*4.2. Model Nesting*

Comparing behavior of the standard model to ones that used less rigid relaxation timescales showed that model nesting helped account for larger-scale currents, improved current velocity skill, and increased stability. Evaluations of model performance for this study considered water velocities because currents are important for sediment fluxes. A. Ogston and R. Hale, UW, provided time series of acoustic Doppler current profiler (ADCP) data from three locations ([29]; see [30], Figures 1 and 7). Overall, stronger nudging to regional circulation did not significantly affect the mean current speeds (Table 5, Figure 7). At the 40 m tripod, time- and depth-averaged current speeds and associated standard deviations for 15 January 2010–20 March 2010 were 10.4 ± 6.3 cm s<sup>í</sup><sup>1</sup> , 10.3 ± 8.3 cm s<sup>í</sup><sup>1</sup> and 9.3 ± 7.7 cm s<sup>í</sup><sup>1</sup> in the standard, moderately-nudged and weakly-nudged cases, respectively. However, stronger nudging near the open boundaries increased the frequency with which along-shore currents switched direction, better matching observations (Figure 7). At the 50 m tripod in Poverty Gap, correlation coefficients between model estimates and observed depth-averaged along-shore velocities increased from 0.21 to 0.42 to 0.47 as the intensity of nesting increased from the weakly-nudged to moderately-nudged to the standard implementation (Table 5).

Model nesting also stabilized currents in areas near the open boundaries, reducing the reflection of the river plume at the grid's edge. Without nudging, the model failed within a couple of days because of excessively high water velocities (over 2 m s<sup>í</sup><sup>1</sup> ) at the boundaries near Mahia peninsula and the northeast coast as the river plume reflected off of the open boundaries creating a gyre within the domain. As expected, stronger nudging limited both the formation of the gyre and reflection at the open boundaries. To evaluate model behavior, the flux of freshwater through the open boundaries was estimated as:

$$S\_{obs} = \iint \hat{\boldsymbol{\mu}} \bullet \hat{\boldsymbol{n}} \, \max \{ \mathbf{0}, \left( \mathbf{S}\_0 - \mathbf{S} \{ \mathbf{S}\_0 \} \right) \, \text{d\tau} \, \, d\mathbf{z} \tag{8}$$

where was the velocity perpendicular to an open boundary, *S* was salinity, and *S0* was the background salinity of 35.1 psu. During the January 2010 river flood (28 January–15 February 2010), the cumulative freshwater flux through the open boundaries increased from 0.12 × 106 m3 to 0.23 × 106 m3 to 1.12 × 10<sup>6</sup> m3 when the nudging relaxation timescales, *TR,i* and *TR0*, decreased from 25 days to 5 days to 2.5 days. These fluxes of water were equivalent to about 1%, 2%, and 11% of the freshwater discharge into the grid. Note that the nudging of tracers from cells near the open boundary but within the grid (Equation (5)) removed freshwater from the grid, removing more freshwater for shorter relaxation timescales. Therefore, the estimates of freshwater flux through the boundaries represent low estimates which removed approximately double the volume of freshwater from the standard model compared to the weakly-nudged simulation. <sup>x</sup> *nu* <sup>ˆ</sup> <sup>U</sup>

Mean current velocities were sensitive to the strength of nudging. During the first tripod deployment, for instance, mean currents in Poverty Gap at 40 m water depth changed from 2.1 to 3.4 to 4.1 cm s<sup>í</sup><sup>1</sup> , and the direction of mean water velocity changed from 104 to 72 to 54 degrees counter clockwise from east for the weakly-nudged, moderately-nudged and standard simulations. Current direction fluctuated frequently, however, so sediment dispersal remained relatively consistent among the different model runs, especially over timescales of months.

Therefore, the partitioning of sediment among different areas of the system (e.g., Poverty Bay *vs.* the rest of the shelf *vs.* off the proximal shelf) was relatively insensitive to the nesting scheme. Over the nine months of the model run, from 15 January to 25 August 2010, there was a 6% decrease in the sediment escaping the proximal shelf, a 6% decrease in sediment on the shelf, and a 13% increase in sediment in the bay for the weakly-nudged test case compared to the standard simulation. Similarly, a numerical modeling study [15] found that nesting increased sediment export from the Mekong delta front by <5%.

#### *4.3. Sediment Erodibility*

Choice of seabed erosion rate parameter (*M* in Equation (4)) influenced the amount of, and location of deposition on the shelf. In general, estimates of resuspension and sediment export from Poverty Bay to the shelf increased with the erosion rate parameter (Figure 12). Sediment fluxes in shallow areas were particularly sensitive to the choice of *M* due to increased sediment resuspension where bed stresses were high. Dispersal of slow settling material that remained suspended for relatively long times was also sensitive to *M*. In contrast, dispersal of sediment settling at 1.0 mm s<sup>í</sup><sup>1</sup> was relatively insensitive to *M*; differences in estimated sediment budgets were within 2% of each other for the cases of low, to spatially-variable, to high erosion rate parameters. For sediment settling at 0.15 mm s<sup>í</sup><sup>1</sup> , however, sediment export from Poverty Bay between 15 January and 7 August 2010 increased from 26% to 44% to 50% for the three cases. Despite the increased influx of sediment onto the shelf during the high *M* test case, however, less sediment was retained on the shelf because the high erosion rate parameter encouraged resuspension and resulted in more sediment export from the shelf compared to the standard model (Figure 14). For the low, spatially-varying, and high *M* test cases, 7%, 14%, and 9% of sediment settling at 0.15 mm s<sup>í</sup><sup>1</sup> remained on the shelf, excluding Poverty Bay. Overall, spatially-varying erodibility increased deposition on the shelf relative to Poverty Bay, consistent with radioisotope-derived estimates of deposition on month long timescales [36]. Results from the standard model were most consistent with studies indicating that about a quarter of riverine material has remained on the shelf over decadal to century–long timescales [38].

**Figure 14.** Sediment Budget. (**a**) Time series of cumulative sediment input, mass of sediment in Poverty Bay (B in (**b**)), and mass of sediment on the shelf (S in (**b**)). Colors indicate sensitivity test. Line style indicates area of model grid included in calculations, as shown in (**b**). "Shelf" includes all areas up to 150 m water depth where no model nudging occurred, excluding Poverty Bay. Model grid boundaries were indicated by dashed line. Bathymetric contours were drawn every 50 m up to 150 m depth.

Use of other seabed parameterizations for erodibility that account for bed consolidation and variations in critical shear stress, e.g., [18,22], could further increase sediment export from Poverty Bay following floods, and further strengthen the spatial trend of decreased seabed level variability in deeper areas of the shelf. For instance, some models account for the dependence of seabed erodibility of muds on depositional history such that the seabed's critical shear stress increase and decrease following erosional and depositional time periods, respectively [22]. Utilizing this type of seabed scheme would likely create areas of low critical stress in depositional areas following floods, such as Poverty Bay, enhancing sediment export in the days following high discharge

events. However, this erodibility parameterization requires additional information about observed seabed critical stress profiles, is more computationally expensive, and has not yet been used for many realistically implemented sediment models (e.g., [83]).

#### *4.4. Computational Concerns*

Many decisions in the implementation of this three-dimensional numerical model required tradeoffs between desired accuracy and spatial resolution, and computational limits. The model had a total of 118 × 287 horizontal grid cells, each with 20 vertical water column layers and 8 vertical sediment bed layers. A total of nine tracer variables were included (salinity, temperature, and seven sediment classes), in addition to the momentum state variables. To provide estimates that overlapped with the Poverty Shelf field experiment, the modeled time period needed to span 13 months, from January 2010–February 2011, and provide estimates of state variables, including velocities, tracer concentrations, and sediment bed characteristics, every three hours for each grid point. ROMS has been parallelized using MPI (Message Passing Interface), which allowed us to run the model on VIMS' High Performance Computing (HPC) cluster using 48 nodes. The full 13-month model run required 9 days to run to completion. Some choices of model implementation significantly slowed the computations, including the MPData algorithm for horizontal advection of tracers, and the nudging of currents and tracers near the open boundaries. These components of the model were, however, important for model stability.

#### **5. Summary**

This project built on previous efforts by using a nested hydrodynamic–sediment transport model with spatially-variable erodibility to examine sediment fluxes on the Waipaoa Shelf. A three-dimensional sediment transport model accounting for a river plume, winds, waves, largerscale currents, and tides was developed and implemented for the Waipaoa Shelf, New Zealand. These processes were represented using the ROMS-CSTMS framework in conjunction with locally-validated observed and modeled datasets described above. By varying horizontal and vertical resolution in the model, we focused on the area of interest and boundary layer processes while maintaining sufficient model efficiency. Sensitivity tests indicated that nesting helped to stabilize currents near the open boundaries, reducing the reflection of the river plume there, but variations in nudging did not notably affect sediment budgets for this implementation of the model. In contrast, a spatially-variable erosion rate parameter was needed to increase the export of material from Poverty Bay and retention of material on the shelf.

## **Acknowledgments**

Funding was provided by NSF MARGINS grant 0841092 (Moriarty and Harris), a VIMS student fellowship (Moriarty), and NIWA as part of its government-funded, core research (Hadfield). Many datasets were useful during development and testing of the model, and these were provided by personnel from NIWA (M. Uddstrom, S. Stephens, A. Orpin), VIMS (S. Kuehl, T. Kniskern), the USACoE (J. McNinch), GDC (G. Hall, D. Peacock), East Carolina University (J.P. Walsh, R. Corbett, J. Kiker), and UW (A. Ogston, R. Hale). Thank you to persons who provided technical assistance, including A. Bever (now at Delta Modeling Associates), A. Miller, M.A. Bynum, and D. Weiss (all from VIMS/William & Mary). Computational facilities at VIMS, the SciClone cluster at the College of William & Mary, and the CSDMS computing cluster at the University of Colorado were supported by the NSF, VA Port Authority, Sun Microsystems, and Virginia's Commonwealth Technology Research Fund. High-performance computing facilities at NIWA were supported by the NZ eScience Infrastructure (NESI) and funded by NESI's collaborator institutions and through the Ministry of Business, Innovation & Employment's Research Infrastructure programme. Comments from 3 anonymous reviewers, C. Friedrichs, S. Kuehl, and L. Schaffner (all at VIMS) benefitted the manuscript's development. This paper is Contribution No. 3356 of the Virginia Institute of Marine Science, College of William & Mary.

#### **Author Contributions**

The authors collaborated closely on this work. J.M. Moriarty did the bulk of the development and analysis of the model as part of her M.S. thesis research, and wrote the manuscript. C.K. Harris designed the model experiments, served as co-PI on the project, edited the manuscript, and supervised Moriarty's M.S. program. M.G. Hadfield provided guidance in model development and data analysis, especially for the open boundary conditions and NIWA data products. He also edited the manuscript.

#### **Conflicts of Interest**

The authors declare no conflict of interest.

#### **References**

