A1

 A1

	Reaction		Uptake coefficient
		Ice	Nitric acid	Sulphate
			trihydrate	aerosol
	ClONO 2 + HCl → Cl 2 + HNO 3	0.3	0.3	f
	ClONO 2 + H 2 O → HOCl + HNO 3	0.3	0.006	f
	HOCl + HCl → Cl 2 + H 2 O	0.3	0.3	f
	N 2 O 5 + H 2 O → 2 HNO 3	0.03	0.006	0.1
	N 2 O 5 + HCl → ClNO 2 + HNO 3	0.03	0.006	0.02
	HOBr + HCl → BrCl + H 2 O	0.25	0.25	0.1
	BrONO 2 + HCl → BrCl + HNO 3	0.3	0.3	0.01
	BrONO 2 + H 2 O → HOBr + HNO 3	0.3	0.001	0.01
	HOBr + HBr → Br 2 + H 2 O	0.25	0.25	0.1
	HOCl + HBr → BrCl + H 2 O	0.25	0.25	0.02
	ClONO 2 + HBr → BrCl + HNO 3	0.56	0.56	0.02
	BrONO 2 + HBr → Br 2 + HNO 3	0.3	0.3	0.01
	N 2 O 5 + HBr → BrNO 2 + HNO 3	0.05	0.001	0.02

lists the new heterogeneous reactions added to the UKCA module together with the uptake coefficients on ice, nitric acid trihydrate and sulfate aerosol. This can be compared to Table

1

in

[START_REF] Dennison | Improvements to stratospheric chemistry scheme in the um-ukca (v10.7) model: solar cycle and heterogeneous reactions[END_REF]

. We use the method in

[START_REF] Shi | Kinetic model for reaction of clono2 with h2o and hcl and hocl with hcl in sulfuric acid solutions[END_REF]

Table B1 .

 B1 in a pre-industrial atmosphere. Volcano Eruption date Arrival date Peak Depth (m) Start Depth (m) Zielinski et al. (1994) b Langway Jr. et al. (1995) Volcanic horizons identified from the sulfate and electrical meltwater conductivity records. Eruption date of the volcano and arrival dates of the sulfate in the ice core are obtained from Zielinski et al. (1994) and Langway Jr. et al. (1995) except for the Unknown 1228/30 volcano where the precise eruption date is not known. We choose 1229 as the eruption and arrival date for dating purposes. IST grant ANR16-CE01-0011-01) and the INSU program LEFE-CHAT for supporting the stable isotope laboratory. This is a publication of the PANDA platform on which isotope analysis were performed. PANDA was partially funded by the LabEx OSUG@2020 (ANR10 LABX56). We would like to thank British Antarctic Survey (BAS) and Alfred Wegener Institute (AWI) staff for field and logistical support at Halley Station and Kohnen Station, respectively. Technical support for nitrate isotope analysis at the Institut des Géosciences de l'Environnement (IGE), Grenoble was provided by Pete Arkers. In addition, we thank Lisa Hauge, Emily Ludlow, Shaun Miller, Catriona Sinclair, Rebecca Tuckwell, Sarah Jackson, Julius Rix and Liz Thomas for technical support at BAS. We would like to thank Bodeker Scientific, funded by the New Zealand Deep South National Science Challenge, for providing the combined NIWA-BS total column ozone database. The ice-core data set is available through the Polar Data Centre (Winton et al., 2019). This work used Monsoon2, a collaborative High Performance Computing facility funded by the Met Office and the Natural Environment Research Council. This work also used JASMIN, the UK collaborative data analysis facility. The model data is archived on the MONSooN2 platform and available upon request. The importance of enso phase during volcanic eruptions for detection and pack nitrate related to post-depositional processes in eastern dronning maud land, east antarctica. GEOCHEMICAL JOURNAL, 52 (2), e7-e14. doi: 10.2343/geochemj.2.0519 O'Connor, F. M., Johnson, C. E., Morgenstern, O., Abraham, N. L., Braesicke,

	Kuwae a	1450	1454	61.01	61.13
	1285 b	1285	1285	75.12	75.22
	1277 b	1277	1277	75.77	75.9
	1269 b	1269	1269	76.41	77.46
	Samalas 1257 b	1257	1259	77.12	77.23
	Unknown 1228/30 b	1229	1229	79.33	79.43

a doi/abs/10.1029/JD095iD04p03493 doi: 10.1029/JD095iD04p03493 Lehner, F., Schurer, A. P., Hegerl, G. C., Deser, C., & Frölicher, T. L. (2016).

Acknowledgments

This project was funded by a National Environment Research Council (NERC) Standard Grant (NE/N011813/1) to MMF. VHLW would like to thank the University of Cambridge Doctoral Training Program (DTP) for funding a NERC Research Experience Project (REP) that contributed to this manuscript. JK received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 603557 (StratoClim). MD was supported by the Joint UK BEIS/Defra Met Office Hadley Centre Climate Programme (GA01101). AEJ was funded by the Natural Environment Research Council as part of British Antarctic Survey's programme "Polar Science for Planet Earth". JS and NC thank the ANR (Investissements d'avenir ANR-15-IDEX-02 and EAI-

Appendix B Ice core analysis

Table B1 shows the volcanic horizons identified from the sulfate and electrical meltwater conductivity records in the ISOL-ICE ice core.


Mohammad Alkhatib

Adel Hafiane

Pierre Vieyres

Alain Delbos

Deep visual nerve tracking in ultrasound images

Keywords: Nerve tracking, visual tracking, deep-learning, ultrasound images, regional anesthesia. I

Ultrasound-guided regional anesthesia (UGRA) becomes a standard procedure in surgical operations and pain management, offers the advantages of nerve localization, and provides region of interest anatomical structure visualization. Nerve tracking presents a crucial step for practicing UGRA and it is useful and important to develop a tool to facilitate this step. However, nerve tracking is a very challenging task that anesthetists can encounter due to the noise, artifacts, and nerve structure variability. Deep-learning has shown outstanding performances in computer vision task including tracking. Many deep-learning trackers have been proposed, where their performance depends on the application. While no deep-learning study exists for tracking the nerves in ultrasound images, this paper explores thirteen most recent deep-learning trackers for nerve tracking and presents a comparative study for the best deep-learning trackers on different types of nerves in ultrasound images. We evaluate the performance of the trackers in terms of accuracy, consistency, time complexity, and handling different nerve situations, such as disappearance and losing shape information. Through the experimentation, certain conclusions were noted on deep learning trackers performance. Overall, deep-learning trackers provide good performance and show a comparative performance for tracking different kinds of nerves in ultrasound images.

by these breakthroughs, several deep-learning based trackers have been developed in order to significantly improve the tracking performance. These works showed promising results for different tracking applications, such as [START_REF] Danelljan | Beyond correlation filters: Learning continuous convolution operators for visual tracking[END_REF]- [START_REF] Song | Crest: Convolutional residual learning for visual tracking[END_REF].

In the literature, few methods introduced tracking using deep-learning in US images. In [START_REF] Carneiro | Combining multiple dynamic models and deep learning architectures for tracking the left ventricle endocardium in ultrasound data[END_REF], the authors built a deep neural network observation distribution to track the left ventricle endocardium in US images. In [START_REF] Nascimento | Tracking and segmentation of the endocardium of the left ventricle in a 2d ultrasound using deep learning architectures and monte carlo sampling[END_REF], The authors used deep neural networks to build a new observation model in a particle filter to track and segment the left ventricle in US images. To the best of our knowledge, this is the first deeplearning study on nerve tracking in US images.

Here, we introduce a deep-learning approach to robustly track nerve structures in US images. We conducted a comparative study of thirteen deep trackers for two types of nerves, median and sciatic.

The major contributions of this paper can be summarized as follows:

• Tracking of nerve structure in ultrasound images.

• Comparative study of recent deep-learning tracking techniques.

• Addressing new medical applications (Regional anesthesia). The structure of our paper is as follow. Section. II details the deep-learning trackers. Followed by experimental results and discussion in Section. III. The paper ends with final conclusions in Section. IV.

II. DEEP VISUAL TRACKERS

This paper aims to track nerves in US images using deeplearning methods, and as such these methods should be robust enough to track different nerve situations. The visual tracker starts by generating the target model in the first frame, then extracts features in the next frame to find the candidate models, and find the best match between target and candidates models. Most existing deep trackers use CNN either to generate appearance models, to match object model with its candidates, or to distinguish the object from the surrounding areas. Therefore in the following, 13 deep-learning tracking methods are discussed where CNN is used.

A. Continuous convolution operators tracker

Continuous Convolution Operators Tracker (C-COT) [START_REF] Danelljan | Beyond correlation filters: Learning continuous convolution operators for visual tracking[END_REF] employed a new technique that solves the learning problem by using an interpolation model which enables the integration of multi-resolution feature maps. This model takes the advantages of performing the convolution in the continuous spatial domain to obtain high results in the visual tracking problem. To reach precise sub-pixel localization, C-COT obtains the predicted score as a continuous function. Furthermore, C-COT's multiresolution feature maps facilitate each visual feature to choose the region-size independently.

C-COT integrates the feature map x to the continuous spatial domain t ∈ [0, T ) by introducing an interpolation model J d for each feature channel d

J d x d (t) = N d -1 n=0 x d [n]b d t - T N d n (1)
where x d represents visual features, N d is each feature resolution, and b d is an interpolation kernel.

To predict the matching scores of the target image region, the convolution operator S f {x} is parametrized by a set of continuous T -periodic multi-channel convolution filters f ,

S f {x} (t) = f * J {x} = D d=1 f d * J d x d ( 2
)
where D is the number of domain dimensions, and the filters are learned by minimizing the following,

E (f ) = M j=1 α j S f {x j } -y i 2 L 2 + D d=1 wf d 2 L 2 (3)
where M is the number of training samples, α j is the weight of sample x j , y i is the labeled detection scores of x j sample and represented by periodically repeated Gaussian function, w parameter is used to reduce the effect of periodic assumption, and the L 2 -norm is weighted classification error.

B. Efficient convolution operators

Efficient convolution operators (ECO) [START_REF] Danelljan | Eco: Efficient convolution operators for tracking[END_REF] is based on C-COT and aims to reduce the C-COT model size, the training set size, and excessiveness and sensitivity of the model update. In other words, ECO aims to reduce the redundancy in the sample set of C-COT.

Unlike C-COT which learns one separate filter for each feature channel, ECO provides a smaller set c of filters by using a factorized convolution operator P . Therefore, ECO replaces Eq. 2 by,

S P f {x} (t) = P f * J {x} = c,d P d,c f c * J d x d = f * P T J {x} (4)
C-COT collect new samples in each frame, which leads to sampling set redundancy. For that, while preserving the samples diversity, ECO reduces their number in the learning phase by a generative model of the training sample space. The generative model finds the filter that minimizes the expected correlation error,

E (f ) = E S f {x} -y 2 L 2 + D d=1 wf d 2 L 2 (5)
The model strategy in C-COT is updated in each frame which leads to slow tracking procedure. ECO uses a sparse updating scheme to reach more fast and robust tracking. This scheme is concluded by updating the model once a sufficient change happens.

C. Convolutional network based tracker

Convolutional Network based Tracker (CNT) [START_REF] Zhang | Robust visual tracking via convolutional networks without training[END_REF] considered a simple two-layer convolutional network that developed a robust sparse representation for visual tracking. CNT uses CNN network to extract mid-level features from the image. These features are then distinguished into positive and negative ones by learning a classifier. Using a k-means algorithm, CNT initializes fixed filters by extracting a set of normalized patches from the target region. Around the target region, these filters define a set of feature maps which encode target local structural information. These feature maps construct the first layer, while the second layer consists of the encoded target local structural information. To adapt to target appearance variations, an online strategy is employed to update the model. The online strategy is a sparse representation which adapts a simple temporal low-pass filtering method,

c t = (1 -ρ)c t-1 + ρĉ t-1 (6)
where c t is the target template at frame t, ρ is a learning parameter, and ĉt-1 is the sparse representation of the tracked target at frame t -1.

D. Multi-domain convolutional neural networks

Multi-Domain convolutional neural Networks (MDNet) [START_REF] Nam | Learning multi-domain convolutional neural networks for visual tracking[END_REF] has five hidden layers which consist of shared layers and multiple branches of domain-specific layers. These Domains correspond to individual training sequences and each branch is representing binary classification to identify the target in each domain. MDNet has K branches in the last fully connected layers, where each K branch contains a binary classification layer. These binary classification layers are to distinguish the target and the background in each domain. Using a large set of videos with tracking ground-truths, MDNet trains each domain to construct a target representation.

MDNet trained CNN using the Stochastic Gradient Descent (SGD) method, wherein each iteration of each domain is handled separately. MDNet tracks the target by evaluating the randomly sampled candidate windows around the target region in the previous frame. While tracking, MDNet incorporates the shared layers in the pre-trained CNN with a new binary classification layer to develop a new network. In order to update the network, MDNet applies short-term and long-term update strategies. Furthermore, MDNet adapts bounding box regression technique for more precise target localization.

E. Structure-aware network

In general, Structure-Aware Network (SANet) [START_REF] Fan | Sanet: Structure-aware network for visual tracking[END_REF] follows the same strategy as MDNet but with an additional recurrent neural network (RNN) based structure for improving object representation. Fig. 1 shows the structure of SANet and how RNNs is utilized. Using multiple RNNs, SANet models object structure during learning then combines it into CNN. SANet consists of two fully connected layers and one fully connected classification layer which concatenated with the recurrent layers using a skip concatenation strategy. For training, target tracking, model update, and target localization, SANet adapts the same strategies as MDNet.

F. Fully-Convolutional Siamese Networks

Fully-Convolutional Siamese Networks (SiameFC) [START_REF] Bertinetto | Fully-convolutional siamese networks for object tracking[END_REF] utilize a sliding-window evaluation by using a bilinear layer that computes the cross-correlation of its two inputs. SiameFC starts by initializing the interested object location (x ) in the first frame and the search area in the next frame (z ). A convolutional embedding CNN function (f ρ ), with learnable parameter ρ, is used to represent each feature map for the inputs. To find the similarity between these inputs, SiameFC computes the cross-correlation between the two feature maps f ρ (x ) and f ρ (z ) using,

g ρ (x , z ) = f ρ (x ) f ρ (z ) (7)
where ρ is a learnable parameter. The goal of Eq. 7 is to find the best value between the two input feature maps. And to achieve this goal, SiameFC offline trains the network with a huge number of random targets taken from a large database of videos. A spatial map of labels c i is assembled for each sample. The training is performed by minimizing an element-wise logistic loss over the training set,

arg min ρ i (g ρ (x i , z i ), c i ) (8)
The tracking process is performed by comparing the target object with the candidate's locations. These candidates are located in the search region which is centered in the same previous target location center but four-times bigger in size. The new target location is found by taking the candidate with the highest similarity score.

G. Correlation filter network

Correlation Filter Network (CFNet) [START_REF] Valmadre | End-to-end representation learning for correlation filter based tracking[END_REF] based on Siamese networks by modifying the correlation filter learner as a differentiable layer in the deep neural network. The correlation filter block between the interested object location x and the cross-correlation operator is set as,

h ρ,s,b (x , z ) = s w(f ρ (x )) f ρ (z ) + b (9)
where the scalar parameters s and b ,the scale and the bias respectively, are used to make the score range suitable for logistic regression. z is the search areas in the next frame. f ρ is a convolutional embedding CNN function. Also, w is the standard convolution filter template computed by the convention filter block from the training feature map x = f ρ (x ).

H. Discriminant correlation filters network

Discriminant Correlation Filters Network (DCFNet) [START_REF] Wang | Dcfnet: Discriminant correlation filters network for visual tracking[END_REF] is based on Siamese network and aimed to do simultaneously convolutional features learning and correlation tracking. DCFNet added a correlation layer for backpropagation to Siamese network using an object location probability heat map.

The discriminant correlation filter w can be obtained by,

ŵl = φl (x) ŷ * D k=1 φl (x) ( φl (x)) * + λ (10)
where ŵl presents filter w of channel l, ϕ ∈ R M ×N ×D is the target patch features, y ∈ R M ×N is the ideal reaponse, λ is the regularization coefficient constant, the (ˆ) represents discrete Fourier transform F, ( * ) is the complex conjugate of a complex number y, and refers to Hadamard (element-wise) product.

In the new frame, DCFNet detection process starts by cropping a search window and finding the features inside it. Then DCFNet estimates target translation by using correlation response map maximum value,

g = F -1 D l=1 ŵl * φl (z) (11)
DCFNet uses incremental filter update which regards it as an RNN network. DCFNet incrementally updates the filter over time t during the online tracking which gives the advantages of maintaining only a small sample set. Filter update can be found using,

ŵl p = p t=1 βŷ * φl (x t ) p t=1 β t D k=1 φk (x t ) ( φk (x t )) * + λ ( 12
)
where β t is the impact of sample x t .

I. Multi-task correlation particle filter

Multi-task Correlation Particle Filter (MCPF) [START_REF] Zhang | Multi-task correlation particle filter for robust object tracking[END_REF] takes the benefits of controlling the particle sampling in particle filter using a multi-task correlation filter. The learning process of the correlation filter leads to using fewer particles which decreases the computation cost. MCPF learns the correlation filter jointly by including different feature inter-dependencies.

Multi-task correlation filter (MCF) learned z k to differentiate discriminative training samples x k of target from the background, where K is the features (CNN or HOG). To find the features with similar z k which are more stable, MCF applies circular shifts to z k , where all possible circular shifts of an image patch of M × N pixels are x m,n ∈ {0, 1, ..., M -1} × {0, 1, ..., N -1} which represent the possible locations of the target object. After that, MCF learns the correlation filters for z k using,

min {z k } K k=1 k 1 4λ z k G k z k + 1 4 z k z k -z k y + γ Z 2,1 (13)
where

Z = [z 1 , z 2 , ..., z K ] is obtained by gathering learned z k of K different features, λ is a regularization parameter, G k is equal to X k X K , X k
donates all training samples with Gaussian function label y, γ is a tradeoff parameter between reliable reconstruction and joint sparsity regularization. Finally, to find multi-task correlation filter z k for each type of feature, Eq. 13 is solved using the Accelerated Proximal Gradient method.

MCPF first step consists of generating the particle, followed by predicting the particle location using the probabilistic framework. After that, MCF is applied to each particle with the aim of shifting the particles to a stable location using its circular shifts. Then MCPF updates the weights using the response map,

r = k F -1 F(z k ) F y i t , x (14)
where z k is the learned MCF, x is the target appearance model, y i t is the observation of particle i at time t, donates Hadamard (element-wise) product, and F and F -1 are the Fourier transform and its inverse, respectively.

The optimal state can be formulated as,

E [s t | y 1:t ] ≈ n i=1 w i t S mcf s i t ( 15
)
where each particle s i t is shifted S mcf s i t , and w i t is particle weights and is proportional to the response of the MCF.

MFCF updates MCF using an incremental strategy which only utilizes current frame new samples x k ,

F (x k ) t = (1 -η) F ( xk ) t-1 + ηF (x k ) t F (z k ) t = (1 -η) F (z k ) t-1 + ηF (z k ) t (16)

J. Hedged deep tracking

Hedged Deep Tracking (HDT) [START_REF] Qi | Hedged deep tracking[END_REF] is based on adaptive hedge method which solves the online learning problems in a multi-expert multi-round setting. HDT takes the advantages of VGG-Net [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF] deep architecture to extract feature maps of convolutional layers from image regions. To generate response maps, each feature map is convolved by correlation filters to generate a weak tracker (expert). HDT hedges these trackers into a stronger one using an online decision-theoretical Hedge algorithm as shown in Fig. 2. At time t, the target position (x * t ,y * t ) can be found by the position with the best response,

(x * t , y * t ) = K k=1 w k t . x k t , y k t ( 17
)
where w k t is the weight at time t for expert k. w k t uses new samples X k in the current frame to update the previous models which reflect each expert's decision loss,

Z k * , * ,d = Y X k . X k + λ X k * , * ,d W k t = (1 -η)W k t-1 + ηZ k t ( 18
)
where W k t is the k-th filter which modeled in the Fourier domain, X represents the new samples in the current frame k-th convolutional layer, Y is a 2D Gaussian distribution with zero mean and standard deviation proportional to the target size, denotes the Hadamard (element-wise) product, λ is a tradeoff parameter, and η is the learning rate.

K. Hierarchical convolutional features tracker

Hierarchical Convolutional Features Tracker (HCFT) [START_REF] Ma | Hierarchical convolutional features for visual tracking[END_REF] utilizes large-scale datasets to learn rich feature hierarchies of CNNs. HCFT is robust to appearance variations due to keeping target objects semantics in the last convolutional layers. Target appearance is encoded using a correlation filter on each convolutional layer. HCFT uses the hierarchies of convolutional layers to find the maximum responses that locate the target.

HCFT employs VGG-Net [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF] Convolutional feature maps to encode target appearance. Followed by finding the maximum response using correlation filters in the frequency domain,

W d = Y Xd D i=1 X i Xi + λ ( 19
)
where D is the number of channels, Y is a Fourier transform of a Gaussian function y, X is the feature vector of the d channel, the bar refers to the complex conjugation, is Hadamard (element-wise) product, and λ is a regularization parameter.

HCFT finds the response map in the new frame by providing the feature vector ‡ ( Z using Fourier transform) on the l -th layer of a patch,

f l = F -1 D d=1 W d Zd (20)
The new target location is set to the patch with the maximum response. HCFT update the model using moving average technique for the numerator A d and denominator B d of the correlation filter W d ,

A d t = (1 -η)A d t-1 + ηY Xd t , B d t = (1 -η)B d t-1 + η D i=1 X i t Xi t , W d t = A d t B d t +λ ( 21
)
where t is the frame index and η is a learning rate.

L. Convolutional residual tracker

Convolutional RESidual Tracker (CREST) [START_REF] Song | Crest: Convolutional residual learning for visual tracking[END_REF] uses end-toend training and reformulates Discriminant Correlation Filters (DCFs) as a one-layer convolutional neural network. The residual learning process is adopted to reduce model degradation and to be more invariant to appearance changes.

DCF learns a filter W by solving the minimization problem arg min

W W * X -Y 2 + λ W 2 ( 22
)
where X is the input sample, Y is its corresponding Gaussian function label, and λ is the regularization parameter.

CREST initializes the model by extracting features, mapping the response, and setting the distribution parameters in the base and residual layers. For the new frame, CREST generates the response map and sets the new target location to the patch with the maximum response. CREST handles scale changes by extracting different scale patches around target new location center. These patches are sent to the response map and the patch with the maximum response sets to be the target new scale.

CREST initializes a ground-truth response map in each frame and the search patch is adopted as a training patch. These ground-truth maps and the training patch update online the network.

M. Deep-learning tracker

Deep-Learning Tracker (DLT) [START_REF] Wang | Learning a deep compact image representation for visual tracking[END_REF] adopts the neural networks outputs as object features to localize the target object. DLT learns generic image features using stacked de-noising autoencoder (SDAE). Followed by transferring the offline training to online tracking. Using continuously tuned classification neural networks and feature extractor, DLT adapted to target object appearance changes.

DLT starts by collecting features from the target and its surrounding areas, then pass it to SDAE for offline training. For the new frame, DLT adopts particle filter technique by spreading particles around the previous target location. Using the network, a confident map is determined for each particle and the new location sets to the particle with the highest confidence. If all particles have the same confidence, this concludes an appearance change of the target and the network should be tuned again.

III. EXPERIMENTS ,RESULTS AND DISCUSSION

In UGRA, the anesthetist starts by using the US probe to scan a part of the body back and forth in order to locate and track the nerve. This step is important to stabilize the probe in a good position to visualize the nerve and insert the needle.

In this paper, we conduct the experiment on two different nerves which have different characteristics, median and sciatic. The median nerve is one of the major nerves in the arm, it starts from the brachial plexus to innervate the intrinsic muscles of the hand. The sciatic nerve is located in the leg, more specifically in the popliteal fossa. The median nerve presents a circular, oval or elliptic shape, whereas the sciatic nerve sometimes presents an irregular shape which makes it harder to visualize and to track [START_REF] Heinemeyer | Ultrasound of radial, ulnar, median, and sciatic nerves in healthy subjects and patients with hereditary motor and sensory neuropathies[END_REF].

This study shows the feasibility of nerve tracking in US images using deep-learning approaches. This experiment provides a performance comparison and evaluation of deeplearning approaches for nerve tracking in ultrasound images. Each method is analyzed in term of accuracy, consistency, time cost, and handling different nerve situations. In this section, we first describe the used dataset and setup, then analyze and discuss results and performances.

A. Dataset and Setup

Experiments were conducted on sonographic videos of the median and sciatic nerves obtained from 42 anonymous adult patients using an ultrasound machine with an MHz transducer frequency (one video per patient). A total number of 10337 ultrasound images of the nerve were used, which include 25 videos of median nerves with an average of 335 image per video, and 17 videos of sciatic nerves with an average of 120 image per video. The dataset is ethically approved, and it was acquired in real conditions at the Medipole Garonne hospital in Toulouse (France). The ground-truth was provided by two regional anesthesia experts.

It is well known that the visual properties of US images are degraded by many effects such as artifacts, signal degradation, The experiments were carried out with a core 7 Duo 3.50 GHz processor with 32GB RAM under Matlab. In this experiment, we conduct a comprehensive experimental evaluation of 13 deep visual trackers introduced in Section. II and one visual tracker for nerve tracking from [START_REF] Alkhatib | Adaptive median binary patterns for fully automatic nerves tracking in ultrasound images[END_REF]. In [START_REF] Alkhatib | Adaptive median binary patterns for fully automatic nerves tracking in ultrasound images[END_REF], the authors tracked the median nerve using hand crafted features, where AMBP texture descriptor with Particle filter showed the best results. In this paper, AMBP-PF is tested, as the best method obtained in [START_REF] Alkhatib | Adaptive median binary patterns for fully automatic nerves tracking in ultrasound images[END_REF], to provide a comparative study between hand crafted features and deep-learning features. The 13 deep visual trackers have achieved top performance on OTB-100 [START_REF] Wu | Object tracking benchmark[END_REF], TC-128 [START_REF] Liang | Encoding color information for visual tracking: Algorithms and benchmark[END_REF] and VOT2015 [START_REF] Kristan | The visual object tracking vot2015 challenge results[END_REF] datasets. For evaluating each method, the same parameters provided by the original papers were used along with the source codes that have been made available by the original authors. In this experiment, VGG-Net [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF], very deep convolutional networks (up to 19 layers) are adopted for feature extraction. Overall, this experiment shows the benefits of exploiting deep-learning visual tracking in US images.

B. Results

For more accurate and extensive results, two evaluation procedures are performed in this experiment. The first accuracy evaluation is assessed by the bounding box overlap ratio between the estimated nerve position and the ground-truth. The overlap ratio is based on pixels percentage in the intersection area. The second evaluation methodology is precision and success plots [START_REF] Wu | Object tracking benchmark[END_REF]. The trackers are ranked in terms of Distance Precision (DP) and Area Under the Curve (AUC), respectively. The precision plot represents the percentage that the center location error is below a predefined threshold (20 pixels in this experiment), where the center location error uses the average Euclidean distance between target estimated center and ground-truth center. The success plot shows if the target is being tracked successfully by finding if the overlap score between the estimated bounding box and the ground-truth is larger than a predefined threshold (0.5 in this experiment). Fig. 3 illustrates the tracking methods accuracy for median nerve, where ECO, C-COT, and SANet achieved the best results, while other methods suffer from less stability and less performance accuracy. Also, it can be seen that CREST gave good results but with less stability. On the other hand, compared to a median nerve, a sciatic nerve is harder to track due to its location, shape, and appearance which is almost the same as the surrounding areas in certain frames. In Fig. 5, ECO provided the best performance and it can be seen that HDT and MCPF gave a good performance but with less stability. Fig. 4 shows qualitative results of tracking median and sciatic nerves using ECO method. As we have previously stated, Fig. 4 provides the ground-truth.

Fig. 6 reports the precision plot and the success plot over the median and sciatic nerves videos, where it illustrates a comparison of all deep trackers. DP and AUC scores for each tracker are shown in the figure legend. For the median nerve and among the compared methods, ECO tracker provides the best results with DP and AUC scores of 95% and 75%. SANet tracker achieves the second best results in both DP and AUC scores. For sciatic nerve, ECO and HDT trackers reach more than 72% for DP score and more than 61% for AUC score. Overall, it can be noticed ECO tracker outperforms other trackers and achieves the best results in both precision and success plots.

C. Discussion

In this paper, we addressed a challenging problem in UGRA which is nerve tracking. To deal with this problem several CNN-based methods have been introduced. Tab. I depicts tracking methods performance for median and sciatic nerves. For the median nerve, using ECO provides the best results, where these results are obtained due to transferring prior visual via pre-training and capturing any appearance changes via online learning. C-COT adopts the same maneuver as ECO, but ECO provides a better generalization of the target by avoiding the over-fitting. Other good trackers for median nerve are SANet and MDNet which achieved a good score caused by using a particle filter framework in its design. As well as this, SANet incorporates with an RNN scheme which leads to an increase in the tracking accuracy. For the sciatic nerve, using ECO or HDT achieves the best results, where the HDT results are obtained as a result of its hedging properties. CNT tracker uses one convolutional layer, while others use deeper convolutional layers such as ECO and HCFT. In this experiment, it was observed that using more deep layers results in a better performance and improves the tracking accuracy.

For the median nerve and comparing between CNN-based deep trackers and traditional (hand crafted features) trackers such as particle filter (PF) with Adaptive Median Binary Pattern (AMBP) features [START_REF] Alkhatib | Adaptive median binary patterns for fully automatic nerves tracking in ultrasound images[END_REF], PF-AMBP achieves good results and outperforms few deep-learning trackers. While for the sciatic nerve, the CNN-based deep tracking algorithms achieved a better performance than the traditional trackers in terms of accuracy and stability thanks to deep features strong representation. Finally, it can be observed that ECO tracker provides the best results among CNN-based deep trackers for both median and sciatic nerve tracking and gives the best stable results. Overall, the accuracy of CNN-based deep trackers is competitive and provides good performance for tracking the median and sciatic nerves.

Time complexity is considered a crucial point and an important aspect for visual tracking, especially in medical applications. The used dataset was recorded at 20 f rames/s. Tab. II demonstrates the running time for each method where it shows that DCFNet provides the best processing time. While ECO is slow, C-COT, SANet, and HDT are much slower. 0.13 0.14 CN T [START_REF] Zhang | Robust visual tracking via convolutional networks without training[END_REF] 0.63 0.65 M DN et [START_REF] Nam | Learning multi-domain convolutional neural networks for visual tracking[END_REF] 1.00 1.20 SAN et [START_REF] Fan | Sanet: Structure-aware network for visual tracking[END_REF] 1.63 1.74 SiameF C [START_REF] Bertinetto | Fully-convolutional siamese networks for object tracking[END_REF] 0.26 0.31 CF N et [START_REF] Valmadre | End-to-end representation learning for correlation filter based tracking[END_REF] 0.45 0.49 DCF N et [START_REF] Wang | Dcfnet: Discriminant correlation filters network for visual tracking[END_REF] 0.04 0.05 M CP F [START_REF] Zhang | Multi-task correlation particle filter for robust object tracking[END_REF] 0.60 0.66 HDT [START_REF] Qi | Hedged deep tracking[END_REF] 0.89 1.30 HCF T [START_REF] Ma | Hierarchical convolutional features for visual tracking[END_REF] 0.27 0.31 CREST [START_REF] Song | Crest: Convolutional residual learning for visual tracking[END_REF] 0.9 1.5 DLT [START_REF] Wang | Learning a deep compact image representation for visual tracking[END_REF] 0.33 0.42 P F -AM BP [START_REF] Alkhatib | Adaptive median binary patterns for fully automatic nerves tracking in ultrasound images[END_REF] 0.59 0.63 Important aspects affect the running time for CNN-based deep tracking algorithms, which are the number of layers and model update strategy. Some trackers use more deep layers while others use fewer layers which makes the tracker run faster. The other important aspect is the tracker model update strategy, where it can be noticed that updating the model after each frame is time-consuming. For that, ECO updates its model every few frames which make the process run faster. Another strategy to update the model is using Siamese network to model prior information that accelerates the running process such as CFNet, DCFNet, and SiameseFCs. While ECO is not the fastest method but, at the same time, it provides a good trade-off between tracking accuracy and time complexity.

The experiments faced some challenges when the nerve disappeared or appeared to be almost as identical as the surrounding areas. Losing the nerve and failing to re-track it leads to tracking failure, which makes this challenge significant. The MCPF tracker uses particle filter principle which gives it the ability to re-track the nerve in case of disappearance. Other trackers expand their localization to re-track the nerve once its appears again such as ECO and DCFNet. On the other hand, CREST tracker failed to re-track the nerve rapidly after it appeared again. Fig. 7 shows an example of how MCPF succeeds in tracking the nerve even when the nerve almost disappeared.

IV. CONCLUSION

Accurate and consistent nerve tracking is essential for safe and efficient Ultrasound-Guided Regional Anesthesia operation. In this paper, we perform nerve tracking in ultrasound images using deep-learning techniques. Recent deep-learning trackers are introduced to track nerve regions in ultrasound images. Different procedures were used to evaluate and compare the deep-learning trackers to demonstrate the effectiveness, robustness, and speed of the deep trackers. In this study, nerve tracking was performed directly on the original environment ultrasound images without any prior image enhancements which makes it a very challenging task. Our findings show that ECO, SANet, and C-COT outperform other techniques for tracking the median nerve, and ECO, HDT, and MCPF for tracking the sciatic nerve. Overall, deep-learning trackers showed good performance and handled noise suppression without pre-filtering the images. In future work, tracking techniques will be assessed on other types of nerves in order to improve the performance.

Fig. 1 :

 1 Fig. 1: Illustration of SANet tracker [35].

Fig. 2 :

 2 Fig. 2: Illustration of HDT tracker [40].

Fig. 3 :

 3 Fig. 3: The performance of deep-learning trackers for the median nerve, where accuracy and stability are shown.

M edian 10 Fig. 4 :Fig. 5 :

 1045 Fig.4: Nerve tracking using ECO tracker on median nerve and sciatic nerve (red rectangle for ECO method and a green rectangle for the ground-truth).

Fig. 6 :

 6 Fig. 6: Precision plot and success plot over 42 US videos on 14 tested trackers.

Fig. 7 :

 7 Fig. 7: Nerve tracking using MCPF tracker. Although the existence of nerve disappearance, the tracker succeeded to predict the nerve location (red rectangle for MCPF tracker and a green rectangle for the ground-truth).

TABLE I

 I

	: Tracking scores (%) comparison between the pro-
	posed tracking methods
		N erves
	Method	M edian Sciatic Overall
	C -COT [31]	0.94	0.73	0.84
	ECO [32]	0.94	0.80	0.87
	CN T [33]	0.79	0.73	0.76
	M DN et [34]	0.93	0.73	0.82
	SAN et [35]	0.94	0.76	0.85
	SiameF C [36]	0.82	0.74	0.78
	CF N et [37]	0.85	0.77	0.81
	DCF N et [38]	0.86	0.73	0.79
	M CP F [39]	0.89	0.79	0.84
	HDT [40]	0.87	0.80	0.83
	HCF T [41]	0.85	0.78	0.82
	CREST [42]	0.92	0.73	0.83
	DLT [5]	0.86	0.75	0.80
	P F -AM BP [25]	0.87	0.71	0.82

TABLE II :

 II Tracking Speed (spf ) between the proposed tracking methods

		N erves
	Method	M edian Sciatic
	C -COT [31]	0.65	0.67
	ECO [32]

ACKNOWLEDGEMENTS

This work is part of the DANIEAL 2 project supported by Centre Val de Loire Region (France) grant 2016 -00108375. We would like to thank Region Centre Val de Loire for supporting the work.