**A Hydrodynamic and Sediment Transport Model for the Waipaoa Shelf, New Zealand: Sensitivity of Fluxes to Spatially-Varying Erodibility and Model Nesting**

#### **Julia M. Moriarty, Courtney K. Harris and Mark G. Hadfield**

**Abstract:** Numerical models can complement observations in investigations of marine sediment transport and depositional processes. A coupled hydrodynamic and sediment transport model was implemented for the Waipaoa River continental shelf offshore of the North Island of New Zealand, to complement a 13-month field campaign that collected seabed and hydrodynamic measurements. This paper described the formulations used within the model, and analyzed the sensitivity of sediment flux estimates to model nesting and seabed erodibility. Calculations were based on the Regional Ocean Modeling System—Community Sediment Transport Modeling System (ROMS-CSTMS), a primitive equation model using a finite difference solution to the equations for momentum and water mass conservation, and transport of salinity, temperature, and multiple classes of suspended sediment. The three-dimensional model resolved the complex bathymetry, bottom boundary layer, and river plume that impact sediment dispersal on this shelf, and accounted for processes including fluvial input, winds, waves, tides, and sediment resuspension. Nesting within a larger-scale, lower resolution hydrodynamic model stabilized model behavior during river floods and allowed large-scale shelf currents to impact sediment dispersal. To better represent observations showing that sediment erodibility decreased away from the river mouth, the seabed erosion rate parameter was reduced with water depth. This allowed the model to account for the observed spatial pattern of erodibility, though the model held the critical shear stress for erosion constant. Although the model neglected consolidation and swelling processes, use of a spatially-varying erodibility parameter significantly increased export of fluvial sediment from Poverty Bay to deeper areas of the shelf.

Reprinted from *J. Mar. Sci. Eng.* Cite as: Moriarty, J.M.; Harris, C.K.; Hadfield, M.G. A Hydrodynamic and Sediment Transport Model for the Waipaoa Shelf, New Zealand: Sensitivity of Fluxes to Spatially-Varying Erodibility and Model Nesting. *J. Mar. Sci. Eng.* **2014**, *2*, 336-369.

#### **1. Background**

#### *1.1. Sediment Transport Models*

Field experiments carry a high cost and are hampered by difficulties of observing water column sediment fluxes during energetic conditions such as floods and storms, except at discrete points served by deployed instruments. Numerical models based on the relevant processes for transport can be used to extrapolate point observations to continuous spatial scales, beyond the spatial and temporal coverage of field experiments. Here, we present a numerical model that complements a 13-month field campaign on the Waipaoa shelf, New Zealand.

Three-dimensional circulation and sediment transport models, such as the Community Sediment Transport Modeling System (CSTMS; [1]) resolve horizontal and vertical gradients, all of which can be important in the coastal ocean. The CSTMS has been implemented within the numerical hydrodynamic model ROMS (the Regional Ocean Modeling System; [2–5]). Although increased model complexity and resolution carries a heavier computational load, a three dimensional model was necessary to represent the complex bathymetry, bottom boundary layer processes, and river plume dynamics on the Waipaoa River continental shelf, New Zealand.

Many three-dimensional coastal sediment transport models have either neglected larger-scale currents or simplified them by using temporal and/or spatial averages to specify currents at the model's boundary, e.g., [6–10]. For example, a numerical model for Poverty Bay, the coastal portion of the Waipaoa Sedimentary System, which accounted for wind, wave, tidal, and river plume processes was developed by [6]. At the open boundaries, [6] accounted for tides and allowed disturbances to propagate through the boundary by using Chapman [11], Flather [12], radiation [13], and no-gradient boundary conditions for the free surface, two and three dimensional currents, and tracers, respectively. Recently, however, numerical models of continental shelf sediment transport have specified conditions along open boundaries based on estimates of coastal currents, temperature, and salinity from larger-scale, lower resolution models [14,15]. Like these examples, we build on previous efforts by nesting a finer-scale grid within a larger-scale hydrodynamic model, thereby accounting for larger-scale circulation patterns. For the event-driven Waipaoa shelf model, nesting not only allowed us to account for larger-scale currents, but was necessary to increase the stability of the model by reducing the reflection at the open boundary of sediment and freshwater from the river plume.

In many coastal environments, sediment fluxes are also affected by seabed erodibility, which can be defined as the amount of sediment available for entrainment into the water column at a given bed shear stress (see [16]). The treatment of erodibility is a distinguishing characteristic of cohesive and non-cohesive models (see [17,18]). For models of muddy cohesive seabeds, erosion typically depends on the seabed's critical shear stress, *IJcrit*, and an erosion rate parameter, *M*, which regulates the rate of sediment resuspension (e.g., [1,17]; see section 2.4). Observations show that both parameters may vary with seabed porosity, the depositional history of the seabed, biological processes and other factors, e.g., [19–21]. For instance, recently-deposited sediments were easier to erode than material from consolidated, older seabeds in the York River estuary [16]. Based on seabed erodibility experiments, a bed consolidation scheme in which critical shear stress varied in time, space, and with depth into the seabed, depending on depositional history of the seabed, has been developed and implemented within numerical models [18,22]. Here, we developed a simpler parameterization that modified the erosion rate parameter to account for spatial variations in erodibility, based on seabed microcosm erodibility experiments (see section 3.6).

#### *1.2. Study Site: Waipaoa River Continental Shelf, New Zealand*

Located on an active tectonic margin and draining a small mountainous catchment, the Waipaoa River delivers material to the ocean primarily during floods [23,24]. The Waipaoa exports about 15 million tons of sediment annually, primarily through either gullying or landsliding, depending on riverine conditions [24]. This material is primarily mud, with a median grain diameter of 8.5 ȝm during flood conditions, and approximately 1% of the load is sandy bedload [23,25]. Because of the river's small catchment, rain storms induce flooding throughout the drainage basin, and delivery of sediment to the coastal zone typically coincides with energetic oceanic conditions [23].

Riverine sediments are delivered to Poverty Bay, an about 50 km2 embayment that opens onto the continental shelf through a 10-km wide mouth (see Figure 1A). A counter-clockwise gyre driven by river discharge and the Coriolis force typically dominates currents in Poverty Bay [26–28]. On the shelf, water velocities during January 2010–February 2011 were primarily along-shore, but switched direction often, with an average current of 1.6 cm s<sup>í</sup><sup>1</sup> to the NE and a mean speed of 26.3 cm s<sup>í</sup><sup>1</sup> (data obtained from Hale, R. and Ogston, A., University of Washington (UW) [29]; tripod set-up described in [30]). Local winds, as well as larger-scale wind driven currents, southward travelling eddies, and coastally trapped waves likely drive water velocities [26,31–33]. Surface wind and swell waves on the shelf have average periods of 9–10 seconds and significant wave heights of 0.8–0.9 m, although longer-period waves can reach the shelf from the Southern Ocean [28,34]. Wave-induced motion dominated bed shear stress calculations by an order of magnitude compared to current-induced stress [30,35]. During 2010 at a tripod deployed in 50 m of water near the Southern depocenter, bed stresses exceeded 0.15 Pa, a threshold for fine-sediment resuspension, for 46% of the deployment period (data from [30]).

Over decadal and Holocene timescales, sediment accumulation on the shelf has occurred in two bathymetric lows to either side of Poverty Bay, but deposition is more variable over day- to month-long periods. Tripod observations and model estimates indicated that material is temporarily deposited in Poverty Bay following floods, and then, in the subsequent days to weeks, waves resuspend sediment and currents carry it to the shelf [6,28,35]. Observations of <sup>7</sup> Be activities also indicate that deposition over month-long timescales varies, depending on weather conditions [36,37]. For instance, <sup>7</sup> Be inventories from successive research cruises indicated that both erosion and deposition of terrestrial sediments occurred over different parts of the shelf during the January 2010 flood [37]. Over longer timescales, seismic profiles and 210Pb radioisotopes (22.3 year half life) indicated two depocenters with maximum accumulation rates of ~1 cm year<sup>í</sup><sup>1</sup> occur located in bathymetric lows to either side of Poverty Bay, bordered by the coast and offshore anticlines (Figure 1; [38,39]).
