Miage Glacier (Figure 1), located on the southern side of the Mont Blanc massif in the western Italian Alps (45°47′N, 06°52′E), has a total area of 10.5 km² and an elevation range of 1,740–4,640 m above sea level (a.s.l.) (Fyffe et al., 2014). The lowest 5 km² of the glacier, below approximately 2,500 m a.s.l., is almost completely covered by coarse, angular rock debris, dominated by mica-schists, gneiss, and granite, with smaller amounts of amphibolite, slate, fault breccia, quartzites and limestone, with iron oxidation common (Deline, 2002; Franzetti et al., 2013). Debris thickness increases downglacier from a thin and patchy cover <0.10 m thick in the upper ablation zone, to >0.50 m on the terminal lobes, and thickness is predominantly in the range 0.20–0.40 m over large areas of the tongue (Mihalcea et al., 2008; Foster et al., 2012) except for isolated blocks and debris mounds which may exceed 10 m thickness (Deline, 2009). The debris primarily originates from rockfalls and mixed snow and rock avalanches from the surrounding valley walls (Deline, 2009) and melt out of englacial debris forming moraines in the ablation area (Deline et al., 2012). In vertical profile, debris cover typically exhibits downward fining from an open-work cobble/boulder layer at the surface, through pebbles and granules, to sands and silts at the debris-ice interface. Brock et al. (2010) recorded mean ablation season melt rates ranging from 33 mm water equivalent (w.e.) d⁻¹ beneath 0.04 m of debris to 6 mm w.e. d⁻¹ beneath 0.55 m debris, with the lowest layers of debris normally saturated with water during the ablation season. Temperatures over the debris-covered area were almost continuously positive in the June-September period, with frosts at the debris surface recorded on average only every 10 nights, although decreasing temperature with depth implies that frosts could be more frequent at the base of the debris layer at the ice interface. Fyffe et al. (2019b) recorded surface streams draining debris-covered sub-catchments, supplied by meltwater flowing through the base of the debris matrix. This observation implies a dynamic water table in debris, rising in the morning as dilute meltwater floods the lower layers, and falling during the evening and overnight due to declining melt rates and drainage. Furthermore, Brock et al. (2010) recorded daytime evaporation rates over debris as high as 1 mm h⁻¹ suggesting that capillary action draws liquid water upwards into the warmer open-work cobble layers, which are open to atmospheric turbulence. Debris cover is highly mobile on moraine slopes and in the vicinity of streams and ice cliffs, and its distribution is intimately linked to spatial patterns of surface ablation (Fyffe et al., 2014; 2020; Westoby et al., 2020).

Direct measurement of the near-surface vertical CO₂ flux in mg m⁻² s⁻¹, F _c , was made using an open-path eddy covariance system, referred to as the EC system hereafter, consisting of a CSAT3 three-dimensional sonic anemometer and an EC150 CO₂/H₂O open path infra-red gas analyser, supplied by Campbell Scientific Ltd., Loughborough, United Kingdom (Table 1). The principles of trace gas flux measurement over glaciers using EC systems have been explained elsewhere, e.g., Wang and Xu (2018), and so are not repeated here. The EC system was installed at two separate sites in two different years to examine F _c variation over differing debris thickness and elevation: i) a lower weather station (LWS) at 2,000 m a.s.l., with mean debris thickness of 0.23 m, typical of the relatively thick debris present over much of the lower glacier, in the 2013 ablation season; and ii) an upper weather station (UWS) at 2,380 m a.s.l, with mean debris thickness of 0.04 m, representative of thin debris on the upper part of the continuously debris covered zone, in the 2016 ablation season. Both sites were located at the centre of level areas of the glacier surface, with little elevation variation within ∼50 m of the LWS, and ∼10 m of the UWS, with an upglacier slope of ∼6° starting at a distance >10 m from the UWS (Figure 2). Surface debris around the measurement sites was mainly in the size range 0.10–0.40 m (long axis), with occasional boulders >1 m, at the LWS, and mainly <0.05 m (long axis) at the UWS. EC instruments were mounted surface parallel on cross arms at 1.83 m height, attached to a free-standing tripod, and oriented towards the dominant wind direction (westerly at the LWS and north-westerly at the UWS) to minimise airflow shadowing by the tripod and the mounting apparatus. The measurement height at a little below 2 m was considered a suitable distance from the surface to capture dominant turbulent eddies in the airflow, whilst not seriously violating the assumption of the constant flux layer. Previous work at the LWS site revealed an absence of katabatic flows, due to convection from the debris cover, with the wind speed maximum normally located above 2 m from the surface (Brock et al., 2010).

EC measurements were conducted between 26th June and 6th September 2013 at the LWS, and 24th June and 8th September 2016 at the UWS. 20 Hz measurements were recorded on a Campbell Scientific CR3000 datalogger and processed into 30-min averages using Campbell Scientific Open Path Eddy Covariance software (www.campbellsci.com). Corrections to the raw data were applied as follows: removal of unreliable values using sonic anemometer and gas analyser diagnostic codes; removal of low signal strength values (<90% full signal); lagging of CO₂ measurements against sonic wind measurements using a covariance maximisation procedure; and application of the “WPL” flux correction for air density fluctuations (Webb et al., 1980). Outlying values in the 30-min averages, defined as F _c fluxes greater than +/- 3 standard deviations about the mean, were also removed prior to further analysis. The majority of removed data were due to: i) rain or condensation lying on the sensor nodes reducing signal strength; and ii) data gaps due to power or logger failures, in particular between 16 July and 10 August 2013. The number of remaining half hour values were 1,941 at the LWS and 2,928 at the UWS. Measurement sites were monitored every 1–2 days in late June, early July, and early September, and on 1 day in early August, and minor adjustments made to level instruments due to differential ablation beneath the tripod feet.

Under stable atmospheric conditions with low wind speed, turbulent mixing may be insufficient for CO₂ absorbed or released at the surface to reach the instrument level. Estimation of the sub-instrument CO₂ storage is an important consideration in ecological studies where instrument heights are typically several metres above the vegetation surface and biological activity and surface roughness are high. However, over supraglacial debris, unstable atmospheric conditions dominate during ablation periods and wind speeds are high and sustained, even during the night (Brock et al., 2010). Only 0.3% of the total half hour records had a friction velocity <0.05 m s⁻¹, and no records had a friction velocity <0.01 m s⁻¹, indicating that periods of weak turbulent mixing were rare. Wang and Xu (2018) identified the daily atmospheric CO₂ storage in the debris area of Koxkar glacier to be less than 1% of net glacier carbon exchange, which they attributed to the low instrument height (2 m) limiting space for CO₂ storage and the porous nature of the surface material. Due to the low likelihood of substantial surface CO₂ storage, it was not considered in analysis of F _c in this study.

Both EC measurement sites were equipped with additional meteorological sensors to enable analysis of F _c variations using independent environmental variables. Air temperature, T _a (°C), and relative humidity (%) were measured using a HMP45C temperature and relative humidity sensor, housed inside a naturally ventilated Met21 radiation shield (both Campbell Scientific Ltd.). The Met21 radiation shield has been shown to be effective at protecting temperature sensors from anomalous solar heating on a debris-covered glacier (Shaw et al., 2016). The 4 components of the surface radiation balance (incident and reflected shortwave radiation, S↓ and S↑, respectively, and incoming and outgoing longwave radiation, L↓ and L↑, respectively; all in units of W m⁻²) were measured using Kipp and Zonen CNR1 (LWS) and CNR4 (UWS) radiometers. All instruments were mounted at 1.83 m, except the radiometers, which were mounted at 1.6 m. The instrument setup was very similar to that described in Brock et al. (2010) and full sensor specifications can be found in that paper. Hourly precipitation totals were obtained from the Lex Blanche weather station, operated by Regione Valle d’Aosta, 4 km west of the LWS at 2,162 m a.s.l. in both 2013 and 2016. Additional hourly precipitation data were available from a rain gauge at 2,340 m a.s.l. on Miage Glacier in 2013. The incoming and outgoing longwave radiation fluxes were used to calculate debris surface temperature, T _s , using a surface emissivity of 0.94, following Brock et al. (2010). Wind speed, u (m s⁻¹), was calculated from the two horizontal wind speed components recorded by the sonic anemometer.

To help understand processes controlling F _c recorded at the EC stations, the upwind contributing glacier surface areas, or footprints, were calculated. A particular consideration at the LWS site is the presence of forested areas 0.5–1.0 km distant which could influence F _c through photosynthesis and soil microbial processes. We calculated contributing areas using the Agroscope Reckenholz Tanikon (ART) footprint tool (Version 1.0, 13.03.2007) developed by the Swiss Federal Agricultural Research Center (Neftel et al., 2008). The ART footprint model is based on the analytical footprint model of Kormann and Meixner (2001) and has been successfully applied in the complex terrain of a debris-covered glacier (Wang and Xu, 2018).

Using analysis for all days of EC data, the glacier surface footprints at each site remain constant throughout the season and are dominated by areas <200 m from the EC stations (Figure 2). The main contributing areas are upglacier from the measurement sites corresponding with dominant wind direction (Figure 3); to the west of the LWS, with a small additional component from the south-east, and to the northwest of the UWS. The contribution of non-glacier areas was <0.1% at both sites, and hence off-glacier photosynthesis and respiration can be discounted as a significant influence on F _c recorded at the EC stations. No snow was recorded in the vicinity of the LWS during the 2013 measurement period. At the UWS, there was a continuous snow cover starting a few metres upglacier of the EC station in late June, coincident with the main contributing area. The snow cover had retreated several hundred metres upglacier by mid-July. Snow cover will therefore influence F _c at the UWS only in the first 2–3 weeks of the 2016 measurement period.

In the results section, F _c is presented visually for each site as daily and half-hourly time series, and as mean daily cycles using season-averaged values for each hour of the day. Regression analysis of half hourly F _c on independent meteorological variables (S↓, T _s , T _a , and u) is conducted on day (S↓ >0 W m⁻²), night (S↓ ≤0 W m⁻²) and half season (June-July = early season; August-September = late season) data subsets. The former subdivision is made due to the contrasting temperature regimes of debris in the day and night, and the latter subdivision is made to aid assessment of potentially influential long-term changes such as snow cover retreat, depletion of available reactive sediment within debris covers, and decline in S↓ between the early and late season. An alpha level of 0.05 is used to identify significant relationships. As is conventional in glaciological research, in this study fluxes of energy and mass are considered positive when directed towards the surface and negative when directed away from it.

At the LWS, daily net total F _c is positive for most days of the 2013 ablation season, with a mean of 1.58 g m⁻² d⁻¹, indicating a net downward flux of CO₂ into the debris (Figure 4A, top trace). In the late June to mid-July period, daily total F _c varies between 1.5 and 3.0 g m⁻² d⁻¹, except for a value of 0.6 g m⁻² d⁻¹ on 9 July. Daily net total F _c remains positive on most days from mid-August to early September, but values are slightly lower, typically in the range 0.8–2.4 g m⁻² d⁻¹, with negative values on 19 and 24 August, and values close to zero on 23 and 27 August, and 4 September. Daily net total F _c does not exceed 2.0 g m⁻² d⁻¹ after 29 August.

F _c values at the LWS broadly correspond with the pattern of daily average S↓, T _a , and T _s over the 2013 season, particularly in June and July (Figure 4A). Days with high positive F _c are generally concurrent with high S↓ and T _s , indicating warm and sunny weather conditions, while low positive or negative daily F _c totals, e.g., on 9 July, and 19, 24, and 27 August, correspond with marked drops in S↓ and T _s (Figure 4A), associated with relatively cool and cloudy conditions. There are some exceptions, e.g., daily F _c values decline between 4 and 7 July, while T _a and T _s increase, and S↓ remains steady, over the same period, and daily F _c totals appear to be independent of S↓, T _a , and T _s in the first week of September. There is no clear relationship between u and F _c at the LWS site, with days of high u corresponding with both high and low F _c . The days with the highest positive F _c totals in their respective half season periods: 30 June (2.8 g m⁻² d⁻¹) and 4 July (3.0 g m⁻² d⁻¹), and 25, 26, and 29 August (2.1–2.4 g m⁻² d⁻¹), are preceded by days of heavy rainfall (daily totals in the range 6–33 mm) and, in most cases, very low debris surface temperatures. T _s minima were <0°C on the mornings of 28 and 29 June, and <0.5°C on the mornings of 26 and 28 August. A data gap on 25 June means the minimum for that morning is not known. However, T _s remained well above 0°C throughout 4 July, and several days in August had F _c totals >2.0 g m⁻² in the absence of rain or very low T _s .

At the UWS site, daily total F _c totals are predominantly negative, or close to zero, in the early season June to July period, with a mean of −0.5 g m⁻² d⁻¹, indicating a net upward flux of CO₂ from debris to the atmosphere (Figure 4B, top trace). Daily F _c totals are most strongly negative in June and the first half of July, with values in the range −2.5 to +0.2 g m⁻² d⁻¹. In the second half of July, daily F _c totals are close to zero, ranging from −1.0 to +0.6 g m⁻² d⁻¹, except for a notable high positive total of 1.9 g m⁻² d⁻¹ on 15 July. In contrast to the June-July period, daily F _c totals are generally slightly positive in August and September, typically ranging from −0.6 to +1.7 g m⁻² d⁻¹, with a mean of +0.4 g m⁻² d⁻¹, indicating a net downward flux of CO₂ to the debris in the second half of the 2016 season. There are large positive totals of 2.6 and 2.2 g m⁻² d⁻¹ on 10 and 11 August, respectively, and a large negative total of −1.4 g m⁻² d⁻¹ on 18 August. The mean daily total F _c at the UWS site over the 2016 season is −0.06 g m⁻² d⁻¹; one-16th of its magnitude of the LWS site in 2013, and of opposite sign.

There is no clear visual relationship between daily total F _c and daily mean S↓, T _a , T _s , and u at the UWS in the period from late June to the middle of August 2016 (Figure 4B). A weak direct relationship between daily total F _c and daily mean S↓, T _a and T _s is apparent in the second half of August and first week of September, however, but F _c still appears to be independent of u. In similarity to the LWS, the days with the highest positive daily F _c at the UWS, in the range 1.7–2.6 g m⁻² d⁻¹ on 15 July, and 6, 10, and 11 August 2016, all occurred on days with morning T _s <0°C, following heavy rain on the previous day (Figure 4B). Meteorological conditions were similar on these days, but not unusual in comparison to the rest of 2016, with relatively high S↓, and slightly below average T _a and T _s . Other days with morning T _s values <0°C: 27 June, 3 July, and 22 August, also show increased F _c totals compared with neighbouring days. Similarly, the 6 July, the only day in the first 3 weeks of the 2016 season with a positive F _c , total had low T _s (<0.5°C in the early morning) following heavy rain on the preceding day.

At the LWS, hourly-averaged F _c displays a strong diurnal cycle with an approximately bell-shaped curve of positive daytime values, centred on an early afternoon peak, while the night-time F _c is characterised by negative values of smaller magnitude, with no clear relationship to the time of night (Figures 5A, 6A). On an average day in the 2013 season, the LWS F _c is positive for 12 h between 8.00 and 20.00, peaking at >90 mg m⁻² s⁻¹ (>0.3 g m⁻² h⁻¹) between 14.00 and 15.00, while night-time F _c drops to −14 mg m⁻² s⁻¹ (−0.05 g m⁻² h⁻¹) between 22.00 and 23.00, and then varies in a narrow range between −8 and −15 mg m⁻² s⁻¹ (approximately −0.03 to −0.05 g m⁻² h⁻¹) until 8.00. Peak half-hour F _c exceeds 140 mg m⁻² s⁻¹ (>0.5 g m⁻² h⁻¹) in several days in June, July, and August (Figure 5A). Both the magnitude and variability of night-time F _c increases from late June to the middle period from mid-July to mid-August, with peak half-hour F _c occasionally exceeding −50 mg m⁻² s⁻¹, (−0.18 g m⁻² h⁻¹) before reducing in magnitude again in late August and early September, although still with a high amount of variability (Figure 5A).

At the UWS site, hourly-averaged F _c shows a similar pattern of positive daytime, and negative night-time values, but with lower magnitude in the daytime, around one-third of that at the LWS, while night-time values are in a similar range at both sites (Figures 5B, 6B). The UWS site also shows greater temporal variability in both day and night F _c over the 2016 measurement period compared with the LWS site (Figure 5). At the UWS, F _c transitions from the early period up to the middle of July, which is dominated by relatively high negative night-time flux and weak positive daytime flux, through the second half of July when positive daytime and negative night-time fluxes are approximately in balance, to the August-September period when positive daytime fluxes generally exceed negative night-time fluxes. On an average day in the 2016 season, the UWS F _c is positive for 7 h between 10.00 and 17.00, peaking at 27 mg m⁻² s⁻¹ (∼0.1 g m⁻² h⁻¹) between 13.00 and 14.00, while night-time F _c drops to −16 mg m⁻² s⁻¹ (−0.06 g m⁻² h⁻¹) between 20.00 and 21.00, and then gradually increases over the remainder of the night, reaching −5 mg m⁻² s⁻¹ (−0.02 g m⁻² h⁻¹) between 8.00 and 9.00 (Figure 6B). Daytime, half-hour F _c rarely exceeds 60 mg m⁻² s⁻¹, (∼0.2 g m⁻² h⁻¹) but peak fluxes over 110 mg m⁻² s⁻¹ (∼0.4 g m⁻² h⁻¹) are recorded on 3 days, all of which had morning T _s <0°C (Figure 5B).

There is a striking similarity in the form and temporal alignment of the mean daytime cycles of F _c , T _s , and S↓ at both sites (Figures 6A, B). At the LWS site, the initial morning rise and daytime peak of S↓ occur 1 hour earlier than the corresponding inflection points in the F _c curve, whereas T _s and F _c vary in unison, with temporally aligned inflection points in the morning, early afternoon, and evening. At the UWS site, the initial morning rise in S↓ occurs 1 hour earlier than the corresponding rises in F _c and T _s , however, the peak values of all 3 variables occur together between 13.00 and 14.00, and their evening inflection points are similarly temporally aligned. While S↓ is of similar magnitude at the LWS and UWS in the 10.00–17.00 high flux period, with mean values of 747 and 743 W m⁻², respectively, F _c and T _s values over the same period are much lower at the UWS, at 28% and 67% of their LWS values, respectively. The duration of high S↓ values over 100 W m⁻² is 3 h shorter at the UWS compared with the LWS due to topographic shading in the early morning and evening. During the night, hourly mean T _s gradually decreases from the late evening to a minimum value between 5.00 and 6.00 at both sites, while over the same period F _c contrasts between a gradual and variable increasing trend at the UWS, and no trend with small variability at the LWS.

Results of the statistical analysis are presented in Tables 2, 3; Figures 7, 8.

Daytime F _c has significant direct relationships to T _s , and S↓ at both the LWS and UWS sites and in both half-season and full season data sets. The simple linear regression relationships are strongest at the LWS, particularly in the June-July period when T _s , and S↓ each account for >60% of the variance in daytime F _c , with the slight lag between daytime cycles of F _c and independent variables (Figure 6) and associated hysteresis accounting for some of the unexplained variance. The relationships of F _c to T _s , and S↓ at the UWS are weak, although significant, in the June-July period but become much stronger in August-September when S↓ explains a greater amount of F _c variance than at the LWS. The slope coefficients for the regressions of F _c on T _s , and S↓ at the LWS decrease between June-July and August-September indicating a lower sensitivity of F _c to debris surface temperature and incoming shortwave radiation in the second half of the season. In contrast, at the UWS the corresponding slope coefficients increase between June-July and August-September, approximately doubling the sensitivity of F _c to T _s , and S↓ in the second half of the season, although still with lower sensitivity than at the LWS. The scatter of high magnitude negative daytime F _c values, visible in the LWS graphs, particularly in August-September (Figure 7 top two panels and Figure 8), is mostly associated with rainfall events when it is possible that water interfered with gas analyser measurements, even though the instrument signal strength was above threshold. Hence, the decrease in slope coefficients and R ² values between June-July and August-September for the relationships of F _c to T _s , and S↓ at the LWS may be at least partly due measurement error, rather than purely due to change in physical process.

Daytime F _c has significant direct relationships to T _a and u at the LWS, with the slope coefficient and R ² value for the T _a relationships quite consistent between June-July and August-September but dropping markedly for the u relationships over the same period (Table 2). In contrast, daytime F _c has a weak, although significant, dependency on T _a at the UWS, changing from an inverse to a direct relationship between June-July and August-September. The relationship of daytime F _c to u at the UWS is significant and inverse in both periods, changing from a moderately strong relationship in June-July to a very weak relationship in August-September. The night-time relationships of F _c to T _s and T _a at the LWS are either weak or non-significant, but F _c has a moderately strong and significant inverse night-time relationship to u in June-July, becoming weak, although still significant, in August-September (Table 2; Figure 7). In contrast, at the UWS night-time F _c has moderately strong and significant inverse relationships to T _s , T _a , and u in both June-July and August-September. In particular, u accounts for almost half of night-time F _c variance at the UWS in June-July, and over a third in August-September.

A stepwise regression procedure was used to develop multivariable relationships to explain F _c variance, whilst accounting for collinearity between independent variables, with the resulting significant relationships for F _c in mg m⁻² s⁻¹ as follows:

LWS daytime: F u l l   s e a s o n : F c = − 6.7 + 4.6 T s − 5.42 T a + 0.0303 S ↓ + 6.1 u , R 2 = 0.69 . (1) J u n − J u l : F c = − 23.3 + 3.17 T s − 3.4 T a + 8.0 u + 0.0533 S ↓ , R 2 = 0.805 . (2) A u g − S e p : F c = 7.2 + 5.22 T s − 6.69 T a + 0.0177 S ↓ + 5.1 u , R 2 = 0.608 . (3)

UWS daytime: F u l l   s e a s o n : F c = 8.3 + 0.0251 S ↓ + 0.9 T s − 8.1 u , R 2 = 0.477 . (4) J u n − J u l : F c = 15.4 + 0.0278 S ↓ − 8.1 u − 0.38 T a , R 2 = 0.433 . (5) A u g − S e p : F c = 11.5 + 4.82 T s − 5.3 T a + 1.4 u , R 2 = 0.605 . (6)

LWS night-time: F u l l   s e a s o n : F c = 8.8 − 4.9 u + 2.23 T s − 2.13 T a , R 2 = 0.111 . (7) J u n − J u l : F c = 7.4 − 6.17 u − 0.52 T a , R 2 = 0.258 . (8) A u g − S e p : F c = 8.9 − 4.8 u + 2.5 T s − 2.28 T a , R 2 = 0.097 . (9)

UWS night-time: F u l l   s e a s o n : F c = 23.5 − 10.4 u − 0.69 T a , R 2 = 0.435 . (10) J u n − J u l : F c = 25.6 − 11.3 u − 0.45 T a , R 2 = 0.468 . (11) A u g − S e p : F c = 23.4 − 10.9 u − 0.65 T a , R 2 = 0.385 . (12)

All four meteorological variables (T _s , T _a , S↓ and u) independently explain part of the daytime F _c variance at the LWS, with T _s accounting for the largest portion, and S↓ and u the least, and these relationships have very high coefficients of determination, particularly in June-July (Eqs 1–3). F _c sensitivity to T _s and T _a increases between June-July and August-September but decreases for S↓ and u. Interestingly, the T _a slope coefficient reverses from a positive value in the simple linear regressions (Table 2) to a negative value in the multiple regression relationships (Eqs 1–3). This implies that the apparent positive relationship of F _c to T _a in the simple linear regressions is most likely spurious and due to the strong positive correlation of T _a with T _s and S↓ (Table 3). The UWS June-July daytime multiple regression relationship (Eq. 5) has a lower R ² and a different form to the LWS daytime relationships (Eqs 1–3), with F _c most strongly dependent on S↓, independent of T _s , weakly dependent on T _a , and with an inverse relationship to u. In contrast, the UWS August-September daytime multiple regression relationship and coefficient of determination (Eq. 6) are similar to the August-September daytime LWS relationship (Eq. 3), except that F _c at the UWS is independent of S↓.

The LWS night-time multiple regression relationships account for only a small proportion of F _c variance, almost entirely associated with the inverse relationship of F _c flux to u, despite the inclusion of T _s and T _a as independent variables (Eqs 7–9). By comparison, the UWS night-time relationships have higher coefficients of determination, particularly in June-July, which again is almost entirely dependent on the inverse relationship of F _c flux to u, with T _a accounting for only a small part of F _c variance (Eqs 10–12).

The seasonal F _c values infer that thick supraglacial debris is a net CO₂ sink over the ablation period, while on thin supraglacial debris net CO₂ exchange is close to zero. Assuming the LWC EC measurements are representative for thick debris generally, the mean downward flux of 1.58 g m⁻² d⁻¹ would equate to 1.58 t CO₂ km⁻² d⁻¹. With thick debris extending well over 3 km² over the glacier’s surface (Mihalcea et al., 2008; Foster et al., 2012) total drawdown over a 100-day ablation season (a conservative estimate for Miage glacier; Brock et al., 2010) could be of the order of 500 t CO₂ (0.5 Gg CO₂). In units of carbon, the total ablation season drawdown for the thick debris area at Miage Glacier would be ∼43 t C km⁻². For comparison, this is 4 times the very high drawdown rate estimated for marginal surface areas of the Greenland Ice Sheet associated with CO₂ consumption by photoautotrophic algae (Cook et al., 2012).

EC measurements of F _c over supraglacial debris are rare. To our knowledge, the only other comparable study is that of Wang and Xu (2018), who reported a net downwardly oriented F _c of 58.68 mmol m⁻² d⁻¹ (equivalent to 2.58 g m⁻² d⁻¹) over 2 years of EC measurements at Koxkar Glacier, western Tien Shan. The Koxkar Glacier site was at higher elevation (3,212 m) and on thicker debris (0.72 m) than the Miage glacier sites and included measurements during the winter accumulation and spring snow melt periods, as well as the summer ablation season. However, the magnitude of F _c is similar at both glaciers, and this strongly suggests that debris-covered glaciers with extensive covers of thick cover of silicate rocks are important to local and regional carbon cycling. Without data from outside of the ablation season, the net annual F _c at Miage glacier cannot be determined, although the small number of measurements at T _s <0°C suggest F _c magnitude becomes very small at negative temperatures. Wang and Xu (2018) observed that low rates of CO₂ drawdown continued in winter at Koxkar Glacier, even when debris was snow covered and melting absent.

The high magnitude daytime downward F _c at the LWS site, and at the UWS site in the mid July to early September period, is most likely due to CO₂ drawdown induced by a combination of hydrolysis and carbonation reactions. During the day, the debris is warmed by solar radiation, and heat energy is conducted downwards through the debris layer leading to melting of ice at the debris interface (Reid and Brock, 2010). The rates of both diffusion of atmospheric CO₂ into meltwater and rock chemical weathering will increase when T _s increases, because: i) the supply of fresh low p(CO₂) meltwater is greatest when debris surface temperature is highest; and ii) the rate of chemical reaction increases with temperature (Arrhenius principle). These interlinked processes generate a daytime F _c cycle which corresponds closely with, but slightly lags, the daytime cycles of S↓ and T _s (Figure 6). Fyffe et al. (2019b) established that surface meltwater at Miage Glacier flows through debris and drains into supraglacial streams, and so water in the debris matrix could be replenished by new ice melt before it becomes saturated in dissolved CO₂. The combination of the melt-driven supply of fresh dilute water, high temperatures, and reactive mineral surfaces open to the atmosphere makes supraglacial debris an ideal environment for rock chemical weathering and consumption of atmospheric CO₂ during the ablation season. With these conditions, daytime CO₂ drawdown rates can exceed 0.5 g m⁻² h⁻¹ when T _s exceeds 30°C, but approach zero when T _s ≤0°C (Figure 7). S↓ and daytime T _s both correlate strongly with F _c (Table 2) but this consideration of processes, and the lag between increasing S↓ and F _c in the morning (Figure 6), points to a primary role for insolation in providing energy to heat debris and drive melting, rather than being a direct control on F _c . Similarly, daytime T _a and u correlate with F _c primary because their daily cycles are controlled to a great extent by T _s (Brock et al., 2010).

The strong relationship of F _c to T _s and S↓ is consistent between the early and late season at the LWS, and late season at the UWS (Table 2; Eqs 2, 3, 6; Figures 7, 8). The early season period at the UWS is distinct, however, with F _c only weakly dependent on S↓ and T _s (Table 2; Eq. 5; Figures 7, 8), and of much lower daytime magnitude, particularly in the first 3 weeks, than in the remainder of the 2016 season (Figure 4B, upper trace). This cannot be explained by changing meteorological conditions because T _s , T _a , S↓, and u are very similar between the early and late ablation season (Table 4). The most likely explanation is the presence of extensive snow cover in the area upwind from the UWS in the early part of the 2016 ablation season. Trace gases can diffuse through seasonal snow cover (e.g., Seok et al., 2009) so the likely control of snow cover on F _c is the inhibition of processes of CO₂ uptake in debris. The high albedo and low thermal conductivity of snow will strongly reduce the heat flux to the underlying debris, suppressing ice melt and rock weathering, and limiting the consumption of atmospheric CO₂ through carbonation. The UWS site itself was already snow free when the EC station was installed, enabling the debris there to warm in response to daytime insolation. Hence, there would have been a mismatch between the sample area of S↓ and T _s , unaffected by snow cover at, or close to, the UWS site, and the snow-covered CO₂ footprint area extending 200 m upglacier, resulting in weak relationships of F _c to S↓ and T _s . Over time, the snow cover retreated, gradually increasing the area of exposed debris in the UWS contributing area. The 4-day rain event from 11 to 14 July 2016 (Figure 4B) likely removed most of the remaining snow cover within 200 m of the UWS, and subsequently daytime F _c magnitude increased (Figure 5B) and daily F _c totals transitioned from strongly negative to close to zero (Figure 4B).

Two pieces of evidence imply that the rate of daytime CO₂ drawdown is sediment limited. First, the sensitivity of daytime F _c to T _s is lower at the thin debris UWS site compared to the thick debris LWS site (Table 2; Figure 7) and F _c is greater at the LWS than the UWS for the same debris surface temperatures at all values of T _s > 8°C. Meltwater supply rate cannot be the reason for lower daytime F _c at the UWS since ice melt rates would generally be higher at the UWS due to the lower thermal resistance of thin debris cover (Reid and Brock, 2010; Fyffe et al., 2014). The likely explanation for lower F _c at the UWS is the smaller debris-water contact area in the 0.04 m debris layer, compared with the 0.23 m layer at the LWS, resulting in a lower rate of hydrolysis and atmospheric CO₂ drawdown.

Second, daily total F _c is higher on days following rain-debris frost events. At the UWS, daily F _c totals on 15 July and 6, 7, 10, and 11 August 2016 are >1.5 g m⁻² d⁻¹, much higher than the mean daily UWS flux of −0.06 g m⁻² d⁻¹ and comparable to the mean daily F _c total at the LWS of 1.58 g m⁻² d⁻¹ (Figure 4). Similarly, the second highest daily F _c total at the LWS occurred on 30 June following a rain-debris frost event (Figure 4). These results implicate the role of frost shattering in supplying comminuted reactive sediment for chemical reactions in the debris layer, particularly in thin debris covers. Freshly exposed mineral surfaces are highly reactive in contact with water (St Pierre et al., 2019; Wadham et al., 2019) and would be rapidly chemically weathered with the onset of debris warming and ice melt in the day following the frost, in turn leading to a transitory acceleration in atmospheric CO₂ drawdown. Saturation of rocks by rain followed by sub-zero temperatures, as occurred in the debris frost events identified (Figure 4), creates ideal conditions for mechanical fracture of rock clasts, due to the stress applied by expansion of freezing water in pores and along grain boundaries (Matsuoka, 1990). During fieldwork, recently shattered clasts were frequently observed on and in the debris cover, particularly in the higher parts of the debris-covered zone. There were some days at the LWS site when daily total F _c exceeded 2 g m⁻² d⁻¹ without preceding rain or frost, suggesting the availability of recently shattered sediment is less of a control on CO₂ drawdown rate in areas of thick debris. It is possible, however, that alluviation of shattered sediment by rain at the LWS on the 3 July 2013 supplied fresh reactive material to the lower water-saturated horizon of the debris layer, leading to the highest daily F _c total on 4 July. At the UWS, increases in F _c following debris frosts on 27 June and 3 July 2016 were of likely of small magnitude due to widespread snow cover at the time.

Night F _c is predominantly negative with similar magnitude at both sites: LWS night mean = −41 mg m⁻² h⁻¹ and UWS night mean = −35 mg m⁻² h⁻¹. The flux of CO₂ to the atmosphere in the night is most likely due to respiration by debris-dwelling microorganisms dominating net surface CO₂ exchange while hydrolysis and carbonation rates are low. Microbially-mediated sulphide oxidation, if present, could generate high p (CO₂) in immobile pore waters located above the night-time water table, potentially adding to night-time CO₂ emission. It is also possible that expulsion of dissolved CO₂ during overnight freezing of water in the debris periodically contributes to the negative night-time F _c . In the daytime at low T _s , F _c is also negative and of similar magnitude to the night-time, for example, for T _s <6°C, daytime mean F _c is −32 mg m⁻² h⁻¹ at the LWS and −27 mg m⁻² h⁻¹ at the UWS. Hence, microbial respiration is not restricted to night-time, but its impact on net F _c in the daytime is normally masked by the much higher magnitude of CO₂ consumption by hydrochemical reactions.

A noticeable difference between the two sites is that night-time F _c at the LWS is independent of T _s and T _a , and only weakly dependent on u, whereas at the UWS night-time F _c is significantly inversely dependent on all three independent variables (Table 2; Figure 7). The apparent relationship of night-time F _c to u, T _s and T _a at the UWS is likely to be spurious, however, because all four variables depend strongly on time of the night, with seasonally averaged hourly values decreasing almost monotonically from 8 p.m. to 8 a.m. For example, hourly averaged F _c and u correlate more strongly with hour since 7 p.m. (Pearson’s r values = 0.955 and 0.944, respectively) than they do with each other (Pearson’s r = 0.882). An alternative explanation for the night-time trend of decreasing F _c at the UWS lies in the differing water retention between thick and thin debris layers. Daytime meltwater would be expected to drain quickly from the thin debris layer at the UWS but be partly retained within thick debris at the LWS (Fyffe et al., 2019b). Heterotrophic activity in soils is known to be moisture limited (Manzoni et al., 2012). Hence, the decreasing magnitude of F _c over the course of the night at the UWS might be due to decreasing water availability limiting microbial activity, while water availability is not a restrictive factor at the LWS (Figure 6). In this context, the diurnal cycle of F _c (Figure 6) can be at least partly explained through the dynamics of the debris water table, with daytime flooding and night-time drainage of meltwater varying the mixing ratio of mobile low p(CO₂) meltwater to immobile high p(CO₂) porewater dominated by microbial respiration. Differences in respiration rate between the UWS and LWS might also relate to spatial variation in microbial communities on DCGs, which have been observed to increase in complexity and become increasingly heterotrophic downglacier, with increasing debris thickness and age (Franzetti et al., 2013; Darcy et al., 2017). At the UWS site, net release of CO₂ during the early season (Figure 5B) suggests microbial respiration may be important during the late winter and early ablation period of snow cover retreat.