## 1. Introduction

[2] The world's largest rivers remain significantly understudied, despite the fact that they dominate the Earth's surface in terms of drainage and basin sedimentation, with almost half of the Earth's surface drained by its 50 largest rivers [*Potter*, 1978; *Ashworth and Lewin*, 2012]. Evidence also suggests that not all processes that influence river dynamics scale uniformly with increasing channel size. For example, *Parsons et al.* [2007]reported a marked lack of secondary flow structure in a large confluence-diffluence of the Río Paraná Argentina. Although*Parsons et al.* [2007]noted that dune morphology appeared to scale with flow depth, they observed that the channels had a high width-depth ratio and also there may be a much slower adjustment of dune morphology to changes in river discharge, both of which might dampen the formation of secondary circulations. Such observations emphasize the need for investigation of roughness effects in large rivers.

[3] A typical large river has lengths, widths, and depths of the order 10^{3} km, 10^{3} m, and 10^{1} m, respectively, with discharge and sediment loads up to 200 × 10^{9} m^{3} and 1 × 10^{9} t yr^{−1} [*Gupta*, 2007]. These large scales have been a prohibitive factor in field studies, constraining our ability to investigate flow and morphology. However, technological innovations, notably in remote sensing of river-bed topography and measurement of river flow, have made quantitative investigations of large rivers increasingly feasible [e.g.,*Richardson and Thorne*, 1998; *McLelland et al.*, 1999; *Ashworth et al.*, 2000; *Rennie et al.*, 2002; *Kostaschuk et al.*, 2004, 2005; *Parsons et al.*, 2005, 2007; *Rennie and Rainville*, 2006; *Viscardi et al.*, 2006; *Lane et al.*, 2008; *Szupiany et al.*, 2009].

[4] There is also a growing track record of effective application of hydrodynamic models to the quantification of river-channel hydrodynamics in both two dimensions (2-D) and three dimensions (3-D) [e.g.,*Olsen and Stokseth*, 1995; *Hodskinson*, 1996; *Ferguson et al.*, 2003; *Lane et al.*, 1999, 2000, 2004; *Ma et al.*, 2002; *Booker et al.*, 2001, 2004; *Rodriguez et al.*, 2004; *Nicholas*, 2001, 2005; *Ruther et al.*, 2005; *Ruther and Olsen*, 2007; *Tritthart and Gutnecht*, 2007; *Abad et al.*, 2008; *Shen and Diplas*, 2008; *Tritthart et al.*, 2009], and some of these studies have begun to consider large rivers [e.g., *Kleinhans et al.*, 2008; *Ercan and Younis*, 2009]. A critical element of such application is the representation of bed roughness elements, which range from individual grains of sand up to large bedforms such as dunes. Modeling these elements is explicitly possible at very high resolutions [e.g., *Lane et al.*, 2004; *Hardy et al.*, 2006], but for river-scale applications, resolving even dune-size bedforms can be difficult due to the computational resources required as well as the availability of topographic data that are constantly evolving. Recent advances in numerical modeling techniques have been aimed at improving this situation. For example,*Nabi* [2008a, 2008b]used an unstructured grid that could be refined in all dimensions, in particular close to the bed, and successfully coupled a discrete particle model to a large eddy simulation. This technique may provide an alternative method for specifying bed topography. However, it still does not address the computational demands associated with running models with resolutions of a meter or less (to resolve dunes, for example) over spatial scales of several kilometers. It also does not address the fact that large-scale bathymetric surveys are required that may only be applicable to a small range of flow conditions. For this reason, parameterization of bed roughness remains necessary.

[5] In both one-dimensional (1-D) and 2-D simulations of river flows, velocity predictions have proven to be highly sensitive to roughness parameterization [*Lane and Richards*, 1998; *Lane*, 2005], and this has made it a primary modeling consideration. Much of this work has focused upon developing robust mathematical descriptions to capture the interactions between near-bed flow velocity, grain, and bedform descriptors of the river-bed surface and fluid turbulence [e.g.,*Clifford et al.*, 1992; *Ferguson*, 2007]. However, in practice, bed roughness tends to be used as a calibration parameter so as to force agreement between model predictions and field observations [*Lane*, 2005].

[6] The majority of hydrodynamic models of river flow parameterize roughness effects through the application of a logarithmic friction law [e.g., *Hodskinson*, 1996; *Hodskinson and Ferguson*, 1998; *Lane et al.*, 1999, 2000, 2004; *Booker et al.*, 2001; *Morvan et al.*, 2002; *Booker*, 2003; *Olsen*, 2003; *Booker et al.*, 2004; *Dargahi*, 2004; *Rodriguez et al.*, 2004; *Ruther et al.*, 2005; *Ruther and Olsen*, 2007; *Tritthart and Gutnecht*, 2007; *Abad et al.*, 2008; *Kleinhans et al.*, 2008; *Shen and Diplas*, 2008; *Ercan and Younis*, 2009; *Tritthart et al.*, 2009]. In this formulation, the roughness parameter *k*_{s}, often referred to as Nikuradse sand roughness [*Nikuradse*, 1933], is used to characterize the effect that roughness elements have on the flow. The value of *k*_{s}is normally set as a function of a measured grain-size diameter [e.g.,*Abad et al.*, 2008; *Shen and Diplas*, 2008]. The development of more sophisticated roughness parameterizations to deal with other types of energy losses, such as those associated with secondary circulation [e.g., *Blanckaert and de Vriend*, 2003, 2010] and curvature-driven turbulence [e.g.,*Blanckaert*, 2009], have also been investigated.

[7] In many of the above examples, roughness is being used as an effective parameter in an auxiliary relationship that is required to represent energy losses that are not otherwise being represented explicitly. The simplest approach to this problem is to identify a generic auxiliary relation (i.e., one that applies throughout the computational domain) and then to consider how to represent the roughness parameter. This has involved both friction factor-based [e.g.,*Dargahi*, 2004] or an analytical [e.g., *van Rijn*, 1984, 2007; *Olsen*, 2003; *Ruther et al.*, 2005; *Ruther and Olsen*, 2007; *Paarlberg et al.*, 2010] upscaling to the sand roughness. Some applications have explored the sensitivity of model predictions to roughness parameterization [e.g., *Kleinhans et al.*, 2008; *van Balen et al.*, 2010]. Less common approaches include inference of the sand roughness from estimates of Manning's *n* [*Morvan et al.*, 2002] and the use of roughness lengths measured directly from velocity profiles [*Hodskinson*, 1996]. A small number of studies (including the present paper) have sought to optimize model predictions (e.g., water-surface elevation; velocity) on experimental or field measurements by adjusting the roughness length [e.g.,*Booker*, 2003; *Rodriguez et al.*, 2004; *Tritthart and Gutnecht*, 2007; *Tritthart et al.*, 2009]. The majority of these approaches apply estimates of sand roughness that are derived from reach to bar-form scales, and thus are more suited to 1-D and 2-D approaches. For example, the*van Rijn* [1984, 2007]roughness predictors are based on depth-averaged values of flow, whereas friction factor- and Manning's*n*-based estimates provide a reach-averaged approximation.

[8] Other studies have shown the merits of moving away from the log-law formulation altogether through new types of auxiliary relations. Both*Nicholas* [2005] and *Carney et al.* [2006] developed formulations more sensitive to the presence of bedforms, whereas *Kang and Sotiropoulos* [2011] solved the boundary layer equation, and *Constantinescu et al.* [2011]employed a detached eddy simulation (DES) that is capable of resolving near-wall flow with more accuracy than wall functions. A very fine mesh is employed with only grain roughness parameterized, and so application here would not be possible, given computational restraints especially at these large scales.*Escauriaza and Sotiropoulos* [2011] also applied DES coupled with a sediment transport model, using a numerical scheme that contains predetermined dissipation to include the effect of subgrid topography that is scale dependent and requires parameterization [*Escauriaza and Sotiropoulos*, 2011]. The double-averaging approach [*Nikora et al.*, 2007a, 2007b] appears to offer a way forward in this respect. The resulting set of equations, known as the double-averaged Navier Stokes (DANS) equations, include an additional stress term that is referred to as the form-induced stress. This is analogous to the Reynolds stress but results from spatial rather than temporal variations in mean velocity. Near the bed, this stress can be a similar order of magnitude to the Reynolds stress [*Nikora et al.*, 2007b]. Adopting such an approach to estimate roughness, a priori, in a mathematical model, requires very high-resolution field data to calculate the DANS terms, and such data may not be available in large river studies, although this is the approach that is likely to be most robust in this kind of study.

[9] In summary, the application of a 3-D model that captures bedform roughness effects is possible. At very large scales, this becomes increasing difficult, and thus parameterization of bedform roughness elements may be required. However, there is no clear established theory for defining what the effective roughness length should be in a 3-D simulation. This length should vary with both unmeasured elements of bed topography and be dependent on the data-collection spacing (e.g., dune morphology) and the resolution of numerical discretization. This variation should also be both temporal [*van Rijn*, 1984, 2007] and spatial [*Nicholas*, 2005; *Zeng et al.*, 2008; *van Balen et al.*, 2010], but, in a deterministic sense and with the resolution of topographic data that can be achieved over large extents in wide rivers, such a deterministic approach is not possible. Additionally, the sensitivity of models to a spatial variability in roughness specification has been tested and revealed relatively small differences in the global flow distribution [*Viscardi et al.*, 2006; *van Balen et al.*, 2010], although some differences in secondary flow characteristics and bed shear stress distributions were observed [*van Balen et al.*, 2010]. Moreover, there are few comparisons of different wall treatments and a limited number of studies that have fully tested the sensitivity of model predictions to model parameterization, although *Ercan and Younis* [2009] and *Kleinhans et al.* [2008] are notable exceptions. *Kleinhans et al.* [2008]studied the dynamics of channel bifurcations and tested a 3-D model for sensitivity to a number of factors, including the type of roughness specification.*Kleinhans et al.* [2008]employed both uniform Chezy and Colebrook-White formulations, and their results did not indicate a preference for either parameterization.*Ercan and Younis* [2009]investigated the uncertainty in model predictions of flow along a reach of the Sacramento River and tested the sensitivity of the model predictions to various modeling parameters, such as grid resolution, turbulence closure, and roughness parameterization. To assess the sensitivity of model predictions to the type of roughness formulation, they compared their predictions with measured data, and the model predictions were obtained using their 2-D model with Colebrook-White, Manning, and Blasius formulations to specify roughness. The Colebrook-White and Manning formulations were found to give similar results and compared more favorably to measured data than the Blasius formulation.

[10] The aim of the present paper is to explore the impacts of roughness length upon key characteristics of the 3-D flow field in large rivers and to consider its implications for parameterization of roughness effects in both 3-D and 2-D depth-averaged model formulations. The purpose of this study is as follows: (1) to assess roughness length parameterization in the application of computational fluid dynamics (CFD) of large rivers, (2) to test the sensitivity of the model to roughness length specification, (3) to assess the implications of roughness treatments that assume the velocity profile is log-linear and 3-D simulations that use the fully rough log-law, and (4) to investigate the flow field using CFD output. This is achieved through the application of a CFD model informed by field measurements of flow and bed topography. The model is run with a roughness-length parameterization, and a range of roughness-length values are implemented, allowing investigation of this influence on flow routing and validation with measured flow data. These results are analyzed in four parts: (1) modeled and measured data are directly compared and a number of metrics are used to assess the optimal roughness length; quantitative assessment of the spatial velocity fields is also given; (2) the sensitivity of flow routing is investigated; (3) assessment of a number of velocity profiles extracted from the CFD predictions distributed spatially through the reach is presented; these results are used to quantify the convergence between 3-D models that use the fully rough log-law and those that assume the flow to be logarithmic over the entire depth, and (4) primary and secondary flow patterns around, and in, the lee of a large bar are presented using the optimal CFD results. The paper commences by detailing the methods used to obtain the field data and the CFD model applied. This is followed by a presentation and discussion of the results obtained insection 3 followed by the conclusions in section 4.