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A probabilistic sediment cascade model of sediment transfer in the Illgraben

2014; Wiley; Volume: 50; Issue: 2 Linguagem: Inglês

10.1002/2013wr013806

1944-7973

Georgina L. Bennett, Péter Molnár, Brian W. McArdell, Paolo Burlando,

Hydrology and Watershed Management Studies

Water Resources ResearchVolume 50, Issue 2 p. 1225-1244 Research ArticleFree Access A probabilistic sediment cascade model of sediment transfer in the Illgraben G. L. Bennett, G. L. Bennett Institute of Environmental Engineering, ETH Zurich, Zurich, Switzerland Now at Department of Geological Sciences, University of Oregon, Eugene, Oregon, USASearch for more papers by this authorP. Molnar, Corresponding Author P. Molnar Institute of Environmental Engineering, ETH Zurich, Zurich, SwitzerlandCorrespondence to: P. Molnar, [email protected]Search for more papers by this authorB. W. McArdell, B. W. McArdell Swiss Federal Institute of Forest, Snow and Landscape Research, Birmensdorf, SwitzerlandSearch for more papers by this authorP. Burlando, P. Burlando Institute of Environmental Engineering, ETH Zurich, Zurich, SwitzerlandSearch for more papers by this author G. L. Bennett, G. L. Bennett Institute of Environmental Engineering, ETH Zurich, Zurich, Switzerland Now at Department of Geological Sciences, University of Oregon, Eugene, Oregon, USASearch for more papers by this authorP. Molnar, Corresponding Author P. Molnar Institute of Environmental Engineering, ETH Zurich, Zurich, SwitzerlandCorrespondence to: P. Molnar, [email protected]Search for more papers by this authorB. W. McArdell, B. W. McArdell Swiss Federal Institute of Forest, Snow and Landscape Research, Birmensdorf, SwitzerlandSearch for more papers by this authorP. Burlando, P. Burlando Institute of Environmental Engineering, ETH Zurich, Zurich, SwitzerlandSearch for more papers by this author First published: 22 January 2014 https://doi.org/10.1002/2013WR013806Citations: 56AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract We present a probabilistic sediment cascade model to simulate sediment transfer in a mountain basin (Illgraben, Switzerland) where sediment is produced by hillslope landslides and rockfalls and exported out of the basin by debris flows and floods. The model conceptualizes the fluvial system as a spatially lumped cascade of connected reservoirs representing hillslope and channel storages where sediment goes through cycles of storage and remobilization by surface runoff. The model includes all relevant hydrological processes that lead to runoff formation in an Alpine basin, such as precipitation, snow accumulation, snowmelt, evapotranspiration, and soil water storage. Although the processes of sediment transfer and debris flow generation are described in a simplified manner, the model produces complex sediment discharge behavior which is driven by the availability of sediment and antecedent wetness conditions (system memory) as well as the triggering potential (climatic forcing). The observed probability distribution of debris flow volumes and their seasonality in 2000–2009 are reproduced. The stochasticity of hillslope sediment input is important for reproducing realistic sediment storage variability, although many details of the hillslope landslide triggering procedures are filtered out by the sediment transfer system. The model allows us to explicitly quantify the division into transport and supply-limited sediment discharge events. We show that debris flows may be generated for a wide range of rainfall intensities because of variable antecedent basin wetness and snowmelt contribution to runoff, which helps to understand the limitations of methods based on a single rainfall threshold for debris flow initiation in Alpine basins. Key Points A probabilistic sediment cascade model of a debris flow catchment is developed Sediment storage (history) and triggering (climate) are key for sediment yield Debris flows are simulated for a wide range of rainfall intensities 1 Introduction Mountain basin sediment discharge is inherently nonlinear and stochastic in its relationship to climatic forcing and sediment production. This leads to difficulties in the prediction of sediment discharge and making inferences about environmental change from sediment yield data alone [e.g., Jerolmack and Paola, 2010; Van De Wiel and Coulthard, 2010]. The nonlinearity in sediment discharge may arise from several sources, of which storage effects, geomorphic thresholds, and connectivity are generally thought to be the most important [e.g., Walling, 1983; Phillips, 2003, 2006]. Transient sediment storage in various landscape compartments (hillslopes, debris cones, river terraces, etc.) determines the availability of sediment for transport and as a result sediment discharge may be transport or supply limited [e.g., Bovis and Jakob, 1999; Lisle and Church, 2002; Otto et al., 2009]. Geomorphic thresholds are tipping points in the system at which events take place or the system behavior changes either by internal adjustment or external forcing [e.g., Schumm, 1979]. Hydrological connectivity of sediment sources to channels modulates sediment delivery and its distribution in time and space [e.g., Reid et al., 2007; Fryirs, 2013]. And finally stochasticity in climate, in the processes of sediment production, the mobilization of grains and pathways they follow in the landscape, all lead to an inherent variability and uncertainty in sediment transport and limit deterministic predictions [e.g., Benda and Dunne, 1997, Fuller et al., 2003; Malmon et al., 2003]. The aim of this paper is to implement the effects of storage, thresholds, and connectivity in a simple conceptual model of sediment transfer with which the nonlinearity and stochasticity in sediment discharge can be captured. The model is based on the notion of a sediment cascade, which conceptualizes the fluvial system as a cascade of connected reservoirs representing different landscape compartments (e.g., hillslopes and channels) where sediment goes through multiple cycles of storage and remobilization before being discharged from the basin [see Burt and Allison, 2010, and references therein]. The transfer of sediment is determined by fluvial processes and sediment storage, while the triggering of events supplying sediment may be stochastic or related to climatic variables. This conceptualization is founded on observations which have shown debris flows to be triggered by rainfall and conditioned on basin wetness [e.g., Badoux et al., 2009], yet at the same time limited by the availability of sediment [e.g., Bovis and Jakob, 1999; Jakob et al., 2005]. The application presented in this paper is intended for a mountain basin where sediment is produced by hillslope landslides and exported out of the basin by floods and debris flows generated by runoff in the channels. Numerical modeling is a useful tool for understanding and developing hypotheses about mountain basin sediment transfer because it allows for full control over initial conditions and parameters, which is difficult to achieve in either field or laboratory studies [Van De Wiel et al., 2011]. Sediment transfer modeling approaches range from simple empirical sediment budget models to complex physically based models that attempt to represent the processes of sediment transfer in as much detail as possible, such as landscape evolution (long term) and soil erosion (short term) models based on the 1-D or 2-D application of equations of motion for water and sediment. While they can be used for detailed simulations in space and time of sediment transfer through the drainage basin [e.g., Coulthard et al., 2000; Tucker et al., 2001; Molnar et al., 2006; Coulthard and Van De Wiel, 2007; Van De Wiel and Coulthard, 2010], they assume sediment transport laws and are heavily data dependent. As such they are subject to uncertainties that are difficult to evaluate, leading to an overparameterized problem where observed data are sometimes not sufficient to justify the model complexity. Our intention in this paper is to develop a model that is lumped in space and incorporates the minimum process representation required to reproduce first-order properties of sediment transfer in a mountain basin, such as sediment discharge volumes, event frequency, residence times, and their statistical properties. A key element is the use of the modeling approach in a probabilistic framework, allowing for stochasticity in landslide triggering and reconstructing the resulting probability distributions of sediment discharge by floods and debris flows from system behavior. This inverse approach has been used for instance for avalanche modeling [Ancey et al., 2003]. It allows us to include the inherent uncertainty in sediment input and its effect on sediment discharge, which would not be possible with deterministic models. Some other examples of this approach in geomorphology can be found in Benda and Dunne [1997], Fuller et al. [2003], Tipper [2007], Van De Wiel et al. [2011], among others. We propose that the value of this modeling approach comes from its compatibility with available observations, the inclusion of uncertainty and randomness in sediment production and transport, and the suitability for scenario analysis. Although in the development of the sediment cascade model in this paper we specifically have a landslide and debris flow catchment in mind, the concepts are generally applicable to any basin that can be schematized into a cascade system, e.g. see Lu et al. [2005, 2006] for an application to explain the sediment delivery ratio. We apply the model to the Illgraben in Switzerland, where a unique continuous 10 year record of debris flows provides the opportunity to calibrate it. In addition to the record of sediment discharge, the probability distribution of landslide volumes for the catchment has been estimated [Bennett et al., 2012], and there are estimates of erosion and storage of sediment on the hillslopes and in the channel [Berger et al., 2011; Bennett et al., 2013], as well as all necessary climate data. The hillslope-channel cascade approach has been qualitatively described in the Illgraben by Bardou and Jaboyedoff [2008], including important debris flow generating mechanisms [Bardou and Delaloye, 2004; Badoux et al., 2009]. Importantly, previous studies in the catchment enable the independent estimation of the majority of model parameters such that calibration of the model does not involve extensive fine tuning. We have three main objectives in this paper: (1) We develop the concept and apply the sediment cascade model to the Illgraben and investigate the conditions that lead to the transformation of the probability distribution of slope failures into that of debris flows in terms of the stochastic triggering and sediment transport mechanisms in the basin. (2) We investigate the impact of sediment storage in the Illgraben cascade on simulated sediment discharge events in general, and their division into transport and supply-limited events. (3) Our premise is that the storage and availability of water and sediment (system memory) and triggering potential (climate) drive sediment discharge behavior. On this basis, we investigate the rainfall that leads to debris flows in the model in order to understand and quantify the limitations of rainfall intensity thresholds for debris flow initiation. Although our application is based only on the Illgraben, we attempt to present the approach and results in a general way, inviting comparisons with any mountain basin with similar hydrological and geomorphological processes. 2 Slope Failures and Debris Flows in the Illgraben The Illgraben is a small (4.6 km2), NE facing catchment discharging into the Rhone Valley in southwest Switzerland (Figure 1), formed within highly fractured Triassic metasedimentary rocks, predominantly quartzites, limestones, and dolomites [Gabus et al., 2008]. It is of great research interest because of its large sediment output into the Rhone River of ∼60,000–180,000 m3 yr−1 mostly in the form of debris flows [Berger et al., 2011]. As a result, the Rhone River downstream of the Illgraben has developed a braided morphology over a reach more than 6 km in length. Figure 1Open in figure viewerPowerPoint Location of the Illgraben in the Rhone Valley and Switzerland. Large debris flows have been measured at the bottom of the Illgraben fan since 2000 by the WSL. We utilize part of this record from 2000 to 2009, containing 36 debris flows with estimated volumes between 2900 and 107,000 m3 [e.g., McArdell et al., 2007; Schlunegger et al., 2009; Bennett, 2013] to calibrate parts of our model. The largest documented event with a total volume of several hundred thousand cubic meters occurred on 6 June 1961, causing considerable damage on the debris flow fan. The sediment discharge regime is also characterized by floods and smaller debris flows (<3000 m3), but these are minor contributions to the sediment budget. In 2007 when more detailed measurements were made, 16 of 19 events were floods contributing ∼1600 m3 of sediment, or 8% of the 20,000 m3 of sediment transported by the three large debris flow events. Instrumentation is removed from the channel at the end of October and reinstalled at the beginning of May. Therefore, sediment discharge is only recorded from May to October. Several studies have investigated the production and transfer of sediment through the Illgraben [e.g., Bardou et al., 2003; Bardou and Delaloye, 2004; McArdell et al., 2007; Bardou and Jaboyedoff, 2008; Schlunegger et al., 2009; Berger et al., 2011; Schürch et al., 2011]. In a previous study, we used digital photogrammetry to produce a record of erosion and deposition in the upper catchment between 1963 and 2005 [Bennett et al., 2012, 2013]. More than 2000 landslides occurred between 1986 and 2005 from the most active slope in the catchment (our study area), spanning 6 orders or magnitude in volume and producing a mean erosion rate 0.39 ± 0.03 m yr−1 [Bennett et al., 2012]. The probability distribution of the landslides, with rollover below 233 m3 and power-law tail above this volume, was attributed to two types of slope failure—shallow slumps and slides making up the rollover and deep-seated bedrock failures making up the power-law tail. The latter are the most significant for the sediment budget, accounting for more than 98% of the total sediment supply [Bennett et al., 2012]. We use this distribution to determine the volumes of slope failures in the sediment cascade model. Large slope failures are also documented earlier in the 20th century, in 1920, 1928, 1934, and 1961 [Lichtenhahn, 1971; Gabus et al., 2008]. The largest rock avalanche was on 26 March 1961 with a volume in the range of 3–5 × 106 m3. The sediment generated by this event presumably led to the largest recorded debris flow later that year. The controls on the hillslope erosion rate are ambiguous but a thermal control seems present. Bennett et al. [2013] showed that an increase in the mean rate of hillslope erosion in the 1980s in the Illgraben is most likely explained by the increased exposure of the hillslope to thermal weathering due to a significant reduction in snow cover in warmer periods. Berger et al. [2011] illustrated the occurrence of channel filling during the winter and spring seasons by slope failures between 2007 and 2009, supporting the hypothesis that thermal weathering could be the most important control on slope failure. We implement this potential thermal triggering of landslides in the model by conditioning landslide occurrence on the absence of snow cover, but we also experiment with other hypothetical triggering mechanisms and sediment input scenarios. Another important observation in the Illgraben is that hillslopes are eroding independently of channel incision and that a downstream-directed coupling is the dominant process in the catchment at this time scale [Bennett et al., 2013]. There are several possible triggering mechanisms of debris flows in the Illgraben channel system [Bardou and Delaloye, 2004; Badoux et al., 2009]. The largest debris flows, such as the one documented in 1961, are probably associated with failures of landslide dams [Bardou et al., 2003]. Debris flows may also result from hillslope landslides with additional entrainment along the channel [Burtin et al., 2012]. Bardou and Dalaloye [2004] argue for climatic triggers related to temperature, e.g., snowmelt runoff from avalanche deposits or frost cracking due to ground freezing. However, the most frequent mechanism of debris flow generation is thought to be by entrainment of sediment stored in the channel during runoff events that are predominantly generated by heavy summer rainstorms [Badoux et al., 2009; Bennett et al., 2013]. We therefore conceptualize debris flow triggering in the model by surface runoff and subsequent entrainment. Because snowmelt can play an important role in conditioning or even triggering debris flows in the late spring and early summer, our modeling approach includes the simulation of hydrological processes of precipitation, snow accumulation and melt, and evapotranspiration, which together determine runoff and the conditions for generating floods and debris flows. 3 Model Structure and Calibration The sediment cascade model SedCas is a conceptual water and sediment transfer model that is spatially lumped at the basin scale (Figure 2). It consists of two parts: a hydrological and a sediment model. The hydrological model simulates the water balance for the basin including all relevant hydrological processes that lead to surface runoff generation. The sediment model simulates the cascade of sediment from landslides to hillslopes and into channels, and together with the runoff simulated by the hydrological model determines sediment discharge events in the form of sediment-poor floods, sediment-laden floods (or debris floods), and debris flows. The time step of both models is daily. The calibration of the SedCas model components for the Illgraben was performed as much as possible by independent estimation of model parameters and without fine tuning of the model output. All model parameters are summarized in Table 1. Figure 2Open in figure viewerPowerPoint SedCas model structure. The probability distribution of slope failures is from Bennett et al. [2012]. The distribution of sediment discharge events (debris flows) are those measured at the catchment outlet from 2000 to 2009. Table 1. Model Parametersa Parameter Description Value T* Threshold temperature for snow accumulation, melt, and melt of water frozen in the ground 0˚C m Snowpack melt rate factor 2.2 mm °C−1 d−1 δsum Albedo (summer) 0.3 x δwin Albedo (winter) 0.8 x α Parameter in the calculation of evaporation efficiency γ 0.2 mm−1 Swcap Basin-wide water storage capacity 21 mm x k Residence time of water in the storage reservoir 2 days xmin Minimum landslide volume from the power-law tail 233 m3 x β Power law scaling exponent in landslide distribution 1.65 x μ Mean of the lognormal distribution of landslides < xmin 3.36 m3 x σ Standard deviation of lognormal distribution of landslides < xmin 1.18 m3 x dh Hillslope redeposition rate 0.12 x Shcap Hillslope storage volume threshold 7.5 × 104 m3 x sdls Threshold snow depth for landslides triggered by thermal weathering (procedure 1; in SWE) 12 mm x rls Threshold rainfall for landslides triggered by rainfall (procedure 2) 8 mm d−1 x Qdf Critical discharge to generate a sediment discharge event 0.33 m3 s−1 x smax Maximum potential ratio of sediment to water in the flow, which equates to a maximum sediment concentration of 0.39 0.65 x a Parameters estimated independently are indicated with x. The hydrological model is a lumped model based on the linear reservoir concept which is the basis for many conceptual watershed models [e.g., Eriksson, 1971; Kirchner, 2009]. The water storage reservoir is fed by rainfall and snowmelt and depleted by evapotranspiration and runoff. Daily precipitation is derived from the MeteoSwiss RhiresD gridded product as a mean depth over cells that cover the Illgraben basin. The interpolation method in RhiresD follows that of Frei and Schär [1998]. The area-integrated precipitation estimates from RhiresD are more reliable than ground measurements in the Illgraben. Daily air temperature is measured at Sion, ∼15 km SW of the Illgraben, and interpolated to mean basin altitude with a monthly lapse rate estimated from Illgraben station data [Bennett et al., 2013]. Daily solar radiation and cloud cover data are also measured at Sion. Precipitation is separated into solid and liquid phase by a temperature threshold and a degree-day model is used to estimate snowmelt. Details of the hydrological model and its calibration are in section 3.1. The sediment model is a lumped model of the sediment transfer system and consists of two sediment storage reservoirs, one for the hillslope and the other for the channels. Sediment is supplied stochastically into the reservoirs by slope failures derived from a probability distribution of landslides on the hillslopes. In our application to the Illgraben, we consider the hillslopes at the head of the main debris flow channel to be our main sediment production area, as these have been shown to be the most active in the basin [Schlunegger et al., 2009; Berger et al., 2011]. This area is marked as the study slope in Figure 1 and the probability distribution of landslides has been developed for it by Bennett et al. [2012]. The study area does not include downstream tributaries to the main channel which may produce occasional sediment input, but are generally much less active. The hillslope reservoir represents the storage of sediment at the base of the hillslopes in the study area into which a fraction of sediment from slope failures is temporarily deposited en-route to the channel reservoir (see Figure 2) [Bennett et al., 2013]. The channel reservoir represents the portion of the main debris flow channel between the base of the hillslopes in the study area and the fan apex (near to CD19 in Figure 1). See Bennett et al. [2013] for a schematic and further explanation of the sediment routing system. Details of the sediment model and its calibration are in section 3.2. Hydrological Model 3.1.1 Snow The hydrological model uses a simple description of snow accumulation and melt to predict snow depth at a point as a function of elevation, temperature, precipitation, and a constant melt factor [e.g., Perona et al., 2007; Molini et al., 2011]. Accumulation of the snowpack occurs through cumulated precipitation events when temperature is below a threshold T*. On days when temperature exceeds T* the snowpack melts at a rate proportional to temperature, s(t) = m(T − T*) where s is daily snowmelt and m is the melt-rate factor. Snowmelt feeds the water storage reservoir together with rainfall. The model may be driven by observations of daily precipitation and temperature or stochastic simulations thereof. For the calibration of the snow module, we used snow depth data from the Grimentz station 6 km to the southwest of the Illgraben (Figure 1), chosen from several surrounding stations due to its similar elevation to the study area. We converted snow depth into snow-water equivalent (SWE) using a constant density 0.3 g cm−3, which was an average of fresh and old snow measurements taken at the nearby Arolla glacier [Carenzo et al., 2009] assuming an equal contribution of old and new snow to the snowpack. We calibrated T* and m based on the duration of snow cover and snow depth for the period 2000 to 2009. We found that having the same threshold temperature T* = 0°C for accumulation and ablation and m = 2.2 mm °C−1 d−1 produced the best results (RMSE = 1.5 mm d−1). Figure 3a shows an example of the time series of modeled snow depth compared to the observed snow depth at Grimentz (in SWE), along with modeled snowmelt and rainfall. The assumption of a constant snow density does not allow the degree-day model to capture the fluctuations in SWE accurately; however, the duration of snow cover, which is the key component for us, is represented reasonably well together with the probability distribution of snow depth (Figure 3b). A more complex snow accumulation and melt model would be needed in spatially distributed applications. Figure 3Open in figure viewerPowerPoint (a) Example of time series of modeled daily snow depth, rainfall, snowmelt, and measured snow depth (in SWE) at Grimentz. (b) Cumulative distribution of modeled and measured daily snow depth for the period 2000–2009. 3.1.2 Water Balance The water balance in the hydrological model is solved with a linear reservoir model at the daily time scale. The water storage reservoir represents the capacity of the soil (weathered bedrock) in the basin to store and discharge water. It is fed by snowmelt and rainfall and depleted by evapotranspiration and runoff: (1)where Sw is water storage in the reservoir, r is rainfall, s is snowmelt, AET is evapotranspiration, and Q is runoff. All of these are daily basin-averaged values in millimeters. Actual evapotranspiration is modeled as a fraction of daily potential evapotranspiration (PET) which is computed with the Priestley-Taylor method [Priestley and Taylor, 1972]. This requires time series of mean daily temperature, solar radiation, cloud cover, and values for albedo and elevation. We obtained the time series from the MeteoSwiss weather station in Sion and used the mean elevation of the study site as the representative point. Albedo was δsum = 0.3 for the summer and δwin = 0.8 for the winter, which are average values for bare ground and snow, respectively. AET is computed as a fraction of PET, (2)where γ is an efficiency parameter which is determined as a function of catchment water storage following Tuttle and Salvucci [2012], (3)where α is a parameter that determines how water availability in the subsurface limits evapotranspiration at the potential rate. The parameter α = 0.2 mm−1 was calibrated to reproduce the mean annual AET for the study region [Hydrological Atlas of Switzerland]. Runoff from the water storage reservoir takes place under two conditions. When the water storage capacity Swcap is not reached, outflow is computed as a function of the stored amount assuming a linear reservoir relation. When the capacity is exceeded, then all excess water generated by rain and/or snowmelt is discharged into the channel system and out of the basin: (4) The residence time k represents the attenuation of runoff through subsurface flow paths. Based on our observations in the Illgraben, we allow runoff from the subsurface reservoir only when T > T*. During the winter months, water in the subsurface reservoir stored in bedrock fractures, coarse sediment deposits and soil is assumed to be frozen. Only when the temperature rises above T* draining of water is initiated. We made a best guess of k = 2 days based on observations of discharge in the channel in days following rainfall; however, we note that the model results, including debris flow timing, are not very sensitive to k. The water storage capacity Swcap was independently estimated from the difference in observed runoff and basin-integrated rainfall for several flood and debris flow events in the catchment in 2005 and 2006 [Nydegger, 2008]. For rainfall events without snowmelt we argue that the maximum observed difference represents the catchment storage capacity. Averaged over the catchment this results in Swcap = 21 mm. This is a low estimate because it is based on only 2 years of data and assumes water storage was empty at the beginning of the events. In the calibration of the model, we investigated the effect of larger values as well. Figure 4 shows the seasonal distributions of modeled hydrological variables for the period 2000–2009. Rainfall is maximum during the summer months, but AET removes a large fraction of the water during this time, reducing discharge. Discharge is highest in the spring as a result of large inputs of snowmelt and low values of AET. Mean annual values of rainfall, AET, and discharge after calibration are 1018, 362, and 657 mm, respectively. These agree with values reported for the region in the Hydrological Atlas of Switzerland and a recent study by Fatichi et al. [2013]. We have no other means of calibrating the hydrological outputs in more detail without continuous discharge measurements at the catchment outlet. Figure 4Open in figure viewerPowerPoint Seasonal distribution of modeled hydrological variables. Plotted are the monthly means over the simulation period 2000–2009. Sediment Model 3.2.1 Sediment Supply by Slope Failure Sediment is delivered into the hillslope storage reservoir by slope failures at an average annual hillslope erosion rate equal to the observed rate [Bennett et al., 2012]. We experimented with five scenarios/procedures of sediment input into the model. The first three procedures are stochastic and slope failures are drawn from the probability distribution determined from observations by Bennett et al. [2012], while the remaining two procedures are hypothetical deterministic reference cases. Procedure (1) simulates triggering related to freezing. Large failures are triggered on days with air temperature T ≤ 0°C and snow depth sd < sdls. This procedure is based on the argument that freezing conditions without an insulating layer of snow on the ground are conducive to thermal weathering and slope