## 1. Introduction

[2] How river deltas emerge and how they evolve are classic questions in geomorphology [*Bates*, 1953; *Coleman and Gagliano*, 1964; *Wright and Coleman*, 1973; *Galloway*, 1975; *Orton and Reading*, 1993]. Coastal deltas are morphologically very active sedimentary landforms where strong deposition caused by the high sediment supply from the river is competing with reworking wave and current action. The deposition of coarse sediment at the mouth of the delta is often accompanied by the formation of oil and coal reservoirs [*Morgan*, 1977; *Coleman*, 1975; *Coleman and Prior*, 1980; *Allen et al.*, 1981]. As a result, the first field studies investigating the geological structure of coastal deltas were carried out early in the 20th century primarily by oil companies, for example in the Mississippi Delta [*Fisk*, 1947, 1952; *Kolb and van Lopik*, 1958; *Coleman and Gagliano*, 1964, 1965]. Today the gulf of Mexico at the mouth of the Mississippi is one of the major offshore oil fields in the United States. The understanding of the facies, relationships and mechanisms responsible for the development and distribution of deltaic deposits therefore is essential for efficient exploration and oil extraction [*Bates*, 1953; *Coleman and Prior*, 1980]. Six major lobes of the Mississippi Delta have been identified and their ages have been determined using radiocarbon dating [*Fisk and McFarlen*, 1955; *McFarlen*, 1961; *Saucier*, 1963; *Frazier*, 1967; *Törnqvist et al.*, 1996]. More recent studies have shown that, beside the major lobes, there are also three to six sublobes [*Penland et al.*, 1987]. The main lobes of the delta are shown in Figure 1.

[3] In recent years the study of changes in deltaic topography has come into focus because of coastal land loss related to the rising sea level combined with extreme weather events causing significant damage. Coastal hazards have an immense economic impact as 25% of the world's population live on deltaic coastlines and wetlands [*Giosan and Bhattacharya*, 2005; *Syvitski et al.*, 2005]. To obtain a deeper understanding of the dynamic processes involved in delta formation, laboratory experiments have been set up in recent years in order to quantify sedimentation and erosion processes in a delta. Experiments have been carried out with some success in the “eXperimental EarthScape” (XES) facility of the St. Anthony Falls Laboratory [*Kim et al.*, 2006; *Swenson et al.*, 2005; *Paola et al.*, 2001; *Sheets et al.*, 2002]. Other recent laboratory experiments have shown that the cohesion of the sediment transported by the stream is an essential factor in the formation of elongated birdfoot deltas such as the Mississippi. Because of the cohesion of the sediment, the channel beds are stabilized which leads to more distinct channel patterns and lower channel migration. In nature this channelization happens because of riparian vegetation which stabilizes the bed at the river banks and bars [*Hoyal and Sheets*, 2009].

[4] Although the techniques for topographic measurements and experimental setups have advanced considerably, computational modeling of deltas has proven to be very difficult as the systems are highly complex and large time scales have to be taken into account. Physically based models generally combine hydrodynamics derived from the Navier-Stokes equations with an empirical sediment transport law based on bottom shear stress and sediment continuity. This set of partial differential equations is then integrated using finite element or finite volume techniques. Fully three-dimensional simulations with hydrodynamic-topographic coupling have been carried out by *Harris et al.* [2005] using ECOM-SED and by *Edmonds and Slingerland* [2007, 2008], who applied the Delft-3D model to study the mechanics of river mouth bar formation. Although the models based on partial differential equations describe the details of the flow, numerical simulations of realistic river basins and delta formation over geological times are far beyond today's computational power. Usually these models cover only small sections of some kilometers over several months or years.

[5] In contrast, our knowledge of the topography and channel dynamics is derived from digital elevation model (DEM) data and sediment records covering scales of broadly 10^{0} − 10^{6} m and 10^{−1} − 10^{5} years. Process models are required that include the changing boundary conditions governing land-surface changes and mass fluxes over these scales [*Brasington and Richards*, 2007]. While for the very small and very large scales well-developed models exist, the mesoscale is still not yet well understood [*Wolinsky*, 2009]. Thus the challenge of geomorphological modeling is to reduce the complexity of the microscopic physical equations without modifying the characteristic mesoscopic behavior of the system [*Coulthard*, 2001]. During recent years “reduced complexity models” (RCMs) based on the idea of cellular automata [*Wolfram*, 2002] have proven to be very successful in modeling the time evolution of geophysical processes [e.g., *Paola et al.*, 2001; *Coulthard et al.*, 2007]. The motivation for this type of modeling is not to simulate the detailed evolution of a given river, but to identify the essential physics of the underlying processes [*Murray*, 2003]. The results of these simulations then can be compared and validated with appropriate coarse-grained field measurements and laboratory experiments. Recent advances in this field have sought to achieve these ends through the development of novel cellular discretization methods efficiently describing the evolution of the topography combined with an increasing reliance on high-quality topographic data [*Brasington and Richards*, 2007; D. Divins and D. Metzger, NGDC Coastal Relief Model, Central Gulf of Mexico Grids, 2006, http://www.ngdc.noaa.gov/mgg/coastal/coastal.html (hereinafter referred to as Divins and Metzger, 2006)]. RCMs are based on simplified equations that still capture the essential morphodynamics of the landscape changing processes. These simplifications introduce a new set of problems as the model equations are often based on empirical descriptions instead of previously well-understood physical properties and variables. Additional complications then emerge because of the fact that the nature of these new parameterizations may themselves be both scale and grid dependent and not easily transferable to real scales [*Brasington and Richards*, 2007; *Murray*, 2003, 2007]. The work of Murray and Paola on braided river streams [*Murray and Paola*, 1994] is often considered as the seminal work in applying RCMs in geomorphology. Other more recent examples are CEASAR [*Coulthard et al.*, 1998] and EROS [*Davy and Crave*, 2000] for river channel dynamics and alluvial sediment transport or LISFLOOD [*van der Knijff and de Roo*, 2008] for modeling flood plain dynamics. Reduced complexity models have also been applied to delta formation by *Sun et al.* [2002]. This model is completely topography driven and does not account for subaqueous sediment transport at the delta front or backwater and overbank effects. Other models like the two-dimensional DELTASIM [*Hoogendoorn and Weltje*, 2006] include subaqueous sedimentation, but lack the description of lateral sediment transport. A comparison and discussion of the different models and strategies are given by *Overeem et al.* [2005].

[6] On the basis of RCM ideas, *Seybold et al.* [2007] presented a new model to simulate the time evolution and formation of river deltas. This model combines the simplicity of the cellular models with the essential hydrodynamic features necessary to reproduce realistic river delta patterns, which cannot be obtained by classical topography driven flow equations such as Manning-Strickler. The model describes a subaerial and subaqueous growth of the deltaic deposits using a simple hydrodynamic routing with an explicit water surface coupled to the topography by an erosion and deposition law. By modifying the erosion-deposition law, the model reproduces the formation of the Galloway [*Galloway*, 1975] end-member delta types, namely, river-, wave- and tide-dominated. Furthermore several characteristics of the time behavior of real delta formation such as lobe switching could be observed [*Seybold et al.*, 2007].

[7] In this paper we apply the model to the case of a river-dominated delta and focus on the specific static and dynamic features of this delta type. We compare the model dynamics with that of the Balize Lobe of the Mississippi Delta and show that the model captures the key features of the delta formation process, such as the self organized formation of subaerial and subaqueous natural levees. We investigate the simulated delta evolution and the internal behavior of the model by comparing the model parameters with measured data obtained for the Mississippi. Our aim is to show that the model is internally logical and gives physically meaningful results, that the dimensionless parameters may be rescaled consistently to fit observations, and that the model produces long-term simulated dynamics of the delta formation process with a complex temporal correlation structure.

[8] The paper is organized as follows: in section 2 we present a description of the model implementation and the details of the model equations, followed by section 3, which summarizes the model parameters used for the simulation of the birdfoot delta lobe. The simulated delta dynamics and the consistency of the RCM equations are checked by comparing the simulation results with data from the Mississippi. In section 5 we investigate the simulated long-term dynamics of the delta growth.