Effects of erosion-induced changes to topography on runoff dynamics

Journal of Hydrology 573 (2019) 811–828

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Research papers

Effects of erosion-induced changes to topography on runoff dynamics ⁎

T

Shahin Khosh Bin Ghomash, Daniel Caviedes-Voullieme , Christoph Hinz Chair of Hydrology, Brandenburg University of Technology Cottbus-Senftenberg, Germany

A R T I C LE I N FO

A B S T R A C T

This manuscript was handled by Marco Borga, Editor-in-Chief, with the assistance of Christian Massari, Associate Editor

Runoff generation from rainfall events is a complex, spatial and temporally dependent process strongly governed, among other factors, by catchment surface topography. Although it is widely known that many catchments experience morphological evolution, it is often ignored in analysis for different reasons ranging from simplification to lack of data. However, young catchments and early landscapes (such as those which are affected by natural or anthropogenic disturbances) do exhibit topography changes which in turn affect catchment hydrodynamics, hydrology and in particular runoff. In this work, we study the runoff generation and hydrodynamics of the Hühnerwasser artificial catchment (Brandenburg, Germany) during a period of erosion-based topographical changes (2006–2010). Nine Digital Elevation Models from such period were used as topography over which physically-based simulations were performed. The results suggest that topographic evolution in this catchment mostly affects the onset of runoff, whereas peak discharges and receding hydrograph limbs are less affected. These differences in hydrological signatures can be explained through the changes in the spatial distribution of runoff hydrodynamics and their impact on surface runoff connectivity. Relatively small topographical differences produce changing ponding conditions and modify flowpaths which becomes evident only through inspection of the spatial distribution of hydrodynamic variables. Moreover, the study shows that in order for simulations to be able to capture such responses, appropriate computational mesh and topographical data resolution are critical, since connectivity itself can be greatly affected by low resolution data or representation.

Keywords: Rainfall/runoff simulation Runoff generation Topographic evolution Catchment morphodynamics Surface runoff connectivity

1. Introduction Landscape evolution is the result of many different geomorphological and hydrological processes (e.g., surface runoff, sediment transport) (Hüttl et al., 2014; Troch et al., 2015; Tucker and Hancock, 2010). These topographic changes have a significant impact on the hydrological response of a catchment (Appels et al., 2016). They can affect the flow paths, rainfall-runoff-infiltration partitioning, and so on (Moussa, 2008; Schaaf et al., 2013a,b). Therefore, understanding the possible impacts of topographic changes is of interest to understand how catchments evolve, how they have matured and how different ecohydrological processes interact. However, because of the unique evolution of each catchment, and because evolution of mature catchments occurs at very slow rates, generalization of some of the observed impacts of changing topographies is very difficult (Merz et al., 2004; Mazur et al., 2011). Moreover, given that the complexity of processes contributing to morphological changes within the catchment and the corresponding alteration of runoff signatures, single catchment experiments and even comprehensive monitoring programmes of whole catchments will neither allow to decipher all processes interaction nor ⁎

will it allow to apply a statistically derived experimental, design commonly used in agriculture and ecological field studies. Hydrological processes play a significant role in the evolution of landscapes in many ways, one of which is through sediment transport processes. Surface runoff is largely responsible for the redistribution of sediment across spatial scales, from the plot scale, to the hillslope scale and to the catchment scale (Cuomo et al., 2016). At the hillslope scale the net effect of erosion is an evolving topography, and the amount of transported sediment is related to the magnitude of topographic change (Heckmann and Vericat, 2018). There is a clear feedback between the hydrodynamic/hydrological processes and the geomorphological change, i.e., hydrodynamics drive erosion, erosion leads to a change in topography which in turn constrains and reshapes hydrodynamics. Landscape evolution models (LEM) (e.g., Chen, 2014; Tucker and Hancock, 2010) attempt to model such interactions, originally at geological spatiotemporal scales, but also being applied into smaller scales (Coulthard et al., 2013), also addressed, usually in small catchments by hydraulic-based models (Cuomo et al., 2015; Juez et al., 2018). It is also relevant to highlight that the magnitudes of morphological change are also different depending on scales and governing process, e.g., erosion

Corresponding author. E-mail address: [email protected] (D. Caviedes-Voullieme).

https://doi.org/10.1016/j.jhydrol.2019.04.018 Received 9 November 2018; Received in revised form 7 March 2019; Accepted 4 April 2019 Available online 04 April 2019 0022-1694/ © 2019 Elsevier B.V. All rights reserved.

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observed and frequently the only source of hard data (Bracken and Croke, 2007). Although many connectivity metrics and indices exist (Antoine et al., 2009; Borselli et al., 2008; Bracken et al., 2013; Lane et al., 2009; Mayor et al., 2008), many of them only consider structural, static connectivity, disregarding the dynamic connectivity which occurs as a response to the transient hydrodynamics of runoff (Borselli et al., 2008, Cammerat, 2002, López-Vicente and Ben-Salem, 2019). Physically-based models allow another approach to link spatial distributions and hydrological signatures, since they represent and resolve processes at resolutions which are compatible to the scales and distributions at which the processes occur. Commonly, rainfall/runoff processes are modeled by means of empirical and lumped approaches, mainly due to their inherent simplicity and low computational cost (Hollander et al., 2009; Caviedes-Voullieme et al, 2012). It has been shown that the spatial distribution of different hydrological properties such as microtopography, and processes, e.g., infiltration can have significant effects on surface runoff generation, rainfall-runoff-infiltration partitioning (Thompson et al., 2010), on the resulting hydrographs (Appels et al., 2011) and vegetation growth (McGrath et al., 2012). However, such lumped models fail to account for the spatial distribution of hydrological properties and processes. Furthermore, they often mask and mix effects of different properties and processes, since they allow for large parameter freedom, enabling to achieve correct hydrological signatures (typically hydrographs) without any certainty of the internal distribution of water, as it is mostly controlled by tunable parameters. Physically-based models usually have stronger constrains on parameter freedom, thus, when calibration is achieved, results are more accurate and meaningful (Fernández-Pato and García-Navarro, 2016). An added advantage is that the spatially distributed hydrodynamic fields that these models produce, can lead to the study of hydrological connectivity as an emergent property of the system (Keesstra et al., 2018; Lesschen et al., 2009). The comparatively large computational cost of physically-based models has limited their use in the past to a small variety of applications such as runoff simulation in small scale catchments and urban catchment areas (Caviedes-Voullieme et al, 2012; DaeHong and Yongwon, 2013; Simons et al., 2014). However, increased computational power, new hardware paradigms and more efficient numerical methods enable the application of physically-based, distributed models to a wider range of applications. Recently, rainfall/ runoff simulation of large catchments and high resolution flood simulation in urban and rural areas is becoming common (Chen et al., 2017; Costabile et al., 2017; Paniconi and Putti, 2015). The Hühnerwasser catchment (located in northeast German) offers an interesting opportunity to observe topographical changes and morphological evolution in the time span of a decade, as the catchment quickly evolved from a highly perturbed landscape into a maturing catchment (Hüttl et al., 2014; Maurer and Gerke, 2016). The sustained monitoring effort produced a sequence of catchment digital elevation models (DEM) throughout multiple years which documents the catchment’s topographic evolution, offers an opportunity to simulate the hydrological response under such evolution, removing the interference of additional factors and thus study a simplified system in which only topography is changing and address the need to robustly identify to what extent the hydrological processes in the catchment are affected by these changes. From a modelling perspective, it is also crucial to be aware of the degree to which the data resolution is able to properly represent the hydrologically-relevant geomorphic features of the catchment which therefore allow to capture the small scale hydrological processes that are involved. The significance of small scale processes on runoff generation and other hydrological responses (such as surface storage and surface flow connectivity) has been shown in previous studies (Appels et al., 2011; Hallema et al, 2016; Thompson et al., 2010), clearly signaling that proper spatial representation is key. Currently, high resolution topography at the catchment scale is feasible, although still not ubiquitous and running physically-based simulations on such high-

on hillslopes produces comparably low magnitude changes in contrast to the relief-forming processes of geological catchment evolution (Cuomo et al., 2015). The available literature includes a number studies of LEM applications in the coupled hydromorphological process (e.g., Perron and Fagherazzi, 2012; Salles and Duclaux, 2014) and the impact of hydrological factors and processes on the morphological evolution (e.g., Hancock et al., 2006; Hoober and Cohen, 2017). In contrast, research seems to be scarce on how the evolving topography affects the hydrodynamics and therefore the hydrology of hillslopes. There are arguably several reasons for this gap. One is that Hydrology is often concerned with systems which change at very slow rates, which makes the topographic changes driven by hillslope erosion negligible when studying hydrological responses to rainfall events, for example. Furthermore, if there is topographic change, it is often not measured, since full-scale DEM acquisition has been historically nonfeasible to perform frequently. Current technology does allow for temporal DEM datasets, enabling studying the transient topographies and DEMs of Differences (DoD) (e.g., Heckmann and Vericat, 2018). Moreover, monitoring of evolving systems also has allowed to record topographic evolution from sediment processes at the hillslope scale (Hofer et al., 2012; Schneider et al. 2013). The availability of these datasets allows to pursue modelling studies which may provide insights into how erosion-caused topography evolution on hillslopes can affect hydrological processes, which in turn affect both the overall ecohydrological and morphological evolution of the hillslope and even perhaps cascade along the landscape (Sweeney et al., 2015). Although observations and monitoring are key for a better understanding of these issues, modelling is also an essential tool. Observations are, by their own nature, constrained by the events which occur, when they occur. Therefore, replications and their analysis are nearly impossible to conduct. In the case of evolving topography, it is of course possible to register the dynamic surface, and to monitor rainfall and runoff, but the same rainfall will not occur over different topographies, making direct comparisons impossible. Modelling is the only tool which systematically allows to study sensitivity of the system to variations in processes, and to make systematic observations of the response of the system to controlled forcing. We focus in this work on the effects that topographic change due to erosion processes has on surface runoff generation. The hydrological significance of the rainfall/runoff process and the need for its modelling and simulation has been widely pointed out (Beven, 2001; Birkel, et al., 2012; Paniconi and Putti, 2015; Rodriguez-Iturbe, 2000). The dependence of runoff response on catchment structure remains only partially understood since many factors interact (topography, vegetation, geology) with varying degrees of relative influence across a range of spatiotemporal scales (Jencso and McGlynn, 2011). The possibility to model such processes and responses enhances our understanding and prediction capabilities of different hydrological responses and to assess the effects of climate and land use change on the hydrological behavior of systems (Hölzel et al., 2011). Although historically hydrologists have focused on the hydrograph as the main source of information from a catchment (Sivapalan, 2018), the spatial distribution and flow paths of runoff in a catchment, heavily influenced even by small topographical features, may become a primary player when attempting to understand not only hydromorphological interactions (Czuba and FoufoulaGeorgiou, 2015), but also biogeochemical hotspots (Frei et al., 2012; Groffman, 2012; McClain et al., 2003) and long term vegetation development (e.g. McGrath et al., 2012). Many authors have proposed different approaches to link signatures such as the hydrograph to structural and morphological properties of the catchment, either by observations or conceptual models (e.g., Karalis et al, 2014; Kirchner, 2009; Moussa, 2008; Post and Jakeman, 1996). Furthermore, the understanding of how small scale runoff generation and its patterns reflect in the catchment runoff response is still lacking (Ries et al., 2017). Hydrological connectivity can further help relating the spatial hydrodynamic features to the hydrological signatures which are easily 812

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Fig. 1. Conceptual diagram of topographic, hydrological and vegetation change in the Hühnerwasser catchment.

have been run on nine different DEMs with 1 m resolutions of the Hühnerwasser catchment throughout the years 2006 to 2010. The high resolution data used in this study enables a reasonable representation of the topographic features of the catchment and allows for accurate hydrodynamics to be achieved (Mazur et al., 2011).

resolution, large scale surfaces remains challenging. In physically-distributed simulations, a high computational cost exists due to the nonlinearity of the governing equations and the large number of cells that is usually required to represent the topography and achieve sufficient accuracy of the discrete solution (Wood et al., 2011; Fernández-Pato et al., 2018). One way to reduce the computational costs is mesh coarsening, which reduces resolution, accuracy and computational cost (Yu and Lane, 2006; Ozgen et al., 2015). The degree of the accuracy loss is highly dependent on to what extend the chosen mesh is able to capture the microtopography and the small scale hydrological processes of the terrain. This is non trivial, as complex interactions exist between mesh resolution and surface features, physical properties of the flow (namely friction) and even infiltration properties (Yu and Lane, 2006; Caviedes-Voullieme et al, 2012; Fernández-Pato et al., 2016) making model results strongly depending on mesh selection. It is therefore relevant to assess what the possible effects of the (often) relatively low resolution available DEM data, or resolution reduction (Sampson et al., 2012) for computational reasons on the hydrological signatures and, most importantly, on spatial distributions, flow paths and connectivity (López-Vicente and Álvarez, 2018). This is of course of particular importance when dealing with evolving topographies. This work is concerned with studying the individual effects that evolving topography has on the rainfall/runoff response of the Hühnerwasser catchment. We aim to observe characteristic catchment signatures and runoff flow fields. The goal is to characterize how morphological changes interact with different rain intensities and how this manifests in hydrological responses. An additional research question which strongly relates to topographical evolutions is: how much does the topography resolution and its representation in a hydrological model artificially generate signatures? That is, for topographical evolution to be analyzed, it is necessary to ensure that numerical artifacts (often generated by inappropriate computational meshes) are kept to a minimum. We therefore perform simulations which cover the topographical evolution throughout 2006 to 2010 in the Hühnerwasser catchment by means of a 2D zero-inertia solver. To facilitate the assessment of the effects of topographical evolution our simulations remove most sources of complexity such as complex rain signals, infiltration and other involved processes which can strongly influence runoff generation and the resulting hydrographs as well as introducing added uncertainty and the models’ reducing explanatory power (Jencso and McGlynn, 2011). Indeed the issue of selecting which processes and model components to keep and which to simplify or discard is at the core of Hydrology (Kirchner, 2006, 2009). Therefore, in this work, we focus on conditions where infiltration has been completely removed and surface friction has been kept minimal and homogeneous in order to be able to clearly observe the different impacts of morphological evolution as well as the numerical effects of different mesh properties on the rainfall/runoff simulation results, although we also contrast with simulations considering infiltration. We highlight that although an erosion-driven topography change underlies the study, erosion and sediment transport processes are not modelled, and their effects are only present by the differences in the measured DEMs. The simulations

2. Materials and methods 2.1. The catchment The Hühnerwasser ('Chicken Creek') catchment is located in southeast of Brandenburg, near the city of Cottbus, in the plain areas of northeast Germany. It lies within a post-mining landscape, in the rehabilitation area of an open-cast lignite mine. The catchment construction was completed in September 2005 to serve as a new artificial headwater that replaced the previous stream “Chicken Creek” that was destroyed as a result mining activities in the 1980s. Contrary to the surrounding landscape, the catchment was not ecohydrologically rehabilitated, but has been left unmanaged in order to monitor and document its morphological and ecohydrological evolution. The development of the catchment has been reported to be fast in its first year, with the formation of morphological components such as rill networks (Schneider et al, 2013) and the initial development of vegetation, but subsequently the catchment has seen a more gradual development (Gerwin, et al., 2011; Hofer et al., 2012), in which the initially dominating physical processes slowly lose dominance in favor of chemical and biological processes (Raab et al., 2012). For details on the morphological changes of the catchment, and assessments of the sediment balances, we refer to Schneider et al. (2011, 2012, 2013). To illustrate the initial evolution of the topography the catchment and its possible effects on surface water dynamics, Fig. 1 presents a conceptual line including key morphological and ecohydrological processes, based on the account by several authors (Gerwin et al., 2009; Hüttl et al., 2014; Schaaf et al., 2013a,b; Schneider et al., 2013). The catchment has an area of around 6 ha and has been constructed as a small hillslope with an elevation difference of about 15 m along the main axis and with the average longitudinal slope of 3% with the absolute heights of the catchment area ranging from 125 m.a.s.l. up to 140 m a.s.l (Gerwin, et al., 2009). The precipitation intensity of the area is reported to be from 1.2 mm/h up to 25 mm/h between the years 2007 and 2009 with the maximum rain rate generating a runoff of around 126 m3/h at the gauge located in the lower part of the catchment (Mazur et al., 2011). It has also been reported that in the initial years of the catchment’s development, a minimum rain intensity of 9 mm/h was required for runoff to be registered in the catchment (Hofer et al., 2011). The runoff response of the catchment to rain events has also been reported as fast with small delays (Mazur et al., 2011). At the lower part of the catchment, a pond was constructed by the introduction of a depression in the clay layer construction. The morphological evolution of the catchment was monitored by performing a set of aerial digital photogrammetry surveys between 2006 and 2010. Nine DEMs with 1 m resolution (Schneider et al., 2012) have been selected for this 813

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heterogeneity of sediment properties at the catchment scale in hydrological modeling and therefore highlighting the importance of the spatial distribution of the processes involved. Hollander et al. (2009), using several models, both lumped (for surface and subsurface flow) and distributed (based on methods such as the Green-Ampt and Richards equations for generating infiltration in the saturated and unsaturated zones respectively), studied the influence of the modeler’s choice in defining the boundaries and parametrization on model results and found that the modelers’ experience and preferences have significant impacts on the results of the model. Hofer et al. (2011), using a physically based approach (for 2D subsurface flow), investigated the influence of the connectivity of drainage pathways in the catchment on the runoff generation process and found that the connectivity is highly sensitive on the antecedent soil water content and is also dependent on factors such as topography and soil hydraulic properties. Hofer et al. (2012), with the use of two different physically based models (for surface flow) based on Manning’s equation and self-organized critical networks, studied the development of rill networks in the catchment and was able to reproduce the rills with small differences in the geometric characteristics such as length and depth in contrast to the observed data of the catchment. All the aforementioned studies have emphasized on the importance of the spatial distribution of the processes involved and the resolution of the data being used in the modeling procedure of the hydrological processes. Fig. 2 shows, exemplary, the change in topography between November 2007 and August 2008 and between August 2008 and June 2009. The figure illustrates the magnitude of the topographic changes in the catchment. It shows that there is mostly a reduction of elevation as the catchment evolves, which is the result of erosion processes. During these years the catchment was undergoing the initial phases of vegetation development, therefore it was still rather prone to erosive processes.

Table 1 DEM and computational mesh properties. Alias

Production Date

Number of Cells

Avg. rill length [m]

Avg. rill width [m]

Mean drainage density [km/ km2]

11/06 11/07 04/08 08/08 12/08 05/09 06/09 12/09 03/10

November 2006 November 2007 April 2008 August 2008 December 2008 May 2009 June 2009 December 2009 March 2010

44,957 51,983 51,983 51,983 48,882 51,955 51,983 49,810 49,810

17.83 15.85 19.05 – – 18.85 – – –

0.93 0.65 0.61 – – 0.71 – – –

38.68 72.88 47.39 – – 34.14 – – –

study and summarized in Table 1. In this study, the DEMs were cut to remove the pond area. This is due to a set of reasons. Firstly, the photogrammetry surveys did not provide real bathymetric data for the pond. The existing data for the pond is extrapolated from additional observations and does not necessarily account for sediment depositions in the pond bed at the time the surveys where performed. Secondly, the pond acts a severe runoff buffer. If simulated runoff is monitored downstream of the pond, hydrographs are severely dampened and delayed, and hydrograph properties are very strongly dominated by the buffering capacity of the pond, thus destroying the hydrograph response to changes in morphology. Therefore, it is convenient to monitor simulated runoff upstream of the pond, and the pond becomes unnecessary. Finally, horizontal water surfaces (such as the pond) present a challenge to the stability of the selected numerical model (CaviedesVoullieme et al., 2018). By removing the pond, stability constrains are alleviated, time-steps are larger and computational time is kept low. Table 1 summarizes the selected DEMs, the number of cells which they contain after removal of the downstream pond region in all cases, and geomorphic indicators (average rill length, average rill width, and mean drainage density) as reported by Schneider et al. (2013) which show the relatively small morphological variations that the hillslope experienced. The Hühnerwasser catchment has been subject of hydrological modeling studies. Hölzel et al. (2013), used a spatially-distributed hydrological water balance model and found that artificial sediment structures (pour-ribs dumped by stackers during the construction phase) in the catchment have a reduction effect on the runoff generated as a result of different rain events, since they act as hydraulic barriers and increase the water-ponding capacity of the catchment. Hölzel et al. (2013) further emphasized the importance of considering the

2.2. The model The core hydrodynamic process in the mathematical and numerical model is free surface flow. We solve the 2D zero-inertia approximation (eq (1)) to the shallow water equations (Caviedes-Voullieme et al., 2018).

∂h h5/3 + ∇ ⎛⎜ Z ⎞⎟ = R − I ∂t n ⎝ ∥Z∥ ⎠

(1)

where h is water depth [m], t is time [s], n is Manning’s roughness coefficient [ms−1/3], Z is the water surface gradient [−], R is the

Fig. 2. Elevation difference in meters between Nov. 2007 – Aug. 2008 and Aug 2008 – June 2009 DEMs. 814

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Complementary, two different rain signals from an event reported in 2007 in the area have also been used to provide a comparison between the catchments response to complex precipitations and simple continuous rain. The storm with largest accumulated rainfall (71.1 mm) recorded in the Cottbus weather station. This rainfall event was recorded at an hourly resolution, and the storm duration was 310 min. A microcanonical random cascade model (Pohle et al., 2018) was used to generate plausible sub-hourly (10 min) resolution rainfall distributions. Sixty distributions were stochastically generated, of which two were chosen for simulations (shown in Fig. 17 together with runoff results). The two rain events, herein called R1 and R2 have the same rainfall volume, however, their temporal distributions and intensities differ strongly. The R1 event has very low precipitation early on followed by an intense 10 min peak at 151.7 mm/hr. The R2 event has a gradually growing intensity, peaking late in the storm at 70.3 mm/hr. The average intensity is 13.76 mm/hr for both cases, putting it just above the LIR rainfall which has a similar duration (300 min). The R1 and R2 events were used with three dx = 1 m DEMs (April 2008, June 2009 and March 2010) in order to explore the catchment response throughout different years to real rain signals, resulting in 3 DEMs and 2 rainfall setups. The simulations were run with an idealized setup that included no infiltration and very low, homogeneous values of friction in order for the results to demonstrate only the effects of morphological change and different mesh properties on the generated runoff. This also allowed to achieve maximum steady discharges and to have very small delays between precipitation and the catchments response that noticeably reduced the required computational costs of the simulations. A homogeneous surface roughness represented by Manning’s coefficient set to 0.009 s/m1/3, which is practically equivalent to the smoothness of a glass surface and is in contrast, considerably smoother than the actual catchment surface. Ideally friction would be set to zero, but due to the nature of the ZI equation this would introduce an indefinition (Caviedes-Voullieme et al., 2018). It is therefore kept non-zero, but artificially extremely low. Stability was enforced by setting a CourantFriedrichs-Lewy value of 0.9 was chosen for the simulations. Simulation and rainfall durations were chosen so that the discharge in the hydrographs reached a clear steady state and the simulations ran for enough time for the water to leave the catchment. Runoff in the model has been measured at a defined outlet, which was set to act as an outfall boundary, at the same location for all the DEMs at the lower western part of the catchment on the main rill. All other boundaries of the catchment were set as closed reflective boundaries.

rainfall intensity [m/s] and I is the infiltration rate [m/s]. We solve the equation using a first-order Finite Volumes scheme for spatial discretisation and a first-order explicit Euler scheme for temporal integration (Caviedes-Voullieme et al., 2018), where i refers to a computational cell, and ω to the edges of such cell, Ai is the cell area [m2], Lw is the length of a cell edge [m], and superindex n denotes the time level.

hin + 1 = hin + Δt (R|in − I|in ) −

Δt Ai

Nω

∑ ω=1

(hωn )5/3 nω ∥Zωn ∥

Zωn. nω Lω

(2)

The numerical scheme is conditionally stable, and the time step is estimated following

L Δt < CFLmin ⎛ ω ⎞ ⎝ vω ⎠ ⎜

⎟

(3)

in which CFL is the Courant-Friedrich-Lewy number (CFL ≤ 1), Lω is the length of a cell edge [m] and vω is the water velocity at the cell edge [m/s]. Infiltration capacity fp [m/s] is estimated by the Green–Ampt model as:

fp (t ) = Ks +

Ks ψΔθ F (t )

(4)

In which Ks (m/s) is the saturated hydraulic conductivity, ψ (m) represents the average suction head at the wetting front and Δθ = θs-θi (m3/m3) is the difference between soil porosity θs (m3/m3) and the initial volumetric water content θi (m3/m3). The infiltration rate is related to the accumulated infiltration F (m), which is estimated from Eq. (5)

F (t ) ⎤ Ks t = F (t ) − ψΔθln ⎡1 + ⎢ ψΔθ ⎥ ⎣ ⎦

(5)

The actual infiltration rate is determined, as usual, by comparing rainfall and infiltration capacity. 2.3. Study setup 2.3.1. Simulation setup The simulations were run on nine different elevation models between the years 2006 and 2010. Selected DEMs are illustrated in Fig. 3. From the November 2006 DEM until the November 2007 DEM the catchment has been reported to experience an expansion of rill networks while subsequently the patterns have remained comparably stable (Schneider et al., 2013). It has also been reported that the rills were widest in 2006 and have become narrower until the year 2008, whereas from 2008 up to 2009 they have seen a minor increase in their mean width (Schneider et al., 2013). Also, a noticeably strong variation in drainage patterns for the November 2006 and November 2007 DEMs is reported. The variations indicate straightening of rills and rills becoming more equally spaced. Throughout the November 2007 to March 2010 DEMs, the drainage network has been reported to appear comparably stable (Schneider et al., 2013). In order to reduce the complexity of the simulations and to allow for reasonably straightforward and clear analysis and conclusions, the use of real rainfall signals has only been partially considered. In turn, two uniform rain intensities have been used for most of the simulations. A low precipitation intensity of 10 mm/h (exceeding the 9 mm/h threshold which has been reported for runoff generation in Hühnerwasser) and a very high 100 mm/h intensity were chosen in order to be able to clearly assess the influence of different rain intensities on the runoff generation processes in the catchment. Uniform (and long enough) rain signals allow for a clear steady state discharge to be achieved while complex rain events, due to their varying intensity, may fail to clearly describe such a steady discharge. Altogether, this accounts for 9 DEM and 2 uniform rainfall setups.

2.3.2. Selected meshes Meshes can consist of structured or unstructured grids with different cell shapes such as squares or triangles. Finer resolution meshes have a higher number of cells and a smaller cell size that result in higher required computational costs and data storage. Coarser mesh resolutions, on the other hand, have a lower number of cells with larger cell sizes. However, topography attributes in them only represent averaged properties of the surface that can result in a reduction in model accuracy. To observe the difference between the behavior of coarser and finer meshes, square structured meshes with the cell sizes of 0.5 m, 1 m, 2 m, 4 m, and 8 m were generated. The base data used for mesh generation were the nine 1 m resolution DEMs throughout the years 2006 to 2010 of the catchment resulting in a total of 45 computational meshes. The square structured meshes were generated in a way that the length of the edge of each cell was a result of a multiplication of the pixel edge length of the origin raster. Once generated, the elevation of each cell in the mesh was the result of the average elevation of the raster data cells. The five different meshes generated from the December 2008 DEM are shown in Fig. 4. In order to clearly illustrate the difference in how the different mesh resolutions represent the slope and elevation in the catchment, a close view of a surface located in the southern part of the December 2008 DEM with meshes with the cell 815

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Fig. 3. Selected DEMs between 2006 and 2010.

sizes of 1 m and 4 m is shown in Fig. 5. The figure shows the vertical dimensions scaled 10 times to allow its understanding. It can be observed that as a result of coarsening, the surface suffers a data loss and the small scale features of the morphology are smoothed out and no longer distinguishable in contrast to a finer mesh.

of the hydrograph. We further define a normalized steady discharge Qstn [−]. This indicator is the difference of steady discharge between some mesh Qstx and the corresponding 1 m resolution mesh Qst1, normalized by the steady discharge of the corresponding DEM with a resolution of 1 m Qst1, as shown in Eq. (6). Analogously, we also define α [-] for each DEM as the normalized T50 difference, as shown in Eq. (7), in which T50x is the time when the discharge reaches 50% of the steady discharge for a mesh with the resolution of x and T501 [s] is the same indicator for the dx = 1 m mesh resolution. The model was configured to produce spatial results of hydrodynamic fields every 60 s. The transient water depth fields are then thresholded by a binary filter, so that cells with depths lower than 2 mm are flagged as dry, and those with higher depth are flagged as wet. This produces a binary map with wet and dry clusters, as described by Renard and Allard (2013). These clusters are simply a group of cells with the same state (wet/dry) which share a common edge (see Renard and Allard (2013)). We then identify

2.4. Postprocessing The model results in this work have been post-processed into multiple signatures and indicators by ad-hoc R scripts. A brief description of the indicators and the procedure to obtain them is presented here. Steady discharge Qst [m3/s] values have been estimated by computing the mean discharge using the last ten entries prior to the end of rainfall, point at which the falling limb of the hydrograph starts. We also define T50 [s] an indicator of time to 50% steady discharge, estimated simply by linear interpolation of the appropriate data points in the rising limb

Fig. 4. Meshes with the cell sizes of 0.5 m, 1 m, 2 m, 4 m and 8 m of the December 2008 DEM from left to right respectively. 816

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Fig. 5. Comparison between 1 m (left) and 4 m (right) resolution in the December 2008 DEM.

affected by the change in morphology in the different years of the catchment. Steady discharge is always achieved (sooner or later), and it is very similar for all DEMs, as expected, given the lack of infiltration and the steady rainfall. Nonetheless, it must be highlighted that the steady discharge is not identical. This is due to slightly different catchment areas in each DEM (Fig. 13). The falling limbs see to be affected only very mildly by topographical evolution. It is possible that larger differences in runoff generation could be observed during the formation of the rill network, however, since DEMs are not available in this case it has not been possible to assess this. The different mesh resolutions result in much larger differences in the onset of runoff, while the steady state and the receding limbs are only mildly affected. Mesh coarsening typically results in a significant delay in the onset of runoff and a delay in achieving the steady state.

the number of wet clusters, and use this as a connectivity metric (Renard and Allard, 2013; Antoine et al., 2009). An ad-hoc R script was created for this purpose, based on ‘raster’, ‘biclust’ and ‘SDMTools’ packages. This number of (disconnected, wet) clusters is a quantitative indicator of connectivity, in particular of dynamic connectivity, and therefore dependent on the hydrodynamics, and not only the DEM. A higher number of wet clusters, for a constant flooded area, implies lower surface water connectivity, and viceversa. That is, for example, when 80% of the catchment is flooded, having 20 disconnected wet clusters implies a higher connectivity than having 200 disconnected wet clusters. The limit is obviously having only a single cluster, with a 100% flooded area, implying that the entire catchment is connected. We highlight the need to always consider the flooded area together with the number of clusters to draw this interpretation. When comparing across different meshes (with different number of cells) the number of clusters is normalized by the number of cells to allow for comparison.

Qstn

Q − Qst1 = stx Qst1

(6)

∝=

T50x − T501 T501

(7)

3.2. Surface flow hydrodynamics and connectivity The lag observed in the onset of runoff among the different meshes can be linked to the connectivity degree among the water mass throughout each simulation. This issue can be observed in the spatial distribution of the depth field. Fig. 8 illustrates the spatial distribution of the flow field in the catchment at time 1000 s, which is approximately the time when the discharge reaches 50% of the steady discharge, for the December 2008 and May 2009 simulations, both with a finer mesh (dx = 1) and a coarser mesh (dx = 8). It can be seen that the flooded areas more disconnected in the coarser mesh compared to the finer mesh. Due to this, the water is capable of reaching the outlet at a considerably shorter time in the finer mesh compared to the coarser mesh setup. This issue mainly arises due to the poor representation of topography in the coarser mesh. Due to this, there is an underestimation of the local maxima and an overestimation of local minima of the terrain in the coarser meshes which result in larger area ponds compared to the finer mesh. Consequently more water is stored in the coarser meshes during the simulations in contrast to the finer mesh. This can also be observed in the differences among the runoff volumes resulting from different meshes (most clearly seen in Figs. 6(e) and 7(e)). It is evident that the coarser meshes store a higher volume of water after the rain event compared to finer meshes and hence a lower volume of water outflows, resulting in smaller volume values for the coarser mesh (dx = 4 m,dx = 8 m) in comparison to the finer mesh (dx = 0.5 m , dx = 1 m). The only exceptions are the November 2006 simulations in which all mesh resolutions approximately show the same

3. Results and discussion 3.1. Hydrological signatures: hydrographs, volume In this section, the hydrographs and runoff volumes of the simulations are presented. The results for the lower intensity rain (LIR) cases are shown in Fig. 6 and for the higher intensity scenario (HIR) are presented in Fig. 7. The figures show that all hydrographs (for all meshes and DEMs) achieve a steady state in a relatively short time. This can be explained by the absence of infiltration, which allows for the onset of runoff to follow very quickly the beginning of the rain, and the very low value of friction used which enables a fast routing of water in the catchment. Each of the hydrographs can be divided into three sections, the rising limb that characterizes the onset of runoff, the steady state discharge and the falling limb. From the point of view of topographical evolution, the hydrographs exhibit differences among the steady discharges and the rising limbs throughout the different topographies of the catchment with the original resolution (1 m). It is mostly the onset of runoff which is clearly 817

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Fig. 6. Hydrographs and volumes for the LIR scenario for dx = 0.5, dx = 1, dx = 2, dx = 4 & dx = 8 [m] meshes. Solid lines represent discharge, dashed lines represent cumulative runoff volume.

Moreover, it can be seen that for both DEMs the reduction in resolution produces a complete disconnection (at this time) of the central rill from the outlet. Secondary rills are also all disconnected from the outlet. Some of the intermediate-sized clusters completely disappear in the coarse meshes, and the ones connected to the output do so no longer. Interestingly, the largest cluster is, in all cases, the one corresponding to the central rill. For 2008 the cluster nearly doubles its size, while dramatically decreasing in length and increasing in width. Additionally, comparing across DEMs (Dec. 2008 vs May 2009), under high resolution, also shows a change in terms of size, location and number of wet clusters, even a redirectioning of the west clusters. Fig. 10 shows an equivalent figure, but during the steady state (t = 300 m). It shows that, even at steady state, the connectivity of the catchment is considerably different when reducing resolution, even at steady state. Most of the minor rills are lost. At low resolution, the catchment behaves like a Vshaped surface. For the 2008 case, the largest cluster doubles its area, even though that large cluster encompasses several rills under high resolution. In low resolution only the central rill is part of the largest

behavior. This may be due to the base data of that DEM having a lower resolution than 1 m, therefore causing coarsening to have small effects on the topographic features of the catchment. It might also be due to the fact that the topographic features of the catchment were not as prominent in the initial years in comparison to the later DEMs. There is uncertainty associated to the data acquisition and post-processing strategy which allows for different causes of this (Schneider et al., 2012). The transient water depth maps shown in Fig. 8 can be thresholded into binary wet/dry maps, as the ones shown in Fig. 9 (showing the same cases and the same time as Fig. 8) during the onset of runoff. The gray areas in Fig. 9 represent dry regions, while the colored areas represent wet clusters. The color scales indicates the size of the wet cluster in terms of the fraction of area of catchment it occupies. The figure shows how a change in resolution changes drastically not only the number of wet clusters, but the shape, size and even location of them. As is to be expected, all the small local depressions are lost when coarsening, thus eliminating all the low area fraction clusters. 818

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Fig. 7. Hydrographs and volumes for the HIR scenario for dx = 0.5, dx = 1, dx = 2, dx = 4 & dx = 8 [m] meshes. Solid lines represent discharge, dashed lines represent cumulative runoff volume.

The figure shows that the normalized number of clusters increases from zero (representing a dry catchment) during the rising limb of the hydrograph and eventually becomes steady during the state stage of the hydrograph. High resolution meshes result in a lower number of clusters per cell than coarse resolution meshes, i.e., finer meshes have a higher degree of connectivity (more cells are part of a smaller number of connected clusters) than the coarse mesh. The flooded areas at time t = 280 min (with at least 2 mm water depth) account for 16.06% of the total catchment area with the dx = 1 m resolution and 19.5% with the dx = 8 m resolution in the December 2008 simulations. These values were 14.98% and 17.11% for the May 2009 simulations respectively. At t = 280 min the number of clusters has achieved a clear steady state in all four simulations in Fig. 11. Since the flooded area (deeper than 2 mm) is very similar for both resolutions, but the number of clusters is different, it ensures that the cluster number is a proxy for connectivity. In short, the higher connectivity between hillslope and the drainage network increases the flashiness of the runoff response, as has been highlighted by Hallema et al. (2016), also suggesting that connectivity

connected wet cluster, with severely overestimated width, and with underestimated flow length. For the 2009 case, the area of the largest cluster is tripled, the maximum flow length is similar, but with severely enlarged width, clearly showing how severely the spatial distribution of water and the hydrological connectivity is ill-represented by the coarse mesh. From 2008 to 2009 (at high resolution) the change in rill connectivity is quite clear. The changes in connectivity (both real, as those which are artifacts of low resolution) may not be very relevant for reproducing steady hydrographs, but may be essential to model responses to intermittent rainfall, sediment transport, ecological processes (vegetation establishment, seed transport) and morphological evolution of the catchment. Fig. 11 shows the evolution of the number of clusters normalized by the number of cells of each DEM, for simulations with the December 2008 and May 2009 DEMs, with both fine (1 m) and coarse (8 m) resolution. The reason for normalization responds to the fact that the meshes have huge differences in number of cells, making the comparison of cluster numbers (which may include individual cells) difficult.

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Fig. 8. Spatial distribution of the flow field at T = 1000 s with dx = 1 (left) and dx = 8 (right) in the December 2008 (bottom) and May 2009 (top) DEMs.

2010 simulation with the use of the 1 m resolution mesh. From the figure it is evident that mesh resolution has small impacts on the steady discharge values estimated by the model with the coarser meshes having a difference of up to 6% with respect to the 1 m resolution mesh. The steady discharge values of the 0.5 m mesh are all in line with the 1 m mesh results with differences smaller than 1%. This suggests that 0.5 m resolution is unnecessary in terms of the quality of estimating steady discharge. Additionally, the figure shows that the catchment area is not constant among the DEMs, and that the differences in simulated steady discharge among the DEMs are mostly determined by the differences in area. Recall that from a morphological point of view, the onset of runoff which is mostly affected by the change in morphology (Figs. 6 and 7). To further study this, consider Fig. 13 which shows that the steady discharges achieved among the different DEMs is mostly impacted by the area size of that DEM. Complementary, Fig. 14a shows the depression storage volume for all DEMs and resolutions. This is a topological feature of each discretized surface. There is a general trend across resolutions: coarser implies a larger depression storage, meaning that the volume of local minima are mostly overestimated with coarser resolutions. Along time, it is clear that there is initially a mild reduction in depression storage, but in 2009 a high storage is registered, which then falls back to the previous levels. Comparing this to Fig. 12, shows a very strong correlation between T50 and depression storage, suggesting it is precisely the filling of local depressions which is strongly responsible for the delays in the onset of runoff. Fig. 14b shows the ratio of static storage (depression storage volume) to the maximum dynamic storage (maximum detention volume), for both the LIR and HIR rainfall. Firstly, the figure shows that this ratio is inversely proportional to resolution for both LIR and HIR, meaning that depression storage takes a larger role in surface detention for coarser meshes. The trend in time is similar to the trend of surface depression storage (Fig. 14a) and T50 (Fig. 12). Moreover, clearly higher intensities (HIR, dashed lines)

metrics complement hydrograph data very well, so that further insights can be drawn from the combined signatures. 3.3. Interpreting hydrographs through connectivity and the onset of runoff These delays in the onset of runoff, caused by different mesh resolutions, can be seen in a higher detail in Fig. 12, which illustrates the time when the discharge reaches 50% of the steady discharge, (indicator for how fast runoff develops) for different topographies and different meshes as a result of the LIR and HIR rainfalls. It can be seen that 0.5 m and 1 m meshes show similar predictions of the onset of runoff in most cases (with variances below 20% of the 1 m mesh results). The 2 m resolution mesh shows differences of up to 50% in comparison to the 1 m mesh. With the coarser meshes, the differences rise up to about 440% in contrast to the results generated by the 1 m reference mesh, making the results completely inadequate in terms of the onset of runoff. These differences clearly indicate that the impact that topography data/representation can have on model results can be very large. Fig. 12 also shows that topographic evolution of the catchment has a moderate impact in how runoff is initiated. The time tends to increase towards a maximum for the June 2009 DEM, then falling back to similar times as in 2006. Importantly, the figure clearly shows that for this catchment, mesh resolution can have a much more significant effect on the onset of runoff than the topographic evolution. This highlights the importance of simulating runoff processes at an appropriate resolution, so that the effects of morphological evolution are not overwhelmed or dampened by the numerical artifacts introduced by the computational mesh. To get a better understanding on how mesh resolution affects the predicted steady discharge values in the model, Fig. 13 shows the steady discharge values simulated in the different DEMs with different mesh configurations as a result of the HIR and LIR scenarios. All the values have been normalized with respect to the results from the March 820

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Fig. 9. Area of disconnected wet clusters during the onset of runoff (t = 1000 s = 16.6 min) with dx = 1 (left) and dx = 8 (right) in the December 2008 (bottom) and May 2009 (top) DEMs. Colors represent areas of wet clusters, and shows dry regions.

number of small disconnected flooded areas in comparison to the April 2008 and March 2010 simulations. Both the 2008 and 2010 DEMs produce a higher flow concentration in their main rill at the same time of the simulations. The high number of small clusters or ponds in the 2008 DEM shows relevant microtopographic features present in the interrill surfaces. They appear to allow for significant ponding thus not allowing for high flow concentration in the rills. Comparing the 2008 and the 2010 DEMs it appears that the 2010 DEM results in higher flow concentration overall, in the entire rill network than 2008, perhaps signaling that the microtopography in the interrill surfaces plays a smaller role, or that the rill network is more strongly defined. Furthermore, the flow fields in Fig. 15 offer a clear explanation of why the June 2009 DEM results in the largest delay in the onset of runoff as shown in Fig. 12 and the lowest flow rate at t = 1000 s (hard to appreciate in Fig. 6). Clearly the extent of microponding and the lower flow concentration are responsible for this. Interestingly, as Fig. 12 shows, the onset of runoff is very similar for the April 2008 and March 2010 DEMs, which can also be appreciated in the flow fields. Regarding low (LIR, 10 mm/h) and high (HIR, 100 mm/h) rainfall intensities, the obvious differences in runoff response is that steady state discharge is ten times higher for HIR than for LIR (Figs. 6 and 7). Given the absence of infiltration, steady discharge is mostly determined by rainfall intensity. Fig. 16 shows a comparison of runoff indicators between the two rainfall intensities. Fig. 16(a) and 16(b) represent T50 [s] under both rainfall intensities for the different DEMs with four mesh resolutions. Fig. 16(c) and 16(d) show the normalized steady discharge (Qstn [-]) for both HIR and LIR. Fig. 16(a) shows that different rainfall intensity results in smaller differences in α for the 0.5 m resolution mesh (less than 25%) than for the 2 m resolution mesh (up to 110%).

decrease the fraction of stored surface volume in depressions, but the trends remain unchanged. The trend of how this morphological change has affected runoff generation in the catchment can be seen from Fig. 12. The onset of runoff experiences a delay over time from November 2006 up to June 2009 and then a turn is seen in this trend with the delay decreasing until March 2010. These differences in the onsets of runoff among the different years clearly indicate the extent to which morphological change can impact the hydrological processes involved in a catchment. Fig. 15 presents the instantaneous flow field at time 1000 s (16.6 min) for the simulations on the April 2008, June 2009 and March 2010 DEMs, with the 10 mm/h rain intensity (LIR), for a 1 m resolution. This time is early on during the onset of runoff. These flow fields allow to observe clearly how differently runoff builds up on the surface of the catchment, and allow to explain some of the behaviors observed in the hydrographs (Fig. 6) and summarized also in the onset of runoff indicator in Fig. 12. Although hard to appreciate in Fig. 6, all three hydrographs result in different flowrates at t = 1000 s. The June 2009 DEM produces a discharge roughly 3 times smaller than the discharge for the March 2010 case. The April 2008 DEM results in a discharge slightly (around 10%) larger at such time. More importantly, the shape of the hydrograph at such time is very similar for the April 2008 and the March 2010 cases, but it is characteristically different for the March 2010 case. The collective analysis of signals and spatial distributions consistently links the differences in the onset of runoff to changes in surface water connectivity caused by small topographic features, which has been also recently been noted for agricultural catchments (LópezVicente and Álvarez, 2018). Fig. 15 shows that the June 2009 simulation results in a higher 821

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Fig. 10. Area of disconnected wet clusters at steady state (t = 300 min_ with dx = 1 (left) and dx = 8 (right) in the December 2008 (bottom) and May 2009 (top) DEMs. Colors represent areas of wet clusters, and shows dry regions.

and HIR setups. These differences rise up to 4% for the dx = 2 mesh size and up to 6% for the two coarser mesh configurations. It can be concluded that different mesh resolutions have small effects on the steady discharge estimates of the model under different single pulse intensities. However the absence of some processes such as infiltration, soil heterogeneity and surface friction must be kept in mind while observing these results. With the introduction of these processes, the results are expected to alter and the degree in which the cell size of the mesh is capable of capturing these processes will become a significant

The differences rise significantly with the coarsening of meshes, with the dx = 4 mesh having differences up to 200% and the dx = 8 producing differences up to 300%. These results show that there may be interactions between the rainfall signal and mesh resolution and thus suggest that mesh resolution analysis should be always assessed before using real rain signals for rainfall/runoff simulations. Fig. 16(c) and (d) show that the dx = 0.5 mesh has an almost identical behavior while estimating the peak discharge under different rain events with a maximum difference of less than 1% between the LIR

Fig. 11. Number of disconnected clusters (wet-dry threshold of 2 mm) normalized by cell number, for simulations on the December 2008 and May 2009 DEMs with both 1 m and 8 m mesh resolutions. Solid lines represent discharge, dashed lines represent the normalized number of clusters. 822

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Fig. 12. Comparison of the time when the discharge reaches 50% of the steady discharge.

Fig. 13. Comparison of steady discharge values and DEM areas.

Fig. 14. Surface depression storage and maximum detention storage for all DEMs. In figure b dashed lines represent the HIR and solid lines represent the LIR rain setups.

(d) show results corresponding to the same DEMs. As is expected, the R1 rainfall results in higher runoff than the R2 rainfall, consistently with their peak intensities. Both rain events show that different topographies result in different hydrographs, but mostly for the onset of runoff and the peaks flows. The intermediate flow rates and the drainage limbs of the hydrographs are almost identical for all three DEMs, regardless of the rain event. A comparison with the LIR and HIR cases

factor in shaping the results.

3.4. Non-uniform rainfall Fig. 17 shows the resulting hydrographs from the April 2008, June 2009 and March 2010 DEMs under two different rainfall signals (R1 and R2) and the LIR and HIR scenarios. For comparison, Fig. 17(c) and 823

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Fig. 15. Spatial distribution of the flow field at t = 1000 s for the April 2008, June 2009 and March 2010 DEMs.

Fig. 16. Comparison of time of 50% steady discharge and steady discharge values under the two rain scenarios.

cases is 1.043. Interestingly, the ratio for the R1 rain is 1.033 and for R2 is 1.043. The ratios for both R1 and R2 are very similar to the LIR and HIR ratios, suggesting that the change in peak discharge is almost the same to the change in steady state discharge (for steady rains) which is mostly dominated by the difference in catchment area (Fig. 13). That is, the difference in peak discharge is a result of the change in catchment

shows that the hydrographs behave essentially in the same way for R1 and R2, i.e., it is the onset of runoff which is delayed and milder for June 2009 compared to March 2010 and the April 2008. The March 2010 DEM results in lower maximum discharge values in contrast to the other DEMs under the time-dependent rainfall. The ratio of maximum discharge between the April 2008 and March 2010 in the LIR and HIR 824

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Fig. 17. Hydrographs of the April 2008, June 2009 and March 2010 DEMs under different rain events.

Fig. 18. Hydrographs until T = 50 min of dx = 2 m meshes with (right) and without (left) infiltration under the HIR rainfall.

3.5. Reintroducing infiltration: Preliminary assessment

area, not a result of introducing further rainfall complexity. Overall, results from the R1 and R2 events show that the effects of changing topographies (in the absence of infiltration) manifest qualitatively in the same way independent of rainfall distribution.

For the sake of completeness, and in order to contextualize the aforementioned results, Fig. 18 presents simulation results computed considering infiltration. For this set of simulations only the 2 m resolution meshes have been used. We show simulations only with the

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topographic evolution on catchment hydrodynamics are very weakly dependent on rainfall properties. This may only be true in the absence of infiltration, since morphological features can in fact amplify or reduce infiltration. This remains to be studied systematically. The results in this work highlight the fact that a deep understanding of catchment dynamics through computational modelling requires a systematic approach, as multiple physical processes and numerical artifacts interact, overlap and may dominate the indicators and signatures used to characterize and evaluate the response. Topographical effects may be completely drowned by numerical artifacts from the mesh and the emerging interactions between topography, rainfall distribution and heterogeneous infiltration are not easy to untangle, and in fact modelling is perhaps the only approach which allows to explore it. The natural continuation of this work is to therefore explore the role of these interactions, and whether or not the behavior of signatures observed in this work are amplified or simply completely overrun by other responses. This has been pointed out as an evermore relevant issue in Hydrology (Jencso and McGlynn, 2011) This work is consistent in offering outlook towards further exploration of the effects of evolving catchment properties such as vegetation cover (Donohue, et al., 2007; Birkel et al., 2012), climate (Li et al., 2012) and infiltration (Horton, 1931; Shuster et al., 2007) on hydrological processes.

HIR rainfall, since for the selected infiltration parametrization, the LIR rain results in a trivial response without any runoff. Infiltration has calculated using the Green Ampt method with a simplistic domain-wise homogenous saturated hydraulic conductivity of 2.53*10−6 ms−1 and suitable parameters for loamy sand soil: average suction head at wetting front ψ = 0.0613 m and porosity η = 0.437 (Schaaf et al., 2017). Fig. 18 shows the hydrographs only until t = 50 min to enable a good resolution of the onset of runoff. Fig. 18(a) shows results without infiltration (corresponding to results originally presented in Figs. 7 and 18b) shows results with infiltration. Obviously, runoff is reduced in the presence infiltration. Infiltration has additional effects. Firstly, there is an increased delay to the onset of runoff which amplifies the differences across different topographies. Moreover, the asymptotic trajectory towards the steady state is significantly extended. These results suggest that the onset of runoff variations in response to morphological evolution studied in an idealized form, without infiltration, hold or might even be amplified by infiltration. This remains to be studied systematically as it is a numerical experiment in its own right. 4. Conclusions The results of this study suggest that topographic evolution in the catchment can generate mild differences in the runoff generation process. In particular, the early stages of runoff -the onset of runoff- is mostly affected. The changes appear to be related to the smoothening of the surface and the subsequent changes in runoff connectivity on both hillslopes and to a certain extent in the rill network. Since the variations in the onset of runoff appear to be related to connectivity and ponding, it is expected that with the re-introduction of the missing hydrological processes, in particular infiltration, the effects of topographic evolution on surface flow to become amplified in terms of hydrological partitioning. The results suggest that a catchment which is experiencing rather small topographic changes in the interrill surfaces and to a very small extent in the rill network, the process of runoff generation can be affected by small scale surface features. This points out to the importance of interrill microtopography and its effect on hydrological partitioning (Thompson et al., 2010; McGrath et al., 2012) but as this study shows, also in the transient states and the sequence of how runoff is produced. The changes in the onset of runoff can be related to surface dynamic connectivity which allows to explain in a succinct way how the spatial distributions of runoff correlate and are likely responsible for features of the hydrograph. Moreover, despite the relatively small topographic changes, significant differences can be appreciated in the spatial distribution, flow paths and connectivity of surface runoff, thus implying that even such small topographic evolution can have impacts in the formation of morphological, ecological and biogeochemical hotspots. Additionally, the results show that mesh resolution can have a significant impact on the runoff signatures and flow fields. The poor representation of terrain features and inability of coarse meshes to capture the small scale processes involved manifests in a lower runoff connectivity, which in turn manifests in runoff signatures as a delayed onset of runoff. This numerical artifact is similar to -and can overlap with- that of a changing topography, therefore highlighting the need of appropriate mesh selection to perform simulation-based analysis of these systems. In a broader outlook, the artifacts introduced by computational resolution mimic the effects of field observations at different scales, and the differences in connectivity from numerical resolution may also be analogous to scale-dependent connectivity (Bracken et al., 2013). The simplistic precipitations used in the majority of this study interact with mesh resolution to produce different signatures: coarser meshes show a larger response variation when changing rainfall intensity. Interestingly, the signatures response to topographic evolution seems to be relatively insensitive to rain intensity and intrastorm rainfall distribution. This suggests that the expected effects of

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