Boundary condition control of fluvial obstacle mark formation – framework from a geoscientific perspective

Obstacle marks are sedimentary bedforms, typically composed of an upstream local scour hole and a downstream sediment accumulation in the vicinity of an obstruction that is exposed to a current. However, specific morphologies are variable in fluvial, coastal and submarine environments. Although obstacle marks and the phenomenon of local scouring are subject to different scientific disciplines, the objectives of investigations are rather incoherent and no systematic framework for analysing and evaluating boundary condition control exists yet, especially concerning limited knowledge of the cause and effect relationship of obstacle mark formation at instream boulders or vegetation elements in variable environmental conditions. Thus, a parameter framework is developed which identifies a spectrum of extrinsic and intrinsic boundary conditions that control the major process dynamics of obstacle mark formation. The framework is composed of dimensionless control parameters that are separated by a hierarchical order regarding their significance for obstacle mark formation. Primary control parameters determine the geometrical scale of flow field at the obstacle, and therefore control the potential maximum size of the obstacle. Secondary control parameters affect the dynamics of the flow field in geometrical scale and limit the potential maximum size of the emerging sedimentary structure if thresholds are crossed. The framework is supposed to be a foundation for subsequent quantification and determination of thresholds by systematic laboratory studies. To elucidate this, flume‐based research is presented, evaluating the influence of different flow levels at boulder‐like obstacles of different shapes. The results show that obstacle mark dimensions were maximized at shallow flow depths compared to obstacle dimensions, while deep flows at submerged boulder‐like obstructions caused considerably smaller obstacle marks. In interdependency with a rounded and more streamlined obstacle shape, deep flows even cause a deviation of morphology if the flow depth above an obstacle exceeds 1.6 times the obstacle's dimensions. © 2020 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.


Introduction
In general, obstacle marks are morphological features formed by coherent vortex structures induced by obstacles exposed to a current (e.g. Karcz, 1968;Richardson, 1968;Allen, 1984;Paola et al., 1986). Initially, the presence of an obstruction confines the approaching flow field and leads to areas of potential scouring in front and around the obstacle, as well as depositional areas in the wake of the obstacle, due to local acceleration and deceleration of flow around the obstacle. Although obstacle marks are considered here as bed features of the fluvial environment, similar morphologies are reported from the seabed at shipwreck sites (e.g. Quinn, 2006;Garlan et al., 2015;Quinn and Smyth, 2017), in the aeolian environment at sandy surfaces (e.g. Leenders et al., 2007;Bishop, 2011;Luo et al., 2012;McKenna Neuman et al., 2013) and snow (Allen, 1965;Filhol and Sturm, 2015). In the fluvial environment, numerous natural elements are capable of serving as obstacles (e.g. boulders, deadwood and vegetation elements) (Figure 1). Studies of different scientific disciplines in Earth-science lead to synonymous expressions of erosional and depositional bed features induced by obstructions, including obstacle scour mark (Dżułyński and Walton, 1965), current crescent and current shadow (Peabody, 1947;Allen, 1984), comet mark (Werner et al., 1980), obstruction-formed pool (Buffington et al., 2002;Hassan and Woodsmith, 2004;Comiti et al., 2005) and vegetation-induced sedimentary structure (Nakayama et al., 2002;Rygel et al., 2004). scour phenomenon lead to numerous physical modelling studies and deterministic approaches to evaluate the significance of various boundary conditions, including flow conditions, sediment characteristics, geometric characteristics of the obstruction and time (Breusers and Raudkivi, 1991;Hoffmans and Verheij, 1997;Melville and Coleman, 2000;Sumer and Fredsøe, 2005;Ettema et al., 2011). Traditionally, the motivation of this research is to estimate the potential maximum scour depth at technical infrastructure subjected to flood events as a design parameter for foundation depth or as a proxy for risk assessment procedures (e.g. Melville and Sutherland, 1988;Chang et al., 2004;Sheppard et al., 2014). Most equations are derived through empirical approaches and rely on independent non-dimensional control parameters that represent boundary conditions. Naturally, these approaches do not consider specific properties of natural instream obstructions (e.g. boulders and vegetation elements) (Shamloo et al., 2001;Euler and Herget, 2012;Euler et al., 2017). Thus, the impact of many non-dimensional parameters on local scouring at technical infrastructure has been identified and isolated by the hydraulic engineering community, while knowledge of the boundary condition control of obstacle mark formation at natural instream obstructions is rather scarce. What is most lacking is a systematic framework that analyses obstacle marks as complex and self-organizing bedforms (e.g. Werner, 1999Werner, , 2003, not just components of it (i.e. potential maximum scour depth). In this perspective, environmental boundary conditions and derived control parameters govern the shape and dimension of the evolving bedform Kocurek et al., 2010;Chojnacki et al., 2019). Obstacle mark formation is interpreted as a system of interconnecting influences, which induce positive and negative feedback loops when thresholds of control parameters are crossed.
We propose a systematic parameter framework that sorts control parameters by different categories and classifies them based on two hierarchical levels. The impact of individual control parameters is quantified by critical thresholds derived from various references on the topic. In order to assess the complex-ity of boundary condition control on obstacle mark formation at natural instream obstructions, specific control factors are introduced that have not been considered so far.
The framework is established as a means to investigate the interplay of environmental conditions with erosional and depositional processes at obstructions within the fluvial system and to identify sensitivity by performing systematic laboratory parameter studies. It brings together knowledge from extensive literature on local scouring at artificial structures, and reveals gaps where the impact of individual control parameters is as yet inadequately explained. Besides purely academic relevance in the course of basic research on obstacle mark formation, growing knowledge of boundary condition control is supposed to be beneficial for application perspectives at field sites (cf. Figure 1).
1 Persistent obstacle marks are suitable indicators for the estimation of past local flow conditions (e.g. Herget et al., 2013). However, a systematic framework of boundary condition control on obstacle mark formation can refine existing procedures to use obstacle marks as hydraulic indicators. 2 Instream solid and permeable obstacles have significant effects on structural dynamics of rivers due to sediment mobilization, sediment trapping and pioneer island formation, and are frequently used to enhance the habitat quality of degraded rivers (e.g. Radspinner et al., 2010). The extent of these effects is controlled by thresholds of boundary condition, and further knowledge would be beneficial in the course of valuable and sustainable river restoration practices. The aims of this paper are: (i) to review obstacle marks as sedimentary structures combining knowledge and experiences from different disciplines; (ii) to give a comprehensive overview of morphodynamic processes leading to the emergence of these structures; (iii) to review existing knowledge of boundary conditions and control factors of obstacle marks formation across different scientific disciplines; (iv) to sort boundary conditions and control parameters of obstacle marks formation at natural instream obstacles by different categories and hierarchies in a novel parameter framework; (v) to evaluate the effects of different water levels at the obstacle and obstacle shape on obstacle marks formation based on a laboratory flume study, to underpin the relevance of the parameter framework.  In engineering science, the expression 'local scour' is utilized to account for morphodynamic processes at man-made obstructions, such as bridge piers, river training structures and pipelines. Safety problems at these structures due to the local Obstacle Marks as Sedimentary Structures on Different Spatial Scales Typically, obstacle marks are regarded as sedimentary structures that develop in non-cohesive and cohesive sediments (e.g. Briaud et al., 1999;Brandimarte et al., 2006;Debnath and Chaudhuri, 2010) and also in bedrock channels (e.g. Richardson and Carling, 2005;Yin et al., 2016).
Obstacle marks are assembled structures, typically composed of an upstream conical depression wrapping laterally around an obstacle in the downstream direction, denoted as a scour hole, and a contiguous depositional region in the wake of the obstruction, termed a sediment ridge. The obstacle itself is considered as an integral component of the structure and consists of a large bed obstruction, typically with a diameter greater than the grain size of the surrounding alluvium (Judd and Peterson, 1969;Lisle, 1981;Thompson, 2008). The entire pattern can be characterized by certain morphometric variables characterizing length values of the scour hole, including scour depth (d s ), scour width (w s ), scour length (l s ), as well as length values of the sediment ridge (L r ), including ridge height (h r ), ridge width (w r ) and ridge length (l r ) (cf. Figure 2A) (Euler and Herget, 2012). Scour hole and sediment ridge volumes (Vol s and Vol r ) can be estimated by multiplying the morphometric variables, although this procedure does not account for the specific shape of the structures and might lead to overestimation (Euler and Herget, 2012). The upstream scour slopes in front of the obstacle, in the plane of symmetry as well as perpendicular to it, are separable into upper and lower slope. The transition is characterized by a berm or rim as a type of 'knickpoint', which separates the steeper inner scour hole from the outer scour hole (cf. Figure 2B) (Dargahi, 1990;Hoffmans, 1993;Link et al., 2008). Close to the obstacle front, a flat semi-circular scour hole is located.
Field evidence of obstacle marks at a solid obstruction has been reported on different spatial scales, resulting from overland flow at rock fragments (e.g. Poesen et al., 1994), at boulders as remnants of flood events in ephemeral streams (Karcz, 1968;Euler et al., 2017) and at icebergs during glacier outburst floods (jökulhlaups) (Russell, 1993;Russell et al., 2006;Høgaas and Longva, 2016). Amongst the greatest obstacle marks (dimensions up to 10 2 m) are reported as evidence of Quaternary megafloods (peak discharge > 10 6 m 3 s À1 ) at large boulders and bedrock hills (Baker, 1978;Baker and Bunker, 1985;Carling et al., 2002b;Herget, 2005). Their macroscopic pattern is thereby consistent on different spatial scales (cf. Figure 2A). However, Nakayama (1992) describes scour holes in the wake of large boulders, while a frontal scour hole is missing. A connection can be drawn to the impact of boulders in high-gradient streams or rock sills, which are capable of inducing local scour formation in their wake due to overtopping and jet stream motion at their wake side (Buffington et al., 2002;Comiti et al., 2005;Endreny et al., 2011;Pagliara et al., 2018). However, beyond the description no further explanation based on dominant boundary conditions is available to account for this kind of 'inverse' obstacle mark.
Concerning solid instream roughness elements, like boulders in upper segments of gravel bed rivers, similar sedimentary structurescalled particle clustersare well documented as small-scale bedforms (Dal Cin, 1968;Strom and Papanicolaou, 2008;Papanicolaou and Tsakiris, 2017). Contrary to obstacle marks, no local scour hole is formed at the obstacle frontal face (stoss side). Instead, the obstacle serves as an anchor particle that traps incoming finer sediments either on its stoss side or in its wake, depending on the relative submergence ratio (i.e. ratio of flow depth to diameter of the anchor particle) of the obstructions as these bedforms evolve during the rising or falling  Euler and Herget (2012, p. 40). (B) Schematic upstream scour slope profile in the plane of symmetry indicating segments with different inclination, separated at a 'knickpoint' (i.e. berm). Not to scale. limp of a hydrograph (Laronne et al., 2001;Papanicolaou et al., 2011Papanicolaou et al., , 2018Ghilardi et al., 2014b).
Obstacle marks of different spatial extent are also reported at permeable riparian vegetation elements. Rygel et al. (2004) introduced the expression 'vegetation-induced sedimentary structures' (VISS) to describe ancient sedimentary structures at fossil forest in floodplain strata, while Tooth and Nanson (2000), Nakayama et al. (2002), Rodrigues et al. (2007), Euler et al. (2014) and Corenblit et al. (2016) report in-situ evidence at grass colonies, shrubs, sprouts and mature trees. As reported by these authors, shrubs and sprouts tend to favour lee-wise deposition of sediments in their wake (i.e. sediment ridge; cf. Figures 1B and 2A), while scour holes are significantly small or even absent. On the contrary, for mature trees with a single trunk, considerable scour holes are also documented. Obstacle mark formation at individual plant scale is also investigated in laboratory studies to evaluate the impact of permeability and porosity on the flow field around vegetal elements (e.g. Chen et al., 2012;Kim et al., 2015;Yagci et al., 2016).

Morphodynamic Processes at Instream Obstacles
Large bed obstacles exposed to a steady current are capable of modifying the flow field in their vicinity, resulting in the following processes: (1) contradiction of streamline lateral to the obstacle, causing higher flow velocities; (2) a vertical jet-like downflow towards the sediment bed at the obstacle front as a consequence of a vertical pressure gradient at the obstacle frontal face; (3) formation of a horseshoe-vortex system (HSV) at the obstacle base, resulting from the deflection of the downflow against the main flow direction; the HSV extends downstream, past the sides of the obstacle; and (4) a decelerated region of flow in the wake region of the obstacle, including a wake vortex system of detached shear layers with vertical axis of rotation (cf. Figure 3) (Allen, 1984;Dargahi, 1989;Shamloo et al., 2001;Sumer, 2004;Pattenden et al., 2005;Euler and Herget, 2012;Papanicolaou et al., 2012;Sumner, 2013;Hajimirzaie et al., 2014;Bauri and Sarkar, 2016;Launay et al., 2017).
Processes (1) to (4) are capable of amplifying the bed shear stress above the critical bed shear stress for sediment mobilization, inducing local scouring in front and laterally to the obstacle, even though there is no general sediment movement in the surroundings. The main driver of sediment mobilization and local scouring is the HSV (e.g. Dargahi, 1990;Radice et al., 2009;Link et al., 2012;Bouratsis et al., 2017). The HSV is located in the inner scour hole close to the scour hole bottom, where sediment is picked up beneath the HSV by the particle transport modes of saltation and rolling (Dey, 1996;Unger and Hager, 2007;Maity and Mazumder, 2014). The steeper inner scour hole is shaped by the HSV. The rotation of the HSV generally stabilizes the lower slope at an angle greater than the angle of repose (e.g. Hoffmans, 1993;Dey et al., 1995). However, the HSV is an unsteady vortex system that randomly oscillates in time, and thereby temporarily weakens (e.g. Unger and Hager, 2007). Thus, ongoing depth incision and occasional weakening of the HSV destabilize the scour slopes and result in gravity mass movements, causing an enlargement in frontal length and width of the scour hole (cf. Figure 2). Due to the collapses, sediment grains slide into the scour bottom where they get picked up by the HSV and are transported downstream under its expanding legs as bed load. In the mid-to far-wake region the sediment gets deposited as a dune-like sediment ridge due to decreasing bed shear stress (e.g. Oliveto and Hager, 2014). Sediment transport on the sediment ridge is composed of rolling and sliding (e.g. Euler et al., 2017).
Deposition of finer material in the low-energetic wake of large bed obstructions (e.g. boulders) also occurs without indication of local scouring in front of the obstruction (e.g. Thompson, 2008;Papanicolaou et al., 2011Papanicolaou et al., , 2012. Here, fine sediments are transported as sheets or in suspension and form a tapered sediment ridge or sand shadow (Werner et al., 1980) (cf. Figure 1B). However, the unique aspect about obstacle marks is that they can develop even when the threshold for general sediment movement is not exceeded (Euler and Herget, 2012). Scour depth incision is characterized by a non-linear development until an equilibrium condition is reached. The scour depth is then referred to as the equilibrium scour depth and is determined as the maximum depth of the scour hole measured from the undisturbed bed level. The equilibrium scour depth is reached asymptotically in time (cf. Figure 4).
As reported from laboratory flume studies, initial scour incision is characterized by positive feedback mechanisms due to the fact that the HSV sinks into the developing scour hole (e.g. Dey, 1996Dey, , 1999Muzzammil and Gangadhariah, 2003;Dey and Raikar, 2007a). With ongoing temporal evolution and increasing size of the scour hole, the cross-section of the vortex increases and the shear stress under the HSV decreases as less energy per unit mass is available (e.g. Kothyari et al., 1992;Mia and Nago, 2003;Li et al., 2018). Thus, the feedback mechanism turns negative and dampens further evolution of scouring (Muzzammil and Gangadhariah, 2003;Muzzammil et al., 2004). Once shear stress induced by the HSV is well below the critical shear stress, the equilibrium condition of scour incision is attained while gravitational movements at the upper slope also relax. If the alluvial material is non-uniform, an armour layer of coarser sediments develops at the scour hole bottom which has a reductive impact on scour depth incision and the equilibrium condition is reached more quickly (e.g. Dey and Raikar, 2007b). From laboratory data it is known that almost 80% of equilibrium scour depth is developed within only 5-40% of the duration of experimental runs, while the time scale to reach equilibrium scour depth depends on flow conditions and sediment characteristics (Melville and Chiew, 1999).
At equilibrium conditions, the morphometric characteristics of the scour hole show a distinct relationship at which wide and long frontal scour holes belong to deeply incised scour holes, while the sediment ridge width also has a linear relationship to scour depth (Euler and Herget, 2012;Euler et al., 2017). Laboratory observations indicate that feedbacks loops, resulting from dynamic interactions between hydraulic and sedimentary processes, lead to non-linear development in time towards equilibrium, although the external energy input (e.g. discharge) is constant (Euler et al., 2017). This behaviour is commonly known as self-organization (e.g. Coco and Murray, 2007), and depends on the thresholds of external environmental boundary conditions as a type of cause and effect relationship (e.g. Murray et al., 2014).

Review of Boundary Conditions of Morphodynamic Processes at Instream Obstructions
By referring to the advanced knowledge from hydraulic engineering science on the phenomenon of bridge pier scouring, environmental boundary conditions of local scouring are grouped into: (1) flow conditions; (2) sediment characteristics; (3) geometric characteristics of the bridge pier; and (4) time, indicating the multi-dimensional complexity of the phenomenon (e.g. Breusers and Raudkivi, 1991;Hoffmans and Verheij, 1997;Melville and Coleman, 2000;Sumer and Fredsøe, 2005;Ettema et al., 2006Ettema et al., , 2011Williams et al., 2017). Boundary conditions are composed of various influence factors that operationalize conditions (i.e. 'flow conditions') into measurable quantities (i.e. mean flow velocity and depth). Upon application of dimensional analysis and the Buckingham π-theorem (e.g. Barenblatt, 2003), these influence factors are transformed into non-dimensional, scale-invariant control parameters and displayed as functional relationships that can reasonably be analysed in physical modelling studies (e.g. Ettema et al., 1998;Williams et al., 2017). Local scour depth is basically controlled by flow depth (d w ; dimension L) relative to pier/obstacle width (w o [L]), approach mean flow velocity (U m [LT À1 ]) relative to critical mean approach velocity for entrainment of bed sediment , pier/obstacle width relative to median grain diameter (D 50 [L]), the gradation coefficient of sediment (σ G = (D 84 /D 16 ) 1/2 [M 0 L 0 T 0 ]), pier/obstacle shape, pier/obstacle alignment and time (t [T]) (e.g. Breusers and Raudkivi, 1991;Hoffmans and Verheij, 1997;Melville and Chiew, 1999;Melville and Coleman, 2000;Sumer and Fredsøe, 2005;Ettema et al., 2011). Detailed descriptions of parameter influenceincluding envelope curves and empirically determined thresholdare given in the aforementioned references.
Obviously, the research of hydraulic engineers on local scouring has a technical background, as the potential failure of technical infrastructure due to local scouring is the motive to investigate the phenomenon. In this regard, the height of the obstruction is neglected as the obstruction (i.e. bridge piers) protrudes above the water surface. Thus, obstacle height (h o [L]) is always greater than flow depth (i.e. emergent flow prevails, d w ≤ h o ). This perspective might be insufficient concerning natural large bed elements, like solitary boulders located at the streambed, as it neglects flow over the obstruction (i.e. submergence, d w ≥ h o ). Obstacle mark formation at submerged obstacles like pipelines was investigated by Dey et al. (2008) and Sarkar (2014) in laboratory studies, while Euler and Herget (2011)  ), leading to an adapted obstacle Reynolds number (Re o = U m L o / ν). The exponents were chosen to account for the impact of obstacle height (h o ) on local scouring at submerged obstacles and derived from a data analysis on pier and abutment scouring reported in Oliveto and Hager (2002). Re o expresses the ratio between turbulent and viscous stresses at the obstacle (Euler and Herget, 2011;Lança et al., 2016;Manes et al., 2018) and thresholds for the initiation of obstacle mark formation based on the Re o number are formulated (Euler and Herget, 2012). The product of U m and L o thereby controls the turbulence and erosive energy of the HSV as it determines the flow separation and adverse pressure gradients at the obstacle frontal face (Muzzammil and Gangadhariah, 2003;Muzzammil et al., 2004). However, the size of the HSV also depends on flow depth (d w ) and the structure of the approaching boundary layer ; see Figure 3.3 therein). Although the flow over the obstruction (d w > h o ) is a common feature at boulder-like obstacles, its implication for local scouring and obstacle mark formation has been considered in only a few empirical studies so far (Fisher and Klingeman, 1984;Shamloo et al., 2001;Tominga, 2014). As opposed to this, the influence of emergent (d w < h o ) and submerged (d w ≥ h o ) flow has been analysed sufficiently in the course of bed load transport around large roughness elements and pebble cluster formation in gravel bed rivers, identifying the submergence ratio (d w /h o ) as a dominant control parameter for the deposition of incoming sediments Papanicolaou and Kramer, 2006;Papanicolaou et al., 2010;Ghilardi et al., 2014a), while the boundary conditions of the surrounding alluvial bed material in relation to the diameter of the roughness element inhibit the formation of a local scour hole in front of the obstruction. Considering a solitary solid boulder-like obstruction located in a straight, moderately sloped channel with subcritical (Fr < 1) flow conditions and cohesion less alluvial sediment (i.e. plane bed-type streams; Simons and Richardson, 1966), local scour incision can functionally be determined by: , Mb is an indicator for the mobility of a boulder-like obstruction, due to tilting into the scoured depression which limits further evolution of local scouring and induces equilibrium more quickly (e.g. Truelsen et al., 2005;Friedrich et al., 2016;Euler et al., 2017;Rennie et al., 2017), ρ s is sediment density and d sed is the thickness of the alluvial layer [L]. Considering a solitary riparian vegetation element (i.e. mature tree or shrub) exposed to a current, local scouring is anticipated to be functionally determined as: where I o is the inclination of the stem in the streamwise direction [M 0 L 0 T 0 ], V p is the porosity of a permeable obstruction [M 0 L 0 T 0 ], which triggers bleed-flow (i.e. flow through the obstruction) instead of downflow and HSV formation (e.g. Schnauder and Moggridge, 2009) and h d is the deflected height of a flexible vegetation element exposed to a current [L].
Equations (1) and (2) state that d s depends on 16, respectively 17, variables (denoted n) in three basic dimensions (denoted m) that define the problem's inherent degrees of freedom (e.g. Sonin, 2004). Assuming constant relative sediment density (ρ s À ρ)/ρ (i.e. neglecting ρ and ρ s and introducing Euler and Herget, 2011) reduces the degrees of freedom in both equations. Furthermore, application of the π-theorem (e.g. Barenblatt, 2003) to Equations (1) and (2) reveals n À m nondimensional control parameters. Among other expressions, we get: where U m /g * L o 1/2 is the obstacle Froude number (Fr o ), U m * L o /ν is the obstacle Reynolds number (Re o ), L o /B is the blockage ratio, Sh (L o /le o ) describes the hydrodynamic shape of a body, generally differing between streamlined obstructions with cross-flow dimensions smaller than stream-wise dimensions (Sh ≤ 0.5) and bluff obstructions with cross-flow dimensions comparable to stream-wise dimensions (Sh ≥ 0.8) (e.g. Douglas et al., 2001) and t e is the time scale to reach equilibrium [T], which is a function of d w /L o , U m /U c and L o /D 50 (e.g. Melville and Chiew, 1999).
Considering a permeable vegetation element, Equation (2) can be expressed as: where I v is the perpendicular alignment of the obstruction to the streambed (90°). According to Manes and Brocchini (2015) and Manes et al. (2018), flow intensity (U m /U c ) is often somewhat artificially included in the dimensional analysis of local scouring, because it has the important physical meaning of discerning between clear-water (U m /U c < 1) and live-bed conditions (U m /U c > 1) of the approaching flow (e.g. Melville and Coleman, 2000;Ettema et al., 2011). For the latter, sediment mobilization is not only occurring in the vicinity of the obstruction, but also in the undisturbed flow upstream. However, as highlighted by Simarro et al. (2007), the usage of U c (i.e. U m /U c ) introduces technical difficulties in the analysis as: which can be expressed as a non-dimensional equation, applying dimensional analysis: Comparison of Equations (3), (4) and (6) indicates the analogy of several control parameters, although different reference lengths (L o and D 50 ) are used. It becomes obvious that the control parameters d w /L o , Re o and Fr o are linked due to the consideration of U c /U m , because U m /U c * U c /g * D 50 1/2 generates a derivative of Fr o and g * D 50 3 /ν 2 can be rearranged to a derivative of Re o (cf. Lança et al., 2016). Thus, technically speaking, the right-hand sides of Equations (3) and (4) are not independent and one of the control parameters (i.e. d w /L o , Re o or Fr o ) has to be excluded (Simarro et al., 2007;Lança et al., 2016). As it is preferred to keep U m /U c , Fr o is excluded and the functional relationships reduce to: Furthermore, due to shape similitude of the local scour hole (e.g. Euler and Herget, 2012), it is possible to replace d s /L o in Equations (5) and (6) by any characteristic length of the scour hole (cf. Figure 2A): By comparing Equations (7), (8) and (9), (10), d s /L o can substitute any of the non-dimensional parameters on the right side of Equations (5) and (6) (cf. Chreties et al., 2008), underlining the dependence of scour depth incision for the evolution of the scour hole width (w s ) and length (l s ), besides other control parameters. Equations (7) and (8) compromise the control parameters of obstacle mark formation at natural obstructions by including well-known parameters from hydraulic engineering research on the topic, as well as parameters that account for specific properties and characteristics of natural obstacles. However, technical considerations reveal that control parameters d w /L o and U m /U c in Equations (7) and (8) are connected due to the variables d w and U c [cf. Equation (5)]. Thus, a variation of one control parameter along an axis of influence often causes the variation of another parameter, which then affects the morphodynamic processes and size of the emerging obstacle mark (Ettema et al., 2011).
A further systematization of the control parameters included in Equations (7) and (8) is proposed, which classifies the control parameters based on two different hierarchical levels and quantifies their impact for obstacle mark formation and size of the emerging structure based on thresholds.

Parameter Framework of Boundary Condition Control on Morphodynamic Processes at Natural Instream Obstacles
Obstacle marks are complex geomorphic systems (e.g. Werner, 1999Werner, , 2003, characterized by feedback loops of hydraulic and sedimentary processes and showing a non-linear evolution in time towards the equilibrium condition. More specifically, this behaviour is commonly known as self-organization (e.g. Coco and Murray, 2007), which depends on the thresholds of control parameters. It is supposed that the impact of control parameters on obstacle mark formation and dynamics can be assessed by thresholds of two different categories: (1) control parameters that have to be crossed to initiate local scouring and (2) control parameters that mark conditions at which obstacle marks are spatially maximized. Consequently, between these thresholds of control parameters, the size of the obstacle and its characteristic morphometric variables (cf. Figure 2A) is reduced compared to the potential maximum. From this perspective, the control factors of Equations (7) and (8) can be classified into hierarchical levels regarding their significance for obstacle mark formation and size of the emerging structure, while interconnections are also considered by this procedure. Therefore, the 'typical' obstacle mark pattern emerging form the erosive action of the HSV and scour depth incision serves as a target of the parameter framework. Here, the control factors are grouped into extrinsic and intrinsic categories and further distinguished into levels of effectuality, including (1) hierarchy and (2) impact. Figure 5 depicts a graphical scheme that compactly demonstrates dimensional influence factors and nondimensional control parameters of obstacle mark formation at natural instream obstacles, which are further outlined in detail.

Categories
Control parameters are separated into intrinsic and extrinsic categories. Extrinsic control parameters cluster the hydraulic conditions and alluvial characteristics as well as time, while intrinsic control parameters characterize properties of the obstacle such as geometrically definable roughness element and integral component of the emerging obstacle mark. Regarding natural instream obstacles, characteristics of solid obstacles (i.e. boulder-like) and permeable obstacles (i.e. vegetation elements) are distinguished (cf. Figure 5). For solid boulder-like obstructions, Sh and Mb belong to the intrinsic control parameters. Here, bluff obstructions (Sh ≥ 0.8) offer higher resistance to the approaching flow and generate higher-pressure gradients at the obstacle frontal face, which results in a stronger HSV and more intense local scouring processes. Boulder-like obstructions are also mobile (Mb). In the course of high-energy flows (i.e. Fr ≥ 1), this might result in the mobilization of the obstacle itself and transport downstream (Carling et al., 2002a;Alexander and Cooker, 2016;Bressan et al., 2018). In the course of obstacle mark formation, the mobile obstacle is not transported downstream, but tilts into the evolving scour hole, if a critical scour depth is reached. This self-burial limits further scour incision and induces equilibrium more quickly (e.g. Euler et al., 2017).
In contrast, shrubs are permeable obstacles. The porosity of the frontal area leads to flow penetrating the obstruction irrespective of water level (i.e. emergent or submerged) (Lee et al., 2018). Vegetation porosity (V p ) represents the fraction of void spaces in relation to the total body volume and is commonly expressed as a dimensionless quantity between 0 and 1 (e.g. Grant and Nickling, 1998;Montakhab et al., 2013). Indeed, porosity is not a fixed value as it depends on number and size of stems and leaves per unit area, which vary during the annual growth cycle due to exfoliation (e.g. Schnauder and Moggridge, 2009). If the obstacle is too porous, frontal scouring is inhibited due to absent downflow. Nevertheless, sediment trapping of incoming sediments is still observable (e.g. Leenders et al., 2007) (cf. Figure 1B). No systematic investigation on the influence of V p as intrinsic control parameter of obstacle mark formation has been conducted so far. Additionally, the stems and leaves of shrubs are flexible and tend to bend in a stream-wise direction as a reaction to flow passing over or through (e.g. Nikora et al., 2008;Nikora, 2010). According to Okamoto and Nezu (2010), the deflected height (h d ) is an appropriate measure of the flexibility, which is primarily dependent on the rigidity of the vegetation element. The rigidity of a vegetation element determines the extent to which it offers resistance to the flow, generating pressure drag to induce local scour incision (e.g. Nikora, 2010). Thus, if the deflected height (h d ) in relation to the obstacle height (h o ) (without bending) exceeds a critical threshold, local scouring is inhibited, while again trapping of incoming sediments might still be possible (e.g. Nikora, 2010). Again, no critical threshold of h d /h o is formulated so far. However, the impact of inclination in a stream-wise direction (I o ) is similar to the deflected height (h d ), which is described for tree trunks of matured riparian vegetation due to local scouring (e.g. Nakayama et al., 2002).

Hierarchy
Intrinsic and extrinsic control parameters are distinguished by two hierarchical levels, regarding their significance for the size of the morphometric parameters. The hierarchical levels consider connections of control parameters depicted in Equations (7) and (8).
Primary control parameters define the geometrical scale of the HSV at the obstacle and determine the potential maximum size of the morphometric variables (e.g. scour depth; cf. Figure 2A). It is supposed that the size of an obstacle mark is maximized at distinct values or within small ranges of the primary control parameters that can be interpreted as thresholds. From these thresholds, an increase or decrease of a primary control factor affects the geometrical scale of the HSV and limits the spatial extent of an obstacle mark (expressed due to the size of the morphometric variables). For given primary control parameters, the actual size of the morphometric variable is further impacted by the secondary control parameters as they influence the dynamics of the flow field at the obstacle. Generally, they characterize limitations of scour hole incision and sediment ridge accumulation and limit the potential maximum obstacle mark size below or beyond a distinct threshold (cf. Ettema et al., 2011).
The control parameters L o /D 50 , L o /B, d w /L o and Sh are considered as primary control parameters for obstacle mark formation at solid boulder-like obstructions, as they affect the geometrical scale of the HSV at the obstacle, while for vegetation elements porosity (V p ), relative inclination of the stem in the streamwise direction (I o /I v ) and relative defected height of the flexible parts (h d /h o ) are additional primary control parameters.
Within the geometrical scale, the control parameters U m /U c , Re o , σ G , d sed /L o , t/t e and Mb (only for solid boulder-like obstructions) are considered as secondary control parameters which, above or below certain thresholds, impact the potential maximum size of the morphometric variables for given primary control parameters (see next section).

Impact
The impact of primary and secondary control parameters on the size of the morphometric variables is quantified by thresholds, differing conditions for which morphometric variables are potentially maximized, conditions for which morphometric variables are limited compared to a potential maximum and conditions for which obstacle mark formation is even completely inhibited. As a synthesis, these thresholds are gathered from empirical evidence reported in various references on local scouring, while scour depth (d s ) is chosen as target morphometric variable. Table I gives a comprehensive overview of known threshold ranges of primary and secondary control parameters used for the present framework, which can be summarized as follows.
1 Relative coarseness (D 50 /w o or D 50 /L o ): d s is maximized for relative coarseness w o /D 50 ≈ 25-50 (Lee and Sturm, 2009). For w o /D 50 > 60-10 000, d s is reduced, because in noncohesive alluvial sediment, ripple formation at the subthreshold condition of motion (U m /U c < 1) can cause sediment transport into the scour hole. If w o /D 50 < 8, alluvial sediment particles are too coarse compared to the obstacle size and inhibit local scouring completely, because of the dissipating effects of large sediment particles on the HSV (e.g. Firat and Gungor, 2009 (Euler et al., 2014). Here, wake vortices create a zone of recirculating currents in the obstacle wake, causing scouring in the wake as a type of 'inverse' obstacle mark.
For I o /I v >> 1.3, no frontal scour hole will emerge. 5 Porosity (V p ): d s is supposed to be maximized if V p = 0, so that no bleed-flow occurs. Unfortunately, there is neither empirical data available nor thresholds of V p > 0 formulated that limit d s . 6 Relative defected height of flexible parts (h d /h o ): no thresholds have been described so far. 7 Flow intensity (U m /U c ): for U m /U c > 1, d s is reduced due to the passage of bedforms like ripples or dunes (e.g. Melville and Coleman, 2000;Hong et al., 2017). For U m /U c ≤ 0.3, no local scouring is initiated at the obstacle front, irrespective of flow depth (d w ) and obstacle size (L o ) (Chiew, 1995). 8 Obstacle Reynolds number (Re o ): for Re o < 3000, viscous stresses dominated at the obstacle that inhibit the formation of an HSV and the emergence of a frontal scour hole, irrespective of flow depth (d w ) and obstacle size (L o ) (Euler and Herget, 2012). 9 Gradation coefficient (σ G ): for σ G > 1.3 and non-uniform alluvial sediment, d s is limited (e.g. Raudkivi and Ettema, 1985). Frontal scouring is supposed to be prevented if D 84 /L o < 8. As reported by Sheppard and Miller (2006), d s is largely independent of σ G at live-bed conditions (U m /U c > 1). 10 Mobility (Mb): if an obstacle is considered mobile, local scouring can undermine the obstacle and result in a tilting into the scour hole that will limit further d s incision. Cleary, the tilting of a mobile obstacle depends on d s , so that the designation of distinct thresholds is crucial. Nevertheless, Euler et al. (2017) experimentally determined the onset of tilting at d s /le o > 0.6. 11 Relative sediment thickness (d sed /L o ): if an obstacle is located in a thin alluvial sediment layer above bedrock (i.e. d sed /L o < 1) (e.g. Hodge et al., 2011;Church and Haschenburger, 2017), d s incision is significantly limited, while slight enlargement of w s and l s could be observed (Schlömer and Herget, 2016). If d sed /L o = 0, the formation of obstacle marks as a sedimentary structure is inhibited. 12 Time scale (t/t e ): d s is potentially maximized at equilibrium conditions (t/t e = 1). From laboratory studies on bridge piers it is known that t e is reached after several days, depending on flow conditions and sediment characteristics (e.g. Melville and Chiew, 1999). Scour depth (d s ) will not reach equilibrium if t/t e < 1. 13 Submergence ratio (d w /L o ): d w /L o is considered as a primary control factor and thresholds are quantified via a laboratory study hereinafter.

Evaluation of Submergence Ratio and Obstacle Shape as Primary Control Factors of Obstacle Mark Formation at Solid Boulder-Like Obstacles
Submergence ratio (d w /L o ) and obstacle shape (Sh) are considered as primary control parameters defining the geometrical scale of the HSV, because they control the adverse pressure gradients formed at the obstacle frontal face and determine the potential maximum size of the obstacle mark. Considering a solid boulder-like instream obstruction, the variable d w is the key determinant to attain varying ratios of d w /L o , as the height and width (i.e. L o = h o 2/3 w o 1/3 ) of the boulder-like obstruction are not supposed to change during a flood event (Lacey and Rennie, 2012). This perspective is in contrast to prior investigations on local scouring at submerged structures, where different ratios of d w /L o were modelled by changing the obstruction height (h o ) of a cylinder protruding into flow, keeping the flow depth (d w ) constant (e.g. Dey et al., 2008;Sarkar, 2014). This   (1999) a Local scouring is reported in bedrock channel (Richardson and Carling, 2005;Yin et al., 2016), but not as sedimentary structure.
In a first set of experiments (series A), individual experiments were designed to represent steady flow conditions at constant mean approach velocity (U m = 0.2 m s À1 ), whereas d w was varied from 0.02 to 0.14 m for individual runs in different intervals (0.005 to 0.02 m) by adjustment of a tail-gate at the end of the flume. The procedure resulted in submergence ratios (d w /L o ) ranging from 0.55 to 3.83, indicating emergent conditions (obstacle's top protruded the water surface, d w < L o ) to fully submerged conditions (d w >> L o ) to mimic natural conditions at instream boulders adequately. Flow depth (d w ) in the working section (~2.7 m downstream of the inlet) was measured by punctual measurements of the water surface profile along the plane of symmetry by an ultrasonic distance meter (Mic +25, Microsonic ® , accuracy ±0.1 mm). By applying the principles of continuity (Q = U m * B), different discharges (Q) were calculated that ensure constant U m at different d w based on the fixed cross-section of the flume (B). Water flux was provided by a recirculating pump (Lowara FCE-series ® ) and discharge was measured by a magnetic/inductive discharge meter (Schwing MS 1000 ® , accuracy ±1%).
For a given D 50 , varying d w while keeping U m constant impacts the shear velocity (u* [LT À1 ]) at the undisturbed bed, which can be explained by Keugelan's resistance law for dynamical rough beds (e.g. Muste, 2017): Here, u* decreases with rising d w , if U m is kept constant (e.g. Breusers and Raudkivi, 1991). Recalling Equation (5) and the interdependence of hydraulic control parameters, a variation of d w for a given D 50 yields different U c : for which u c * is the critical shear velocity [LT À1 ] that can be estimated by a procedure given by Melville and Coleman (2000, p. 194): u c Ã ¼ 0:0115 þ 0:0125 D 50 1:4 valid for 0:1 mm < D 50 < 1 mm ð Þ (13) so that: By applying Equations (13) and (14) to the conditions of series A experiments, it becomes obvious that the secondary control parameter U m /U c was varied for different submergence ratios (d w /L o ), ranging from 0.65 (for d w /L o = 3.83) to 0.89 (for d w / L o = 0.55), which could have been compensated by changing the slope of the flume. Unfortunately, changing the slope is not possible at the flume used. Nevertheless, recalling the underlying assumptions of the parameter framework, d w /L o controls the potential maximum size of the morphometric variables as it determines the geometrical scale of the HSV, while the secondary control parameter U m /U c controls the dynamics of the HSV within that geometrical scale and affects the actual size of the morphometric variables.
Series A experiments were designed to determine the threshold conditions of d w /L o at which morphometric variables are maximized and analyse implications for the size of the morphometric variable below or beyond this threshold condition. In the present investigation, morphometric variables of the scour hole (cf. Figure 2A) and its simplified volume Vol s = d s * w s * l s were analysed, normalized by Vol s 1/3 /L o .
Series B experiments were repeated on the cuboid obstacle (Sh ≥ 0.8) for the same ratios of d w /L o , keeping U m /U c constant (U m /U c = 0.72). From this, the observed thresholds of series A experiments are evaluated. In order to keep U m /U c constant at different flow depths (d w ), U m had to be varied (0.162-0.22 m s À1 ). This procedure also affected the secondary control parameter Re o , which was varied for different ratios of d w /L o , ranging from 5928 (at d w /L o = 0.55) to 8050 (at d w /L o = 3.83).
For the present investigation, the following primary and secondary control parameters were constant: L o /D 50 = 66.5, L o / B = 0.11, σ G < 1.3, d sed /L o > 1, t/t e ≥ 1 and Mb is neglected, thus Equation (7) reduces to: for series A and for series B. Table II lists conditions and results of all 44 experimental runs (series A and B). The obstacles were placed in the test section of the flume (~2.7 m downstream of the inlet) in the plane of symmetry to minimize sidewall effects (e.g. Nezu and Nakagawa, 1993). Obstacles were buried 0.005 m deep in the sediment layer and mounted on a plate attached to the flume bottom to prevent tilting. The elliptical sandstone pebble was aligned with its longest axis parallel to the flow direction. For most experiments, one-dimensional vertical velocity profiles of the undisturbed approaching boundary layer were measured 0.10 m upstream of the obstacle using a miniature velocity probe (Streamflow 403, Nixon Flowmeter ® , accuracy ±1.5%) to ensure the boundary layer was fully developed in the test section and followed a logarithmic distribution. Especially for low water depth (0.02-0.04 m), this procedure was not feasible, nevertheless discharge was recorded continuously by a magnetic/inductive discharge meter. During selected runs at fully submerged conditions (i.e. flow depth 0.12 m), a downlooking acoustic Doppler velocimeter (ADV) (Vectrino, Nortek AS ® , accuracy ±1%) was used to measure three-dimensional velocities and turbulences in the vicinity of the obstacles along two-dimensional profiles in the plane of symmetry. The sampling frequency was 25 Hz and the flow velocity and turbulence were sampled for 60-90 s at each measuring point. Intervals in the longitudinal direction were 0.01-0.05 m, and 0.005-0.01 m in the vertical direction. Data were collected near to the end of each experimental run (>22 h) and raw data were post-processed using WinADV (Version 2.031) (Wahl, 2000), applying a spike removing and a correlation filter (e.g. Goring and Nikora, 2002;Chanson et al., 2008). For the calculation of shear stress, the turbulent kinetic energy method (TKE) (e.g. Kim et al., 2000;Biron et al., 2004) was used, considering variances of the streamwise, cross-channel and vertical components of flow. In order to ensure obstacle marks are near equilibrium (cf. Figure 4), a runtime of 24 h was chosen (cf. Melville and Chiew, 1999). After 24 h the flume was drained and the characteristic morphometric variables of the obstacle mark were measured with point measurements of a laser distance meter (ODAM S14C, Baumer Electric ® , accuracy ±1.5 mm) mounted on a carriage on top of the flume.

Impact of submergence ratio (d w /L o ) on obstacle mark formation
The submergence ratio is classified based on disturbances of the water surface profile due to the presence of the obstacle (e.g. Shamloo et al., 2001). At fully submerged conditions (d w / L o > 2), no disturbance of the water surface profile could be observed, indicating a free flow of the approaching boundary layer above the obstacle top. At shallow submerged conditions (1 < d w /L o < 2) the obstacle top was only slightly below the water surface, causing the water level to drop above the obstacle top. In addition, a bow wave piles up at the obstacle front. During unsubmerged conditions (0 < d w /L o < 1), the obstacle top was above the water surface and also a bow wave at the obstacle front could be detected, while in mid to far wake, irregularities of the water surface indicate the presence of trailing vortices due to detached shear layers. The disturbances of the water surface profiles were similar at the different obstacle shapes and for both experimental series (cf. Figure 6).
For series A experiments the typical obstacle mark pattern controlled by the action of the HSV developed at the bluff cuboid obstruction (Sh ≥ 0.8) for all ratios of d w /L o , while this was not applicable for the spherical obstacle (Sh ≤ 0.4) and the streamlined pebble (Sh ≤ 0.4) (cf. next section). Concerning the typical obstacle mark morphology, the morphometric variables d s , w s and l s and the normalized scour hole volume (Vol s 1/3 /L o ) are maximized at d w /L o = 0.8 to 1.0 (experimental runs A8, A9 and A21). An increase or decrease in d w /L o from this threshold causes a limitation of Vol s 1/3 /L o ( Figure 7A). At the threshold condition d w is comparable to L o , thus a high vertical pressure gradient is present at the obstacle front, creating an intensive downflow and efficient HSV system at the obstacle base. At the threshold condition the secondary control parameter U m /U c was 0.83 and 0.81, respectively. Remarkably, although U m /U c was higher at unsubmerged conditions (i.e. U m /U c = 0.86 and 0.89 at d w / L o = 0.68 and 0.55), Vol s 1/3 /L o is reduced compared to the observed maximum at shallow submerged conditions (1 < d w / L o < 2), indicating that within the range of constant primary . U c is estimated from Equations (13) and (14). a Indicates scour holes in the wake. (a) for d w /L o < 0.7, boulder-like obstacles are exposed to a rather shallow flow (i.e. horizontal length scale of flow > vertical scale of flow). For this unsubmerged condition the formation of a bow wave at the obstacle front is observed (cf. Figure 6B). The bow wave interferes with the HSV due to opposite rotation direction (cf. Melville and Coleman, 2000), which limits the spatial extent of the HSV. For d w /L o = 0.55, obstacle mark formation could be observed in the present investigation. Unfortunately, d w /L o < 0.55 could not be physically modelled in the laboratory facility. Thus, the threshold of d w / L o where the HSV ceases to persist due to the interference of the bow wave could not be detected.
(b) for d w /L o > 1.1 rising flow depth at the boulder-like obstructions results in a weakening of the vertical pressure gradient in front of the obstacle and eases downflow at the obstacle front. As a consequence, a smaller HSV prevails, because much of the approaching current flows over the obstacle top. The weaker downflow and HSV system damp the incision of d s and the enlargement of w s and l s . Thus, Vol s 1/3 /L o at fully submerged conditions (d w /L o > 2) is 60% smaller than maximum Vol s 1/3 /L o at d w /L o = 0.8-1. The observed threshold condition for maximized Vol s 1/3 /L o at d w /L o~1 could be validated by series B experiments on the bluff cuboid obstacle (Sh ≥ 0.8). The actual value of Vol s 1/3 /L o is slightly smaller than for series A experiments, because U m / U c = 0.72 (U m /U c = 0.81 at d w /L o~1 for series A experiments). Moreover, the trend of decreasing Vol s 1/3 /L o compared to the observed maximum is obvious for an increase or decrease of d w /L o , which is equivalent to observations of series A experiments (cf. Figure 7B)   dependent on the primary control parameter d w /L o , while the secondary control parameters U m /U c and Re o impact the actual value of Vol s 1/3 /L o as envelopes to this trend (cf. Figure 7C). Due to restrictions of the laboratory facility, it was not possible to physically model conditions of d w /L o > 3.83. Thus, thresholds at which local scouring at the bluff angular obstruction (Sh ≥ 0.8) is completely inhibited could not be determined. Impact of obstacle shape (C d ) on obstacle mark formation For the spherical obstacle (Sh ≤ 0.6), Vol s 1/3 /L o is maximized for unsubmerged conditions at d w /L o ≈ 0.7 (run A21, cf. Figure 8 A), while Vol s 1/3 /L o is 20% less than for the bluff angular obstruction (cf. Figure 7A). Remarkably, an increase in d w /L o towards shallow submergence (1 < d w /L o < 2) emerged as a different morphology of the obstacle mark. Contrary to the typical obstacle mark morphology, the sedimentary structure is then composed of a minor frontal scour hole and two lateral depressions in the wake (runs A17-A19; cf. Figure 8B). For d w /L o > 1.6, an 'inverse' obstacle mark prevailed at the spherical obstacle (Sh ≤ 0.6) that is composed of two lateral depressions in the wake and adjacent sediment ridge, while a frontal scour hole is absent (cf. Figure 8C). The morphology of an inverse obstacle mark prevailed for the elliptical obstacle (Sh ≤ 0.4, runs A23-A33) irrespective of d w /L o , while the dimensions of the downstream depression (depth, width and length) decreased with rising d w /L o .
At fully submerged conditions (d w /L o = 3.28), the flow field at the spherical and elliptical obstructions revealed insignificant downflow due to a weak vertical pressure gradient at the obstacle front. Vice versa, the HSV at the base is relatively small in its size, actually smaller than the measuring grid of the ADV measurements (i.e. 0.01 m in the horizontal direction and 0.005 m in the vertical direction) (cf. Truelsen et al., 2005). In the near-wake region, recirculation of approaching flow was present, which is responsible for the observed wake scouring due to turbulence-induced high shear stresses (cf. Figure 9).

Conclusions and Perspectives
Boundary condition control of obstacle mark formation at natural instream obstructions (solitary boulders and vegetation elements) is assessed by a novel parameter framework that incorporates the large body of knowledge derived from hydraulic engineering on local scouring at technical infrastructure (e.g. bridge piers, abutments and pipelines). In total, 13 nondimensional and scale-invariant control parameters are identified that impact morphodynamic processes at natural instream obstructions. Control parameters are integrated into a systematization that classifies their significance for size of morphometric variables of an obstacle mark based on two hierarchical levels. Seven primary control parameters control the geometrical scale of the turbulent HSV at the obstacle and determine the potential maximum size of the structure, while six secondary control parameters impact the dynamics of the HSV within the geometrical scale and characterize sensitivities of obstacle mark formation. Both hierarchical levels are based on empirical thresholds that are partially derived from an interdisciplinary review on the phenomenon of local scouring at artificial instream obstructions. The purpose of the framework is to identify conditions at which the morphometric variables are maximized, conditions at which morphometric variables are limited compared to the maximum stage and conditions at which the formation of obstacle marks is completely inhibited.
To underpin the proposed classification with an empirical base and to determine threshold conditions of the primary control parameters submergence ratio (d w /L o ) and obstacle shape (Sh) at which morphometric variables are maximized, two series of small-scale flume experiments were conducted. The submergence ratio (d w /L o ) was modelled by varying the flow depth (d w ) at obstacles of nearly identical size (L o ) but different shape (angular, spherical, elliptical), while the secondary control parameters U m /U c and Re o were also slightly varied.
The normalized scour hole volume (Vol s 1/3 /L o ) in a nearequilibrium condition (after 24 h) is maximized at angular (Sh ≥ 0.8) and spherical obstacles (Sh ≤ 0.6), if d w is nearly equal to L o at d w /L o = 0.8-1.0, while Vol s 1/3 /L o on average is 20% larger for Sh ≥ 0.8, irrespective of d w /L o . For d w /L o = 0.8-1, a high-pressure gradient exists at the obstacle frontal face and a large HSV prevails at the obstacle base, while an increase or decrease in d w /L o from this threshold condition limits the spatial extent of the HSV and vice versa Vol s 1/3 /L o . At the spherical obstacle (Sh ≤ 0.6) no typical obstacle mark (frontal scour hole and downstream sediment accumulation) emerged for d w /L o > 1.6, while the streamlined shape of the elliptical obstacle (Sh ≤ 0.4) inhibited the formation of an HSV capable of inducing local scouring in front of the obstruction irrespective of d w /L o . Furthermore, the observed dependence of Vol s 1/3 /L o on d w /L o is also valid for a variation of the secondary control parameters U m /U c and Re o that impact the dynamics of the HSV, representing envelopes to this trend (cf. Figure 7C). The experimental results confirm the classification of the parameter framework.
The validity of the defined threshold ranges has to be tested empirically for more complex scenarios as an approximation to natural conditions at instream obstructions and their impact on obstacle mark formation. Particularly, flume studies aiming to mimic unsteady discharge events and associated variations in d w /L o and U m /U c over time (t) are needed. Here, physical modelling studies offer the advantage to gradually and systematically vary control parameters to identify cause and effect relationships and quantify sensitivities, assuming scale independency of processes. Besides the purely academic relevance, increasing knowledge on boundary condition control of fluvial obstacle mark formation and dynamics will refine existing approaches for hydraulic interpretation of preserved obstacle marks that can be used to estimate past flood events (Herget et al., 2013).

Data availability statements
Research data are not shared.