Pulse-Doppler radar measurements of debris flows: High-resolution monitoring of surge dynamics from two events in the Gadria Creek (Italy)

. As a consequence of their spontaneous occurrence, and frequent formation of multiple surges with high sediment loads, debris flows are considered one of the most hazardous gravity-driven mass movements in montane regions. Field measurements of surface velocities are an essential link in the chain of understanding fundamental process dynamics and applied protection against debris flows. In order to measure the velocities of multiple consecutive surges within a single debris-flow event, a PD radar (pulse-Doppler high-frequency radar) sensor for high-resolution real-time debris-flow monitoring has been developed. In this contribution we present PD radar measurements of two debris flows, that occurred at the Gadria creek in Italy on July 26, 2019, and August 10, 2020, over a torrent length of 250 meters. We record over 55 high-amplitude surges that overlap and superimpose at the front of the debris flow, but also subsequently throughout the debris-flow body. Our results demonstrate applicability of a PD radar for debris-flow monitoring and serve as a data source for modelling surge dynamics in debris flows.


Introduction
In recent decades, various non-contact debris-flow monitoring methods for velocity measurement have been developed [1]. A sensor system that is particularly promising is the pulse-Doppler high-frequency (PD) radar [2]. In this contribution, we present first measurements of this system at the study site Gadria creek. We first provide a description of the method, with a special focus on the PD radar system. Subsequently, we use derived surface velocities and independently measured flow depths to characterize the surge dynamics of two debris flows. Finally, we discuss the challenges and limitations we have experienced and provide an outlook.

Test site and methods
The Gadria creek is located in the autonomous province of Bolzano in the Eastern Italian Alps. The steep slopes, the highly weathered metamorphic rocks and the glacial deposits, which can easily be eroded by heavy convective rainfall in the summer months, form the basis of this remarkably high debris-flow active catchment area [3,4] In 2016, a monitoring barrier was installed that provides flow height measurements in addition to a wide range of flow parameter [5]. In 2017, a PD radar unit was installed on the dam of the retention basin. The radar's main antenna beam is directed PD radar features the capability to detect moving objects at velocities > 0.2 m/s with a size of 1 m 2 up to a distance of 2,500 m by emitting a pulsed electromagnetic beam and processing the echo signal in a discrete-time manner. Within this range, a distance resolution, socalled range gates (Fig. 1), with a width from 15 to 150 m can be selected [2]. Velocities are determined using the Doppler effect. A fast Fourier transform (FFT) is used to convert the discrete-time echo signal into Doppler spectra (frames). Note that a single frame consists of an absolute frequency distribution where the velocities correspond to the classes and the frequency itself is defined as the echo intensity [6]. To simplify the information from the Doppler spectra for further calculations, we extract a maximum, median and mode velocity value per frame (Fig. 2).

Results and analysis
During the summer months of 2019 and 2020, a total of four debris flows occurred in the Gadria creek. One event took place on July 26, 2019, and the others were initiated at short intervals on August 02, 10, and 12, 2020. In this study we focus on the July 26, 2019 (t0 = 12:11:46 UTC) and August 10, 2020 (t0 = 17:50:33 UTC) debris flows. Both events were characterized by a distinct granular front, a solids-rich body with highamplitude surges, and a watery tail similar to [7]. We were able to fully record both debris flows with PD radar and flow height sensors. For characterizing and comparing surge dynamics, we calculate the amplitude A of each surge as the difference between the maximum flow height h with the depositional height h+ in the intermediate region with A = h -h+ and the surge period T as the time from the maximum flow height of a surge to the subsequent one [8]. The Froude number is based on the median velocities vmed at the peak of the surges and corresponding flow height h (Fig. 3). Finally, we also calculated the peak discharge Q with is composed of the flow height h and the corresponding cross-sectional area of the trapezoidal channel at respective times. For a suitable averaged surface velocity value, we opted for the median of the Doppler spectra vmed. Following this calculation, the estimated total volume is about 2000 m 3 for DF19 and about 10000 m 3 for DF20. The 2020 event has significantly higher flow height at the front, but thereafter the median value of flow height h and depositional height h+ is found to be notably lower than in the 2019 event (Fig. 3). Examining the flow velocity vmed, DF20 also shows significantly higher peak velocities. Interestingly, the average surge period T and the mean surge amplitude A are rather similar. The averaged values are given as A equals 0.57 m and T equals 20 s for DF19 and A equals 0.54 m and T equals 27 s for DF20.   4 shows the binned and normalized echo intensity for each range gate plotted against time as well as the respective distance of 25 m between the range gates. For the fourth dimension, we plotted the medium velocity vmed in the same way as echo intensity, but assigned it a color scale. The individual surges have been highlighted to provide a better sense of the dynamics. Around t840, at a range of ~ 250 m the front approaches with vmed of over 6 m/s, but between t850 and t870 a small surge subsides from a distance of 160 m. In nearly the same time slot from ~ t860 a following surge comes into the picture, where vmed even increase to ~ 9 m/s when entering range gate 8 at a distance of ~ 205 m. Shortly thereafter, at range gate 5 the front which is additionally slowed by the impact on the monitoring barrier, is caught up by the following surge and the two merge.

Discussion
The major difference between DF19 and DF20 resides in the flow regime. In DF19, the Froude numbers occur almost exclusively in the subcritical flow regime, while for DF20, they are found in the supercritical regime greater than 1. We tested the Froude numbers from both events against h+. DF20 exhibits moderate correlation (R 2 = 0,421) with h+ and DF19 shows no correlation at all (Fig. 5). Note that for DF20, the higher the Froude numbers (in the supercritical regime) at the crest of the surge, the lower the deposition h+. However, this observation does not hold for DF19, where a clustering occurs when the Froud numbers are less than 1. We note that in the event of DF20 h+ also represents a critical deposition height. The reason is that at an average height h+ of ~ 0.52 (m), the flow became stationary. At DF19, 6 of the total 16 surges came to a complete halt in the intermediate sections with an average h+ of ~ 1.20 m. We could not find any relation between vmed and respective amplitudes A and do not find high-amplitude surges traveling faster than smaller ones. What is the reason for the different flow regimes in the two events? According to independent measurements of basal normal stress and flow height [9], the bulk density of DF19 was between 2000 and 2300 kg/m³ and the mean bulk density of DF20 varied around 2000 kg/m³. What these measurements do not explicitly reveal is the water content and the overall grain size distribution, especially the fines content in the form of clay and silt, which controls the viscosity of the fluid. Based on visual video analysis, we hypothesize that DF20 had a higher fines content than the DF19, causing higher flow velocities and lower deposition heights. For DF19, we speculate that flow dynamics were more likely controlled by inter-particle collisions.

Conclusions
In this study we apply a novel non-contact and highresolution PD radar to monitor surface velocities in natural debris flows. We analyze the results together with independent flow height and basal normal stress measurements. The key conclusions are:  The PD radar system is applicable for continuously monitoring surface velocities of debris-flow surges.  Data analysis in the form of range-timeintensity-velocity (RTIV) diagrams shows that surges can superimpose and merge with the debris-flow front, but also with one-another.  Surges of two debris flow events at Gadria creek show surprisingly consistent surge dynamics.  Depositional height h+ in surge-intermediate stationary regions can be linked to different flow regimes.  High-amplitude surges do not necessarily flow at higher velocities than low-amplitude surges.  High Froude-numbers surges seem to be associated with lower inter-surge flow depth.