4.1. Controls on Rates of Respiration and Photosynthesis on Svalbard Valley Glaciers
 There were significant (p < 0.05) correlations between rates of respiration (in units of volume) with both sediment thickness and organic carbon, explaining a combined total of 72.7% of total variation in the respiration rates (Table 2). The significant increase in respiration with increasing sediment depth is likely due to increases in both the amount of labile organic matter and number of microbial cells within the incubations, since cryoconite samples were added to the bottles in bulk. The simplest explanation for the significant correlation between TOC and respiration is that a relatively constant fraction of TOC between sites is bioavailable, and hence increasing TOC increases the amount of available carbon for respiration. The reason for the small (6.8% of total variation; see Table 1) but significant negative relationship of VB site to respiration (Figure 5) is unclear. One possibility is that cryoconite holes on VB contain a higher proportion of refractory to labile carbon, although we have no data to further test this hypothesis.
 The lack of any significant relationship (p < 0.05) between photosynthesis (in units of volume) and sediment thickness is consistent with light limitation within deeper sediment layers. Incident PAR is typically completely attenuated at thicknesses of <1 mm in silty sediments restricting photosynthesis to the upper submillimeter depth of sediment grains [Jorgensen and DesMarais, 1986; Garcia-Pichel and Bebout, 1996]. The significant correlation (p < 0.05) of TOC with photosynthesis, accounting for 26.1% of the total variation of photosynthesis (Table 2), is unlikely to be because in situ photosynthesis within the cryoconite holes forms the majority of TOC. We show in section 4.3 that the measured rates of NEP are unlikely to be able to produce more than a small fraction of TOC within the studied cryoconite holes on a reasonable timeframe. An alternative explanation for the positive correlation between TOC and photosynthesis is that the breakdown of organic matter allochthonous to the cryoconite holes (although potentially produced autochthonously elsewhere on the glacier) is supporting photoautotrophic growth, perhaps by the supply of essential nutrients such as nitrogen or phosphorus [Tranter et al., 2004; Stibal et al., 2008b, 2009].
 Less than half of the variation in rates of gross photosynthesis could be explained by the measured variables in this study (Table 2), indicating that additional factors are likely important. One key missing variable measured in this study for explaining rates of gross photosynthesis is the availability of photosynthetically active radiation (PAR), which changes with season, cloud cover, and shading effects by cryoconite hole walls and local topography [Hodson et al., 2010b]. The availability of nutrients such as phosphorus and nitrogen may also be an important factor for microbial growth and activity [Stibal et al., 2008b; Telling et al., 2011]. Phosphorus has previously been shown to be limiting in the water phase of cryoconites [Mindl et al., 2007]. Further, some cryoconite holes on AB, ML and VB can become depleted in available aqueous and sediment-bound nitrogen resulting in microbial nitrogen fixation [Telling et al., 2011]. Microbial nitrogen fixation could feasibly have a negative impact on rates of microbial growth and activity since it is an energetically costly process relative to the uptake of aqueous nitrogen species [Gutschick, 1978; Telling et al., 2011].
 The strong positive correlation between respiration and photosynthesis in cryoconite holes, with a tendency to net autotrophy within <3 mm thick sediments (Figure 3), is consistent with a closely coupled microbial carbon loop where labile carbon produced by phototrophs supports the majority of the measured rates of respiration [Hodson et al., 2010a]. Therefore while the majority of organic carbon within Svalbard cryoconite holes is not likely formed in situ within the holes via photosynthesis (see section 4.3), conversely the recycling of labile organic carbon produced by photosynthesis within cryoconite holes may support a significant fraction of the total microbial activity within the holes.
4.2. Controls on Net Ecosystem Production on Svalbard Valley Glaciers
 The only significant (p < 0.05) measured environmental control on NEP was sediment thickness, accounting for 55.7% of total NEP variation (Table 2). The strong control of sediment thickness on NEP is clearly shown in Figures 3 and 6 and indicates that NEP in cryoconite holes tends to net autotrophy at sediment thicknesses of <3 mm (where rates of photosynthesis are typically greater than rates of respiration) and toward net heterotrophy at sediment thicknesses of >3 mm (where rates of respiration typically exceed those of photosynthesis). The relative increase in respiration over photosynthesis at sediment depths >3 mm (Figures 3 and 6) may be explained by light limitation in thicker sediments owing to shading by cryoconite grains.
 The mean rate of NEP on the valley glaciers (−0.12 ± 4.1 μg C g−1 d−1) was slightly net heterotrophic, although close to the detection limit. Although there appears to be little or no overall accumulation of autochthonous organic carbon in the cryoconite holes of this study, there are likely to be loci of net autotrophy and net heterotrophy which are strongly controlled by sediment thickness. Importantly, cryoconite debris in hydrologically isolated cryoconite holes on Arctic glaciers tend to form uniform one grain layers owing to the effect of lateral as well as vertical melting of ice by cryoconite grains heated by solar radiation [Cook et al., 2010]. There may therefore be a tendency for net autotrophy in more hydrologically stable regions with lower slopes and less water flow, allowing time for cryoconite to equilibrate to a one grain thick layer. Conversely, cryoconite holes with higher slopes and more rapid streamflow may have a tendency toward net heterotrophy owing to greater flushing of cryoconite holes and the subsequent piling up of thicker sediment. For example, a previous glacier wide survey of cryoconite coverage on ML toward the end of the main melt season demonstrated that cryoconite holes on the lower half of ML (where cryoconites in this study were focused; see Figure 1) were dominated by stream cryoconite holes with relatively high rates of supraglacial flushing, while the upper half of ML was dominated by relatively isolated cryoconite holes with relatively low rates of supraglacial flow [Hodson et al., 2007]. The potential for organic carbon from autochthonous origin to accumulate at higher and less hydrologically disturbed parts of the Greenland Ice Sheet ablation zone has been recently demonstrated [Stibal et al., 2012]. We hypothesize that rates of significant net organic production on ML may therefore be focused in the upper half of ML where thin one grain layer cryoconite may dominate. Furthermore different surface regions on valley glaciers may switch between overall net autotrophy to net heterotrophy throughout the melt season owing to changes in the hydrological regime.
4.3. Sources of Organic Matter in Svalbard Cryoconite Holes
 We assess the potential importance of net autotrophy for producing organic carbon in thin (1 to <3 mm thick) cryoconite layers using equation (1):
where melt seasons is the number of melt seasons to produce the TOC or estimated phototroph biomass of the cryoconite hole, cryoconite organic carbon (in units of μg C g−1) is either TOC or estimated phototroph biomass (the latter estimated by converting the measured concentrations of chlorophyll a to phototroph carbon biomass using a ratio of 1:47) [Riemann et al., 1989], moraine organic carbon is the mean TOC value of moraine debris on ML (4900 μg C g−1), NEP is in units of μg C g−1 d−1 for holes with autotrophic growth only, and time is the typical length of a melt season on ML (60 days) [Hodson et al., 2007]. Although the moraine organic carbon values in equation (1) are based on just three samples of a lateral moraine from ML, their low TOC values (relative to cryoconite) are consistent with previous reports of moraine from the glaciers. A value of 3000 μg C g−1 has been reported from lateral moraine on ML [Borin et al., 2010], while the TOC content of barren soils and subglacial derived sediment in the forefields of VB, ML and AB has been reported as typically below detection (<1% dry weight) while cryoconite debris TOC on the three glaciers was typically several percent dry weight [Kaštovská et al., 2005].
 The mean time needed to form the estimated phototroph biomass in thin (1 to <3 mm sediment thickness) autotrophic cryoconite holes is 3.3 ± 3 years (1σ), with a minimum of 1 year and maximum of 14 years (Figure 7). The mean time required to form the mean TOC in the same holes is 105 ± 91 years (1σ), with a minimum of 20 years and a maximum of 348 years (Figure 7). The typical residence time of cryoconite in stream washed holes on Svalbard valley glaciers has been estimated to on the order of <1 year to several years [Stibal et al., 2008a; Hodson et al., 2010a]. Thin (1 to <3 mm) cryoconite sediments on Svalbard valley glaciers may therefore have sufficiently high rates of autochthonous carbon production to support the growth of a relatively small (compared to TOC) phototrophic biomass, but likely not more than a fraction of their TOC. More hydrologically stable (isolated) cryoconite holes elsewhere however could have substantially greater residence times on the ice surface, and hence a greater potential for autochthonous organic matter accumulation. For example, cryoconite on sections of the Greenland Ice Sheet may have a residence time of >100 years on the ice surface [Nobles, 1960], and autochthonous organic carbon production provides one explanation for the higher TOC content of cryoconite debris documented on parts of the Greenland Ice Sheet (e.g., 13–20% TOC by dry weight) [Gerdel and Drouet, 1960] relative to Svalbard valley glaciers (Figure 4).
Figure 7. Estimates of the number of melt seasons required to produce organic carbon in thin (<3 mm thick) autotrophic cryoconite sediment: (a) time required to form total organic carbon and (b) time required to form the estimated phototroph carbon biomass of cryoconite. These time estimates were calculated using equation (1) (see section 4.3). Phototroph biomass was estimated by assuming a 1:47 ratio between the measured chlorophyll a concentrations of cryoconite and phototroph carbon biomass (after Riemann et al. ; see section 4.3).
Download figure to PowerPoint
 The above calculations indicate that at the time of sampling overall rates of net autochthonous organic carbon production within the cryoconite holes were unable to account for the majority of organic matter in the cryoconite. This discrepancy in the organic carbon budget of the cryoconite holes can be explained in one of three ways. First, there may be allochthonous inputs of organic carbon from environments external to the glacier into the cryoconite holes. Second, there may be autochthonous organic carbon production in alternative supraglacial habitats on the glacier surface which is subsequently washed into the cryoconite holes. Third, NEP rates in nascent cryoconite holes may have been substantially higher than in the holes at the time of sampling.
 Input of allochthonous organic carbon into cryoconite holes is likely, although the magnitude of this flux is currently unknown. Windblown organic matter from adjacent tundra [Stibal et al., 2008a] is perhaps the most likely source. There may also be input of organic carbon near the terminus of the glaciers however from subglacial debris pushed up to the surface in the form of pressure ridges, although reported values of for subglacial debris samples at the front of AB, ML and VB are low (<1% TOC dry weight) [Kaštovská et al., 2005].
 The autochthonous production of organic carbon in alternative habitats on the glacier surface, and subsequent washing into cryoconite holes, is also feasible. The snowpack overlies the entire surface of Svalbard valley glaciers at the start of the season and retreats upslope as the melt season progresses [Hodson et al., 2008], while dispersed cryoconite lying on the ice surface can constitute up to half of the total mass of cryoconite on Svalbard valley glaciers [Hodson et al., 2007]. The NEP of the snowpack and dispersed cryoconite environments is currently unknown [Hodson et al., 2008] but could potentially be significant [Takeuchi, 2002; Hodson et al., 2007].
 The third explanation for the source of organic carbon in cryoconite holes is that rates of NEP are greater in nascent cryoconite holes than in more mature cryoconite holes. This mechanism appears plausible but is currently untested. Microimaging of cryoconite grains indicates that cryoconite in cryoconite holes is typically composed of individual small grains of ≤ 100 μm or less bound together in larger aggregates by exopolysaccharides [Takeuchi et al., 2001; Hodson et al., 2010a; Langford et al., 2010]. Given the negative relationship between cryoconite thickness and NEP (Figures 5 and 6), it is plausible that rates of photosynthesis could dominate over respiration in the initial phase of aggregation resulting in relatively high rates of NEP. In contrast the more mature cryoconite grains in the cryoconite holes of this study had a relatively close balance between photosynthesis and respiration (Figure 3). The lack of cryoconite <0.5 mm thick in the cryoconite holes of this study (Figures 4d and 6) tends to suggest however that either the initial aggregation of cryoconite debris is extremely rapid, or that the initial aggregation does not occur within the cryoconite holes themselves but instead within either the snowpack and/or dispersed cryoconite debris on the ice surface [Langford et al., 2010]. Some support for the latter comes from a previous study on an Antarctic glacier that demonstrated a threshold aggregation size is necessary before cryoconite can absorb sufficient solar energy to melt into the ice to form cryoconite holes [MacDonell and Fitzsimons, 2008]. It is possible that a similar threshold aggregation size mechanism operates on Arctic valley glaciers.