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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 13month 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 (ROMSCSTMS), 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 threedimensional 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 largerscale, lower resolution hydrodynamic model stabilized model behavior during river floods and allowed largescale 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 spatiallyvarying erodibility parameter significantly increased export of fluvial sediment from Poverty Bay to deeper areas of the shelf.
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 13month field campaign on the Waipaoa shelf, New Zealand.
Threedimensional circulation and sediment transport models, such as the Community Sediment Transport Modeling System (CSTMS; [
Many threedimensional coastal sediment transport models have either neglected largerscale currents or simplified them by using temporal and/or spatial averages to specify currents at the model’s boundary, e.g., [
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 [
Located on an active tectonic margin and draining a small mountainous catchment, the Waipaoa River delivers material to the ocean primarily during floods [
Riverine sediments are delivered to Poverty Bay, an about 50 km^{2} embayment that opens onto the continental shelf through a 10km wide mouth (see
Study site on North Island, New Zealand. (
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 monthlong 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 [
Though both seabed and water column data have been collected for the Waipaoa River continental shelf, knowledge of sediment transport mechanisms is benefited by development of a three dimensional hydrodynamicsediment transport numerical model providing spatial coverage unattained by observational efforts. This paper describes the implementation of the ROMSCSTMS numerical model for the Waipaoa continental shelf and examines the sensitivity of sediment flux estimates to model nesting and seabed erodibility parameterizations.
This section describes the equations and numerical schemes used to specify hydrodynamic and sediment transport processes within the model and at the boundaries of the grid.
ROMSCSTMS, a communitydeveloped numerical circulation and sediment transport model, solves the equations for Reynoldsaveraged NavierStokes, tracer advectiondiffusion, and continuity using the hydrostatic and Boussinesq assumptions as described in [
Model parameters as described in this paper.
Parameter  Meaning  Unit 

C_{s,1,}_{ised}  Suspended concentration of sediment class

kg m^{−2} 
c_{x}, c_{y}  Phase speeds for oblique radiation boundary condition  m s^{−1} 
D_{50}  Median grain diameter  M 
E_{ised}  Erosion for sediment class

kg m^{−2} s^{−1} 
F_{cs,ised}  Source of sediment class

kg m^{−2} s^{−1} 
F_{grid}  Parameter specifying spatiallyvariable nudging at open boundaries  nondimensional 
F_{OBC}  Parameter specifying changes to nudging at open boundaries based on current direction  nondimensional 
h  Water depth  m 
h_{transition}  Transitional water depth for erosion rate parameter parameterization  m 
I  Number of grid cells in NWSE direction  nondimensional 
i  Index for model grid in NWSE direction  nondimensional 
ised  Index for modeled sediment classes  nondimensional 
J  Number of grid cells in SWNE direction  nondimensional 
j  Index for model grid in SWNE direction  nondimensional 
k_{1}, k_{2}  Coefficients for active layer formulation  m^{2} s^{2} kg^{−1}; nondimensional 
M  Erosion rate parameter  kg m^{−2} s^{−1} 
M_{min}  Minimum erosion rate parameter  kg m^{−2} s^{−1} 
M_{max}  Maximum erosion rate parameter  kg m^{−2} s^{−1} 
Unit vector perpendicular to open boundary  
p  Seabed porosity  nondimensional 
S  Salinity  psu 
S_{0}  Background salinity  psu 
S_{0BC}  Flux of freshwater through the open boundaries  m^{3} 
T_{R,b}  Relaxation timescale for nudging at open boundaries  s 
T_{R,i}  Relaxation timescale for nudging within model interior  s 
T_{RO}  Relaxation constant for nudging at open boundaries  nondimensional 
t  Time  s 
Current velocity  m s^{−1}  
w_{s,ised}  Settling velocity for sediment class 
m s^{−1} 
x, y  Horizontal coordinates  nondimensional 
z  Vertical coordinate in water column  nondimensional 
z_{a}  Thickness of seabed active layer  m 
z_{s}  Vertical coordinate in seabed  m 
ζ  Variable of interest in boundary condition equations  Same units as velocity, temperature, salinity, or sediment concentrations 
ζ′  Variable of interest in boundary condition equations before nudging  Same as above 
ζ_{obc}  Prescribed value for variable of interest in open boundary condition equations  Same as above 
Maximum wavecurrent induced bed shear stress over a wave period  Pa  
Magnitude of maximum wavecurrent induced bed shear stress over a wave period  Pa  
τ_{crit}  Critical shear stress for the seabed  Pa 
ROMS distinguishes itself from other community hydrodynamic models by its model grid, and timestepping and advective schemes. It uses a curvilinear orthogonal grid in the horizontal and a stretched, terrainfollowing grid in the vertical which allows it to carry high resolution in both the surface and bottom boundary layers [
Numerical Schemes for Waipaoa Shelf model.
Process  Numerical Scheme 

Advection of momentum (Vertical, 3D)  4th order, centered 
Advection of momentum (Horizontal, 3D)  3rd order, upstream 
Advection of tracers  MPData 
Vertical Sediment Settling  PPM 
The surface boundary formulation in ROMS was adopted from the physicallybased COARE (Coupled Ocean Atmosphere Response Experiment) framework [
This implementation of ROMS used the Sherwood, Signell and Warner [
As summarized in
Erosion was calculated following the Ariathurai and Arulanandan formulation [
As indicated in Equation (1), the model assumed continuous deposition so that
Consistent with observations of erodibility on the Waipaoa shelf, the model formulation was modified to encourage erosion of sediment from shallow areas by varying the erosion rate parameter,
Shows (
Sediment bed properties such as grain size distribution were stored for eight seabed layers that each initially represented 20 cm of sediment. Erosion and deposition of multiple sediment classes modified the thickness of seabed layers and the grain size distributions stored for the sediment bed, as described in [
The Waipaoa shelf model grid was bounded by land on the northwestern side (
Similar to other studies [
Nudging, evaluated within grid interior:
NudgingRadiation OBC, evaluated at model boundary:
Observed and modeled datasets used to initialize and force the model are listed in
Designed to include the river mouth, Poverty Bay, and the proximal continental shelf, the model grid (
The model grid had a horizontal resolution of about 450 m on the midshelf and was curved to reduce the number of terrestrial grid cells and to approximately parallel bathymetry (
Four datasets that each had a different focus provided the basis for the model’s bathymetry. Multibeam was used to map Poverty Bay in 2005 and 2006 by J. McNinch (now at USACoE; see [
Datasets used for model initialization and forcing.
Type of Data  Data Description and Source 

Bathymetry to construct model grid  Multibeam surveys [ Bathymetric contours provided by S. Stephens (NIWA) [ Historical gridded bathymetry [ Modeled bathymetry of New Zealand ROMS model (ROMSNZ) 
Currents, temperature and salinity at open boundaries, and for model initialization  Baroclinic version of ROMSNZ ([ 
Wave height, direction, and period  NIWA’s New Zealand Wave (NZWAVE) model (NZWAVE, an implementation of NOAA’s Wave Watch III model; [ 
Wind stress  NIWA’s New Zealand Limited Area Model (NZLAM, an implementation of the UK Met Office’s Unified Model; [ 
Tidal components: open boundary sea surface height and tidal velocities  Tidal velocities, amplitudes and phase components from the Oregon State Tidal Prediction Software TPX07.1 global solution (OTPS; [ 
Meteorological data  Air pressure, cloud cover, precipitation, relative humidity, shortwave radiation, air temperature from NIWA’s National Climate Database web system [ 
River discharge of freshwater and sediment  River gauge measurements provided by G. Hall and D. Peacock (Gisborne District Council, New Zealand) [ 
Sediment properties of fluvial and seabed material (diameter, settling velocity, critical stress for erosion, erosion rate parameter)  River observations [ Observed seabed properties [ ADV and OBS data [ Gust microcosm erodibility experimental data [ 
Seabed characteristics for comparison to model estimates  Radiometric and Xray analysis of cores [ 
Comparisons revealed systematic offsets between the bathymetric datasets. In areas that overlapped (see
Coverage of bathymetric datasets near Poverty Bay mouth. Datasets are labeled by source (see
After gridding, the model bathymetry was smoothed with a Shapiro (1975) filter to improve model stability [
Time series of observed and estimated weather conditions on Waipaoa Shelf. (
Modeled data were used as input to account for spatial and temporal variability in the wind and wave fields. Estimates from NZLAM and NZWAVE (described below;
A local implementation of NOAA’s Wave Watch 3 model [
Both model estimates and observed datasets provided atmospheric input. NZLAM, an implementation of the UK Meteorological (Met) Office’s Unified Model [
Waipaoa River water and sediment discharges were represented as a pointsource entering Poverty Bay at a grid cell located at the river mouth. Observations of river stage were collected hourly at Kanakania Bridge, ~80 km upriver, above tidal influences, by G. Hall and D. Peacock at the Gisborne District Council (GDC) [
Vertical profile of river input showing the partitioning of momentum, fresh water, and river sediment at the river mouth.
Tidal velocities, amplitudes and phase components extracted from the Oregon State Tidal Prediction Software (OTPS) TPX07.1 global solution [
Current velocities, temperature and salinity at and near open boundaries of the Waipaoa grid were nudged toward values from ROMSNZ, a largerscale baroclinic model adapted for northern New Zealand ([
Threedimensional, time dependent current velocities, temperature and salinity estimates from ROMSNZ were linearly interpolated to the Waipaoa shelf grid and used for model initialization and nudging at model boundaries. ROMSNZ estimates were unavailable for some grid cells near the coast in the interior of the grid where the landocean masking differed between the two models. At these sites, current velocities were initialized to zero, and initial temperature and salinity estimates were set equal to values from adjacent grid cells. Since landocean masking was identical between model grids near the open boundaries, these approximations only affected model initialization and not nudging near the open boundaries (see
Model calculations included a total of seven sediment types and eight seabed layers (
Estimates of effective settling velocity based on tripod measurements from the field site (obtained from A. Ogston and R. Hale, UW [
Sediment classes and their characteristics
Sediment Class  Source  % of Riverine Load  Settling Velocity (mm s^{−1})  D_{50}(μm) 

1  Seabed  −  0.1  63 
2  Seabed  −  0.5  500 
3  Seabed  −  125.0  1000 
4  River  53  0.15  16 
5  River  27  0.3  22 
6  River  13  0.5  30 
7  River  7  1.0  40 
For all sediment classes: Critical Shear Stress: 0.15 Pa; Sediment Density: 2650 kg m^{−3}; Porosity: 0.6.
Initial distribution of seabed sediment classes showing fraction of (
Four classes were used to represent sediment delivered fluvially. Their properties were informed by observations that estimated a median grain diameter of 8.5 μm in the Waipaoa River during floods [
Parameters related to erodibility (critical shear stress, erosion rate parameter) were informed by ADV and OBS (Optical Backscatter Sensor) measurements from the first two months of the tripod deployment (data from [
The Waipaoa shelf model described above, called the “standard model”, was implemented for 15 January 2010–27 August 2010.
Results for the standard model are evaluated, and then the sensitivity of estimates to model nesting and seabed erodibility parameterization is discussed.
Time series of tidally and depthaveraged water velocities from the Poverty Gap tripod in 40 m water depth. Observations (grey) and model estimates, including the standard model (thick red line), moderatelynudged (maroon), and weaklynudged sensitivity tests (black).
Both the modeled and observed currents varied spatially and frequently reversed direction (
Map of estimated timeaveraged depthaveraged current speed (shading; m s^{−1}) and direction (black arrows). Long white arrows with blue outlines indicate observed current direction for tripod deployments. Black bathymetric contours indicate every 10 m.
Model estimates of waves, bed shear stresses, and sediment concentrations also captured the timing of observed episodic events (see [
Model evaluation statistics calculated (
( 

Wave Orbital Velocity  0.63–0.85  0.84–1.35  −6.4–1.4 cm/s  
Bed Shear Stress  0.60–0.82  0.72–1.79  −0.20–0.02 Pa  
DepthAveraged Currents (AlongShelf)  0.33–0.79  0.59–0.93  −4.7–10.4 cm/s  
DepthAveraged Currents (AcrossShelf)  0.01–0.24  0.34–1.52  −2.1–7.0 cm/s  
Suspended Sediment Concentrations  0.27–0.52  0.03–0.28  −0.22–0.01 g/L  
( 

DepthAveraged Currents 
Standard  0.33–0.45  0.59–0.74  8.0–10.4 cm/s 
Moderate Nudging  0.40–0.41  0.47–0.79  1.2–10.0 cm/s  
Weak Nudging  0.14–0.23  0.65–0.84  −1.0–13.6 cm/s  
DepthAveraged Currents 
Standard  0.01–0.12  0.35–1.23  −0.8–0.65 cm/s 
Moderate Nudging  0.02–0.07  0.44–1.25  −0.64–1.0 cm/s  
Weak Nudging  0.09–0.30  0.59–1.11  −4.7–1.7 cm/s 
^{1} Correlation Coefficient; ^{2} Ratio of the standard deviation of the model estimates to that of the observations; ^{3} Difference between the mean of the model estimates and mean of the observations.
Erodibility in the model was evaluated by comparing estimates of seabed level variability to observations of eroded mass from Gust microcosm experiments (observations provided by [
Modeled seabed level variability. Shading indicates log_{10} of the modeled seabed level variability, equal to the standard deviation of seabed thickness (cm) for each grid cell.
Patterns of erosion and deposition estimated by the model have been evaluated using seabed observations of ^{7}Be inventories that indicate recent deposition of terrestrially derived material ([
Observations of eroded mass from [
Comparison of seabed level variability to observations of eroded mass from [
Deposition per percent of riverine load following the March wave event for standard, moderatelynudged, low
Overall, sediment fluxes were likely underestimated, but patterns of transport and deposition were consistent with observations. For instance, episodic and energetic waves dominated bed shear stress calculations and determined the timing of seabed resuspension, as seen in observations and other modeling studies (see above,
Observed ^{7}Be inventories from (
Comparing behavior of the standard model to ones that used less rigid relaxation timescales showed that model nesting helped account for largerscale 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 ([
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^{−1}) 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:
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^{−1}, and the direction of mean water velocity changed from 104 to 72 to 54 degrees counter clockwise from east for the weaklynudged, moderatelynudged 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
Choice of seabed erosion rate parameter (
Sediment Budget. (
Use of other seabed parameterizations for erodibility that account for bed consolidation and variations in critical shear stress, e.g., [
Many decisions in the implementation of this threedimensional 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 13month 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.
This project built on previous efforts by using a nested hydrodynamic–sediment transport model with spatiallyvariable erodibility to examine sediment fluxes on the Waipaoa Shelf. A threedimensional 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 ROMSCSTMS framework in conjunction with locallyvalidated 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 spatiallyvariable erosion rate parameter was needed to increase the export of material from Poverty Bay and retention of material on the shelf.
Funding was provided by NSF MARGINS grant 0841092 (Moriarty and Harris), a VIMS student fellowship (Moriarty), and NIWA as part of its governmentfunded, 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. Highperformance 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.
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 coPI 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.
The authors declare no conflict of interest.