Ian A Bouyoucos
email: ian.bouyoucos@my.jcu.edu.au

José E Trujillo

Ornella C Weideli

Nao Nakamura

Johann Mourier

Serge Planes

Colin A Simpfendorfer

Jodie L Rummer

Investigating links between thermal tolerance and oxygen supply capacity in shark neonates from a hyperoxic tropical environment

Keywords: Critical thermal maximum, haematocrit, haemoglobin, oxygen supply capacity, pcrit, reef sharks

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

Introduction

The way in which temperature affects physiological performance of ectotherms is linked to species' biogeography and the potential for local extirpations under climate change [START_REF] Pörtner | Oxygen-and capacity-limited thermal tolerance: bridging ecology and physiology[END_REF][START_REF] Sunday | Thermal tolerance and the global redistribution of animals[END_REF]. In response to temperature variation, species can physiologically acclimate to maintain performance of Darwinian fitness traits and behaviourally select favourable temperatures for performance [START_REF] Angilletta | Coadaptation: A unifying principle in evolutionary thermal biology[END_REF]. These physiological and behavioural strategies serve to establish a 'thermal safety margin' (TSM), which defines the difference between an organism' body temperature and its thermal tolerance limits [START_REF] Sunday | Thermal-safety margins and the necessity of thermoregulatory behavior across latitude and elevation[END_REF]. Thermal safety margins decrease with increasing temperature, and tropical ectotherms appear to have the smallest TSMs [START_REF] Payne | An alternative explanation for global trends in thermal tolerance[END_REF][START_REF] Sunday | Thermal tolerance patterns across latitude and elevation[END_REF]. Climate change is increasing air and sea surface temperatures and the frequency and duration of heatwaves globally [START_REF] Bindoff | Changing ocean, marine ecosystems, and dependent communities[END_REF]. As such, global warming puts tropical ectotherms at a greater risk of shifts in distribution patterns or even mortality relative to temperate species [START_REF] Pinsky | Greater vulnerability to warming of marine versus terrestrial ectotherms[END_REF]. Because the capacity to tolerate high temperatures is an important fitness-related trait, thermal tolerance has been extensively investigated in laboratory studies.

Thermal tolerance can be quantified by measuring the critical thermal maximum (CTMax) metric, which defines the upper temperature where an organism loses motor control following acute exposure (Lutterschmidt and Hutchison, 1997a;[START_REF] Macmillan | Dissecting cause from consequence: a systematic approach to thermal limits[END_REF]. Much of what is known about CTMax in ectotherms comes from studies on fishes [START_REF] Beitinger | Quantification of the role of acclimation temperature in temperature tolerance of fishes[END_REF]Lutterschmidt and Hutchison, 1997a). While not a lethal endpoint, CTMax is essentially 'ecological death', meaning that the organism would no longer be able to serve a functional ecological role in its environment, and survival is limited.

Beyond laboratory approaches, CTMax can be estimated from species' geographic ranges, where the warmest summer temperatures encountered at the equatorial extent are considered proxies for CTMax [START_REF] Sunday | Thermal tolerance patterns across latitude and elevation[END_REF]; although, this approach has highlighted that laboratory estimates are not always representative of in situ limits [START_REF] Payne | Temperature dependence of fish performance in the wild: links with species biogeography and physiological thermal tolerance[END_REF].

Oxygen availability is another important environmental factor that limits the distribution of waterbreathing ectotherms. In water, oxygen concentrations are already quite low (i.e., ~30% lower in water compared to air). Hypoxia (i.e., low oxygen availability) is a widespread phenomenon in the oceans, such as oxygen minimum zones in the deep-sea [START_REF] Seibel | Critical oxygen levels and metabolic suppression in oceanic oxygen minimum zones[END_REF], and limits the distribution of water-breathers.

Climate change is further reducing oxygen availability in aquatic ecosystems, partially because of global warming [START_REF] Breitburg | Declining oxygen in the global ocean and coastal waters[END_REF], and this could further affect species' distributions and survival [START_REF] Wishner | Ocean deoxygenation and zooplankton: Very small oxygen differences matter[END_REF]. However, the oxygen availability that constitutes hypoxia differs between species and is related to the sensitivity of an organism's physiological systems to changes in environmental oxygen. For instance, an often-cited hypoxia threshold of 2 mg O2 L -1 would be fatal for the sandbar shark (Carcharhinus plumbeus; [START_REF] Crear | The impacts of warming and hypoxia on the performance of an obligate ram ventilator[END_REF], but not the clearnose skate (Rostaraja eglanteria; Schwieterman et al., 2019b). Thus, defining hypoxia tolerance is also key in predicting the effects of climate change on water-breathers.

A common measure of hypoxia tolerance, the critical oxygen tension (pcrit), defines the oxygen partial pressure (pO2) below which metabolic rate declines with environmental pO2 [START_REF] Ultsch | The utility and determination of Pcrit in fishes[END_REF][START_REF] Wood | The fallacy of the Pcrit -are there more useful alternatives?[END_REF]. Typically, pcrit is measured when an organism has achieved its standard metabolic rate [START_REF] Rogers | A new analysis of hypoxia tolerance in fishes using a database of critical oxygen level (Pcrit)[END_REF], which represents the metabolic rate of a postprandial organism at rest and at a stable temperature [START_REF] Chabot | The determination of standard metabolic rate in fishes[END_REF]. However, it has recently been suggested that pcrit is not an ecologically relevant measure of hypoxia tolerance [START_REF] Wood | The fallacy of the Pcrit -are there more useful alternatives?[END_REF] and simply represents a rate-specific measure of oxygen supply capacity [START_REF] Seibel | Oxygen supply capacity in animals evolves to meet maximum demand at the current oxygen partial pressure regardless of size or temperature[END_REF]. Thus, when environmental oxygen reaches pcrit for a given metabolic rate, an organism's physiological oxygen supply capacity (α = metabolic rate • pcrit -1 ) is being fully utilised [START_REF] Seibel | Oxygen supply capacity in animals evolves to meet maximum demand at the current oxygen partial pressure regardless of size or temperature[END_REF]. As such, it has been suggested that the oxygen level at which maximum metabolic rate (MMR) is reduced (i.e., pcrit-max) is a more ecologically relevant index of hypoxia tolerance [START_REF] Seibel | Oxygen supply capacity in animals evolves to meet maximum demand at the current oxygen partial pressure regardless of size or temperature[END_REF].

Temperature and oxygen act together on the physiology of marine ectotherms to set biogeographic range limits. This phenomenon reflects the temperature dependence of an organism's hypoxia tolerance [START_REF] Deutsch | Metabolic trait diversity shapes marine biogeography[END_REF]. Conversely, the oxygen dependence of thermal tolerance is less clear [START_REF] Macmillan | Dissecting cause from consequence: a systematic approach to thermal limits[END_REF]. One hypothesis, oxygen-and capacity-limited thermal tolerance (OCLTT), posits that oxygen supply capacity limits thermal tolerance in ectotherms [START_REF] Pörtner | Oxygen-and capacity-limited thermal tolerance: bridging ecology and physiology[END_REF]. One prediction of this hypothesis is that haematological traits (e.g., haemoglobin concentration, haematocrit), which influence blood-oxygen carrying capacity and MMR, are positively correlated with CTMax [START_REF] Pörtner | Oxygen-and capacity-limited thermal tolerance: bridging ecology and physiology[END_REF].

Only a handful of studies have demonstrated intra-specific [START_REF] Muñoz | Hematocrit is associated with thermal tolerance and modulated by developmental temperature in juvenile Chinook salmon[END_REF] and inter-specific [START_REF] Beers | Thermal tolerance of Antarctic notothenioid fishes correlates with level of circulating hemoglobin[END_REF] associations between haematocrit (i.e., the ratio of red blood cell volume to whole blood volume) and CTMax, where others do not demonstrate such associations [START_REF] Brijs | Experimental manipulations of tissue oxygen supply do not affect warming tolerance of European perch[END_REF][START_REF] Wang | Anaemia only causes a small reduction in the upper critical temperature of sea bass: is oxygen delivery the limiting factor for tolerance of acute warming in fishes?[END_REF]. However, such associations do not suggest a mechanistic link, as even haematological traits do not always correlate with hypoxia tolerance traits [START_REF] Mandic | Mechanisms and evolution of hypoxia tolerance in fish[END_REF]. Thus, future studies that continue to test this prediction ought to test whether oxygen supply capacity has a role in the presence or absence of such associations.

Coastal, tropical marine habitats are natural laboratories to study the role of oxygen-supply capacity in the relationship between haematological traits and thermal tolerance. Increases in water temperature correlate with increases [START_REF] Mcarley | Hyperoxia increases maximum oxygen consumption and aerobic scope of intertidal fish facing acutely high temperatures[END_REF] or decreases [START_REF] Fangue | Temperature and hypoxia tolerance of selected fishes from a hyperthermal rockpool in the dry tortugas, with notes on diversity and behavior[END_REF] in oxygen in shallow, coastal habitats, such as rockpools. The relative amount of primary productivity and respiration occurring at high temperatures determines whether these habitats become hypoxic (i.e., when respiration rates exceed photosynthesis rates) or hyperoxic (i.e., when photosynthesis rates exceed respiration rates). In habitats that experience hyperoxia at high temperatures, it is thought that these oxygen conditions support high thermal tolerance by elevating aerobic performance [START_REF] Mcarley | Fish and hyperoxia-From cardiorespiratory and biochemical adjustments to aquaculture and ecophysiology implications[END_REF]. Therefore, if haematological traits and thermal tolerance are related, and this relationship is linked to oxygen supply capacity, supporting evidence should be observable in organisms from hot and supersaturated marine habitats [START_REF] Giomi | Oxygen supersaturation protects coastal marine fauna from ocean warming[END_REF].

The purpose of this study was to test for associations between haematological traits and thermal tolerance and suggest a role for oxygen supply capacity in this relationship using species living near their thermal and oxygen limits. This was accomplished using reef shark neonates as experimental models because they have relatively high thermal tolerance (Bouyoucos et al., 2020a;[START_REF] Gervais | Too hot to handle? Using movement to alleviate effects of elevated temperatures in a benthic elasmobranch, Hemiscyllium ocellatum[END_REF] and relatively poor hypoxia tolerance [START_REF] Routley | Exposure to hypoxia primes the respiratory and metabolic responses of the epaulette shark to progressive hypoxia[END_REF]. The first objective was to describe water temperatures and oxygen levels at the study site. The second objective was to test for in situ associations between thermal habitat characteristics and haematological traits in the two reef shark neonate populations at the study site. The third objective was to test for ex situ associations between experimentally derived thermal tolerance and physiological oxygen supply capacity in the same populations. Together, this study combines field and laboratory data to offer a novel perspective on whether haematological traits are reliable predictors of thermal tolerance as suggested in previous studies [START_REF] Beers | Thermal tolerance of Antarctic notothenioid fishes correlates with level of circulating hemoglobin[END_REF][START_REF] Muñoz | Hematocrit is associated with thermal tolerance and modulated by developmental temperature in juvenile Chinook salmon[END_REF]. Further, these data can contribute to our understanding as to the mechanistic basis of thermal tolerance in marine ectotherms and how tropical fishes might cope with ocean warming and deoxygenation now and in the future.

Material and methods

Ethical approval

All experimental procedures described herein were approved by the James Cook University Animal Ethics Committee (protocols A2089 and A2394). Permission to conduct research on protected shark species in French Polynesia was obtained from the Ministère de la Promotion des Langues, de la Culture, de la Communication, et de l'Environnement (Arrêtés N°9524, N°5129, and N°11491).

Study site

All research was conducted on Moorea, French Polynesia (S 17°30'; W 149°50'). Research effort was focused on ten sites (Apaura, Haapiti, Maharepa, Pointe de Paorea, Papetoai, Pihaena, Tiki, Vaiane, Vaiare, and Valorie) that span Moorea's 60-km coastline. These sites are typically less than 1 m deep, within 50 m of shore, and comprise a homogenous mix of corals, algal turfs, sandflats, and rock substrate.

All sites are contained within Moorea's narrow lagoon system that experiences little variation in tide height (~ 20-30 cm).

Objective 1

Our first objective was to describe temperature and oxygen conditions of the ten study sites. This involved describing associations between water temperature and dissolved oxygen concentration (DO, in mg O2 L -1 ), rates of oxygen decline, and rates of warming. First, paired temperature and DO spot measurements were taken at each site with a YSI Pro20 (YSI Inc., Yellow Springs, OH, USA), approximately once every two weeks from November 2016 through March 2017. During this period, 5 ± 3 measurements (range = 2-24) were taken in two-hour bins from 0630-1830. A simple linear model was then used to model DO by the interaction of site and temperature using the R 'Stats' package (R Core Team, 2018). Next, three representative sites were selected from Moorea's western, northern, and eastern coastline (Apaura, Pihaena, and Valorie, respectively). Sites were sampled three times each from December 2016 through April 2017. Rates of oxygen decline were measured from 1800-0600 using spot measurements taken every 30 minutes. The highest linear rate of oxygen decline was identified over a four-hour window during each sampling night using a rolling regression function ('auto_resp()') in the 'respR' package [START_REF] Harianto | respR-An R package for the manipulation and analysis of respirometry data[END_REF]. Finally, one or two temperature data-loggers (HOBOUA-002-64, Onset Computer Corporation, Bourne, MA, USA) were deployed at each site to record temperature every ten minutes (accuracy = ± 0.5 °C, resolution = 0.14 °C at 25 °C), yielding partial records from November 2015 through February 2019 (Bouyoucos et al., 2020a). Temperature data from four summers (November-February) were selected, and the previously mentioned rolling regression function was applied to identify the highest linear warming rate over a four-hour window for each site during each summer.

Objective 2

Our second objective was to test for associations between in situ thermal profiles of our study sites and haematological profiles of resident reef shark neonates. Thermal habitat profiles were generated for each site from temperature data-loggers (as described in section '2.3. Objective 1') and consisted of the average and maximum temperature. Rather than selecting the single highest measured value as an estimate of maximum habitat temperature, the mean temperature plus three standard deviations was used as a conservative estimate of maximum habitat temperature (Fig. S1). This rationale is also informed by the idea that an organism's upper thermal limits can be roughly estimated from thermal reaction norms of physiological performance traits as three standard deviations above the optimal temperature [START_REF] Deutsch | Impacts of climate warming on terrestrial ectotherms across latitude[END_REF]. Temperature data were available for all ten sites from November 2015 to February 2019.

Haematological profiles were generated for neonatal blacktip reef sharks (Carcharhinus melanopterus, Quoy & Gaimard 1824; n = 170 individuals from eight sites) and sicklefin lemon sharks (Negaprion acutidens, Rüppell 1837; n = 54 individuals from four sites). Both species were collected from eight sites around Moorea during summer parturition months. Sites were monospecific or hosted both species (Mourier et al., 2013a(Mourier et al., , 2013b)). Sharks were collected using gill-nets during two parturition seasons (October 2014 through March 2015 and November 2015 through March 2016). Gill-nets were set from 1700-2000 and were constantly monitored so that sharks could be removed from the gill-net as soon as they were captured to minimize capture-related stress. Blood samples were then collected immediately by inverting sharks and taking 1 mL of blood from the caudal vasculature with 21-23 gauge, heparinwashed needles. Samples were processed immediately in the field or put on ice and stored for up to three hours and processed in the lab; this practice has been shown to not affect values of the haematological metrics (i.e., haematocrit and haemoglobin concentration) that were measured (Schwieterman et al., 2019a). We measured haematocrit (Hct) by centrifuging blood samples in 70 μL microhaematocrit tubes for two minutes at 4,400 g using a portable centrifuge (ZIPocrit, LW Scientific, Lawrenceville, GA, USA), and calculated Hct as the ratio of packed cell volume to total sample volume. Next, haemoglobin concentration ([Hb], in g L -1 ) was measured using a handheld point-of-care device (HemoCue Hb 201, Australia Pty Ltd, Victoria, Australia) and corrected using species-specific equations (Schwieterman et al., 2019a). Mean corpuscular haemoglobin concentration (MCHC, in g L -1 ) was then calculated as [Hb] divided by Hct. Haematological profiles were generated for each species as the site-mean value of each metric, yielding eight values (i.e., eight sites) for C. melanopterus (n = 8-36 samples per site) and four values (i.e., four sites) for N. acutidens (n = 4-24 samples per site). Associations between thermal habitat profiles metrics (i.e., average and maximum habitat temperatures) and haematological profiles (i.e., [Hb],

Hct, and MCHC) were tested for each species using simple linear regression. Statistical significance for regression was determined with a Bonferroni-corrected α = 0.008 to account for multiple comparisons (n = 6 per species).

Objective 3 2.5.1. Experimental design

Our third objective was to test for associations between ex situ haematological traits, thermal tolerance, and physiological oxygen supply capacity. Individual sharks were sampled for every trait (i.e., haematological traits, thermal tolerance, and physiological oxygen supply capacity), but in differing sampling orders. Sharks were fed between trials, allowing at least 48 hours to recover and fast between trials (Bouyoucos et al., 2020a). Sharks were maintained at ambient temperatures to avoid possible confounding effects of thermal acclimation to a regulated tank temperature.

Animal collection and husbandry

Neonatal C. melanopterus and N. acutidens were collected and transported to a laboratory facility at the Centre de Recherches Insulaires et Observatoire de l'Environnement (CRIOBE) in coolers of aerated seawater [START_REF] Bouyoucos | Dead tired: evaluating the physiological status and survival of neonatal reef sharks under stress[END_REF]. At the CRIOBE, sharks were housed in 1250 L (1.5 m diameter and 70 cm deep) circular tanks that received a constant supply of seawater from an offshore pump. Holding tanks were in a covered, open-air facility that exposed sharks to a natural photoperiod; although, tanks were covered with 60% shade cloth to minimize disturbance. To identify individuals, sharks were tagged with passive integrated transponder (PIT) tags (Biolog-id SAS, Paris, France). Sharks were fed ad libitum every other day with fresh tuna (Thunnus spp.). Carcharhinus melanopterus neonates (n = 12; mass = 0.89 ± 0.15 kg, range = 0.67-1.16 kg) were maintained in groups of two or three per tank, and larger N. acutidens neonates (n = 10; mass = 1.30 ± 0.27 kg, range = 0.99-1.76 kg) were maintained in groups of two per tank. Due to constraints on tank space at the CRIOBE, experiments on C. melanopterus were conducted in October 2019 (ambient water temperature = 29 °C) and experiments on N. acutidens were conducted in January 2020 (ambient water temperature = 28 °C). All sharks were released at their original site of capture at the end of experimentation.

Haematological traits

Haematological traits were measured as described in section '2.4. Objective 2'. Sharks were individually captured from holding tanks and inverted so that up to 1 mL of blood could be drawn from the caudal vasculature using 21-or 23-gauge, heparin-washed needles. Handling and blood sampling were under two minutes so that all sharks within a tank could be sampled in rapid succession and on the same day. Blood samples were placed on ice for up to 30 minutes before being processed. Haematocrit was measured in duplicate, using 70 μL microhaematocrit tubes and a benchtop centrifuge to spin samples at 10,000 g for five minutes. Haemoglobin concentration was also measured in duplicate, where blood samples were incubated within microcuvettes for nine minutes before being read by the HemoCue (Schwieterman et al., 2019a). Species-specific corrections were applied to raw [Hb] output (Schwieterman et al., 2019a). The mean Hct and [Hb] values were used to calculate a single MCHC value for each shark.

Thermal tolerance

Thermal tolerance was estimated by measuring the critical thermal maximum (CTMax) metric.

Individual sharks were removed from their holding tank and introduced to a 100 L, 1 m diameter circular tank containing five 300-watt aquarium heaters (Jager 300w, EHEIM GmbH & Co KG, Deizisau, Germany). The tank was continuously aerated with an air stone to maintain oxygen saturation above 80%.

Following a five-minute habituation to the experimental tank, the water temperature was elevated from an ambient temperature of 29.4 ± 0.9 °C for C. melanopterus trials and 28.0 ± 1.5 °C for N. acutidens trials at a constant rate of 0.12 ± 0.02 °C min -1 using the aquarium heaters until the shark began to exhibit muscle spasms (Bouyoucos et al., 2020a). The temperature at which sharks exhibited the onset of muscle spasms (OS) was recorded as an individual's CTMax, where a spasm was defined as any rapid convulsion originating from the animal's trunk. The temperature at OS is a repeatable, non-lethal endpoint for determining CTMax (Lutterschmidt and Hutchison, 1997b). After reaching OS, the shark was immediately returned to its holding tank.

Oxygen supply capacity

Physiological oxygen supply capacity (α, in mg O2 kg -0.89 h -1 kPa -1 ) was calculated by estimating sharks' routine metabolic rate (RMR, in mg O2 kg -0.89 h -1 ) and critical oxygen tension (pcrit, in kPa). To estimate RMR and pcrit, we used intermittent-flow respirometry [START_REF] Svendsen | Design and setup of intermittent-flow respirometry system for aquatic organisms[END_REF]. Sharks were removed from their holding tanks and placed into individual static respirometry chambers. Up to four 32 L chambers (24 cm diameter and 70 cm long) were placed in a single holding tank that was filled to 530 L (1.5 m diameter and 30 cm deep) and received continuous water supply and aeration. Each chamber was fitted with two 2,500 L h -1 pumps (EHEIM GmbH & Co KG, Deizisau, Germany): one was configured in a closed, recirculating loop to mix water within the chamber, and the other was configured to flush water from the holding tank through the chamber and out an overflow pipe above the water's surface. Oxygen was measured in each chamber with a FireSting Optical Oxygen Meter (PyroScience, GmbH, Aachen, Germany). Oxygen probes were placed within each chamber through the overflow pipe and measured DO every two seconds. A single temperature probe was connected to the oxygen meter and placed in the holding tank to correct DO readings for changes in ambient temperature. The average ambient water temperature recorded during respirometry trials was 29.8 ± 0.2 °C for C. melanopterus and 29.4 ± 0.1 °C for N. acutidens. Corrections for salinity were made by manually inputting a single value into the FireSting software, and barometric pressure was accounted for with a built-in sensor. Oxygen probes were calibrated to 100% and 0% saturation before each trial.

Routine metabolic rate was estimated during the first four hours sharks spent in respirometry chambers [START_REF] Heinrich | A product of its environment: the epaulette shark (Hemiscyllium ocellatum) exhibits physiological tolerance to elevated environmental CO2[END_REF]. Classically, RMR was simply defined as any metabolic rate between the standard and maximum metabolic rates [START_REF] Chabot | The determination of standard metabolic rate in fishes[END_REF]. After introducing sharks to respirometry chambers, intermittent cycling of the flush pump was controlled with a custom data acquisition system and software (National Instruments, Austin, TX, USA). Flush pumps were programmed to flush water through chambers for ten minutes, followed by five minutes of inactivity when oxygen uptake rates (ṀO2) could be measured. In total, 16 ṀO2 values were calculated for each shark. To approximate RMR of a minimally active animal, RMR in this study was estimated as the mean of the lowest three ṀO2 values [START_REF] Norin | Aerobic scope does not predict the performance of a tropical eurythermal fish at elevated temperatures[END_REF]. Oxygen uptake rates were calculated by multiplying the rate of linear oxygen decline (in mg O2 L -1 s -1 ; R 2 > 0.95) by the volume of water in the chamber (in L) and dividing by the mass of the shark (in kg). To account for the effects of variation in mass on ṀO2, all ṀO2 values were scaled to the mass of a 1 kg individual using an intra-specific mass scaling exponent of 0.89 [START_REF] Jerde | Strong evidence for an intraspecific metabolic scaling coefficient near 0.89 in fish[END_REF]. All ṀO2 values used to estimate RMR were calculated using custom R script (A. Mercière and T.

Norin, unpublished data).

The pcrit was estimated immediately after estimation of RMR. In this study, pcrit was defined as the oxygen partial pressure (pO2, in kPa) at which a shark's RMR began a linear decline with ambient pO2 [START_REF] Rogers | A new analysis of hypoxia tolerance in fishes using a database of critical oxygen level (Pcrit)[END_REF]. After sharks spent four hours in chambers for estimation of RMR, flush pumps were disabled to allow sharks to consume oxygen within the chambers and experience progressive hypoxia [START_REF] Speers-Roesch | Hypoxia tolerance in elasmobranchs. I. Critical oxygen tension as a measure of blood oxygen transport during hypoxia exposure[END_REF]. This 'closed respirometry' technique is an acceptable method of measuring pcrit relative to other methods (e.g., intermittent-flow or flow-through respirometry), and possibly gives more ecologically relevant estimates of pcrit because low-oxygen environments are typically high in carbon dioxide as a by-product of respiration [START_REF] Ultsch | The utility and determination of Pcrit in fishes[END_REF][START_REF] Wood | The fallacy of the Pcrit -are there more useful alternatives?[END_REF]. Experiments were terminated when DO measurements began to flatten over time, as determined by visual inspection of data in real time, or when DO reached 2.0 mg O2 L -1 , which is a threshold when neonatal C. melanopterus exhibit muscle spasms (Bouyoucos et al., 2020a). Upon termination of the experiment, sharks were then removed from chambers and returned to their holding tanks. To estimate pcrit, we first calculated an ṀO2 value every five minutes during the closed respirometry phase using LabChart software (7.3.8, ADInstruments, Dunedin, New Zealand). Then, simple linear regression was used to fit a line to these ṀO2 values against the first DO reading at which they were measured for each shark. The DO value at which each sharks' RMR intersected this line was recorded as a sharks' pcrit and converted to kPa using temperature, salinity, and barometric pressure data [START_REF] Reemeyer | Standardizing the determination and interpretation of Pcrit in fishes[END_REF].

Physiological oxygen supply capacity could be calculated after estimating RMR and pcrit. In this study, α was defined as the maximum ability of the cardiorespiratory system to provide oxygen to metabolically demanding tissues [START_REF] Ern | Oxygen dependence of upper thermal limits in fishes[END_REF], and is realized at the pcrit of a given metabolic rate [START_REF] Kielland | Warm and out of breath: Thermal phenotypic plasticity in oxygen supply[END_REF]. In other words, α represents the relationship between a given metabolic rate and its critical oxygen tension, and can be calculated by dividing RMR by its pcrit [START_REF] Seibel | Oxygen supply capacity in animals evolves to meet maximum demand at the current oxygen partial pressure regardless of size or temperature[END_REF].

Data analyses

Associations between ex situ haematological traits and thermal tolerance were tested for using simple linear regressions. Specifically, CTMax was modelled as a function of Hct, [Hb], and MCHC in individual models for each species. All analyses were conducted using the 'Stats' R package. Statistical significance for regression was determined with a Bonferroni-corrected α = 0.016 to account for multiple comparisons (n = 3 comparisons per species).

An additional series of analyses were undertaken to estimate the temperature sensitivity of pcrit under the assumption that thermal tolerance and physiological oxygen supply are related. These analyses were performed to test the prediction that, if CTMax and α are related, then pcrit should equal 21 kPa (i.e., airsaturation and pcrit-max) at the measured CTMax [START_REF] Deutsch | Metabolic trait diversity shapes marine biogeography[END_REF][START_REF] Seibel | Oxygen supply capacity in animals evolves to meet maximum demand at the current oxygen partial pressure regardless of size or temperature[END_REF]. Data for both C. melanopterus and N. acutidens were tested. To do this, we used the average temperature sensitivity for pcrit (Epcrit = 0.4 eV) reported in [START_REF] Deutsch | Metabolic trait diversity shapes marine biogeography[END_REF] to estimate CTMax as the temperature where pcrit = 21 kPa using pcrit estimates for both species from our study. Then, we estimated the temperature sensitivity required for measured values of pcrit to equal 21 kPa at the measured temperatures for CTMax in this study. Next, we used previously published standard (SMR) and maximum (MMR) metabolic rates measured in C. melanopterus at 28 and 31 °C (Bouyoucos et al., 2020a) to calculate temperature sensitivities for SMR and MMR (ESMR and EMMR, respectively) so that Epcrit could be estimated using the equation ESMR = EMMR + Epcrit [START_REF] Seibel | Oxygen supply capacity in animals evolves to meet maximum demand at the current oxygen partial pressure regardless of size or temperature[END_REF]. Finally, estimated Epcrit from Bouyoucos et al. (2020a) was used to estimate CTMax for C. melanopterus using pcrit measurements from the current study. For reference, Epcrit was calculated from the only other available data from elasmobranch fishes [START_REF] Butler | The effect of progressive hypoxia on respiration in the dogfish (Scyliorhinus canicula) at different seasonal temperatures[END_REF][START_REF] Crear | The impacts of warming and hypoxia on the performance of an obligate ram ventilator[END_REF]Schwieterman et al., 2019b).

Results

Objective 1

The average temperature calculated from spot measurements across all ten sites was 29.9 ± 0.2 °C (range = 26.5-37.0 °C) and the average DO was 6.32 ± 1.54 mg O2 L -1 (range = 3.10-11.39 mg O2 L -1 ).

Oxygen was positively associated with temperature at each site (Fig. 1; Table S1). Maximum heating rates occurred during 0610-1530 and were 1.4 ± 0.6 °C h -1 (Fig. S2). The average of the maximum temperatures that were recorded across all sites was 34.1 ± 1.7 °C. Maximum rates of oxygen decline between 1800 and 0600 were 0.45 ± 0.18 mg L -1 h -1 (Fig. S3). The average of the minimum DO values that were recorded across three sampling sites across all nine sampling nights was 4.18 ± 0.62 mg O2 L -1 .

Objective 2

The average temperature from 2015-2019 calculated from temperature data loggers across sites was 28.9 ± 0.3 °C, and the average maximum habitat temperature was 34.4 ± 0.8 °C. For C. melanopterus, there were no associations between average habitat temperature and [Hb], Hct, or MCHC (Fig. 2A-C; Table S2). However, maximum habitat temperature was negatively associated with [Hb] but not with Hct or MCHC (Fig. 2D-F; Table S2). For N. acutidens, neither average habitat temperature (Fig. 3A-C; Table S2) nor maximum habitat temperature (Fig. 3D-F; Table S2) were associated with [Hb], Hct, or MCHC.

Objective 3

Average CTMax was 35.9 ± 0.4 °C for C. melanopterus and 35.8 ± 0.6 °C for N. acutidens. The average pcrit measured in resting sharks was 17.46 ± 1.53 kPa (5.32 ± 0.47 mg O2 L -1 ) for C. melanopterus and 16.02 ± 1.66 kPa (4.90 ± 0.51 mg O2 L -1 ) for N. acutidens. Raw traces of ṀO2 used for determining pcrit are presented in the supplementary materials (C. melanopterus, Figs. S4-S5; N. acutidens, Figs. S6-S7). For C. melanopterus, Hct was negatively associated with CTMax (Fig. 4B; Table S3), whereas [Hb] and MCHC were not associated with CTMax (Fig. 4A andC; Table S3). For N. acutidens, CTMax was not associated with [Hb], Hct, or MCHC (Fig. 4D-F; Table S3). MMR were estimated to be 0.739 and 0.727 eV, respectively. From these values, Epcrit was estimated at 0.012 eV for C. melanopterus. However, this temperature sensitivity did not predict an ecologically realistic value of CTMax. Out of all elasmobranch species for which temperature scaling of pcrit could be calculated from the literature (n = 4; Fig. 6; Table S4), Epcrit was 0.43 ± 0.22.

Using our measured

Discussion

Our goal was to test for associations between haematological traits and thermal tolerance in reef shark neonates, and to investigate the possibility of a role for oxygen supply capacity in these associations.

Here, we demonstrated that, when habitats approached the sharks' CTMax, these habitats were also hyperoxic; therefore, environmental oxygen availability should not be limiting for physiological processes. However, this would only be true if oxygen supply capacity has not been compromised.

Second, we demonstrated negative associations between haematological traits and upper thermal limits, both in situ and ex situ, but only in C. melanopterus neonates. This finding suggests that blood-oxygen carrying capacity and CTMax are not correlated, and that laboratory estimates of CTMax do not always approximate maximum habitat temperatures. Yet, associations observed in C. melanopterus neonates appear genuine, and these unique associations could reflect the effects of temperature on blood viscosity and haemoglobin isoform expression. Third, we estimated the temperature sensitivity of pcrit in sharks at rest, under the assumption that thermal tolerance and oxygen supply capacity are related. We found that the average reported temperature sensitivity predicts maximum habitat temperatures for Moorea and the estimated species-specific values fall within the reported range for other elasmobranch species. This provides support for a theoretical relationship between thermal tolerance and oxygen supply capacity in these species; however, we also emphasise that this link has not been demonstrated empirically. Indeed, the temperature sensitivity estimated from previously published data for C. melanopterus do not support the hypothesis of a relationship between CTMax and oxygen supply capacity. Therefore, investigating haematological traits that are related to blood-oxygen carrying capacity alone is likely not sufficient to test links between thermal tolerance and oxygen (see [START_REF] Beers | Thermal tolerance of Antarctic notothenioid fishes correlates with level of circulating hemoglobin[END_REF][START_REF] Brijs | Experimental manipulations of tissue oxygen supply do not affect warming tolerance of European perch[END_REF][START_REF] Muñoz | Hematocrit is associated with thermal tolerance and modulated by developmental temperature in juvenile Chinook salmon[END_REF][START_REF] Wang | Anaemia only causes a small reduction in the upper critical temperature of sea bass: is oxygen delivery the limiting factor for tolerance of acute warming in fishes?[END_REF]. Future studies investigating the thermal dependence of oxygen supply capacity (i.e., pcrit) may shed light on mechanistic links between thermal tolerance and oxygen (Deutsch et al., 2020;[START_REF] Seibel | Oxygen supply capacity in animals evolves to meet maximum demand at the current oxygen partial pressure regardless of size or temperature[END_REF].

Around Moorea, the reef shark neonate habitats approached but did not exceed the two experimental species' upper thermal limits. While the average maximum habitat temperatures across all sites (34.4 °C) did not exceed sharks' measured CTMax (~ 36 °C), individual maximum habitat temperature estimates did match sharks' CTMax at two of the ten sites. Together, this suggests that, during Austral summer months when these sharks are born, they have a thermal safety margin (TSM) of ~ 6 °C. While both species appear equally thermally tolerant, very little is known about the effects of acute temperature changes on the physiological performance of N. acutidens and C. melanopterus. For instance, C. melanopterus do not exhibit changes in maximal maximum metabolic rates (MMR) in situ between 28 and 32.5 °C [START_REF] Bouyoucos | Dead tired: evaluating the physiological status and survival of neonatal reef sharks under stress[END_REF], but mortality may be associated with exercise stress at temperatures above 31 °C (Bouyoucos et al., 2020a). In addition, in vitro studies on C. melanopterus revealed that haemoglobin's affinity for oxygen decreases with increasing temperatures; moreover, in situ, this species is also capable of behaviourally avoiding unfavourable temperatures (Bouyoucos et al., 2020a). However, when temperatures approach their CTMax in their natural habitats, these sharks are predicted to experience water that is supersaturated with oxygen, suggesting that thermal tolerance should not be impaired by ambient oxygen levels, as long as oxygen supply capacity is not compromised. Heating rate is also known to affect CTMax in fishes [START_REF] Illing | Critical thermal maxima of early life stages of three tropical fishes: Effects of rearing temperature and experimental heating rate[END_REF][START_REF] Mora | Effect of the rate of temperature increase of the dynamic method on the heat tolerance of fishes[END_REF]; indeed, maximum environmental heating rates measured in situ (1.4 °C h -1 ) were much slower than experimental heating rates used to measure CTMax ex situ (7.2 °C h -1 ), suggesting that, in situ, shark neonates may have greater TSMs than laboratory results might suggest. Yet, TSMs should decrease as summer temperatures increase [START_REF] Mcarley | Chronic warm exposure impairs growth performance and reduces thermal safety margins in the common triplefin fish (Forsterygion lapillum)[END_REF][START_REF] Sandblom | Physiological constraints to climate warming in fish follow principles of plastic floors and concrete ceilings[END_REF], and indeed, this has been demonstrated, ex situ, with thermal acclimation in C. melanopterus (Bouyoucos et al., 2020a). It is still not clear as to whether heatwaves and/or ocean warming will expose reef shark neonates around Moorea to temperatures exceeding their CTMax, but this is an area important for future investigation.

Dissolved oxygen levels among the reef shark habitats were lower than measured pcrit values for both species. Overnight measurements at three of the ten sites demonstrated that DO fell below the measured pcrit of C. melanopterus in 68% of measurements (~8.1 hours) and in 45% of measurements (~5.4 hours) for N. acutidens. Indeed, neonatal N. acutidens exhibited lower pcrit and higher α than C. melanopterus.

However, a more ecologically relevant pcrit would account for the effects of sharks' activity level and body temperature. Indeed, it is important to consider how pcrit and α vary when measured in immobile animals, as was the case in this study, and in animals that are forced to swim. Both C. melanopterus and N. acutidens typically swim to ventilate their gills but are also known to rest on the substrate and ventilate their gills through buccal pumping. If the capacity of these sharks to ventilate their gills while swimming is greater than their capacity to ventilate their gills through buccal pumping, then it is conceivable that swimming reef sharks could exhibit lower pcrit and higher α, despite their increased metabolic rates relative to resting. Another consideration is the effect of diel temperature fluctuations on pcrit in reef sharks in situ. Moorea's habitats experience declining DO at night when water temperatures are lowest, when pcrit would seemingly decrease, as has been demonstrated in other elasmobranchs [START_REF] Butler | The effect of progressive hypoxia on respiration in the dogfish (Scyliorhinus canicula) at different seasonal temperatures[END_REF][START_REF] Crear | The impacts of warming and hypoxia on the performance of an obligate ram ventilator[END_REF]Schwieterman et al., 2019b). In other tropical elasmobranchs, pcrit is also associated with haemoglobin-oxygen (Hb-O2) affinity, which is often reported as the pO2 at which 50% of the Hb is bound with O2 (p50; [START_REF] Speers-Roesch | Hypoxia tolerance in elasmobranchs. I. Critical oxygen tension as a measure of blood oxygen transport during hypoxia exposure[END_REF]. In this light, increasing Hb-O2 affinity at lower temperatures -as demonstrated in vitro in C. melanopterus (Bouyoucos et al., 2020a) -should be accompanied by increasing pcrit. Thus, accounting for effects of activity level, gill ventilation, and diel temperature changes would produce different pcrit estimates than what we characterized. Finally, prior exposure to supersaturated oxygen conditions during the day could confer greater tolerance to acute declining oxygen conditions that are experienced overnight [START_REF] Giomi | Oxygen supersaturation protects coastal marine fauna from ocean warming[END_REF]. It is probable that neonatal C. melanopterus and N. acutidens use the shallow, nearshore habitats around Moorea for refuge from predators and even thought to stay within these sites without venturing to deeper, possibly well oxygenated waters at night (Bouyoucos et al., 2020b). Thus, C. melanopterus and N. acutidens must be able to tolerate environmental oxygen levels that decline below their estimated pcrit for an immobile animal for at least five hours if they are to remain within the protection of their shallow habitats at night. Haematological traits varied with in situ and ex situ estimates of upper thermal limits in C. melanopterus neonates, but none of the haematological traits we measured were associated with maximum habitat temperature or CTMax in N. acutidens. In C. melanopterus, [Hb] was negatively associated with maximum habitat temperature while Hct was negatively associated with CTMax. In notothenioid fishes and Chinook salmon (Oncorhynchus tshawytscha), Hct has been found to be positively associated with CTMax [START_REF] Beers | Thermal tolerance of Antarctic notothenioid fishes correlates with level of circulating hemoglobin[END_REF][START_REF] Muñoz | Hematocrit is associated with thermal tolerance and modulated by developmental temperature in juvenile Chinook salmon[END_REF], and this finding has been debated as evidence in support of a link between oxygen supply capacity and thermal tolerance [START_REF] Brijs | Experimental manipulations of tissue oxygen supply do not affect warming tolerance of European perch[END_REF][START_REF] Pörtner | Oxygen-and capacity-limited thermal tolerance: bridging ecology and physiology[END_REF][START_REF] Wang | Anaemia only causes a small reduction in the upper critical temperature of sea bass: is oxygen delivery the limiting factor for tolerance of acute warming in fishes?[END_REF]. Finding the opposite trend in only C. melanopterus and not in its congener, N. acutidens, suggests that associations between Hct and CTMax are variable, speciesspecific, and are likely not the best metrics for testing links between thermal tolerance and oxygen supply.

Further, such trends have only been demonstrated over narrow temperature ranges, such as ~1 °C in the present study and ~3 °C in [START_REF] Beers | Thermal tolerance of Antarctic notothenioid fishes correlates with level of circulating hemoglobin[END_REF] and [START_REF] Muñoz | Hematocrit is associated with thermal tolerance and modulated by developmental temperature in juvenile Chinook salmon[END_REF]. The mismatch we observe between field and laboratory trends for different neonate sub-populations around Moorea also suggests disagreement between laboratory estimates of CTMax and maximum habitat temperatures. If CTMax was a reliable proxy for maximum habitat temperature, then we would predict that traits associated with one metric might also be associated with the proxy. Therefore, disparity in trends observed in situ and ex situ in C. melanopterus suggests that CTMax may not be a meaningful proxy for maximum habitat temperature, and the mismatch in the haematological traits between C. melanopterus and N. acutidens suggests that such traits may not reliably predict CTMax.

The strength of observed associations between haematological traits, CTMax, and maximum habitat temperatures in C. melanopterus, however, suggest that these trends were not spurious. Indeed, coefficients of determination for Hct and CTMax (R 2 = 0.63) and for [Hb] and maximum habitat temperature (R 2 = 0.88) were relatively strong. Negative associations between these traits have, to the best of our knowledge, not been previously demonstrated in fishes and suggest a unique, as-of-yet unexplained phenomenon. A negative association between Hct and CTMax could reflect the thermal dependence of blood viscosity. Depending on shear rate, blood viscosity increases as Hct increases [START_REF] Baldwin | Oxygen transport potential in tropical elasmobranchs from the Great Barrier Reef (Australia): Relationship between hematology and blood viscosity[END_REF][START_REF] Wells | Oxygen transport potential in tropical reef fish with special reference to blood viscosity and haematocrit[END_REF], while increasing temperature reduces blood viscosity [START_REF] Brill | The influence of hematocrit, temperature, and shear rate on the viscosity of blood from a high-energy-demand teleost, the yellowfin tuna Thunnus albacares[END_REF]. Thus, it would be expected that C. melanopterus experience reductions in blood viscosity during acute temperature increases during CTMax experiments. It is possible that Hct increases during heating, but this has not been directly tested in C. melanopterus. However, it is important to note that Hct in C. melanopterus does increase with thermal acclimation (Bouyoucos et al., 2020c) and upon exercise stress (Schwieterman et al., 2019a). On the other hand, a negative association between [Hb] and maximum habitat temperature could reflect the expression of fewer, more temperature resistant Hb isoforms in habitats that achieve higher maximum temperatures. For instance, in C. melanopterus living at 27 °C, in vitro experiments suggest a loss of Hb pH sensitivity when temperatures approaching the animal's CTMax (Bouyoucos et al., 2020a). This logic assumes differences in the costs of expressing temperature resistant isoforms. Alternatively, because habitats around Moorea exhibited strong positive associations between temperature and oxygen, lower [Hb] in habitats that achieve higher maximum temperatures could reflect the degree of hyperoxia in those habitats. Clearly, further research is warranted to determine the mechanistic underpinnings and biological significance of the negative associations between haematological traits and thermal habitat characteristics in C. melanopterus. If these are, indeed, robust trends, as they seem to be, increases in maximum habitat temperatures with ocean warming could result in pathologies in sharks with very low Hct and [Hb].

The average temperature sensitivity for pcrit reported by [START_REF] Deutsch | Metabolic trait diversity shapes marine biogeography[END_REF] predicted oxygendependent values of CTMax for C. melanopterus (33.6 °C) and N. acutidens (34.8 °C). This exercise relied on the assumption that CTMax and oxygen supply capacity are related, such that CTMax is defined as the temperature where pcrit equals the prevailing environmental pO2 (i.e., 21 kPa). While these values underestimate CTMax as measured in this study, the predicted values align very closely with measured maximum habitat temperatures in reef shark neonate habitats around Moorea. Further, the estimated CTMax value for C. melanopterus is close to the maximum body temperature of 34.1 °C that was measured in situ for C. melanopterus (Bouyoucos et al., 2020a). Next, predicting the temperature sensitivity of pcrit that is needed to yield the CTMax values that were measured for C. melanopterus and N. acutidens produced values within one standard deviation of the average value for marine ectotherms presented in [START_REF] Deutsch | Metabolic trait diversity shapes marine biogeography[END_REF]. Indeed, [START_REF] Deutsch | Metabolic trait diversity shapes marine biogeography[END_REF] report a mean temperature sensitivity and standard deviation for pcrit of 0.40 ± 0.28 eV (range = -0.2-1.3 eV) for marine ectotherms. In comparison, available data for elasmobranch species (n = 4) produces a temperature sensitivity of 0.43 ± 0.22 (range = 0.16-0.69) [START_REF] Butler | The effect of progressive hypoxia on respiration in the dogfish (Scyliorhinus canicula) at different seasonal temperatures[END_REF][START_REF] Crear | The impacts of warming and hypoxia on the performance of an obligate ram ventilator[END_REF]Schwieterman et al., 2019b), and we estimated temperature sensitivities of 0.22 and 0.32 eV for pcrit in C. melanopterus and N. acutidens, respectively.

Conversely, the very low temperature sensitivity predicted from thermal sensitivities of SMR and MMR in C. melanopterus that predicted an unrealistic value for CTMax could reflect the effects of long-term thermal acclimation (Bouyoucos et al., 2020a), as opposed to short-term acclimation [START_REF] Slesinger | The effect of ocean warming on black sea bass (Centropristis striata) aerobic scope and hypoxia tolerance[END_REF]. Alternatively, these empirical data for C. melanopterus could refute the notion of an association between CTMax and oxygen supply capacity. Unfortunately, CTMax data were not available for the other elasmobranch species for which Epcrit could be calculated. We emphasise, however, that our study does not empirically demonstrate whether CTMax is limited by oxygen supply capacity. Further, pcrit and α values may not reflect these reef sharks' full oxygen supply capacity, and instead reflect pcrit and α for an immobile, buccal-pumping animal. Both of our study species swim nearly continuously in situ [START_REF] Wells | Respiratory function and nucleotide composition of erythrocytes from tropical elasmobranchs[END_REF]; although, both species rest on the benthos and are capable of buccal pumping to ventilate their gills. Notably, MMR can be estimated from α at the prevailing environmental pO2 [START_REF] Seibel | Oxygen supply capacity in animals evolves to meet maximum demand at the current oxygen partial pressure regardless of size or temperature[END_REF], which was ≥ 21 kPa in this study; this exercise underestimated MMR for C. melanopterus based on values previously reported by our group (Bouyoucos et al., 2020a(Bouyoucos et al., , 2020c[START_REF] Bouyoucos | Dead tired: evaluating the physiological status and survival of neonatal reef sharks under stress[END_REF][START_REF] Rummer | Responses of a coral reef shark acutely exposed to ocean acidification conditions[END_REF]. Thus, a swimming reef shark could be able to better ventilate their gills relative to a resting animal, which would theoretically yield a lower pcrit and a higher α despite sharks' having higher metabolic rates. For instance, α • 21 kPa = 136-219 mg O2 kg -0.89 h -1 , whereas measured values range 278-561 mg O2 kg -0.89 h -1 (Bouyoucos et al., 2020c). However, MMR, as reported in these previous studies was measured using the identical respirometry technique described here. Thus, while these data do not preclude the possibility of a relationship between oxygen supply capacity and CTMax in these reef sharks, these data cannot empirically demonstrate such a relationship.

Conclusions

In conclusion, our investigations using reef sharks in a model experimental system do not support the notion that haematological traits can be used to predict intra-specific variation in thermal tolerance. However, our results do not preclude the possibility of a mechanistic link between thermal tolerance and oxygen. To accomplish this fully, in the future, it will be necessary to define the oxygen dependence of CTMax [START_REF] Ern | Oxygen dependence of upper thermal limits in fishes[END_REF] and the temperature dependence of the metabolic phenotype (i.e., SMR, MMR, and pcrit) over a species' full ecologically relevant temperature range [START_REF] Seibel | Oxygen supply capacity in animals evolves to meet maximum demand at the current oxygen partial pressure regardless of size or temperature[END_REF]. Indeed, there are only two fish species for which sufficient data exist to test the latter: the goldfish (Carassius auratus; [START_REF] Fry | The relation of temperature to oxygen consumption in the goldfish[END_REF] and black seabass (Centropristis striata; [START_REF] Slesinger | The effect of ocean warming on black sea bass (Centropristis striata) aerobic scope and hypoxia tolerance[END_REF]. Future studies should also consider testing for a link between oxygen and thermal tolerance between different ontogenetic stages [START_REF] Dahlke | Thermal bottlenecks in the life cycle define climate vulnerability of fish[END_REF] and investigating links between thermal tolerance and different physiological systems [START_REF] Vornanen | Feeling the heat: source-sink mismatch as a mechanism underlying the failure of thermal tolerance[END_REF]. Thus, our data suggest some capacity of reef shark neonates to tolerate further ocean warming, but our findings do not indicate how reef shark neonates will fare under the combined stress of ocean warming and deoxygenation. Additional research into thermal tolerance and oxygen supply capacity in sharks and other water-breathing ectotherms is needed, and future studies can benefit from testing the multiple available hypotheses.

Tables 713 Table 1. Routine metabolic rates (RMR, mg O2 kg -0.89 h -1 ) and critical oxygen tensions (pcrit, kPa) used to 714 calculate physiological oxygen supply capacity (α, mg O2 kg -0.89 h -1 kPa -1 ) in Carcharhinus melanopterus. 715 were collected for the thorny skate, Amblyraja radiata (Schwieterman et al., 2019b), sandbar shark, Carcharhinus plumbeus [START_REF] Crear | The impacts of warming and hypoxia on the performance of an obligate ram ventilator[END_REF], clearnose skate, Rostaraja eglanteria (Schwieterman et al., 2019b), and small-spotted catshark, Scyliorhinus canicula [START_REF] Butler | The effect of progressive hypoxia on respiration in the dogfish (Scyliorhinus canicula) at different seasonal temperatures[END_REF].

ID

Figure captions

Fig. 1 .

 1 Fig. 1. Associations between water temperature and dissolved oxygen at ten locations (A-J) around Moorea, French Polynesia. Shading around regression lines represents 95% confidence intervals. The red line represents 100% oxygen saturation; oxygen values above this line denote supersaturation.

Fig. 2 .

 2 Fig. 2. Associations between haematological traits of blacktip reef shark (Carcharhinus melanopterus) neonates and thermal habitat profiles. Haemoglobin concentration ([Hb]; A, D), haematocrit (Hct; B, E), and mean corpuscular haemoglobin concentration (MCHC; C, F) are presented in response to either the average temperature (A-C) or maximum temperature (D-F) measured at eight sites. For panels A-C, individual observations represent the average temperature at a site from 2015-2019 and the average value of each haematological trait measured in sharks from 2014-2016 at the same sites (n = 8 sites). Error bars represent standard error of the mean. For panels D-F, individual observations represent the maximum habitat temperature at each site (n = 8 sites), calculated as the average from 2015-2019 plus three standard deviations, and the same data for sharks from panels A-C. Regression lines with 95% confidence intervals (i.e., shading) represent statistically significant associations between variables.

Fig. 3 .

 3 Fig. 3. Associations between haematological traits of sicklefin lemon shark (Negaprion acutidens) neonates and thermal habitat profiles. Haemoglobin concentration ([Hb]; A, D), haematocrit (Hct; B, E), and mean corpuscular haemoglobin concentration (MCHC; C, F) are presented in response to either the average temperature (A-C) or maximum temperature (D-F) measured at eight sites. For panels A-C, individual observations represent the average temperature at a site from 2015-2019 and the average value of each haematological trait measured in sharks from 2014-2016 at the same sites (n = 4 sites). Error bars represent standard error of the mean. For panels D-F, individual observations represent the maximum habitat temperature at each site (n = 4 sites), calculated as the average from 2015-2019 plus three standard deviations, and the same data for sharks from panels A-C.

Fig. 4 .

 4 Fig. 4. Associations between critical thermal maximum (CTMax) and haemoglobin concentration ([Hb]; A, D), haematocrit (Hct; B, E), and mean corpuscular haemoglobin concentration (MCHC; C, F) of blacktip reef shark (Carcharhinus melanopterus; A-C) and sicklefin lemon shark (Negaprion acutidens; D-F) neonates. Points represent observations for individual sharks (C. melanopterus, n = 12; N. acutidens, n = 10), and regression lines with 95% confidence intervals (i.e., shading) represent statistically significant associations between variables.

Fig. 5 .

 5 Fig. 5. Temperature sensitivity of critical oxygen tension (pcrit) of four elasmobranch species. The natural logarithm of pcrit (kPa) is plotted against the inverse of temperature (°Kelvin) multiplied by the Boltzmann constant. The slope of this line is the temperature sensitivity (E, in eV). Available data from the literature

  pcrit values of 17.4 kPa at 29.8 °C for C. melanopterus and 16.0 kPa at 29.4 °C for N. acutidens, a temperature sensitivity for pcrit (Epcrit) of 0.4 eV yielded CTMax estimates of 33.6 °C and 34.8 °C, respectively. Conversely, achieving CTMax at measured temperatures (i.e., 35.9 °C for C. melanopterus and 35.8 °C for N. acutidens) would necessitate Epcrit values of 0.22 and 0.32 eV, respectively. Using previously published data for C. melanopterus, temperature sensitivities of SMR and

Table 2 .

 2 Routine metabolic rates (RMR, mg O2 kg -0.89 h -1 ) and critical oxygen tensions (pcrit, kPa) used to calculate physiological oxygen supply capacity (α, mg O2 kg -0.89 h -1 kPa -1 ) in Negaprion acutidens.

		Mass (kg)	RMR	pcrit	α	Temperature (°C)
		1.11	171.15	17.20	9.95	29.6
		0.93	122.07	18.19	6.71	29.6
		0.75	95.53	15.57	6.13	29.6
		0.76	95.89	20.03	4.79	29.6
		0.95	114.13	16.29	7.00	30.1
		0.67	83.63	15.91	5.26	29.9
		1.16	151.96	18.71	8.12	29.5
		0.98	160.55	15.68	10.24	29.5
		0.93	123.10	19.35	6.36	29.6
	10	0.8	137.07	18.33	7.48	30.0
	11	0.77	105.68	16.18	6.53	29.9
	12	1.08	200.03	18.09	11.05	29.9
	716
	717

Acknowledgements

The authors thank staff at the CRIOBE and volunteers of The Physioshark Project. We also thank Eva Jacquesson, Lizzie Duncan, and Kim Eustache for assistance in the field. The quality of this manuscript was greatly improved by the constructive and thoughtful feedback of two anonymous reviewers.

Funding sources

Ian Bouyoucos was supported by a James Cook University Postgraduate Research Scholarship. This research was supported by an Australian Research Council (ARC) Discovery Early Career Researcher Award (PDE150101266; Jodie Rummer), a L'Oréal-United Nations Education, Scientific and Cultural Organisation (UNESCO) Women in Science Foundation fellowship (Jodie Rummer), an Institut des Récifs Coralliens du Pacifique fellowship (Jodie Rummer), an ARC Super Science Fellowship (Jodie Rummer), the ARC Centre of Excellence for Coral Reef Studies (Ian Bouyoucos and Jodie Rummer), the Laboratoire d'Excellence CORAIL (Serge Planes), the Station d'Ecologie Expérimentale of the CRIOBE (Serge Planes), and the French Ministère de l'Environnement (Serge Planes).

Data statement

Data presented in this manuscript are available the Research Data Repository (Tropical Data Hub) at James Cook University: https://doi.org/10.25903/JX5T-8794.


Giacomo Erez

Anthony Collin
email: anthony.collin@univ-lorraine.fr

Gilles Parent

Pascal Boulet

Mathieu Suzanne

Aurélien Thiry-Muller

Measurements and models to characterise flame radiation from multi-scale kerosene fires

Keywords: thermal radiation, multi-scale re tests, modelling, ame shape, ame emission 1

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

Introduction

Heat transfers are one of the main phenomena involved in the ignition and growth of a re. Amongst them, thermal radiation plays a major role, especially for intermediate to large res [START_REF] Babrauskas | Estimating large pool re burning rates[END_REF]. For example, it can control if (and how) combustion will self-sustain, or if a re will spread [START_REF] Burgess | Heat transfer in ames[END_REF][START_REF] De Ris | Fire radiationA review[END_REF][START_REF] Fernandez-Pello | Controlling Mechanisms of Flame Spread[END_REF], at close and long ranges. Its understanding is thus crucial for various elds, from industrial safety to re investigation.

Thermal radiation is usually accounted for using simple correlations (e.g. [p. 2597 in [START_REF] Hurley | SFPE Handbook of Fire Protection Engineering[END_REF][START_REF] Hamins | Estimate of ame radiance via a single location measurement in liquid pool res[END_REF][START_REF] Yang | Estimate of the Eect of Scale on Radiative Heat Loss Fraction and Combustion Eciency[END_REF]) or multiphysics models (e.g. Fire Dynamics Simulator, FDS). The former provide rapid results, but are often limited in terms of applicability, with poor accuracy when it comes to specic fuels or geometries. The latter provide more accurate results but usually require extensive computational time, and can also show some limitations, regarding complex materials properties or the inuence of combustion conditions. Many re science applications could benet from ner measurements and modelling of radiative heat transfers, and particularly regarding full-scale res. Some studies are already available, for example from an experimental point of view [START_REF] Suo-Anttila | Characterization of thermal radiation spectra in 2m pool res[END_REF][START_REF] Boulet | Experimental Investigation of Radiation Emitted by Optically Thin to Optically Thick Wildland Flames[END_REF][START_REF] Parent | Spectral radiation emitted by kerosene pool res[END_REF], and the work presented here is a contribution to this eort, as it aims at providing comprehensive radiation data and models at reduced costs (small-/intermediate-scale tests and computationally ecient models). This paper describes the measurements that were performed to characterise ame radiation, with the example of kerosene res, and how the results were used to model it, using dierent simplied, yet reasonably accurate, approaches.

Generally speaking, ame radiation is characterised by the amount of energy and the directions in which it is emitted. The former can be given by the Radiative Transfer Equation (RTE), which describes the variations of the spectral radiation intensity I σ [W • m =2 • sr =1 • cm] along direction Ω between positions s and s + ds [m] as a function of emission, absorption, and scattering by the medium (here the ame). If scattering is neglected (e.g. see appendix in [START_REF] Parent | Spectral radiation emitted by kerosene pool res[END_REF]), this is expressed as

dI σ (s, Ω) ds = κ a σ I bb σ (T (s)) -κ a σ I σ (s, Ω), (1)
where σ [cm =1 ] is the wavenumber, κ a the absorption coecient [cm =1 ], and I bb the radiation intensity of a blackbody at temperature T [K]. Other simplications can be made, for example by considering that the ame is optically thick or, on the contrary, thin [START_REF] Collin | Evaluation of simple models of ame radiation in the frame of re propagation[END_REF].

These terms refer to the optical thickness of the medium, τ = e β [], where e is the path length [m], and β the extinction coecient [cm =1 ]. The latter accounts for absorption and scattering, as β = κ a + κ s . This means that an optically thick ame is very wide (large e)

and/or attenuates much of the radiation (large β), by absorbing and/or scattering it.

Another approximation is to consider the ame as a grey medium, which means its properties are wavenumber-independent (e.g. [START_REF] Tien | Flame radiation[END_REF][START_REF] Àgueda | Experimental study of the emissivity 378 of ames resulting from the combustion of forest fuels[END_REF]). This simplies both the experimental data acquisition and the models, but may sometimes be inapplicable, for example when the targets are non-grey materials (e.g. [START_REF] Suo-Anttila | Characterization of thermal radiation spectra in 2m pool res[END_REF][START_REF] Boulet | 382 Optical and radiative properties of clear PMMA samples exposed to a radiant heat 383 ux[END_REF]).

The directions along which radiation is emitted are dictated by the ame shape. Unless fully coupled models are used (e.g. FDS), basic proles or geometries (cylinder, cone) are usually considered because they often oer a decent description of the average ame shape and simplify calculations.

The parameters used to describe the ame shape and emission may be determined experimentally. Here, measurements on kerosene res are presented, in order to describe the radiative heat transfer from the ame to external targets. Spectrally resolved radiative properties were determined, as discussed in [START_REF] Parent | Spectral radiation emitted by kerosene pool res[END_REF]. In this paper, total radiative heat uxes will be considered. All results are analysed for multiple re sizes to study possible scale eects, and ideally take them into account. The tests and measuring devices are presented in Sec. 2.

In addition to knowledge acquisition regarding ame emission and geometry, as well as their changes with re size, the experimental data (see Sec. 3) were used as input data to model radiation and predict heat uxes received by targets. Here, four approaches are used and compared, in order to illustrate and evaluate the simplications that can be made when modelling radiative heat transfer, the required input data, and their inuence on the results. They are based on the use of a simplied ame geometry, extracted from the tests.

The ame emission is also modelled based on measurement results, by assuming the ame absorbs more or less radiation, thus theoretically ranging from a blackbody (full absorption) to an optically thin medium (negligible absorption). A ray-tracing method is used to predict the heat uxes for each approach (see Sec. 4). The results are presented and discussed in Sec. 5 and 6.

Fire tests

Overview

In order to investigate the inuence of scale on ame radiation, re experiments were performed at several sizes, with widths of 30, 50, 70, 100, 175 and 250 cm (square surfaces).

The tests discussed here were done using kerosene (Jet A-1, NATO code F-35) because such pool res are widely studied, thus providing data (mass loss rates, ame heights...) for comparison and validation, but also because they display a long steady phase which makes measurements and analyses easier. They were performed in square steel pans with edges 4 mm thick for the largest pans (70 cm or more) and 2 mm thick for the smaller ones. As explained in [START_REF] Parent | Spectral radiation emitted by kerosene pool res[END_REF], the fuel level was not kept constant.

The tests were performed inside two dierent hangars, suciently large to consider the res as well-ventilated while limiting the inuence of wind and possibly rain. The largest res (70 cm or more) were conducted in the rst one (Groupe ADP) measuring 300 × 50 × 17 m 3 (length × width × height). The second hangar (LEMTA, PROMETHEI facility, 20 × 15 × 7 m 3 ) was used for re widths between 30 and 70 cm.

Measurements

Flame radiative properties

Radiation from ames is due to two types of combustion products, namely gases (mainly CO 2 and H 2 O) and solid particles (soot) [12]. For intermediate and large re sizes, the latter become the main emitter [START_REF] Sibulkin | Estimates of the Eect of Flame Size on Radiation from Fires[END_REF][START_REF] Àgueda | Experimental study of the emissivity 378 of ames resulting from the combustion of forest fuels[END_REF], and it was thus chosen to focus on them in the work presented here. It was shown that ame radiation due to soot can be approximated by that of an equivalent medium which is isothermal, homogenous and non scattering [START_REF] Parent | Spectral radiation emitted by kerosene pool res[END_REF].

These assumptions lead to a simplied expression of the RTE given in Eq. 1, that is

I σ = (1 -exp [-κ a σ e]) I bb σ (T ).
(

) 2
The two unknowns, κ a σ and T , were determined using two distinct measurements [START_REF] Parent | Spectral radiation emitted by kerosene pool res[END_REF]: a multispectral opacimetry setup (custom made) and an infrared spectrometer (Matrix model by Bruker).

Flame geometry

Several cameras operating in the visible range (Hikvision DS-2CD4032 FHWD-A or Lumenera Le165MP) were used to determine the ame shape through a Matlab post-processing (default parameters for release 2018a if not specied otherwise).

Images gathered with the Hikvision cameras were converted to grey scale (rgb2gray function), and then to binary (black and white) values by using a custom threshold which selected up to 8 % of the most intense pixels as part of the ame. Images coming from the Lumenera cameras were directly converted to binary (imbinarize function) because they already provided a satisfactory thresholding. Binary images were then used to extract the ame contour (bwboundaries function) and calibration was performed, when possible, by Direct Linear Transformation (DLT, see e.g. [START_REF] Pastor | 389 Computing the rate of spread of linear ame fronts by thermal image processing[END_REF]). Only the images for the largest kerosene res could not be corrected in such way (no adequate calibration target), and the image coordinates were simply converted to real-world coordinates by using two reference points.

The contours were used to determine the ame widths at discrete heights (every 1 or 10 cm depending on the ame size), which in turn provided a prole, used hereafter to represent the ame shape.

Heat uxes

Radiative heat uxes were measured at various locations around the pool res, using 6 vertical cooled (air or water) gauges at ADP (see Fig. 1a) and 8 uncooled ones at repeat to another (max. ±0.2 m), which explains some dierences in the graphs presented afterwards (Fig. 4 and5). Numerical heat uxes were computed over a range of positions in order to take into account such variations and allow for comparisons to the measured values, but also give a sense of the model sensitivity (see Sec. 5).

Experimental results

Flame radiative properties

Results regarding the radiative properties of kerosene ames were reported elsewhere [START_REF] Parent | Spectral radiation emitted by kerosene pool res[END_REF],

and only a summary will be given here. The opacimetry setup allowed to measure transmittance levels at various wavenumbers, which were used to compute the absorption coecient κ a needed in Eq. 2 as

κ a σ = β σ = β 0 σ σ 0 α , (3)
where κ a σ = β σ because scattering in the ame is neglected [START_REF] Parent | Spectral radiation emitted by kerosene pool res[END_REF], β 0 is the extinction coecient at a reference wavenumber σ 0 (arbitrarily set to 4000 cm =1 , in the center of the spectral range considered here), and α is a fuel-dependent exponent [START_REF] Modest | Radiative Properties of Particulate Media[END_REF]. Once the absorption coecient is determined using Eq. 3, the radiation intensities measured using the spectrometer were tted with Eq. 2 to determine the remaining unknown, the equivalent temperature T [START_REF] Parent | Spectral radiation emitted by kerosene pool res[END_REF]. The ame emission was thus described by three parameters, α, β 0 , and T . This procedure was applied to all repeats, and the resulting values showed to be only weakly dependent on re size [START_REF] Parent | Spectral radiation emitted by kerosene pool res[END_REF], which is an interesting information regarding the upscaling of radiative data. Average values were thus calculated, yielding α = 1.07,

β 0 = 1.44 m -1
, and T = 1243 K.

These results are meant to give a spectrally resolved description of soot radiation for kerosene res of various sizes, at a reduced computational cost as Eq. 2 can be solved analytically using Eq. 3. They can also be used to determine an eective absorption coecient κ a e [cm =1 ], which further simplies computations. However it should be noted that this implies that the medium is considered grey, and this simplication is only relevant if the targets are also grey bodies. Here, the numerical results will be compared to measured radiative heat uxes, which are not resolved spectrally: an eective absorption coecient is thus a reasonable approximation. It was computed by integrating Eq. 2 over all wavenumbers, and tting the results with a function of the path line through the ame e, namely I = C [1 -exp(-κ a e e)] (C is a constant, not relevant here). This is illustrated in Fig. 2, with κ a e = 1.09.

Flame geometry

Flame proles were extracted from visible images of one representative test per re size, as described in Section 2.2.2, and averaged over the steady phase. The resulting points were tted using common simple geometries and observations during the experiments.

Each prole, made of N points x exp [m], was tted with a conical and a cylindrical shape (coordinates x t ). The agreement of each t was evaluated based on the Root-mean-square error (RMSE) and the results are shown in Fig. 3a. Overall, the cone geometry provides the best ts for all re sizes, as indicated by smaller RMSE: this shape will thus be used to model ame radiation, with the parameters given in Fig. 3b (diameter d co and height h co insucient: more data are available and have to be analysed in order to determine clear trends for ame geometry. For the models presented here, the cone shapes will thus be set according to the individual values presented in Fig. 3b.

Models

The experimental data gathered regarding the ame geometry and radiation emission were used to compute heat uxes at several positions, which were then compared to the measured values (see Sec. 5). Four modelling approaches will be presented, in order to evaluate the underlying assumptions and assess how well they can predict radiation from kerosene res of various sizes. All the models will focus on the ame, thus considering the surrounding atmosphere as transparent/non-participating (no emission, absorption or scattering).

Emitting-absorbing ame

The most complete approach presented here is based on the equivalent medium described in Sec. 2.2.1 and 3.1, which models soot radiation as that of a homogenous, isothermal and non scattering medium. This means that radiation is emitted but also absorbed within the

I = [1 -exp(κ a e e)] σ SB T 4 π , (4)
where

σ SB is the Stefan-Boltzmann constant [W • m =2 • K =4 ].
The distance travelled inside the ame, e, is based on the ame geometry and target position. The computations were performed using a Monte-Carlo Method (MMC): quanta are randomly shot from or towards the radiation emitter, and followed through the domain in order to determine the variations in energy and direction for each one of them. When a sucient number of rays/quanta is used, this technique allows to predict almost exactly the radiative heat uxes q [W] received by targets, for example here the heat ux meters.

Thin ame approximation

Considering the ame as an optically thin medium means that no absorption takes place:

all radiation emitted from the ame volume can reach external targets. The heat uxes are given by

q = F V P V with P V = 4 V κ a e σ SB T 4 , (5)
where P V is the emissive power [W] of the ame volume V [m 3 ]. The values for V , κ a e and T are taken from the experiments (Sec. 3). The view factor F V [] was determined numerically with a ray-tracing method, that is a MMC where only the direction of the quanta is monitored.

Thick ame approximation

On the contrary, if the ame is considered as optically thick its absorption is so high that all radiation from within the ame is absorbed before reaching its surface, and thus external targets are only aected by radiation emitted by the ame envelope, that is q = F S P S with P S = S σ SB T 4 ,

where P S is the emissive power of the ame surface S [m 2 ], and its emissivity []. The latter is given by = 1 -exp(-κ a e e) (see e.g. [START_REF] Àgueda | Experimental study of the emissivity 378 of ames resulting from the combustion of forest fuels[END_REF]). Experimental values were used to describe the geometry and the radiation emission (see Sec. 3). The view factor F S can be determined analytically for some congurations [START_REF] Howell | Radiative transfer conguration factor catalog: A 397 listing of relations for common geometries[END_REF], but here it was computed numerically (ray-tracing) as it was more convenient and did not add any computational cost.

Black ame approximation

This last assumption is the simplest, and is an extension of the optically thick case (Eq. 6)

where the surface is considered to be a blackbody, thus implying = 1.

Comparisons of numerical and experimental results

Experimental heat uxes are given in Fig. 4 The optically thick and emitting-absorbing ame models also give the best description of medium to large ames (70 to 250 cm, Fig. 4e and f and Fig. 5), while the optically thin approximation now largely overestimates the measured values, as does the black ame.

Discussions

Overall, the largest dierences between numerical and experimental heat uxes are found close to the ame. This is likely due to the fact that, at these locations, the computations are more sensitive to the ame shape, which is one of the approximations made in this work.

As seen on Fig. 4 and5, the emitting-absorbing and optically thick models give good results for all re sizes, as already concluded from a more theoretical point of view by [START_REF] Collin | Evaluation of simple models of ame radiation in the frame of re propagation[END_REF].

The dierences with the experimental values could be explained by the fact that only soot radiation was modelled (Eq. 4). This could be the reason why heat uxes were under-predicted for the 30 cm test (Fig. 4a and4b), as the contribution of hot combustion gases (H 2 O and CO 2 ) was not taken into account, when in fact it could represent a signicant part of the radiation of such small ames. Similarly, the slight over-prediction for larger res could be due to the fact that absorption by cold atmospheric gases was neglected, although it could have had an impact on the measured values, especially for re tests of width 70 cm and above for which the instruments were located far away from the ame (approx. 20 m).

It can also be noted that the optically thick approximation tends towards the emitting-absorbing model as the re size increases. This could be expected because as the ame width, and thus its optical thickness, increase, the optically thick assumption becomes more and more valid.

As mentioned earlier, the black ame model overestimates the experimental values for all the re sizes investigated here. This suggests that even the biggest ames (2.5 m wide kerosene pool res, Fig. 5e and5f) do not emit like blackbodies, and this assumption should thus be used with care, unless conservative results are wanted. This is in agreement with data from the literature, for which ame thicknesses of approximately 3 m are required to reach blackbody radiation [START_REF] Steinhaus | Large-scale pool res[END_REF]. The overestimation by the black ame approximation appears to be caused by the emissivity value ( = 1), because a model considering emission by the ame envelope can yield good results provided that it uses a more reasonable description of the emission, as shown by the optically thick approximation.

The optically thin ame model gives good results for small res (30 and 50 cm, Fig. 4a to d), but not larger ones because it does not take self-absorption into account, which becomes increasingly important with the re size. This is also why this approximation produces higher values than the black ame model for large ames (175 and 250 cm, Fig. 5c to f), even if the latter could have been thought as an upper limit for thermal radiation modelling (a blackbody is a perfect emitter). As noted in [START_REF] Collin | Evaluation of simple models of ame radiation in the frame of re propagation[END_REF], the thin ame approximation should be used with caution, and shows severe limitations for re applications because it is only valid for small ames (here for widths below approx. 50 cm, but this value is fuel-dependent).

It has been made clear that the relevance of each model depends on the re size, and more precisely on the optical thickness of the ame. To illustrate this, the inuence of the absorption coecient on each model is given in Fig. 6

Conclusions

Part of the data gathered during an extensive experimental campaign was analysed to characterise radiation from kerosene res. The ame shape and radiative properties were extracted for a wide range of re sizes (30 to 250 cm wide). A simple cone shape was chosen to represent the average visible ame, and its parameters were determined for all re sizes. It is worth noting that the best shape was independent of re size. The measurements relative to the ame emission (opacimetry and spectrometry) provided detailed and novel data, especially for large scale res. The results showed almost no dependence on the re size, thus suggesting that an upscaling approach is possible. More details for kerosene can be found in [START_REF] Parent | Spectral radiation emitted by kerosene pool res[END_REF].

Regarding the modelling work, the emitting-absorbing ame model shows encouraging results, even with simplied input data (e.g. ame shape) and several assumptions (e.g. homogenous isothermal medium, gases contribution ignored). This suggests that the key phenomena of ame radiation were captured and modelled to a good degree. Although not highlighted in the application presented here, it should be noted that this approach provides spectrally resolved results at reduced computational cost (Eq. 4 is solved analytically).

The optically thick approximation also shows a good agreement with the experimental data, especially for large re sizes. The two other models (optically thin and black ame)

do not provide satisfactory results, as they under/overestimate the measured values depending on the re size, and are thus too limited in terms of applicability. More specically, the optically thin approximation appears to be suited only for small ames, and thus limited to the very beginning of a re or to specic fuels, while the black ame model overestimates emission even for the largest ames investigated here.

The perspectives of this work include additional data processing, as the same tests were also conducted for heptane, diesel, polyurethane foam, and wood res, but also an improvement of the models, for example by including absorption and emission by H 2 O and CO 2 . The ame shape could also be rened, as cameras were located at several viewing angles for most of the tests. It is hoped that this will further contribute to the understanding of ame radiation and how it can be accounted for.

Acknowledgments

The authors would like to thank the sta of the Fire Engineering division at LCPP for performing the large scale tests, and more widely all personnel of the Préfecture de Police who helped setting them up. The Groupe Aéroports de Paris (ADP) and the Direction Générale de l'Armement (DGA) are acknowledged for providing the test site and the fuel respectively. The technical sta at LEMTA is thanked for designing and building measuring devices and other equipment. Positions relative to pan top edge. Vertical targets. Positions relative to pan top edge. Fig. 6.

Figure captions

Inuence of the extinction coecient κ a on the heat ux q , depending on the model used to compute it. Arbitrary horizontal target at (1;0) m (distance;height).

Fig. 1 .

 1 Fig. 1. Radiative heat ux meters layout at ADP and PROMETHEI test sites (not to scale).

Fig. 2 .

 2 Fig. 2. Integrated radiation intensity I as a function of ame width e (solid line), and tted function I = C [1 -exp(-1.09 e)] (dashed line; C is a constant, not relevant here).

ame, as described by Eq. 2 .Fig. 3 .

 23 Fig. 3. Root-mean-square error of the ts of simple shapes (cone or cylinder) on the experimental ame proles for kerosene (Fig. a), and values of the parameters for the selected conical shape (Fig. b). One representative test per re size.

  and 5 as functions of height (xed distance of approx. 1 m) or distance (xed heights of approx. 1 or 2 m), relative to the top edge of the pan. Measurements were averaged over the steady phase of three tests for every re size except 175 and 250 cm (repeated twice and once resp.). The smallest, mean and largest values of these heat uxes are provided (cross and vertical error bar), along with the variations in height or distance from one repeat to another (horizontal error bar). A good repeatability was observed, except for the closest heat ux of the 250 cm wide re (Fig.5e, just below 2 m) because the ame was tilted. Time variations over the steady phase were negligible, and the uncertainty on the heat ux meters was estimated to be 4 %, which is smaller than the spread caused by changes in position shown here (vertical bars). Numerical values were computed over a range of positions encompassing the locations of the experimental measurements (max. ±0.2 m). An average is presented (line), as well as the minimum and maximum values (edges of the shaded area). It can be seen that the impact of changes in location gets smaller with increasing distance or height as well as increasing re size. Comparison of experimental and numerical heat uxes shows that for small res (30 and 50 cm, Fig.4a to d), the black ame model clearly overestimates the measured values, both for the horizontal and vertical orientations. The other models are closer to the experimental values and show similar trends.

Fig. 4 .

 4 Fig. 4. Heat uxes for kerosene res of various widths. Average experimental values (+), with min. and max. values for position and heat ux. Numerical results computed for a range of positions (see subcaptions). Models: emitting-absorbing ( ), optically thin ( ), optically thick ( ) and black ame ( ). Positions relative to pan top edge.

Fig. 5 .

 5 Fig. 5. Heat uxes for kerosene res of various widths. Average experimental values (+), with min. and max. values for position and heat ux. Numerical results computed for a range of positions (see subcaptions). Models: emitting-absorbing ( ), optically thin ( ), optically thick ( ) and black ame ( ). Vertical targets. Positions relative to pan top edge.

Fig. 6 .

 6 Fig.6. Inuence of the extinction coecient κ a on the heat ux q , depending on the model used to compute it. Arbitrary horizontal target at (1;0) m (distance;height).

Fig. 1 .

 1 Fig. 1.Radiative heat ux meters layout at ADP and PROMETHEI test sites (not to scale).

Fig. 2 .

 2 Fig. 2. Integrated radiation intensity I as a function of ame width e (solid line), and tted function I = C [1 -exp(-1.09 e)] (dashed line; C is a constant, not relevant here).

Fig. 3 .

 3 Fig. 3. Root-mean-square error of the ts of simple shapes (cone or cylinder) on the experimental ame proles for kerosene (Fig. a), and values of the parameters for the selected conical shape (Fig. b). One representative test per re size.

Fig. 4 .

 4 Fig. 4. Heat uxes for kerosene res of various widths. Average experimental values (+), with min. and max. values for position and heat ux. Numerical results computed for a range of positions (see subcaptions). Models: emittingabsorbing ( ), optically thin ( ), optically thick ( ) and black ame ( ).

Fig. 5 .

 5 Fig. 5. Heat uxes for kerosene res of various widths. Average experimental values (+), with min. and max. values for position and heat ux. Numerical results computed for a range of positions (see subcaptions). Models: emittingabsorbing ( ), optically thin ( ), optically thick ( ) and black ame ( ).

  for a 250 cm re (target at an arbitrary location, see caption). It can be seen that for low values of κ a (equivalent here of low optical thicknesses), the emitting-absorbing ame model gives the same results as the optically thin approximation. For high values of κ a , the emitting-absorbing ame model tends towards the black ame model. The optically thin and black ame models could thus be regarded as limiting cases, but Fig.6shows that for intermediate absorption coecients they both yield heat uxes greater than the emitting-absorbing ame model. The two simple approximations (thin and black ames) are thus only relevant for extreme κ a values, and only the emitting-absorbing ame model seems to describe the ame emission accurately for all situations. The optically thick approximation also gives decent results for intermediate to high values of κ a , but it seems less accurate for lower ones.