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.