## 1. Introduction

[2] Simulating the hydraulics of large river networks is becoming increasingly important as demands for regional scale hydrological risk assessment increase and interest in estimating river discharge from remote sensing becomes more widespread [*Andreadis et al.*, 2007; *Biancamaria et al.*, 2009, 2011; *Durand et al.*, 2008; *Neal et al.*, 2009b]. Methods for simulating river hydraulics have either concentrated on routing schemes that simulate wave propagation for global or regional hydrological and land surface models [*Ngo-Duc et al.*, 2007; *Oki and Sud*, 1998; *Pappenberger et al.*, 2010] or river and floodplain hydraulic models that simulate both wave propagation and water level [e.g., *Bates and De Roo*, 2000] but typically at model domain scales of <100 km.

[3] This paper presents a hydraulic model designed for large scale simulation of inundation extent, water level, and wave propagation in areas where limited or no ground based data are available. Specifically, this means it must be theoretically possible to build and evaluate the model using only remotely sensed data and that the time required to simulate flow for one year at the continental scale must be no more than a few hours. The model uses a computationally efficient finite difference numerical scheme adapted from the reach-scale inundation model of*Bates et al.* [2010]and utilizes gridded river network data. To run at a computationally feasible resolution at regional to continental scales (∼1 km on present-day computers) the model assumes that channel flows can be represented as a subgrid-scale process and that the same subgrid channel approach can be used to represent the flow connectivity necessary to simulate inundation dynamics on large predominantly natural floodplains at low resolution. The model utilizes only globally and freely available input data sets for topography and channel parameterization and was calibrated and evaluated on an 800 km stretch of the River Niger Inland Delta in Mali to investigate the performance of the model in terms of simulating water surface elevation, inundation, and wave propagation. The model was then used to assess the effect of the floodplain and complex network of floodplain channels on the flow dynamics of this delta. From these results, the impact of floodplain and tributary dynamics on wave propagation and inundation are discussed.Auxiliary material is also presented to validate the subgrid channel model against equivalent channel geometry at higher resolution, demonstrating the numerical stability and scalability of the subgrid approach.

### 1.1. Introduction to Flow Routing and Hydraulic Modeling at Large Scales

[4] Routing models are typically designed to convey runoff generated by global land surface or continental scale hydrological models to the sea, with the aim of accounting for this component of the water cycle. Most approaches apply a storage cell based routing scheme where the change in storage (*V*) over time (*t*) (*dV*/*dt*) is the sum of flows from upstream and runoff from the cell minus river flow to a downstream cell. The downstream cell is predetermined by a river network and flow direction map [*Doll and Lehner*, 2002; *Fekete et al.*, 2001; *Yamazaki et al.*, 2009], while the flow to it can be estimated using a wave velocity obtained via calibration to observations of discharge or a hydraulic equation relating river geometry to wave velocity (e.g., the Manning equation). Although the fundamental design of most routing schemes is the same, a wide range of variants on this theme with different river networks, resolutions, and process representations have been developed, including TRIP [*Oki and Sud*, 1998], TRIP2 [*Ngo-Duc et al.*, 2007], HYDRA [*Coe*, 2000], WTM [*Vorosmarty et al.*, 1989], and CaMa-Flood [*Yamazaki et al.*, 2011].

[5] The simplicity of routing schemes allows ensemble and scenario based prediction of global runoff [*Arnell*, 1999, 2003] and Monte Carlo based approaches to parameter estimation [e.g., *Pappenberger et al.*, 2010]. However, with simplicity comes the neglect of some important dynamic processes. *Gong et al.* [2009]point to the importance of convective delay when simulating wave propagation, where the inflow to a cell many kilometers in length would not be expected to instantaneously affect the outflow as in many routing model. Neglecting this effect can lead to an overprediction of wave speed or a scale-dependent wave speed when the model is calibrated. The method used to determine river network topology will also affect wave propagation and flow connectivity [*Fekete et al.*, 2001; *Oki and Sud*, 1998; *Vorosmarty et al.*, 2000]. For example, *Yamazaki et al.* [2009] illustrate how widely used steepest slope methods to determine flow direction using the eight neighboring cells (D8 algorithms) can lead to incorrect flow paths and accumulations, particularly when defined for low resolution grids (e.g., >10 km). A flow direction map will also be problematic in deltas, in wetlands, and during flood events, where flow networks can be dynamic due to the complex geometry and nonstationary hydraulic gradients [*Alsdorf et al.*, 2007; *Papa et al.*, 2008]. Flooded fraction, modeled as the inundated fraction associated with changing water surface elevation, has been included in routing models [e.g., *Decharme et al.*, 2008] and can have a significant impact on simulated land–atmosphere water vapor flux [*Dadson et al.*, 2010; *Dawson et al.*, 2009; *Pedinotti et al.*, 2012], although there can be distinct hysteresis in the wetting and drying of floodplains not captured by flooded fraction methods [*Bates et al.*, 2006; *Nicholas and Mitchell*, 2003].

[6] Kinematic wave models, where wave speed is determined by channel bed slope and friction, can efficiently simulate wave propagation and water levels from topographic gradients and inflow sources. Models which use such techniques include JULES G2G [*Bell et al.*, 2007] and the LISFLOOD model used by the European Flood Alerts System [*De Roo et al.*, 2000; *Van Der Knijff et al.*, 2008]. However, kinematic models are unable to account for interaction effects with tributaries and may be difficult to use in areas with low relief due to the need for a monotonically decreasing river bed elevation and the presence of strongly diffusive flow regimes in such settings. Schemes based on diffusive wave models allow dynamic wave speeds and thus backwater effects from channels and floodplains to be simulated. Such models are more expensive but can still be applied at global scales. *Yamazaki et al.* [2011] applied a diffusive wave model with floodplain storage areas to simulate global inundation dynamics. The scheme was more accurate on most of the 30 major rivers basins evaluated than both a kinematic wave scheme and a scheme without the floodplain storage. However, the exchange of water between channel and floodplain was assumed to be instantaneous. Conveyance between floodplain units was also not considered in this study, but has subsequently been added to the model and tested in the Amazon basin by *Getirana et al.* [2012].

[7] Reach-scale hydraulic models solve the shallow water equations, or in some cases a simplification of them when the flow conditions are subcritical, and require distributed values for surface friction and ground elevations. They are designed to be utilized with detailed river cross sections and accurate floodplain digital elevation models (DEMs), which are not available globally or in many large catchments. They also require no prior processing of DEM data to determine flow direction and intrinsically represent wetting and drying hysteresis. Typically the spatial domain is discretized in either one or two spatial dimensions, with computational cost mainly depending on the number of dimensions, resolution of the model, and size of the model spatial domain. When used in two dimensions the models can simulate wave propagation across floodplains provided the flow controlling features are captured by the model topography. However, the computational cost and memory footprint will be too large for global applications at the <100 m resolutions typically used. As the resolution of the model decreases, flow controlling features and flow connectivity may be lost and simulation accuracy reduced. Methods have been developed to incorporate smaller scale features into models using porosity based techniques [*Guinot and Soares-Fraza*, 2006; *McMillan and Brasington*, 2007; *Sanders et al.*, 2008; *Yu and Lane*, 2006] adaptive grids [*Liang and Borthwick*, 2009] or 1-D models for the channel component (e.g., coupled 1-D/2-D models), although these were typically designed with urban rather than global scale applications in mind [e.g.,*Schubert and Sanders*, 2012]. Nevertheless, the representation of flow physics in hydraulic models can be substantially more accurate than wave speed based routing models and kinematic wave models, especially in low relief or complex river networks.

[8] There are a number of examples of hydraulic models being implemented over large river catchments in data sparse areas including the Amazon [*da Paz et al.*, 2011; *Wilson et al.*, 2007], Congo [*Jung et al.*, 2010], and Ob [*Biancamaria et al.*, 2009] river basins. These highlight that the spatial scales at which routing and hydrodynamic models are used are converging, while routing models are now starting to include components of floodplain storage. However, despite the advances in modeling capability, it is still unclear to what extent the additional process representation available via the hydraulic modeling approach is necessary to simulate level and wave propagation over large river systems. Similarly, there is no consensus on how to represent floodplains in large scale hydraulic models where fine topographic controls cannot be represented explicitly, as would be the preferred approach at the reach scale. Simulating the hydraulics of large floodplains and wetlands and their effect on flow routing motivated the design of the subgrid hydraulic model that is presented in section 2. This is followed in section 3 by a summary of two synthetic test cases that were implemented to validate the numerical scheme. In section 4 the Niger Inland Delta is introduced as a test site. Finally, the performance of the subgrid model is assessed and compared with a number of alternative model structures in order to better understand the hydraulics of this globally important wetland.