4.1 Discharge components
Figure 4 depicts the updated hydrograph analysis of Wagner et al (2020a), extended by an additional year of data. Master recession curves derived from single recessions to infer a theoretical recession curve over a long period of time indicate at least a fast and a slow flow component. Importantly, runoff at the rock glacier springs is still present in winter (base flow) with a discharge of a few l/s. The additional data strengthen the results of Wagner et al. (2020a), who related this base flow to the unfrozen base layer of the active rock glacier (Hausmann et al., 2012). In general, the variable discharge behaviour ranging from 6,5 l/s up to 718 l/s with a discharge ratio of 110 (Qmax/Qmin) is similar to the pattern observed at karst springs (e.g. Wagner et al., 2020a; Winkler et al., 2016).
[Insert Figure 4]
The results of the artificial tracer tests indicate a fast flow component exhibiting a mean residence time of around 9 hours (Figure 5; 2015: 9:16 hrs; 2017: 8:41 hrs). When the tracer was injected into the glacial meltwater creek, this locally infiltrating meltwater significantly contributes to the fast flow component. Peak flow velocities during the 2015 (recovery rate 45,8 %) and 2017 (recovery rate 40,0 %) tests were 0,061 and 0,047 m/s, respectively, while the mean flow velocity was 0,029 m/s during both tests.
[Insert Figure 5]
The seasonal variations in discharge components are deciphered using natural tracers. EC measured at the gauging station ranges from 68 to 281 µS/cm, indicating an average event water contribution of 42,6 %. The measured EC of glacial meltwater ranges from 1.2 to 4 µS/cm, while the measured EC of a single precipitation sample within the catchment is 42 µS/cm (sampling sites indicated in Figure 1b). The event water end member of the two component mixing model is therefore assigned an EC of 20 µS/cm, similar to values used in alpine catchments by Wetzel (2003) and Winkler et al. (2016). The ground water EC is parametrized using the highest measured EC at the gauging station (281 µS/cm, measured at a discharge of 22 l/s on 5.11.2015). Presumably, even higher EC values would have been measured if the EC probe would not have fallen dry during the winter months characterized by very low discharge.
In general EC and discharge are inversely correlated (Figure 6). The overall variation in discharge components reflects the superposition of several regularly repeating patterns, exhibiting periods ranging from one day to one year (Heigert, 2018). Following the onset of snowmelt in spring, the event water contribution increases until discharge reaches its maximum in early summer (Figure 6a). The exact event water contribution is strongly dependent on local weather conditions, reflecting the variable snowmelt intensity in response to air temperature (note variability in both discharge and EC/event water share during May in Figure 6a). Maximum discharge (several hundred l/s) is reached in early summer, indicating also the maximum level of storage within the rock glacier. At this time event water accounts for up to 75 % of the total discharge and is subject to pronounced diurnal variations (Figure 6a,b). As summer progresses the overall discharge decreases and the event water share reduces accordingly, resulting in a mean contribution of ~60 % during the summer months. Prominent peaks after heavy rainfall on melting snow cover (early summer) and intense thunderstorms (late summer) are superimposed on this pattern, while peak magnitude decreases steadily during summer (Figure 6a,b). Dry, warm summer periods induce pronounced diurnal variation in EC mirroring the diurnal discharge variations (Figure 6b,c). Declining air temperatures strongly reduce discharge as well as event water contribution and attenuate diurnal variations - temporarily during the summer months (Figure 6a around 23.6.2017) but persistently at the beginning of autumn (Figure 6b around 1.9.2017). After the onset of snowfall, spring flow steadily declines and groundwater contribution increases towards 100 % until the next snowmelt in early spring, occasionally intermitted by single peaks in response to warm rainfall events (Figures 2, 6b).
[Insert Figure 6]
Figure 6c depicts the periodic variations in discharge and natural tracers during a dry, warm summer period in early August 2017, following a heavy precipitation event in late July. The time lag between the diurnal air temperature maximum and peak discharge equals 16 hours. Since snow was absent in the catchment, the periodicity is caused by ice melt responding to diurnal variations in radiation and air temperature. Note that EC and δ18O are inversely correlated to discharge due to the dilution with ice melt water exhibiting low EC (~2 μS/cm) compared to groundwater (281 μS/cm), confirmed by the corresponding variation in δ18O. However, differentiating permafrost ice melt from cirque glacier ice melt is not possible due to the lack of data concerning the former.
While the two component mixing model indicates a mean event water contribution of 65 % during the period depicted in Figure 6c, plotting EC against δ18O allows a more detailed analysis of the event water component (Fig. 6d). The observable hysteresis clearly indicates a dynamically changing composition of the event water component (Harrington et al., 2018; Williams et al., 2006). The diurnal variation introduced by periodic dilution of groundwater with meltwater is superimposed on a general trend towards lower δ18O values (Figure 6c). This trend indicates a progressive shift from rainwater (around -8.05 ‰) towards ice meltwater (around -15.3 ‰) constituting the event water component. Decreasing rainwater contributions correspond to continued runoff since the last heavy rainfall event on 29.7.2017. A minor rainfall event that occurred during the night from Aug. 4 to Aug. 5, 2017 (Figure 6c) immediately shifts the diurnal cycle towards higher δ18O values on Aug. 5, 2017 (Figure 6d). The simple two component mixing model is merely a projection of the actual mixing process involving multiple sources as well as temporary storage within the catchment (see section 4.2).
4.2 Recharge components / Discharge pattern
Applying the lumped-parameter rainfall-runoff model yields satisfactorily results visually (Figure 7) as well as expressed in average Nash-Sutcliffe efficiency (\(\overset{\overline{}}{\text{NSE}}\)) criteria (89.6%; Nash & Sutcliffe, 1970). \(\overset{\overline{}}{\text{NSE}}\) values using a split sample test (Klemes, 1986), where the model is calibrated on the first half of the available data set, validated on the second half and vice versa and compared to the complete data set are shown in Table 1 for calibration and validation periods. The model performs in a similar way as for the relict Schöneben rock glacier (\(\overset{\overline{}}{\text{NSE}}\) of 89.5%; Wagner et al., 2016). An average Nash-Sutcliffe efficiency (\(\overset{\overline{}}{\text{NSE}}\)) criteria is computed using a combination of the classic Nash-Sutcliffe efficiency criterion (Nash & Sutcliffe, 1970) and the modified Nash-Sutcliffe criteria based on log-transformed and square root-transformed discharges (see Wagner et al., 2013, 2016). Also here, the physical relevance of model parameters is stressed (Mouelhi et al., 2006; Wagner et al., 2013, 2016). Table 2 shows the model parameter set from the best-fit model for the catchment of the active rock glacier Innere Ölgrube as well as the parameter set from the relict Schöneben rock glacier catchment (cf. Wagner et al. 2016). Comparable to the results of the relict Schöneben rock glacier catchment, a relatively large routing store (x3) is needed to achieve acceptable model fits. This is suggested to be related to the unfrozen base layer within the rock glacier, which was shown to exist by Hausmann et al. (2012) and interpreted to be the dominant shallow aquifer within the spring catchment (Wagner et al., 2020a). The production storage (x1; or soil moisture accounting store) is even smaller than that of the Schöneben rock glacier catchment. Again, this relates physically to the fact that the Innere Ölgrube catchment is basically a bare rock / debris field and evapotranspiration is limited. Interestingly, model parameters x1 to x4 are not very different to those of the relict Schöneben rock glacier catchment. These implications will be picked up later in the discussion section.
[Insert Figure 7]
[Insert Table 1]
[Insert Table 2]
The rainfall-runoff model for the Innere Ölgrube rock glacier spring catchment allows a quantification of relative input of rainfall, snow- and ice melt (Figure 7). The input fractions of rainfall, snowmelt and ice melt for the observed period of time are 36,6, 35,8 and 27,6%, respectively. It has to be noted, that ice melt is considered to be derived mainly from the melt of the cirque glaciers as indicated by artificial and natural tracer analyses (see discussion section). Berger et al. (2004) also reported about 30% of the rock glacier spring runoff to be related to the glacier melt water and serves as an independent (admittedly vague) information.
4.3 Glacier mass loss estimates from glacier inventories
Applying the formula provided by Chen and Ohmura (1990) to compute glacier thickness for the area estimates of the two cirque glaciers of the two glacier inventories, a loss of 1135708 m³ over the time period 2006 to 2015 was calculated, which is 126190 m³ on average per year. This is the same order of magnitude and about twice of what is “needed” in the rainfall-runoff model for the years 2015-2018; however the areal extents of the cirque glaciers are even smaller by now and moreover the difference between ablation and actual melt needs to be considered. Sublimation is not considered here and therefore ablation estimates from the area-thickness relation will be higher than the glacier melt water “input” estimated in the rainfall-runoff model. Moreover, the positive exchange term in the rainfall-runoff model allows for additional “inflow” (x2 being positive; Table 2). The data analysis allows an order of magnitude consistency check, but not more. Approximately 30% of the recharge are derived from melt water of the cirque glaciers. When considering this rather significant contribution, a future glacier loss is supposed to have a significant impact on the runoff pattern.