Reply on RC2

The submitted study shows the timing over 4000 years of debris flow events from transport-limited catchments, much of whose deposits extend into an adjacent Lake, creating subaqueous geomorphic field evidence by lacustric deposits. The knowledge of such a long time series is, besides geomorphological interest, also important in connection with positive trends in climate change, or land use, exposure, etc. and gives valuable insight to recent dynamics in the occurrence of debris flow events. The article is basically well written and understandable. The literature cited is up to date and, and here I focus exclusively on the presentation of an extraordinary time series of debris flow events, an important and pioneering contribution to the research community.

(1) Precisely because, at least to me, no comparably long historical review of debris flow events is known, a publication of such a time series requires precise information on uncertainties due to the applied methodology and a discussion of how to deal with it. Above all I recommend focusing on the creation and trend analysis of the surveyed frequency representation of such a long (and valuable) debris-flow time series, improving reliability of the time series.
(2) We thank the referee for this remark on the reliability of the debris-flow time series. We fully agree that calculating the age model uncertainties is a necessary improvement on the precision of our frequency calculations. In the revised manuscript, we present an improved age model, which now provides ages at 1 mm steps. In addition, we apply a frequency analysis on a data-based bandwidth coupled with the presentation of the age uncertainty also in the occurrence rate plot as provided by the individual simulations of the age-depth modelling software Bacon. For a more detailed answer and the changes in the manuscript, please view our answer to the major comment on uncertainties of age dating below.
(1) All terrestrial and bathymetric observations should be either shifted to a second paper or significantly shortened.
(2) We thank the referee for the suggestion. In the first version of our manuscript, we did not put enough emphasis on describing the necessary and previously underestimated link between on-and offshore morphological studies and the debris flow turbidite record. Finding evidence for the underlying processes was a prerequisite for defining identification criteria and understanding the event stratigraphy in the sediment cores. The geomorphic description of debris-flow fan evolution should therefore not be decoupled from the event deposit interpretation. We shortened the manuscript with regards to recent morphological changes (e.g. section 5.2) and put more emphasis on conclusive system understanding from a source-to-sink perspective. For a more elaborate explanation, please refer to the answer on the first specific major comment below.

Specific major comments
(1) The introduction to the study describes the need for knowledge of long-term time series, with the reader curious about this 4000-year survey. Interestingly, however, it talks about a combination of several geomorphological surveys in different depositional domains. First of all it must be noted that for the creation of the time series it is not comprehensible why on two selected fans a terrestrial and bathymetric evaluation is carried out, which is not related to the time series collected and analyzed due to lacustrine deposits at all. It is argued that the coupled study of debris flow systems on land and underwater will provide new insights into geomorphic expressions from the catchment to the depocenter provide? So what exactly are these new insights and how do they relate to a 4000 year time series? I was under the impression that it was more like two stories in one study. Whereby the terrestrial as well as bathymetric studies are mainly closer in the context of the already published article by Dietrich and Krautblatter (2017). By the way, since the onshore measurement is based on two LiDAR measurements within a year, the question arise how does one use this to elucidate the relationship between terrestrial and subaquatic deposition of recent debris flows? In other words, how and why should the rates differ from chance -based on the scarcity of data? My suggestion would therefore be that the authors refer, in the present article, more or exclusively to the survey of lake sediments and their statements in connection with debris flow frequency. Although the terrestrial and bathymetric investigation contains some interesting and further information, they seem to be dispensable for the creation of the 4000 years time series. It would be more exciting to focus on the time series of debris flows and find out how well you can determine the frequency based on sediment core analyses.
(2) The referee expresses concern on the link between the geomorphic study and the observations in the sediment cores. In this article, we establish a general understanding of how the major debris flows are transported to their final sink and how their deposits are distributed in the basin before interpreting the turbidite layers found in the 4,000 year time series. On-and offshore geomorphic investigations provided the following new insights: (i) we uncover conclusive evidence of subaquatic debris-flow deposits and subaquatic landslide deposits, which enables us to pinpoint the detrital layers to single debris-flow events and subaquatic slope failures in the sediment cores (Fig. 3); (ii) we justify the transect and coring site selection by documenting the recent debris-flow activity and subaquatic expressions on different fan delta types and their catchments (Lines 156-161); (iii) we link wedge-shaped deposits throughout the 4,000 year sediment profile to low-energy debris flow-activity on the juvenile fan delta (Lines 606-614); and (iv) we correlate subaquatic deposits showing high backscatter signals with previously mapped terrestrial debris-flow deposits from 1947 to 2014 (Fig. 2).
The referee doubts the representativeness of our onshore data due to the limited observation period of only three months. We agree on this statement, but by including the bathymetric data and further assessing the evolution of debris flow-deltas, we can understand the geomorphic system and implement the shorter recorded period into a longer framework. The bathymetric data confirmed active progradation on the juvenile fan delta and its significant contribution to the subaquatic sediment deposition, which was indicated by the TLS results. We therefore chose the juvenile fan as a starting point for the core transect. We changed the text (Lines 580-586) accordingly.
(3) > Lines 18-25 "The amphibious geomorphic investigation of two fan deltas in different developmental stages revealed an evolutionary pattern of backfilling and new channel formation onshore together with active subaqueous progradation on a juvenile fan delta and major onshore sediment deposition and only few but larger subaqueous deposits on a mature fan delta. Geomorphic evidence for stacked and braided debris-flow lobes, subaquatic landslide deposits, together with different types of turbidites in sediment cores facilitated a processbased event identification i.e. debris-flow or earthquake-induced turbidite of the 4,000 year sedimentary record. We directly correlate subaqueous lobe-shaped deposits with high backscatter signals to terrestrial debris-flow activity of the last century. Moreover, turbidite thickness distribution along a transect of four cores allows to pinpoint numerous events to debris-flow activity on a juvenile fan delta." > Lines 78-81 "For a conclusive identification of debris-flow turbidites in the sediment core, we map geomorphic landforms in both the subaquatic and terrestrial realms, which document the interplay between the terrestrial source area, the terrestrial and subaqueous sediment transport, potential temporary storage on the fan delta and the final sink in the depocentre." > Lines 156-161 "An amphibious geomorphological investigation allowed to assess the influence of catchment conditions, delta dynamics, and deposition patterns and to define additional identification criteria for different processes in the event stratigraphy. The determination of geomorphic landforms i.e. debris-flow deposits quantitatively onshore on a seasonal time scale, and qualitatively on the subaquatic slope gives a general understanding of the system connectivity. Differences in the subaquatic distribution of deposits due to catchment and delta characteristics can be identified and the selection of a transect and coring site can be justified (see Sletten et al., 2003;Irmler et al., 2006)." > Lines 213-215 "Preceding evaluation of recent fan delta activity in combined LiDAR and bathymetric data defined a suitable fan delta from which the core transect was taken towards the distal depocentre at intervals of 50-75 m (Fig. 1)." > Lines 451-452 "Besides the event-type distinction based on sedimentological and geochemical parameters, identification and mapping of the respective geomorphic expressions in bathymetric data (Fig. 3a) allows conclusive interpretation on df-and eq turbidites." > Lines 580-586 "Due to the limited observation period of three months, the TLS data is not representative when it comes to longer time periods. Nevertheless, we can deduce that deposits currently located in the depositional area of the juvenile fan delta are rapidly subjected to consecutive transport to the lake. Since the juvenile fan contributes more to the subaquatic sediment deposition compared to the mature fan delta, this fan was chosen as a starting point for the core transect. The discovery of lobe-shaped deposits with high backscatter signals on the subaquatic delta continuation of the juvenile fan provides evidence for recent debris-flow activity and active fan progradation on the juvenile fan. In addition, subaquatic landslide deposits reveal a second process contributing to event deposition in Plansee." > Lines 606-614 "In contrast, 14 df turbidites with a major thickness in the fan-proximal cores (black arrows in Fig. 7b) form wedge-shaped sediment bodies near the slope break and can be explained by low-energy debris-flow activity on the juvenile fan, which may be caused by shifts in the delta morphology, (e.g. formation of multiple branching channels) or changes in the connectivity between catchment and depocentre. The linkage of these sediment deposits to the investigated juvenile fan delta reveals that its particular catchment has shown episodic debris-flow activity over at least 4,000 years. Moreover, the sedimentary record holds a short period of exclusively wedge-shaped df turbidite sedimentation ("P" bracket in Fig. 7b), which occurred immediately after the 2120 BCE earthquake expressed as multiple subaqueous mass-wasting deposits overlain by the eq3 turbidite ( Fig. 7a; Oswald et al., 2021)." > Lines 710-715 "Actualistic debris-flow processes and their corresponding deposits are characterized by their geomorphic landforms in both the terrestrial and subaqueous realms. In a transect of four sediment cores from an active juvenile fan towards the distal basin, we distinguish debris flows and earthquakes to be related with different turbidites based on their geomorphological, sedimentological and geochemical characteristics. Debris flows form lobe-shaped deposits with high back-scatter signals on the subaquatic prolongation of a subaerial active channel on the fan delta." (1) Concerning the lacustrine event deposits, I find the methodology for event type differentiation very exciting and comprehensible, also in the awareness that it is one of the rare opportunities to observe the process of debris flow in a relatively uninfluenced setting (which, by the way, is also well executed). Nevertheless, the following data processing raises questions. My mainly concerns regarding this study relate primarily to the uncertainties of age dating. What uncertainties are there in the temporal determination? Which in the event detection? How do these affect the calculated frequency?
(2) We thank the referee for making an important remark on the age-model accuracy. In our new manuscript, we show a revised approach following comments of both referees, which we think greatly improved the age-depth model. We made use of the age uncertainty provided by the age-modelling software Bacon and coupled this with a suitable bandwidth selection test. First, we applied a bandwidth selection test based on the number of df turbidites after Sheather and Jones (1991), which is also widely used e.g. for kernel statistics and often recommended in data science. This results in a bandwidth of 150.2 years for the whole 4,000 year record and in 16.5 years for the last two centuries, where df frequency is clearly enhanced. Second, we applied the frequency analysis using this 150 years bandwidth on the event ages of each of the 6,396 individual age-model simulations derived from Bacon. The frequency analysis on all simulations results in a 95% uncertainty belt providing a general overview of df turbidite frequency over time (Figure 8a), but likely underestimates/smoothens the actual frequency changes where more frequent events occurred, e.g. in the last two centuries. To overcome this issue, we coupled the 150-yr bandwidth occurrence rate diagram with the 21-yr frequency curve of the mean age to also provide a more detailed view on the frequency changes, especially where a higher number of events are present (e.g. the last two centuries). While this 21-yr frequency might be oversampled for the whole 4,000 year record, enough age constraints in the last century (1 coring date, 2 radionuclide ages, 1930 earthquakeinduced turbidite) and high event frequency allows for more detailed bandwidth in the frequency analyses. Although we now provide the 21-yr and the 150-yr frequency curves for the whole record, we only discuss the detailed 21-yr frequency changes for the last century in more detail (see Lines 526-530). The general frequency changes are also represented in the 150-yr frequency plot i.e. increased frequencies after the ~2120 BCE earthquake and for the last century (see Figure 8a), which further supports the interpretation of actual increased df activity at these times. We explain this approach in the methodology section in Lines 271-280 and in the results section in Lines 496-498 in the revised manuscript. Furthermore, we also added the age uncertainty range to the cumulative thickness curve (Figure 8a, Lines 280-281) and to the df turbidite table in the supplement (Table S4). However, we kept the mean ages for the thickness plots, as introducing age uncertainties would make this bar plot unreadable. (3) >Lines 271-281 "Additionally, we calculated the annual occurrence rate of df turbidites using a central running sum with different bandwidths to reconstruct changes in debris-flow frequency over time in different resolutions. First, a suitable bandwidth (150 yrs) was selected based on the average df-turbidite occurrence over the entire core (Sheather and Jones, 1991). We applied this bandwidth on the occurrence rate calculation for each individual simulation of the age-depth model derived from the R-software Bacon v 2.4.3 (Blaauw and Christen, 2011). This results in a data-based frequency analysis that incorporates age-depth model uncertainties. The rather broad bandwidth is suited for showing general changes in frequency over time. To account for a higher resolution in frequency changes especially in periods with higher number of events, we also calculated a bandwidth based on the df occurrence of the last two centuries and applied the resulting 21-yr bandwidth to occurrence rate calculation of the main age. The cumulative thickness over time involves both the thickness and frequency of df turbidites and its slope provides information on df turbidite accumulation rate per year. We calculated the cumulative thickness on the mean values and the 95 % range values of the age-depth model to transfer age uncertainty to the cumulative thickness analysis." >Lines 496-498 "The frequency analysis of the whole 4,000 year df turbidite record is based on a 150-yr bandwidth, whereas especially the higher number of events in the 20 th century requires higher resolution frequency analysis, here on the basis of a 21-yr bandwidth (Fig. 8a)." >Lines 526-530 "Df phase 4.1 is represented by a strong and fast frequency increase at ~1920 CE, followed by a period of highly frequent debris-flow events ~1980 CE. Since then, the current df phase 4.2 has lower frequencies relative to phase 4.1 but still by far higher frequencies than in the main df phases 1-3. Debris-flow frequency in 4.1 increased by a factor of 8 compared to the reference df phase 3. In df phase 4.2, debris-flow frequency increased by a factor of 7 compared to df phase 3." (1) The used age-depth model by Oswald et. Al (2021)  (2) We changed the ages to CE/BCE in the revised supplement.
(1) Table S2 does not provide information on the uncertainties of the top layers or recent past.
(2) We added 95% range values of the age model for every debris-flow turbidite to the supplementary table S4 and stated the mean uncertainties in the text (Lines 510-511).
(3) >Lines 510-511 "Mean age uncertainties are ± 6 years (2018-1960) and ±19 years (1959-1920; see also Supplementary Table S4)." (1) On the one hand, I would expect the deviations from the mean age dating to be given for each identified event in table S4 and, on the other hand, I would find it methodologically very exciting how to deal with these uncertainties when the stratification of different drill cores of the events is known and overlapping by the dating-uncertainties? How to assign the identified df deposits to a specific year? At least in the recent past a validation with e.g. dendrochronological dating would have been useful?
(2) We appreciate the question on how to deal with absolute and relative age uncertainty. We address this problem by applying the frequency analysis on each of the 6,396 iterations of age-model simulation derived from Bacon instead of the mean event ages. The referee suggests to further calibrate the last decades by on-fan dendrochronological dating of the debris flows. We plan to include this technique in our future research to obtain terrestrial evidence and reduce age uncertainties for the lacustrine deposits. The inclusion of dendrochronological methods is, however, beyond the scope of the present study.
(1) This raises further the question whether all identified events can be used for a frequency analysis or for the classification of the four different phases based on different event rates?
(2) We address this comment in the revised discussion of human impact (Lines 636-656) and give more detailed information on human-induced vegetation changes based on pollen records. A period of enhanced forest clearance during medieval times (Kral 1989) is not reflected in a sudden increase in debris-flow frequency in the sediment core archive. Since then, no further increase of forest clearance or wildfires is reported in the area, so we infer that changes in vegetation can be neglected before or during the period of increasing debris-flow frequency in the last century (phase 4). We clarify in the new manuscript (Lines 649-650), that human induced mass wasting in the first half of the 20 th century possibly created subaquatic detrital layers which cannot be distinguished from debris-flow deposits. This influence was considered in the frequency calculation (Lines 695-697).
Kral, F.: Pollenanalytische Untersuchungen im Fernpaßgebiet (Tirol): Zur Frage des Reliktcharakters der Bergsturz-Kiefernwälder, Verhandlungen der Zoologisch-Botanischen Gesellschaft in Wien. Since 2014 "Acta ZooBot Austria", 1989Austria", , 127-138, 1989 (3) >Lines 636-644 "Human-induced vegetation changes are documented since about 1,000 BCE from a pollen record from peat bog remnants at Heiterwanger See a few kilometres west of Plansee (Kral, 1989). A period of enhanced forest clearance in the area happened during medieval times according to this record. The herein presented sedimentary record of Plansee shows no signs of a drastic increase in debris-flow frequency throughout this period of intense forest use. During late medieval times, the climatic deterioration of the Little Ice Age, war, and epidemics led to a decrease in population and in forest clearance, which can be observed in pollen diagrams from the nearby Ostallgäu (Stojakowits and Friedmann, 2013). Since then, no further increase of forest clearance or wildfires is reported in the area. Therefore, we infer that there were no significant changes of vegetation before or during the period of increasing debris-flow frequency in the last century (df phase 4)." >Lines 649-650 "Therefore, some of the df turbidites in the first half of the 20 th century might actually reflect human-induced mass wasting (see also vi)." (1) Is it possible to quantify the classification of the 4 phases by statistical test? However, once the uncertainties of the event frequency is known a trend analyses should be conducted, showing if changes in the occurrence rate or deposition rate/a are distinct or covered within the uncertainty estimates?