3.1.1 Model structure

Adopting a flexible modelling strategy (Clark et al., 2011; Fenicia et al., 2011), which has proven highly valuable for many studies worldwide in the past (e.g. Leavesley et al., 1996; Wagener et al., 2001; Clark et al., 2008; Fenicia et al., 2014, 2016; Gharari et al., 2014; Hrachowitz et al., 2014), we customized and extensively tested a range of functionally different model structures and parameterizations (not shown). The most suitable of these tested model structures, which was subsequently used for the study catchment (Fig. 4), has nine free calibration parameters (Table 1b) and resembles the wide-spread HBV type of models, which were previously successfully applied over a wide range of environmental conditions (e.g. Seibert, 1999; Seibert and Beven, 2009; Fenicia et al., 2014; Berghuijs et al., 2014; Birkel et al., 2015; Hrachowitz et al., 2015; Nijzink et al., 2016b). All model equations are provided in Table S1 in the Supplement.

Table 1(a) Model storages and fluxes and (b) model calibration parameters with their uniform prior parameter distributions and the median as well as the 5–95th percentiles of the posterior parameter distributions of the set of behavioural solutions (for the model structure, see Fig. 4).

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Briefly, the model was implemented with a semi-distributed snow routine, stratified into 100 m elevation zones. In the absence of more detailed data, the volume of water falling as snow (i.e. solid precipitation P_s) and eventually stored in the snowpack (S_snow) was based on a simple temperature threshold method (e.g. Gao et al., 2017). Due to their minor importance in the snowmelt-dominated study catchment (Böhm et al., 2007) and in spite of their potentially distinct accumulation and ablation dynamics, glaciers were included in the snow module by allowing continued release of meltwater (M_glacier) after the depletion of the transient annual snowpack at elevations with observed perennial glaciers.

Rain (i.e. liquid precipitation P_l) and meltwater M (areally weighted sum from all elevation zones) directly enter the unsaturated root zone (S_u), where a runoff coefficient (C_r) controls the proportion of incoming water directly released as preferential percolation (Q_up) to the slow responding groundwater storage (S_s) or as influx (Q_uf) to a fast responding model component (S_f) and the proportion transiently stored as soil moisture in S_u. Water can then leave S_u either through an evaporative flux (E_a), comprising plant transpiration and evaporation, or through percolation (Q_us) that eventually recharges the groundwater storage S_s. Streamflow is then generated from the combined outflow of S_f and S_s, both implemented as linear reservoirs with storage coefficients K_f and K_s, respectively.

The model at hand thus consists of a semi-distributed, elevation-stratified snow routine and a lumped hillslope component. While we tested different levels of spatial distribution due to different hydrological response units, including for example a parallel wetland component, we decided to go for the most parsimonious feasible model architecture, since more complex models neither improved model performance nor notably influenced the runoff behaviour. As flow velocities are very high, due to the elevated elevation gradients, and flow distances are relatively short, channel routing was considered negligible on the timescale of the implementation. Similarly, interception was neglected due to the limited amount of forested areas.

3.1.2 Model calibration and validation

Model calibration, based on Monte Carlo sampling with 10⁶ realizations from uniform prior parameter distributions (Table 1), was performed for 1987–2007. For a robust model that can reproduce several aspects of the hydrological response simultaneously, thereby ensuring consistency of the internal processes (e.g. Gupta et al., 2008; Euser et al., 2013; Hrachowitz and Clark, 2017), a multi-objective calibration approach was applied. This was done by combining three objective functions, i.e. the Nash–Sutcliffe efficiencies (Nash and Sutcliffe, 1970) of flow (E_NS,Q) and the logarithm of flow (E_NS,log(Q)) as well as the volume error of flow (V_E,Q; Criss and Winston, 2008) into the Euclidean distance D_E to the “perfect” model as an overall objective function (e.g. Schoups et al., 2005; Hrachowitz et al., 2014; Fovet et al., 2015; Nijzink et al., 2016a):

In the absence of more detailed information, all three objective functions in D_E were given equal weights. Note that in contrast to the three individual objective criteria, D_E= 0 indicates a perfect fit.

The best performing 0.1 % of parameter sets in terms of D_E, roughly corresponding to a performance threshold of 0.75 for each of the three individual performance metrics (see results section), were retained as behavioural solutions. These solutions were subsequently used to construct ensemble solutions and thus envelopes for the modelled variables, reflecting their respective sensitivities to parameter uncertainty.

The period 2007–2012 was thereafter used for post-calibration model testing and evaluation (“validation”; Fig. 3), based on the set of retained solutions and their performance metrics D_E for that period. In addition, for a post-calibration plausibility check and evaluation of the snow routine at low elevations, we compared the timing of the presence of an observed snowpack (snow present yes/no) at the three climate stations with the modelled timing of the presence of snow storage at corresponding elevations in the model. Note that in the absence of time series of snow density, no more detailed evaluation could be done. For higher elevations we correlated the modelled annual glacier melt dynamics with the annual glacier melt time series from the three glaciers in the adjacent Ötztal valley.

4.3.1 The role of high-intensity precipitation

On the 3 event days with precipitation totals of P > 45 mm d⁻¹ observed at all three stations and thus P_e ≤ 0.01 (nos. 7, 11, and 19), being a lower limit of traditional rainfall intensity-duration thresholds for debris flow initiation (see above; Guzzetti et al., 2008), this heavy (cf. Schimpf, 1970) although not necessarily high-intensity and short-duration convective rainfall is very likely to have a very high relevance as a contributor to initiating the debris flows (Table 2). The values of S_u for these events, with exceedance probabilities P_e ≤ 0.25, suggest some moderately relevant additional contributions from previous water input that left the soil at above-average moisture conditions. Although present at these event days, snowmelt is likely to have low relevance (P_e ≥ 0.40) as a contributor to these debris flow events. Interestingly, while temperatures have been moderate (0.1 < P_e≤ 0.5) for nos. 11 and 19, they have been rather low for event no. 7 (Figs. 5a and 6b). Thus, for this event, the precipitation only fell as rain at lower elevations (< 2000 m a.s.l.) and the debris flows are therefore likely to have been initiated at lower elevations, which is in accordance with the associated observation of these debris flows, located at the lowest section of the inner Pitztal (Fig. 1).

For event nos. 21 and 24, heavy precipitation was likely to have a very high relevance as a contributor to triggering debris flows, as well (Table 2). This is in spite of the catchment average observed precipitation on these days being less extreme, with 0.01 < P_e≤ 0.1. Rather, as shown in Fig. 6a, both debris flows occurred close to the rain gauge, with the respective highest precipitation recorded on that day, i.e. station Plangeroß for no. 21 and St. Leonhard im Pitztal for no. 24 (Fig. 1), both of which reached P_e≤ 0.01. Together with the high temperatures (Fig. 6b), this suggests that the precipitation on these days very likely occurred as highly localized and temporally concentrated convective rainstorms (“thunderstorms”), which potentially exhibited precipitation intensities far above the ∼ 1.9 mm h⁻¹ threshold (as derived as the lower limit from the observed 45 mm d⁻¹ if precipitation is uniformly distributed over 1 day) for debris flow initiation in mountain areas (Guzzetti et al., 2008), at these two stations. In fact, the available high-resolution precipitation data show that exceptionally high maximum intensities (6.3 mm 15 min⁻¹ and 10.8 mm 10 min⁻¹, corresponding to exceedance probabilities of P_e < 0.0001) occurred on these 2 days. Snowmelt had some moderate additional contribution to event no. 24, while its relevance was low for no. 21 (Fig. 6c). Similarly, the largely below-average S_u indicates a low relevance of antecedent soil moisture for these two events (Fig. 6d). A similar reasoning applies to event nos. 3 and 12, albeit somewhat less unambiguously (Table 2). For both events, catchment averaged observed precipitation fell within exceedance probabilities 0.01 < P_e≤ 0.1, and thus below the empirical trigger threshold. However, also in this case, the rain stations recording the highest daily precipitation totals were largely the ones closest to the observed debris flows, i.e. Plangeroß for no. 3 and Jerzens-Ritzenried for no. 12 (Fig. 1). Although the precipitation recorded at these stations for the 2 event days did not reach the P_e≤ 0.01 threshold (Fig. 6a), the high to very high temperatures on these days plausibly suggest the presence of convective precipitation cells and thus of temporally and spatially concentrated and thus high-intensity rainfall. In contrast, while the temperatures for event nos. 1, 16, 22 and 23 were only somewhat above average, the precipitation recorded at gauges close to the respective events (Fig. 1) was mostly closer to the threshold P_e= 0.01 than for event nos. 3 and 12 discussed above (Fig. 6a), implying that a moderate temporal concentration of these values to precipitation durations ≤ 12 h (and thus not necessarily convective) on the respective event days would already result in precipitation intensities exceeding the threshold for debris flow initiation. Again, for nos. 22 and 23 the high-resolution precipitation intensity data show that clear intensity peaks have occurred (Table 2). Conversely, only rather moderate precipitation (0.1 < P_e≤ 0.5), for both the catchment average and the gauge with the respective highest recorded values, was observed for event nos. 4, 5 and 14, albeit most of them with the highest values for the gauges closest to the debris flows. The high temperatures (P_e≤ 0.1) indicate that localized and temporally highly concentrated precipitation from convective events and above the necessary trigger thresholds is not unlikely for these days. Similarly and although the precipitation data do not give any direct evidence, the merely moderate snowmelt and antecedent soil moisture together with maximum temperatures nearly reaching the P_e < 0.1 threshold for event nos. 15 and 18 suggest that highly localized (and thus potentially not adequately recorded) and/or temporally concentrated precipitation may have generated sufficient local precipitation intensities to trigger these debris flows, as well. Lastly, elevated precipitation values (0.01 < P_e≤ 0.1) were observed for event no. 25, therefore suggesting triggering by precipitation, even though temperatures have been – atypically – very low (P_e= 0.99, corresponding to maximum temperatures of −5 to +7 ^∘C (Fig. 6b)). This interpretation is supported by the available high-resolution precipitation data (P_e < 0.01). Please note that the output from the hydrological model suggests that all of the precipitation has fallen as snow (and would therefore not be likely to trigger any debris flow at all); however, this is due to the mean temperature amounting to −3.8 ^∘C and an inherent limitation of using a daily averaged temperature input. The above points suggest, together with the generally low antecedent moisture storage S_u from preceding and potentially more persistent rain and snowmelt (Fig. 6d), that very intense, relatively short-duration precipitation was likely a highly relevant contributor to event nos. 1, 3, 4, 5, 12, 14, 15, 16, 18, 22, 23, and 25, although the level to which this assessment is fully warranted by the available data varies between the events. In addition, debris flow initiation was supported by contributions of snowmelt (nos. 1, 3, 12, 14, 15, 16, and 18; Fig. 6c) for several events. However, as most of the above events occurred during summer (i.e. July and August) after the snowmelt peaks, which typically occur much earlier in the season (i.e. May and June; see Figs. 5 and S2) and thus when only relatively little snow was left, the snowmelt contributions to these events remained quite moderate.

Table 2The 25 recorded debris flow events in the inner Pitztal that occurred at known dates since 1953. For each event the exceedance probabilities P_e associated with the observed variables daily precipitation P, daily maximum temperature T_max and daily mean streamflow Q_obs as well as with the modelled variables daily snowmelt M, daily antecedent moisture content S_u, daily total near-surface water availability S_l and the daily streamflow Q_mod at the day of the respective events are given. Bold and italic values indicate a very high relevance (P_e≤ 0.01) and bold values a high relevance (0.01 < P_e≤ 0.1) of each individual variable for a given event; normal values indicate moderate relevance (0.1 < P_e≤ 0.5) and italic values indicate a low relevance (P_e > 0.5). The columns indicating the relevance of contributing variables show the likely level of importance of the three variables that directly affect debris flow initiation (P, M, S_u), after consideration of supporting evidence from variables, such as T_max, that do not directly affect the triggering of debris flows. As an additional plausibility check of our interpretation, information on high-resolution precipitation data is provided (column $P_{\max ,\mathrm{10}/\mathrm{15}\min })$ when available. The direct support by the data column indicates to which extent the classification of the contributing variables into very high/high, moderate and low is directly supported by daily data ($++$: excellent support, +: strong support, ∼: moderate support), and thus provides an indicative quality check of how likely this interpretation is to reflect the real conditions during debris flow initiation.

⁽²¹⁾ Taschachbach: 6.3 mm 15 min⁻¹ (St. Leonhard im Pitztal-Neurur (TIWAG): 0.7 mm 15 min⁻¹). ⁽²⁴⁾ St. Leonhard im Pitztal-Neurur (ZAMG): 10.8 mm 10 min⁻¹ (St. Leonhard im Pitztal-Neurur (TIWAG): 5.2 mm 15 min⁻¹; Taschachbach: 2.1 mm 15 min⁻¹). ⁽²²⁾ Taschachbach: 6.4 mm 15 min⁻¹ (St. Leonhard im Pitztal-Neurur (TIWAG): 0 mm). ⁽²³⁾ St. Leonhard im Pitztal-Neurur (TIWAG): 0.9 mm 15 min⁻¹ (Taschachbach: 0.4 mm 15 min⁻¹). ⁽²⁵⁾ St. Leonhard im Pitztal-Neurur (ZAMG): 0.9 mm 10 min⁻¹ (St. Leonhard im Pitztal-Neurur (TIWAG): 0.5 mm 15 min⁻¹; Taschachbach: 0.5 mm 15 min⁻¹).

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4.3.2 The role of snowmelt

Event nos. 8, 9 and 10 occurred on days when the modelled snowmelt reached exceedance probabilities of P_e≤ 0.01 (Fig. 6c, Table 2) and only very little to no additional precipitation was recorded. In spite of these exceedance probabilities, the total median melt volumes of about 18–23 mm d⁻¹ on these days, equivalent to melt intensities of 0.75–0.96 mm h⁻¹ for uniform 24 h melt, fall short of the debris flow initiation threshold for precipitation intensities of ∼ 1.9 mm h⁻¹. However, and importantly, it is very likely that the required intensity threshold was exceeded locally. The reasons are that on the one hand most of the meltwater on the event days was generated at high elevations (> 2000 m), leading to locally considerably elevated melt rates and thus intensities at these higher elevations (up to 38 mm d⁻¹ for nos. 8 and 10 and up to 46 mm d⁻¹ for no. 9), which are the source area of debris flows. On the other hand, melt is unlikely to occur uniformly over a 24 h period. This causes further temporal concentrations of meltwater generation, and thus higher peak melt intensities within individual days which will roughly reflect daily temperature variations, yet in an attenuated, temporally lagged manner due to the thermal capacity of the snowpack. Based on the above reasoning, the snowmelt contribution is thus likely to have a very high relevance for the initiation of debris flows on these event days (Table 2). In addition, antecedent soil moisture was also at very high levels, i.e. P_e≤ 0.01 (Fig. 6d). This continuous build-up of antecedent soil moisture by persistent snowmelt and some moderate rainwater input over the preceding days (Fig. 5a), resulting in catchment-wide almost fully saturated conditions, is thus also likely to provide highly relevant contributions to trigger the debris flow event nos. 8, 9, and 10. Indeed, total liquid water availability and also modelled runoff have been at least as high (P_e≤ 0.003) as those of event nos. 7, 11, and 19, which have been identified as triggered by heavy precipitation with a high confidence (Sect. 3.2.1, Table 2). In contrast, the precipitation totals observed on the 3 days exceed P_e > 0.1, with no precipitation recorded at all for nos. 8 and 9. Although localized, high-intensity precipitation missed by the precipitation gauges cannot be ruled out for these event days, given the already high melt rates of up to 46 mm d⁻¹ and the fact that for nos. 8, 9 and 10 most gauges did not observe any precipitation, rainfall is thus considered to make no more than a moderate additional contribution to the initiation of these debris flows.

For no. 17, an extremely low snowmelt exceedance probability of P_e= 0.0001 was estimated, resulting from the highest snowmelt rate that was modelled within the study period 1953–2012. Yet a maximum local melt intensity of “only” 38 mm d⁻¹ has been calculated which equals those of event nos. 8 and 10, due to the snowmelt occurring over a wider range of elevations (> 1700 m a.s.l.) on that day. As at all three climate stations, moderate (0.1 < P_e≤ 0.5) precipitation was recorded, and rainfall will have played a more prominent role than for event nos. 8, 9 and 10, making this event a classical rain-on-snow triggered event (cf. Church and Miles, 1987).

Mirroring the reasoning for event nos. 8, 9 and 10, the snowmelt exceedance probabilities of 0.01 < P_e≤ 0.1 for event no. 20 and 0.1 < P_e≤ 0.5 for no. 2 suggest at least high and moderate snowmelt contributions, respectively, for triggering the associated debris flow. Interestingly, for both events, the snowmelt has been restricted to a smaller elevation band (> 2400 m a.s.l.) than for the other events described above, thus rendering higher local melt intensities. Indeed, for no. 20 maximum melt intensities of ca. 39 mm d⁻¹, equalling those of event nos. 8, 10 and 17, were modelled, and for no. 2, maximum melt intensities of up to 16 mm d⁻¹, which – given a catchment mean snowmelt of only 4 mm d⁻¹ – are also quite noteworthy. Similarly, the absence of observed precipitation and – in case of no. 2 – only moderate maximum temperature, suggests that precipitation is likely to be of low relevance for the initiation of debris flow event nos. 2 and 20, although the occurrence of small convective shower cells cannot be fully dismissed. Note, however, that the direct evidence provided by data in particular for no. 2 is less strong than for event nos. 8, 9, 10 and 17, leaving the assessment of the relative relevance of the individual contributors less robust.

To sum up, event nos. 2, 8, 9, 10, 17, and 20 have been associated with snowmelt as the primary trigger, while the assumed additional influence of rainfall (i.e. “rain-on-snow”) and antecedent soil moisture varies between the events. Additional supporting evidence for the above reasoning is that the general timing of the above events coincides well with the snowmelt season. Snowmelt typically peaks during May and June in the study region (Figs. 5 and S2), while high-intensity, convective rainfall is mostly only observed later in the season (i.e. July and August).

4.3.3 The role of antecedent soil moisture

For event no. 13, the gradual build-up of soil moisture S_u by considerable precipitation in the days before as well as by persistent, low-intensity snowmelt in the weeks before the event to nearly fully saturated levels (Fig. S2f), resulted in a soil moisture level with an exceedance probability of P_e≤ 0.01 (Fig. 6d, Table 2). This suggests that soil moisture had likely a very high relevance to trigger this event. Precipitation and snowmelt rates corresponding to 0.1 < P_e≤ 0.5 provided additional moderate contributions to initiate event no. 13.

A similar pattern can be found for event no. 6, albeit with a lower relative contribution from soil moisture, whose contribution to trigger the event was moderately relevant (P_e= 0.24), as were the contributions of precipitation (P_e= 0.19) and snowmelt (P_e= 0.40).

Interestingly, both events, nos. 6 and 13, occurred in the lowest part of the study area, where relatively large parts are vegetated (Fig. 1), while most of the events associated with high-intensity precipitation (nos. 1, 3, 4, 5, 12, 14, 15, 16, 18, 21, 22, 23, 24, and 25) took place at higher elevations. For these events, the antecedent soil moisture estimates have been mostly below average, which not only backs the interpretation of high-intensity precipitation as dominant trigger (as discussed in Sect. 4.3.1), but may also indicate that the antecedent soil moisture is in general of minor significance at higher elevations, as in it headwaters the catchment is dominated by lower-permeability surfaces (bare rock, sparsely vegetated areas) and shallow soils that only provide limited storage capacities (cf. Berti and Simoni, 2005; Coe et al., 2008; Gregoretti and Fontana, 2008).

4.3.4 Seasonally varying importance of the different trigger contributions

The above analysis illustrated quite clearly that water inputs originating from different individual “sources” can significantly contribute to generate trigger conditions in the study area. The data further suggest that the relative relevance of each these variables contributing to the actual trigger conditions does vary over time. Even more, there is some evidence that among the three tested variables, high-intensity and potentially short-duration precipitation P may be not the consistently most relevant (or “dominant”) contributing factor for all events. Rather, it is not unlikely that also high-intensity snowmelt M and similarly, although with some lower degree of confidence, persistent, lower intensity water input, building up antecedent soil moisture content S_u and eventually causing saturated conditions, can generate the most relevant contributions to reach trigger conditions. More specifically, high-intensity precipitation was likely to be the dominant contributor to trigger debris flows on 17 out of 25 event days (68 %). This corroborates previous studies that this type of precipitation is the prevalent trigger in such environments (e.g. Berti et al., 1999; Marchi et al., 2002; Berti and Simoni, 2005; Coe et al., 2008; Gregoretti and Fontana, 2008; Braun and Kaitna, 2016; Ciavolella et al., 2016). In addition, however, high-intensity snowmelt was likely the dominant contributor on 6 days, corresponding to 24 % of the observed events and antecedent soil moisture on 2 event days (8 %), highlighting their critical individual contributions to debris flow initiation.

Figure 7Individual exceedance probabilities P_e of precipitation (P; x-axis), snowmelt (M; y-axis) and relative antecedent soil moisture (S_u; z-axis) as well as the corresponding joint conditional posterior probabilities of an event occurring given specific values (expressed as classes of exceedance probabilities) of precipitation, snowmelt and antecedent soil moisture, $p\left(E\right|P,M,S_{\mathrm{u}}$).

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Figure 8Debris flow events by month of occurrence and likely dominant trigger; shades indicate the relative strength (the darker the stronger) of the dominant trigger in terms of (1) its relative relevance compared to the other contributing variables and (2) the extent to which it is directly supported by data (see also Table 2).

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A somewhat different, more quantitative perspective is given by Fig. 7, showing the joint conditional posterior probabilities of a debris flow event E occurring, given the exceedance probability of each individual variable P, M and S_u, i.e. $p\left(E\right|P,M,S_{\mathrm{u}})$. Note that $p\left(E\right|P,M,S_{\mathrm{u}}$) is shown in classes of exceedance probabilities with an increment of 0.25 to allow a meaningful visualization of the clustering effects. High probabilities of debris flow events predominantly cluster at low exceedance probabilities of precipitation or in other words, on days with high precipitation totals which were exceeded only in 25 % of all days in the study period (i.e. the right-most slice in Fig. 7). Under such conditions, additional contributions from snowmelt or antecedent soil moisture are not necessarily required to trigger debris flows (e.g. Aleotti, 2004; Berti et al., 2012), which is also reflected in the elevated $p\left(E\right|P,M,S_{\mathrm{u}}$) for low M and S_u in that class of precipitation exceedance probability. However, elevated event probabilities can also occur when little to no precipitation is observed, i.e. at exceedance probabilities of P > 25 %, which is roughly equivalent to P < 6 mm d⁻¹, but when instead higher melt rates and/or, albeit to a lesser extent, antecedent moisture levels are likely to be present, as suggested by the model results. Although both the relative proportions of the different dominant triggers as well as actual values of $p\left(E\right|P,M,S_{\mathrm{u}}$) as shown in Fig. 7, may be subject to some change over time due to the relatively low absolute number of events with respect to the 60-year study period, the general pattern strongly underline the varying roles of the three variables under consideration as individual and potentially dominant contributors to debris flow trigger conditions in the study region.

Most debris flow events in the study area occur between mid- and late summer (Fig. 8), when spring precipitation and persistent snowmelt have developed above-average soil moisture levels and when the frequency of high-intensity, convective rain storms increases (Figs. 5 and S2). Further analysis also revealed a relatively clear pattern in the seasonally changing relative relevance of the three considered variables as contributors to debris flow trigger conditions. In general, three distinct seasonal debris flow trigger regimes emerge from the analysis, which to a high degree reflect both the seasonal cycle in the hydro-meteorological conditions and in debris flow occurrence, from snowmelt- to convective-rainfall-dominated debris flow triggers. While late spring and early summer events are mostly associated with snowmelt in combination with elevated soil moisture and only very minor contributions of high-intensity precipitation, the latter is, for the above reasons, the dominant trigger in summer and early autumn. While the former may be trivial given that significant snowmelt is less common from July onwards, it is interesting to observe that high-intensity precipitation may be, though also sometimes occurring in spring and early summer, less relevant for triggering debris flows at that time of the year. In our dataset, event no. 7 occurring in early June 1965 was attributed to high-intensity rainfall, while event nos. 8–10, occurring in the same month, were predominantly triggered by snowmelt, forming a clear exception to this general rule. Also, in the same month, triggering by elevated soil moisture conditions due to the combined effect of long-lasting rainfall and snowmelt has been observed (event no. 6). This shows how debris flow triggers can change very rapidly following weather changes. The general pattern (high-intensity precipitation in summer vs. snowmelt in spring as the dominant debris flow triggers) mostly arises from a combination of two factors, namely that in spring considerable proportions of precipitation observed at lower elevations (1) still fall as snow, in particular at higher elevations, and (2) are, if falling as rain, intercepted by, transiently stored in and/or potentially refrozen in the snowpack, in particular if the snowpack has not yet reached isothermal conditions at 0 ^∘C throughout the region of interest. Although a mature snowpack later in the melt season may reverse the latter into a positive feedback, i.e. actually reinforcing intensive precipitation in rain-on-snow events (e.g. Harr, 1981; Conway and Raymond, 1993; Cohen et al., 2015), both factors above can, in principle, also cause an attenuation of the observed precipitation intensity as water will be released from the snowpack with some time lags and potentially over a longer time, i.e. at lower rates than the observed ones. The immediate implications are then that thresholds for debris flow initiation estimated from traditional rainfall (but also precipitation) intensity-duration approaches may be suitable for some regions, as for example demonstrated by Berti et al. (2012), who showed that antecedent soil moisture is of limited importance in their study region, but will be unreliable for certain hydrological conditions, in particular in snow dominated regions (cf. Decaulne et al., 2005), and thus insufficient for meaningful predictions of debris flows. As a step forward, it may therefore be beneficial to move towards understanding the problem in a more comprehensive and thus multivariate way, expressing and combining the varying relative relevance of different water “sources” in terms of total liquid water availability S_l (see Fig. 6e as an example) in the source zone of debris flows, as recently also emphasized by Bogaard and Greco (2018).

4.3.5 Discussion

We would like to reiterate here that, as in any hydrological study at scales larger than the hillslope scale, the issue of epistemic errors in data (Beven, 2012; Beven et al., 2017a, b), arising from the typically insufficient spatial but also temporal resolutions of the available observations (mostly precipitation) can introduce considerable uncertainty in the interpretation of a specific hydrological system (e.g. Valéry et al., 2010; Nikolopoulos et al., 2014; Marra et al., 2017) which is further exacerbated by complex, mountainous terrain (e.g. Hrachowitz and Weiler, 2011). This is in particular relevant for debris flows as they depend on the hydrological conditions at the specific location of their initiation, which is frequently of very limited spatial extent. Borga et al. (2014), for instance, reported the occurrence of several debris flows that were triggered by highly localized, high-intensity rainfall > 100 mm h⁻¹, which remained completely unrecorded by rain gauges at a 5–10 km distance.

We also explicitly acknowledge additional uncertainties arising from the use of a simple, semi-distributed model to represent the hydrological system of the study area. Such models are clearly oversimplifications of the detailed processes controlling the storage and release of water. Together with the effect of the above discussed data errors, this explains, why the model cannot fully reproduce some of the features in the observed hydrograph (e.g. Figs. 5b, c and 6f), in spite of its adequate overall performance. Indeed, out of the 6 debris flow days, where both modelled and measured runoff values were available, the modelled runoff in three cases did not correspond particularly well to the measured runoff (Fig. 6f), although in those cases where the runoff was underestimated by the model (no. 20), this was most likely due to unrecorded or underrecorded precipitation. This ambiguity equally affects the estimates for total soil moisture, while the modelled snowmelt and the antecedent soil moisture, in contrast, can be assumed to be more correct, as these variables are integrations over time, in which case erroneous precipitation measurements are likely to be compensated and thus of less consequence (e.g. Hrachowitz and Weiler, 2011). In addition, the spatial integration of local processes is likely to result in a misrepresentation of hydrological conditions for the locations of debris flow initiation.

However, even though the model is rather simple with limited spatial differentiation, we would like to point out that our approach is not due to an ill-advised oversimplification. Rather, it is the (un-)available data that limit a meaningful spatial differentiation. The most crucial meteorological input, namely precipitation, is very often (and also here) not available on a spatially sufficiently distributed basis (see above), let alone for the actual source area of a specific debris flow. Furthermore, the calibration of a more distributed model would be more problematic and – in the case of fully distributed physically based models – would encounter many other sources of uncertainties (e.g. model/parameter equifinality, scale of available field observations of physical parameters vs. scale of the modelling application/grid size, the suitability of the model equations for the scale of the applications). These issues have been acknowledged for quite some time, but no real progress to close the gap between simplicity and complexity has yet been made (e.g. Dooge, 1986; Beven, 1989, 2006b; Jakeman and Hornberger, 1993; Sivapalan, 2005; McDonnel et al., 2007; Zehe et al., 2007, 2014; Clark et al., 2011, 2017; Hrachowitz and Clark, 2017).

More specifically and notwithstanding these limitations, the catchment-wide considerable melt rates M, together with the generally elevated soil moisture S_u during snowmelt-dominated events generated by the model suggest that, in spite of the potential presence of un- or under-recorded precipitation, these two sources contribute considerable volumes of water to the required trigger threshold. Additional precipitation may then further contribute, but this does neither imply that these contributions were actually necessary nor, and even less so, that they were dominant for triggering these events. Moreover, although modelled melt rates and soil moisture levels may not be fully representative for the location of the debris flow initiation, they provide most likely conservative estimates, as their real values are likely to be higher at the location and moment of debris flow initiation due to spatial and temporal concentration effects. Furthermore, soil water storage, besides being largely controlled by low-intensity, larger-scale water input, also acts as a low-pass filter. As such it attenuates spatio-temporal variability in precipitation to some degree and is thus more homogeneous than the precipitation itself (e.g. Oudin et al., 2004; Euser et al., 2015).