Applying dynamically updated nearshore bathymetry estimates to operational nearshore wave modeling

Accepted Manuscript Applying Dynamically Updated Nearshore Bathymetry Estimates to Operational Nearshore Wave Modeling

Spicer Bak, Katherine L. Brodie, Tyler Hesser, Jane M. Smith PII:

S0378-3839(18)30297-7

DOI:

10.1016/j.coastaleng.2018.12.005

Reference:

CENG 3451

To appear in:

Coastal Engineering

Received Date:

25 June 2018

Accepted Date:

15 December 2018

Please cite this article as: Spicer Bak, Katherine L. Brodie, Tyler Hesser, Jane M. Smith, Applying Dynamically Updated Nearshore Bathymetry Estimates to Operational Nearshore Wave Modeling, Coastal Engineering (2018), doi: 10.1016/j.coastaleng.2018.12.005

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Applying Dynamically Updated Nearshore Bathymetry Estimates to Operational Nearshore Wave Modeling Spicer Bak1, Katherine L. Brodie1, Tyler Hesser2, Jane M. Smith2 1Coastal

and Hydraulics Laboratory, US Army Engineer Research and Development Center, 1261 Duck Rd, Duck, NC 27949 2Coastal

and Hydraulics Laboratory, US Army Engineer Research and Development Center, 3909 Halls Ferry Rd, Vicksburg, MS Corresponding author: [email protected] Abstract: Simulations of nearshore waves using the Steady-State Spectral Wave (STWAVE) Model with temporally-varying bathymetric boundary conditions were undertaken for a period of 11 months at the U.S. Army Corps of Engineers Field Research Facility in Duck, NC. Five sets of bathymetry were tested, two of which were derived from survey data (one evolving with each monthly bathymetric survey, one static) and three were derived from the depth inversion algorithm, cBathy, using Argus optical imagery data updated every half hour. The standard cBathy half-hourly Kalman filtered product was used along with two modified versions that filter depth estimates during large waves prior to being assimilated by the Kalman filter using an offshore wave height threshold or an optically derived wave breaking threshold to reduce bottom boundary condition errors. Bathymetry derived from the modified Kalman filter methods were first validated using continuous in-situ sonic altimeter data, and were found to improve RMSEs relative to the original cBathy bathymetry from an average of about 0.09 m and about 0.15 m offshore and onshore of the sandbar, respectively. Wave model results over the five bathymetric boundary conditions show that the thresholded cBathy bathymetry performs similarly (and slightly better in places) to simulations using an evolving bathymetry as new measurements are available. The wave height predictions using the static bathymetry were approximately equivalent in performance (if not, slightly better in places) to that of the original cBathy, while the evolving surveyed bathymetry had similar performance to the thresholded cBathy method. Keywords: Nearshore, surf zone, wave modeling, STWAVE, cBathy version 1.1, remote sensing, coastal model test bed, Argus, CIRN

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1 Introduction Nearshore wave conditions provide the basis to quantify many near-coast processes including loading on structures, radiation stresses (Longuet-Higgins and Stewart, 1964) that drive nearshore wave setup and circulation, and forcing for sediment transport (van Rijn et al., 2007). In order to properly manage coastal resources and protect local infrastructure and communities from waves and high water levels during large storms, researchers, engineers, and coastal planners require tools which can accurately quantify wave forcing close to shore, including past (hindcast, climatology), present (nowcast) or future (forecast) conditions. Continually run nearshore wave models (Anselmi-Molina et al., 2012) are becoming more common along the world’s coastlines and have been used for rip current prediction (Allard et al., 2008; Austin and Masselink, 2008) and surf forecasting, or combined with wave runup estimates (Fuhrman and Madsen, 2008; Stockdon et al., 2006) to predict ocean impacts on the coast (O’Reilly et al., 2016). Nearshore waves are often estimated through application of phase-averaged nearshore wave generation and transformation models. The bathymetric boundary condition used in nearshore models is of primary importance, and has been specifically cited as a key challenge in overall model accuracy for operational modeling (Allard et al., 2008; Austin et al., 2013). Bathymetric data are most commonly provided by hydrographic surveys. This type of surveying usually requires multiple people, significant time, and expensive equipment, and is particularly challenging within the region of breaking waves, necessitating either amphibious vehicles, waders, or coupled jet-ski/topo techniques (MacMahan, 2001). Unless conducted for specific field experiments, typical bathymetric surveys are either sparse in time (e.g., yearly) (Estep et al., n.d.; Farrell et al., 2012) and/or space (e.g., alongshore spacing of miles) (Farrell et al., 2012; Turner et al., 2016). As a result, regional and nearshore wave studies that utilize surveyed bathymetry can be out of date by years (Allard et al., 2008; Anselmi-Molina et al., 2012; Bryant and Jensen, 2017; van der Westhuysen et al., 2013). While nearshore and inner-shelf bathymetry may change infrequently (only during the largest storm events), surf zone bathymetry can evolve rapidly (e.g., hourly to daily) in response to changing wave conditions, making forecasting of wave heights close to shore challenging. Rip current forecasting, for example, is a particular nearshore modeling focus area that is highly sensitive to the accuracy of the bathymetry (Bruneau et al., 2011). To account for outdated bathymetry, some rip current modeling efforts have instead focused on probabilistic approaches which parameterize the likelihood of bathymetric change (and resultant rip current formation) from wave and tide forecasts (Dusek and Seim, 2013). Others have run an operational circulation model with measured bathymetry (Austin et al., 2013), but acknowledge the difficulty of operationally surveying. An alternate approach to hydrographic surveying is to use remote sensing techniques to derive bathymetry from observations of wave propagation (speed) in the surf zone (Holman et al., 2013). These techniques, though not a direct depth measurement, provide up-to-date bathymetry with high spatial and temporal resolution over km-scale alongshore extents with less expense than traditional vessel-based approaches, though often at the cost of accuracy (Brodie et al., 2018; Holman et al., 2013). For example, optical imagery can be continuously collected from fixed towers (Holman and Stanley, 2007), such as the Argus station at the US Army Corps of Engineers Field Research Facility (FRF), or at intervals from unmanned aerial systems (UAS) (Holman et al., 2011). Remotely sensed data can be used to directly calculate bottom boundary conditions or used in data assimilation algorithms (van Dongeren et al., 2008) and in combination with in-situ gauges (Wilson et al., 2014) to improve bathymetry estimates. Recent work has suggested that using remotely sensed bathymetry to frequently update bathymetry in circulation models can improve results (Holman et al., 2014; Radermacher et al., 2018, 2014; van Dongeren et al., 2008), however this has not been done operationally. 2

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The purpose of this paper is to utilize surveyed and remotely-sensed bathymetry to evaluate which bathymetric boundary conditions produce the lowest nearshore wave height residual when running a nearshore transformation model for a range of environmental conditions over 11 months. Five sets of bathymetry were tested: two were derived from survey data (one evolving with each measured bathymetric survey, approximately monthly, and one static) and three were derived from the depth inversion algorithm, cBathy (Holman et al., 2013), using Argus optical imagery data (updated every half hour). Remotely sensed bathymetry was estimated from optical imagery using the original cBathy algorithm as well as two modified versions designed to maximize characterization of true bathymetric evolution while minimizing errors in the remotely-sensed bathymetry during large breaking waves (Brodie et al., 2018). Simulated wave height errors are quantified using in-situ gauges from a cross-shore array of wave measurements from near the shoreline to 8-m water depth. These error estimates are used to investigate whether the increased temporal resolution of remotely-sensed bathymetry as a bottom boundary condition improves nearshore wave height estimates when compared to a more traditional method using a static or monthly bathymetric surveys. This paper is organized as follows: Section 2 summarizes previous work related to cBathy; Section 3 describes the observations and the cBathy algorithm used in this study; Section 4 describes the wave simulation setup and test cases used in this study; Section 5 first presents the results of the modified cBathy estimates and then follows with the wave modeling results; and finally, Sections 6 and 7 provide a discussion and conclusions.

2 Previous work The cBathy algorithm (Holman et al., 2013) applied to continuously collected optical imagery (Holman and Stanley, 2007) provides spatial bathymetry estimates every half hour during daylight hours. This capability potentially captures morphologic change between bathymetric surveys and provides data in places where a bathymetric survey is not possible. The algorithm calculates incident wave speeds from the video imagery and inverts those wave speeds to bathymetry estimates in the nearshore using the linear dispersion relationship. Robustness is added to the algorithm by running the bathymetry estimates in a point-wise temporal Kalman filter providing answers in rain, clouds, and even when a camera goes down for a short period of time. However, estimates of bathymetry from video-based cBathy may be inaccurate when waves break, especially during storms (Brodie et al., 2018), when wave height predictions are critical. Recent work (Brodie et al., 2018) tabulated all prior evaluations of cBathy (0.51 m < root mean square errors (RMSE) < 2.05 m), and extended an evaluation of video-based cBathy to a wide-range of wave conditions (0.3 < significant wave height, Hs < 4.3 m) through comparison to in-situ sonic altimeters at the FRF. During small waves (0.5 < Hs < 1.2 m), Brodie et al. found the Kalman filtered cBathy depth estimates explained 83% of the variance observed in the seafloor elevation changes (offshore of the sand bar) over a 1-year period. However, during large wave events (offshore Hs/zbottom > 0.42) the unfiltered cBathy depth estimates had significant absolute biases (-3 < Zbias < -0.5 m) and RMSEs (1 < RMSE < 3 m). The Kalman filter reduces some of these errors (RMSE < 1.5 m and Zbias < 0.5 m in the same conditions), but during long duration storms, the Kalman filter became inundated with poor estimates, and in turn allowed some of the known poor estimates to influence the filtered results. In addition to some of the depths being overestimated during large wave events, video-based cBathy biased the position of the sandbar shoreward, by between 17 and 40 m, in wave heights above 1.2 m. These breakdowns of bathymetry estimates are attributed to two factors. The first is related to the assumption of linear waves in the surf zone. Wave breaking is a highly nonlinear process (Freilich et al., 3

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1990; Holthuijsen, 2007), and it has been shown in laboratory and field studies (Holland, 2001; Suhayda and Pettigrew, 1977; Thornton and Guza, 1982; Tissier et al., 2011) that measured wave speeds during breaking are larger than those predicted by linear theory. This 20-40% increase in wave speeds could lead to over estimates of depth by the cBathy algorithm, which uses the linear dispersion relationship. The second is related specifically to using the cBathy algorithm on optical imagery data. In imagery data (as viewed with the human eye from the shore), the approaching wave face is viewed as darker than the seaward side of the wave, but during wave breaking, the forward propagating wave face is viewed as lighter (foam) and the seaward side of the wave becomes dark. This transition creates an erroneous phase-shift in the optical imagery that leads to over/under estimates at the initiation and conclusion of wave breaking (Stockdon and Holman, 2000). Bathymetry derived from cBathy has previously been used as a boundary condition for modeling waves and currents. At a wave-dominated inlet in North Carolina, a one-dimensional wave model was run over the course of a 9-day period using radar-based cBathy bathymetry estimates for two transects approximately 1000 m in length. The accuracy of the methodology was evaluated by comparisons with in-situ wave observations showing a correlation between 0.68 and 0.96 and RMSE between 0.05 and 0.19 m (Díaz Méndez et al., 2015). cBathy wave number estimates from imagery and radar have also been tested in an assimilated ensemble Kalman Filter (EnKF) to improve rip current predictions at the FRF (Wilson et al., 2014). Nearshore currents were predicted using both measured bathymetry and cBathy bathymetry as a boundary condition using the Delft3D suite at the Sand Motor in the Netherlands. Results showed RMSE of 0.1 cm/s and 40 degrees in magnitude and direction, respectively, when compared to simulated currents on the measured bathymetry (Radermacher et al., 2014). The authors also noted a significant source of error near the shoreline where the water depth is overestimated. In followon work, errors in the remotely sensed cBathy estimates were quantified using scale-aware validation schemes after manually removing depth estimates outside of a 1.5 m envelope surrounding the nearest ground truth survey. Subsequently, simulations of nearshore hydrodynamics (Delft3D) were performed using both measured and the above cBathy estimates (Radermacher et al., 2018). Results showed that over half (55%) of the observed rip currents were generated using the cBathy boundary condition estimates while only 9% were false positives (generated using the cBathy bathymetry, but non-existent in simulations using measured bathymetry). The performance of the predictions using cBathy bathymetry was found be sensitive to the accuracy of the cBathy algorithm, specifically the pattern and amplitude of the nearshore sandbars between 200 m and 400m length scales (Radermacher et al., 2018).

3 Observations The FRF is a research facility operated by the U.S. Army Corps of Engineers and is located on the northern outer banks of North Carolina, USA. The 1-km alongshore property fronts the Atlantic Ocean, and a 560-m-long research pier extends to 6-m nominal water depth in the center of the property (515 m), shown in Figure 1. A local coordinate system is defined for the facility with the y-axis oriented alongshore (18.2º counter clockwise from true north) and the origin located at the southern edge of the property (36.1776º N and 75.7497º W).

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N

Figure 1. Parent and nested grid domains. The cross-shore wave gauge array is shown as black circles, and the red triangles indicate forcing points for the nested grid. The inner domain used when forcing from the 17 m Waverider is shown with the black line. The nested domain is shown in the bottom right with the survey profiles lines colored by depth.

3.1 Direct Bathymetry Measurements At the FRF, bathymetry data are traditionally collected along cross-shore transects from the dune toe to 8m water depth and spaced at approximately 50 m in the alongshore along a 1-km section of coastline centered on the FRF research pier. Surveys are conducted using RTK-GPS on the Coastal Research Amphibious Buggy (CRAB) (Birkemeier and Mason, 1984) or RTK-GPS coupled with an acoustic sensor mounted on the Lighter Amphibious Resupply Cargo (LARC) vehicle (Forte et al., 2017). The FRF monthly survey typically takes approximately 15 to 20 person-hours (using the LARC) to complete. 5

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Bathymetric surveys conducted with the CRAB and LARC are accurate to ±0.04 m (Forte et al., 2017). During the time period considered in this paper, 1 October 2015 to 1 September 2016, 15 surveys were available (vertical dashed lines, Figure 2a), with more frequent surveys in the month of October due to an ongoing experiment. To supplement the amphibious surveys, acoustic altimeters were used to provide near real-time bottom position measurements at three locations across the nearshore (cross-shore distances of 150, 200, and 300 m in the local coordinate system). These instruments estimate bottom position from backscatter intensity profiles. The documented error of the altimeters is on the order of 0.1 m (Gallagher et al., 1996; Moulton et al., 2014). The instruments are mounted to heavy, 0.05 m diameter, round pipes jetted ∼4.5 m into the seafloor. The position of the gauges was surveyed with RTK-GPS to within ±0.04 m NAVD 88. For more information about the acoustic altimeters and elevation changes observed during this time period, see (Brodie et al., 2018).

3.2 Wave Measurements In-situ instruments at the FRF continuously measure waves, winds, water levels, and currents. Waves are measured with Waverider buoys in depths of 26 and 17 m; with bottom mounted Acoustic Wave and Current profilers (AWAC) in 11, 8, 6, and 4.5 m depths; with an Acoustic Doppler Profiler (Aquadopp) in 3.5 m; and with four buried Paroscientific pressure gauges at nominal depths ranging from 0 – 3 m NAVD88 (Figure 2). The collection of gauges are referred to herein as the cross-shore array (Table 1) and are located approximately 400 m north of the FRF pier (Figure 2) and approximately 12 meters (in the alongshore direction) from the nearest bathymetry survey profile. For the purposes of discussion, gauges ar e referred to by a combination of nominal depth and gauge type (e.g., AWAC-6m) or the crossshore location for the inshore gauges where nominal depth changes frequently (e.g., xp200m). All times are in Coordinated Universal Time (UTC). Table 1. FRF cross-shore array of wave gauges. Gauge Type Waverider Waverider AWAC 8m-array

Nominal Depth, m 26 17 11 8

AWAC AWAC Aquadopp

6 4.5 3.5

Pressure – xp200 Pressure – xp150 Pressure – xp125

2.8 2.1 1.9

Measurement Type Directional wave Directional wave Directional wave and current Directional wave (Long and Oltman-Shay, 1991) Directional wave and current Directional wave and current Directional wave, current, and bottom elevation Point wave and bottom elevation Point wave and bottom elevation Point wave

FRF Cross-shore Coordinate, m 16,266 3,716 1,272 917

FRF Alongshore Coordinate, m 4,136 1,417 910 935

Sample Frequency, Hz 1.28 1.28 2 2

605 400 300

938 940 940

2 2 2

200 150 125

940 940 940

2 2 2

The directional Waveriders collected a 20-min record, while all bottom mounted wave gauges (sampling at 2 Hz) collected a 34-min record. The wave pressure and velocity time series were analyzed using Fourier methods and the spectra are surface corrected using linear wave theory (Long and Oltman-Shay, 1991). Since the bathymetry changes frequently close to shore where the pressure gauges were located, the two outer pressure gauges (xp200, xp150) were co-located with acoustic altimeters, and these data were used to calculate burial depth of the gauges to correct for attenuation due to burial (Raubenheimer et al., 1998). The two-dimensional wave spectra were estimated using the Iterative Maximum Likelihood method (IMLE) (Oltman-Shay and Guza, 1984). All bulk statistics were calculated from the two-

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dimensional wave energy spectra (both from the model and measurements), all of which use the moments of the spectra, where the “nth moment of the spectra” is defined as: ∞

mn =

∫ f E(f)df n

(1)

0

For n = …, -2, -1, 0, 1, 2...

where E(f) is the variance density spectrum and f is frequency. Wave height was calculated from the 0th moment of the frequency spectrum: Hm0 = 4 m0

(2)

where Hm0 is the significant wave height (referred to as Hs). The inverse of the frequency at the peak energy in E(f) is defined as the peak wave period, Tp.

3.3 Experimental Conditions The storm wave climate at the FRF is dominated by both tropical (hurricanes) and extratropical (Nor’easter) systems. Tropical systems usually progress from South to North with a counter-clockwise rotation and can produce both short-period wind sea and long-period swell with wave directions coming from the East to the Southeast (80 – 165 degrees clockwise from North). These storms tend to occur between June and November and move through the region quickly, generating large waves over short periods of time (1-3 days). In contrast, Nor’easters are dominated by short-period wind-sea and swell that originates from the Northeast. Nor’easters can stall offshore blowing strong winds and generating large waves that can persist for many days (5+ days). Nor’easters tend to occur between September and April, but are more prevalent in the winter months (January to March). Summer months are characterized by lower energy swell from the southeast. Wave conditions during the 11-month study October 2015 through September 2016 were fairly typical for the FRF (0.25 < Hs < 5.1 m; 4 < Tp < 18 s, Figure 2a). Between September 2015 and April 2016, several Nor'easters influenced the region generating large waves (Hs > 3 m). At the beginning of the study period, from 4 to 7 October, Hurricane Joaquin passed offshore of the FRF, generating medium period swell (Hs > 4m; 10 < Tp < 13s). From 8 – 26 October the wave conditions were a mix of smaller (Hs < 1 m) short- and long-period waves (4 < Tp < 13 s). The sandbar position along the cross-shore array transect, as identified in Argus time exposure imagery (described in Brodie et al., 2018), ranged from 142 and 286 m in the cross-shore during the 11-month evaluation (Figure 2C). At the start of the study, the sandbar was initially located near xp200. During the winter and spring (February – May) the sandbar migrated offshore to ~300 m (just inshore of the 3.5 m aquadopp), before moving back onshore to ~ 225 m (Figure 2C). The average position of the sandbar was 217 m in the cross-shore with a standard deviation of 27.9 m.

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Figure 2: A) Significant wave height and B) peak period are shown at the offshore boundary using the 26m waverider (blue) and were supplemented with the 17m waverider (cyan) during data gaps. C) peak elevation of the sandbar from (Brodie et al., 2018) is plotted in black over a greyscale time-stack of Argus (Holman and Stanley, 2007) time averaged pixel intensity co-located to the cross-shore array over the duration of the study. The cross-shore location of the three altimeters is also plotted over the duration of the study

3.4 cBathy Algorithm Video-derived bathymetry estimates were calculated using the cBathy algorithm (Holman et al., 2013) (https://github.com/Coastal-Imaging-Research-Network/cBathy-Toolbox, Version 1.1) from half-hourly daylight time series of pixel intensities collected from an Argus coastal monitoring station (Holman and Stanley, 2007) on the FRF property. The Argus station is located at the top of a 43-m-tall tower located approximately 65 m north of the pier and 30 m behind the dune and consists of six 5 Mega Pixel Point Grey Flea3 Cameras. Pixel time series (2-Hz sample rate for 17 min every half hour) were saved every 5 and 10 m in the cross- and alongshore directions, respectively, extending from 0 to 500 m in the cross shore and from 0 to 1250 m in the alongshore (Holman et al., 2013). The cBathy algorithm estimates frequency and wavenumber from these pixel time series at a spatial resolution of 10 and 25 m in the cross- and alongshore directions, respectively, and converts to water depth estimates using the linear dispersion relationship (Holman et al., 2013). Water depth estimates are converted to seafloor elevations by subtracting the local tide elevation. Bathymetric features with a horizontal length scale greater than 10 times the water depth have been shown to be well resolved using this approach (Plant et al., 2008), particularly when waves are small and non-breaking (Brodie et al., 2018; Holman et al., 2013). The cBathy algorithm is well described in (Holman et al., 2013) and therefore is only briefly outlined here. The algorithm consists of three parts. In step 1, the wavenumber and direction at the four most coherent frequencies for a given collection are estimated from cross-spectra computed within a 100(cross-shore) by 200-m (alongshore) region centered on each cBathy output point. In step 2, these four estimates of wavenumber and frequency are combined using a nonlinear weighted fit to the linear 8

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dispersion relationship to produce a single depth estimate, hˆk , and error estimate, εP2, derived from the 95% confidence interval on the weighted nonlinear fit. Depth estimates were converted to seafloor elevations by subtracting the tide elevation (m, NAVD88) measured at the end of the FRF pier. In step 3, a Kalman filter is used to calculate a weighted running average in time, hk , from the half-hourly hˆk and εP2 estimates to reduce noise, thereby improving the quality of the final video-derived bathymetry estimates. The Kalman filter is defined as hk = hk ― 1 + K(hk ― hk ― 1)

(3)

where hk ≡ Kalman filtered depth estimate hk ― 1 ≡ previous depth estimate hk ≡ current sea floor depth estimate (tide corrected)

K, the Kalman gain, is defined as: K≡

Pk―

(4)

Pk― + R'

where R' ≡ (εp2)2 is the measurement error variance at the current time step, and Pk― is the prior estimate of error variance updated from the previous time step’s final error variance, Pk-1, and given by Pk― ≡ Pk ― 1 + Q∆t

(5)

where Q is the process noise covariance, which quantifies the expected hourly bathymetric variability, and Δt is the time change between estimates. The current time step’s error variance, Pk, is then calculated as

Pk  1  K Pk

(6)

The Kalman filtered depth estimate, hk, and estimated error, εP3 = 𝑃𝑘, provide cBathy’s best estimate of seafloor elevation at each time step and a 95% confidence interval for that estimate, which is related to the true error, but may be too small by a factor of seven (Holman et al., 2013). In this paper, based on the findings from (Brodie et al., 2018), two methods were developed in an attempt to mitigate the effects of wave breaking. The specifics of these methods are described in detail in sections 4.2.4 and 4.2.5, but both of these methods utilize a threshold to remove Kalman filter estimates, hk , during times of wave breaking. Equation (3) is updated as follows to incorporate the thresholded cBathy bathymetry method, ℎ𝑘𝑡: ℎ𝑘𝑡 =

9

{

𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 𝑚𝑒𝑡 ℎ𝑘 ― 1 + 𝐾(ℎ𝑘 ― ℎ𝑘 ― 1), ℎ𝑘 ― 1, 𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 𝑛𝑜𝑡 𝑚𝑒𝑡

(7)

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4 Methods 4.1 Domain and Model Setup For this analysis, two wave model grids were used: a regional parent grid and a local nested grid. The parent grid was created using a digital elevation map from Blanton (2008) and extends 17 km in the cross-shore to an approximate depth of 26 m and 38 km in the longshore with a resolution of 50 m. During the study, the 26 m Waverider broke free from its mooring. When there were no wave records at the FRF 26-m Waverider, the offshore boundary was moved to 4.7 km offshore, co-located to the 17-m Waverider (cyan line, Figure 2A, B). The nested nearshore domain is 1600 m alongshore and 1000 m in the cross-shore with a resolution of 10 m, and any updates to the bathymetry are done only in this nested domain. The nested grid construction process starts by interpolating the survey profiles using a scale controlled Loess interpolation algorithm (Plant et al., 2002) with smoothing length scales of Lx = 20 m and Ly = 100 m. The newly created bathymetry grid is integrated into a subset of a background grid using a weighted b-spline method (Ooyama, 1987; Plant et al., 2009). Figure 1 shows the domains for the parent and nested grids and the FRF cross-shore array. The model is forced with two-dimensional frequency-direction spectra (described in 3.2) along the offshore boundary with a linear frequency distribution between 0.04 hz and 0.4975 hz and a resolution of 0.0075 hz and a direction distribution from ± 90 degrees of shore normal with 5 degree resolution. Spatially homogeneous winds and water levels are applied to the model using the measurements from the end of the FRF pier. A Manning’s n friction coefficient of 0.073 is used (Hanson et al., 2009).

4.2 Bathymetry Test Cases The primary focus of this paper is to assess the applicability of the cBathy bathymetry estimates to improve wave height predictions close to shore using five sets of simulations. The first two are derived from surveys: the first of which is referred to as “static” which holds the bathymetry steady over the 11-month study duration; and the second is referred to as “survey” which uses the surveyed bathymetry and is updated approximately monthly. The last three are derived from the Argus video imagery: the first of which is referred to as “cBKF” which updates the bathymetry based on the standard Argus cBathy analysis (Holman et al., 2013) (approximately every 30 minutes during daylight hours); and the last two are based off equation (7), limiting the estimates available to the Kalman filter by identifying when waves are breaking and cBathy is likely to have high error, using either an offshore wave height threshold or an optically derived wave breaking threshold. Simulations utilizing this method are referred to as “cBKF-T”. Table 2 summarizes these five bathymetries for quick reference. Table 2: Reference for bathymetry types

Bathymetry Description Static bathymetry simulations Slow Update Bathymetry Kalman Filtered cBathy Bathymetry Wave Height Thresholded cBathy Bathymetry Variance image thresholded cBathy bathymetry

10

Update None ~ Monthly 30-min in Daylight 30-min in Daylight, H<1.2m 30-min between 1300 and 2100

Section Described 4.2.2 4.2.1 4.2.3

Reference Static Survey cBKF

4.2.4

cBKF-T (Hs)

4.2.5

cBKF-T (var)

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UTC, variance coverage < 13%

4.2.1 Static bathymetry simulations While the FRF collects bathymetric data with relatively high temporal frequency, monthly surveys are not usually feasible for applied coastal engineering projects. To simulate this, the first set of simulations utilized the initial bathymetry for the study period and held it constant for the duration of this study. The bathymetry used for this set of simulations was collected by the LARC on 15 September 2015, approximately 15 days prior to the beginning of the simulation period. This set of simulations is an attempt to represent a typical scenario in which a project lacks the resources to update bathymetry data, and the best available data are out of date (in this case, only by 15 days at the start of the simulations, but 11.5 months by the end).

4.2.2 Slow Update Bathymetry Simulations The second set of simulations were run utilizing the most up-to-date surveyed bathymetry. These surveys were collected with the CRAB or the LARC. Vertical dashed lines in Figure 2A indicates the date of the 15 bathymetric surveys during the 11-month study duration.

4.2.3 Kalman Filtered cBathy Bathymetry Simulations The first remotely sensed test case utilizes the bathymetry produced by equation (3), the standard Kalmanfiltered cBathy bathymetry estimate, updated half-hourly during daylight hours. For this set of simulations, the bathymetry estimates are not quality controlled and are evaluated as an operational product. The cBathy domain is similar to that described in (Holman et al., 2013), but is extended 200 m to the north and incorporated into the background grid as described in Section 4.1. For simulations during times of darkness, the last collection of the day was held constant until a new bathymetry was available.

4.2.4 Wave Height Thresholded cBathy Bathymetry Simulations To mitigate erroneous depth estimates from the Kalman filtered cBathy bathymetry during wave breaking, equation (7) modified the cBathy estimates, including estimates only when the offshore boundary condition significant wave height was below 1.2 m. As in Section 4.2.3, the cBathy domain is the same, and was incorporated into the background grid as explained in Section 4.1. For simulations during times of darkness or large wave heights, the previous bathymetry is held constant until a new bathymetry was available.

4.2.5 Variance Image Threshold Based cBathy Bathymetry Simulations To more directly account for the known issues with cBathy bathymetry estimates during wave breaking, an approach was developed to use variance imagery (a running variance at each pixel during the 10 minute collection) produced from the Argus camera system (Holman and Stanley, 2007) to identify when waves were breaking over the sandbar. The variance image was selected over the timex (time average) image because it was less sensitive to changes in optical conditions (e.g., fog, rain). The image, which highlights areas of wave breaking, was converted to a scaled grayscale image and evaluated over a subdomain surrounding the approximate position of the sandbar, from 150 to 300 m in the cross-shore and 550 to 1250 m in the alongshore coordinate system (blue box, Figure 3B). In the sub-domain, wave breaking was identified by identifying pixels with a variance that exceeded 0.13 (determined by visually comparing variance and timex imagery; red colors, Figure 3C). When identified wave breaking was more than 25% of the sub-domain, the collection is discarded. To remove effects of high or low light with the rising and setting sun, only the variance images between 1300 and 2100 UTC were used. 11

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Figure 3:Time-averaged (A), variance (B), and thresholded variance (C) imagery across the FRF domain for an example time (PROVIDE DATE). The blue box in (B) defines the region where the variance threshold was applied, and the red colors in C show locations where the variance threshold was met (red) or not met (blue).

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4.3 Example Bathymetry Comparison An example of the bathymetry profiles from each of the grids at the cross-shore instrument array used for this study from January 6, at 2000 UTC is shown in Figure 4. At this time, the offshore buoy recorded 2.2 m significant wave height with a peak period of 10.5 s. Leading up to this point in time there had been 60 hours of wave heights over 1.2 m. The static (red, Figure 4) and the survey (blue, Figure 4) bathymetries are 113 and 13 days out of date, respectively at this time. The cBKF bathymetry profile (equation (3)) significantly over estimates the depth by approximately 2 m both offshore and onshore of the sandbar (cyan line, Figure 4), and is significantly biased onshore, compared to the surveyed bathymetry (blue line, Figure 4). The cBKF-T bathymetries (orange and green, Figure 4) show more similar depth estimates to the survey bathymetry, demonstrating how the over estimations from cBKF are mitigated by applying the threshold (equation (7)).

Figure 4: Cross shore profile of wave height and bathymetry at the cross shore array of wave gauges

5 Results 5.1 Validation of the Thresholded Kalman Filter (cBKF-T) Bathymetry Estimates Before utilizing the cBKF-T bathymetry estimates as a bathymetry boundary condition, cBKF-T estimates were evaluated relative to the altimeter data at xp150, xp200, and adop3.5m for the same time period presented in Brodie et al. (2018). The elevations estimated by the cBKF (cyan line, Figure 5A-C) and cBKF-T (orange and green lines, Figure 5A-C) method qualitatively trend with the altimeter measurements (blue line, Figure 5A-C). During large wave heights (Figure 2A) the cBKF (cyan) over estimates depth by up to 2 m, as also seen in (Brodie et al., 2018). It is worth noting that these cBKF results are slightly different from (Brodie et al., 2018) due to the extra smoothing from the bathymetry integration process (explained in Section 4.1). At the offshore altimeter (Figure 5A) the cBKF-T methods remove most of the erroneous depths that are prevalent during large wave events in cBKF (compare cyan and orange/green lines, Figure 4A). At the middle and inner altimeter (Figure 4B and C), respectively, the cBKF-T methods similarly remove many of the over estimations of depth, but shallow anomalies, particularly at the middle altimeter, are still present. There are times when the cBKF-T (Hs) and the 13

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cBKF-T (var) method performance diverges, sometimes one method allowing more estimates while the other stays with a previous estimate longer, but generally the two cBKF-T methods perform similarly.

Figure 5: Comparisons between the estimated bathymetries, cBKF (cyan), cBKF-T (Hs) (orange), cBKF-T (var) (green), and altimeter measurements (blue) at cross-shore location: (A) 300 m; (B) 200 m; (C) 150 m.

The RMSE and bias for the comparison between the cBKF and cBKF-T bathymetry estimation methods and the altimeter measurements are shown in Table 3. The most significant improvements are seen in reducing the RMSE and bias at the 150 m station. At 150 m in the cross-shore, bias is improved 36.6% to -0.19 m using the cBKF-T (Hs) and 56.7% to -0.13 m using the cBKF-T (var) method. Oddly, at the 300 m station the cBKF-T (Hs) and cBKF-T (var) methods have a large increase in bias, while the RMSE is reduced. In the original cBathy (cBKF), the during-storm over estimations of depth balanced the quiescent shallow bias creating a near-zero bias. In the cBKF-T results, the large over estimates of depth are removed but the shallow bias remains during quiescent times (Figure 5A). 14

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Table 3: Bathymetry Comparison Statistics Cross-Shore Position 150 m 200 m 300 m

cBKF -0.30 0.25 0.03

Bias [m] cBKF–T (Hs) cBKF-T (var) -0.19 -0.13 0.24 0.27 0.17 0.21

cBKF 0.51 0.52 0.37

RMSE [m] cBKF–T (Hs) cBKF-T (var) 0.37 0.34 0.47 0.46 0.28 0.29

To investigate the differences in the bathymetries at locations where continuous altimeter estimates are not available, profile envelopes were calculated for the cBKF (Figure 6A), cBKF-T (Hs) (Figure 6B), cBKF-T (var) (Figure 6C) and survey (Figure 6D) bathymetries over the course of the study. The cBKF bathymetry envelope is the largest (Figure 6A), with depths extending to 6 and 7 m at 170 m (in the trough) and 260 m (the offshore edge of the sandbar) in the cross-shore, respectively. Both of the cBKFT methods have a larger envelope when compared to that of the survey bathymetry envelope, but they are more constrained and similarly shaped to the survey bathymetry profiles shown (compare Figure 6B and C to D). The most noticeable (and maybe most impactful) change between the cBKF and cBKF-T estimates occurs around 260 m cross-shore. This location is just offshore of the sandbar position for the majority of the study duration (Figure 2C). The large overestimates of depth on the offshore edge of the sandbar during wave breaking that are apparent in the cBKF bathymetry are removed in both of the cBKF-T bathymetry methods. Also, note the deep estimates near the shoreline in cBKF are also constrained when using the cBKF-T methods. The static bathymetry is at the lower bound of the surveyed bathymetries envelope between 250 and 400 m in the cross-shore and is at the middle of the envelope around 200 m. Onshore of 200 m, the static bathymetry again trends toward the lower envelope bound (compare black line and profile envelope, Figure 6D). The altimeter measurements provide insight to the true envelope, as captured at the alongshore location of the cross-shore array of wave gauges. cBKF estimates match the altimeter maximums at the three stations, but minimums are overestimated (Figure 6A). The envelope from the cBKF-T methods are better constrained, matching the extremes measured by the altimeters (Figure 6B). The cBKF-T (var) method has a slightly deeper, shallower envelope around the 300, 220 m cross-shore mark, respectively, when compared to the cBKF-T (Hs) method. The two cBKF-T methods are otherwise very similar. The minimum altimeter values agree well with the minimum elevations from the surveyed bathymetry envelope (Figure 6C), while the maximum values are underestimated for both of the 150 m and 200 m stations. This is likely due to the temporal sampling scheme and inherent weather limitations of the survey measurements at the FRF.

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Figure 6: A comparison is shown between the 5 sets of bathymetric profiles at the cross-shore array of wave gauges over the duration of the study colored by rate of occurrence. Each plot has the mean acoustic altimeter value plotted (cyan) with the range of measurements over the course of the study. The bathymetry envelope from this study for A) cBKF B) cBKF-T (Hs) C) cBKF-T (var) D) survey with the static bathymetry plotted in black for reference. D) A cross-shore summary of model skill statistics plotted by the significant wave height NRMSE. The time-matched sample count for the gauges are 6807, 6811, 6195, 6685, 6734 moving from offshore to onshore respectively.

5.2 Summary Wave Height Statistics in the Cross-Shore Normalized root-mean-squared errors (NRMSE) in wave height are computed along the cross-shore array for the five bathymetry test cases and summarized for the study duration (Figure 6E). The simulations all perform similarly offshore of 300 m in the cross-shore where bathymetric differences between the cases are small (Figure 6A-D). Onshore of 300 m, differences in performance between the simulations are larger, (12 % < NMRSE < 23% at all gauges). The NRMSE for the static and cBKF simulations (red and cyan lines, Figure 6D) are comparably high relative to the survey, cBKF-T (Hs), and cBKF-T (var) bathymetries, with the exception of the observation location nearest to shore (xp125) where the static simulation has the lowest NRMSE. The cBKF-T (Hs), cBKF-T (var) and survey simulations generally perform best (with the lowest NRMSE), with both of the cBKF-T simulations having a slightly lower NRMSE at the 200-m and 125-m cross-shore location. The similarity in performance between the survey and the cBKF-T (Hs) simulations is due to offshore significant wave heights at the site being below the 1.2 m threshold for 73% of the study duration (Brodie et al., 2018), and therefore the effects of the improved cBKF-T (Hs) bathymetry during large wave events are overwhelmed by time periods in which the cBKF performs adequately (and cBKF-T and cBKF produce the same bathymetry estimates). Given the similarity in performance between the cBKF-T (Hs) and cBKF-T (var), for simplicity only the cBKF-T (Hs) will be considered moving forward and is hereby referred to as simply cBKF-T. 16

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5.3 Nearshore Skill Statistics by Wave Height To elucidate conditions in which the simulation sets perform differently, RMSE and bias in simulated wave height are calculated and binned by wave height for the onshore gauges that are frequently near and in the surf zone (Figure 7). During the experiment, the outer most gauge (aquadopp 3.5m) is either at or just offshore of the sandbar crest, while xp200 was located near the sandbar crest for the first half of the study duration and then onshore of the sandbar for the second half of the study duration (Figure 2). The other two wave gauges are consistently inshore of the sandbar and intermittently in the wave breaking area of the surf zone. During small offshore wave heights (Hs < 2 m), at all of the gauges, the four sets of simulations perform fairly similarly in both RMSE (Figure 7A, D, G, J) and bias (Figure 7B, E, H, K). As wave height increases, the number of observations decrease (Figure 7C, F, I, L) and significant spread was observed in the bias and RMSE for the four sets of simulations, particularly at the three pressure sensors. In general, for almost all wave conditions at all wave gauges, the cBKF simulations performed worse than the static and survey simulations, while the cBKF-T simulations performed similarly to the static and survey simulations. In fact, at xp200, the cBKF-T simulations consistently performed as well as, and in some conditions better, than the survey simulations (compare blue and orange lines in Figure 7D,E). Results were more mixed at the two inner gauges. At xp150, the static and survey simulations had smaller RMSE at higher wave heights compared to the cBKF and cBKF-T simulations, however, the cBKF-T and survey had similarly low biases. At xp125, the static, survey, and cBKF-T again had similarly low biases and RMSEs for all wave heights, while the cBKF simulations had large RMSE and biases at high wave heights.

Figure 7: Skill statistics at the 3.5 m aquadopp (left column), the xp200 m pressure gauge (left-center column), the xp150 m pressure gauge (right-center column), and the xp125 m (right column) are binned by wave height for each of the 4 bathymetric boundary conditions. A) RMSE B) bias C) sample count at the 3.5 m aquadopp (300 m in the cross-shore). D) RMSE E) bias F) sample count at the xp200 m pressure sensor (200 m in the cross-shore). G) RMSE H) bias I) sample count at the xp150 m pressure sensor (150 m in the cross-shore) and J) RMSE K) bias L) sample count at the xp125 m pressure sensor (125 m in the cross-shore).

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6 Discussion 6.1 Overall Performance using Remotely Sensed Bottom Boundary Conditions During lower energy conditions (Hs < 2 m), nearshore wave model estimates using remotely sensed bottom boundary conditions based on the operational cBathy algorithm (cBKF) performed as well as wave height estimates using static bottom boundary conditions (compare red and cyan lines, Figure 6). During these same conditions (Hs < 2m), the modified cBathy algorithm (cBKF-T) outperformed the static bottom boundary condition (compare red and orange lines, Figure 6) and in many cases was comparable (or better) than the survey bottom boundary condition (compare orange and blue lines, Figure 6). These results suggest that remote sensing techniques are a useful bathymetry source to consider for nearshore wave modeling, particularly when budgets are constrained or vessel-based surveying is too risky. For example, in locations without continuously operating towers, an unmanned aerial system (UAS) could be used during small waves, following the methodology outlined by (Holman et al., 2017). This methodology would enable the collection of the imagery and wave speed observations needed to estimate a bottom boundary condition to initialize a nearshore wave model in only a few hours without necessitating a vessel.

6.2 Cross-Shore Variations in Wave Height Dependence Performance of the various bottom boundary conditions varied across the nearshore and surf zone as wave heights increased, and observed errors were complicated by potential errors in the model, including wave breaking parameterization and/or non-linear wave-wave interactions. For example, at the 3.5 m aquadopp, RMSE generally increases for all sets of simulations as the wave height approaches depthlimited breaking (2 m < Hs < 4 m, depending on changing depths at the gauge) before declining at larger wave heights (Figure 7A), with a similar trend in the magnitude of the biases (Figure 7B, note biases happen to be negative and so the shape of the curves is inverse to that of the RMSE). This increase in errors as wave heights approach their breakpoint suggest that the incipient breaking parameterization could be improved. Interestingly, at the 3.5 m aquadopp, the cBKF-T simulations have an increased negative bias relative to the other bathymetric boundary conditions. These results are due to the observed slight shallow bias in water depth at this location (0.17 m, Table 3). A shallow bias in bottom boundary condition likely causes waves to break farther offshore, leading to low simulated wave heights in the cBKF-T simulations at this location. At xp200, which was either near or onshore of the sandbar crest (Figure 2), the cBKF-T, survey, and static simulations performed similarly (0.15 m < RMSE < 0.30 m), with the static simulations performing worse when the wave height approached depth-limited breaking (Hs ~ 2 m) due to out of date bottom boundary conditions. The cBKF simulations had significant biases and large RMSEs at this location at larger wave heights due to the erroneously deep bottom boundary conditions (Brodie et al., 2018). Since xp200 was frequently inside the surf zone, where wave heights are largely depth-dependent, the benefits of temporally varying the bottom boundary condition correctly (in either the survey or cBKF-T simulations) are most obvious at this location: when calculated over the entire study duration, RMSE for these two bottom boundary conditions was significantly lower here when compared to the static or cBKF bathymetry (Figure 5). These results suggest that if the goal of a given modeling study is to provide timevarying accurate wave heights near the sandbar, such as would be needed to predict wave-driven circulation or to drive sediment transport in the nearshore, increased skill in wave forcing can be achieved by temporally varying the bottom boundary condition with either frequent surveys or with estimates derived from remotely sensed data (e.g., the cBKF-T methodology).

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In some cases, at the inner most wave gauges during large waves (xp150 and xp125, Hs > 2m), the static bottom boundary condition actually out performed all of the other boundary conditions, which might suggest there is little utility in having time-evolving bottom boundary conditions close to shore. However, these improved statistics are likely due to the fact that the static bathymetry is simply a deeper profile, which allows more energy to propagate closer to shore. This increases modeled wave heights (since broken waves in STWAVE are dependent on depth) close to shore, which more accurately matches observations. Wave heights may be underestimated in this region as STWAVE is a phase-averaged linear wave model which requires parameterizations of all surf zone processes beyond refraction and shoaling, meaning the model cannot realistically simulate inner-surf zone wave processes like wave nonlinearity, infragravity waves, wave setup, and wave reflection which could lead to larger wave heights.

6.3 Benefits of cBKF-T over cBKF during Storms Examination of a storm from 4 – 14 January 2016 in which the offshore wave height peaked at approximately 3.5 m (Figure 8A) demonstrates the relationship between the time-varying wave height residual (Figure 8B) and the time-varying bathymetry residual (relative to the altimeter observations at xp200 m, Figure 8D). During this storm, the xp200 gauge was located near the sandbar crest (Figure 2C) and consistently within the surf zone, and wave heights were largely controlled by water depth (note oscillation in wave height in the red circles, Figure 8A). The cBKF-T was held static beginning at 4 January 0830 (Figure 8C) when wave heights first exceeded 1.2 m and updated with the cBathy estimate ( hk from equation (7)) at 11 January 2000 UTC, approximately 7.5 days later when wave heights fell below 1.2 m again. In contrast, the cBKF boundary condition was allowed to vary during this same time period (Figure 7C). The survey boundary condition was also static during this time period.

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Figure 8: A) Wave height versus time at the offshore boundary conditions (black circles) and at the xp200 m pressure sensor (red circles) for a storm in January 2016. Wave height residuals (B) and bathymetry elevations (C) and altimeter elevation residuals (D) versus time for the January 2016 storm at the xp200m are plotted for the survey (green), the cBKF (blue), and the cBKF-T (orange), altimeter observations (red).

Wave height prediction residuals at the xp200 m pressure sensor increase with wave height during this period, especially when waves are breaking (04 to 13 January, Figure 7A, B). The highest residuals in wave height (Figure 8B) are seen in the cBKF (cyan) set of simulations, which also has the highest relative residual bathymetric error (Figure 8C). In contrast, the cBKF-T (orange) has the lowest wave height and bathymetric errors for the majority of this duration. For all sets of simulations, the errors (bathymetry and wave height) begin to grow shortly after the storm begins and wave heights increase. As mentioned in Section 6.2, some of these increased errors, during large waves, may also be a function of the simplified breaking criteria applied in STWAVE (Apotsos et al., 2008; Zheng et al., 2008), not just errors in the bottom boundary condition, however investigation of this is outside the scope of this study. It’s also important to note that the differences in bathymetry residuals are not directly proportional to the residuals in wave height as other physical phenomenon are present (e.g., 2D refraction). For example on 8 January, the cBKF and suvery both have the same depth elevations, while the wave height residuals for the cBKF simulations are closer to the cBKF-T. The cBKF-T methods work primarily by limiting some of the over predictions in depth estimates produced during times of wave breaking and in turn wave height predictions from the model. This is 20

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particularly important during long-duration storm events (e.g., October 2015 and January 2016) when the over estimations from hk begin to infiltrate the Kalman filter. As previously described, the 1.2m threshold (used as a proxy for when waves are likely to break over the sandbar at the FRF) is taken from Brodie et al. (2018), who showed good agreement of cBathy and in-situ altimeter and surveyed data during low wave heights (Hs < 1.2 m) when waves infrequently broke over the bar. The cBKF-T methods used here demonstrate two methods to identify and mitigate the overestimations of water depth produced by the cBathy algorithm during periods of large waves and wave breaking (Brodie et al., 2018), so that the bottom boundary condition for operational wave modeling can be updated appropriately. The effort presented here is not designed to fix the cBathy algorithm during these conditions, but instead to identify the utility of the cBathy algorithm as a boundary condition for wave modeling. While the 1.2 m threshold used with the cBKF-T (Hs) method (and cBathy process error in general (Holman et al., 2013)) may be specific to the FRF field site, the cBathy algorithm has been shown to have skill in other locations (Bergsma et al., 2016, 2014; Díaz Méndez et al., 2015; Radermacher et al., 2014) and the use of an optically-derived wave breaking threshold to identify times of poor data showed similar performance to the wave height threshold. This optically-derived method could easily be transferred to other locations. In this work, the choice of a wave-height threshold may either fail to filter out overestimations of depth (if the wave height threshold is set too low) allowing them to penetrate into the bathymetry solution, and in turn create overestimations of wave height produced by the model, or prevent measured change from being properly incorporated into the bathymetry solution (wave height threshold set too high). Since the overestimations of depth will tend to create larger wave height errors, it may be better err on the side of a stricter threshold. Future development of the cBathy algorithm should aim to provide better calibrated uncertainty, which would allow the Kalman filter to properly assimilate half-hourly depth estimates and remove the need for any thresholding methodology.

7 Conclusions Five sets of nearshore wave height simulations over varying bathymetric boundary conditions for 11months with the STWAVE model at the Field Research Facility were evaluated relative to observations across the surf zone. Of the five sets of bathymetry, two of the sets utilized survey data, one static while the other evolved with the most recently measured bathymetry (survey). The other three utilized optically remotely sensed data and the cBathy algorithm to estimate the bathymetry. The first utilized the operational estimates from cBathy version 1.1 (cBKF), while the other two – cBKF-T (Hs) and cBKF-T (var) – limited estimates to time periods during minimal wave breaking. When compared to the acoustic altimeter measurements, bathymetric estimates using both of the cBKF-T approaches had lower or comparable RMSE at all comparison stations and the bias was better at two of the three stations than estimates from the cBKF. The bias from the last station is a misleading statistic as the large overestimations of water depth (during large waves) balance out the shallow bias in the cBKF method. The wave height simulations using either of the thresholded Kalman filter methods as a bathymetric boundary condition (cBKF-T) perform similarly to those using the most recently measured bathymetry (survey), at some places outperforming the survey, while at others slightly underperforming. The original operational cBathy bathymetry estimates from the Argus observations (cBKF), and the static simulations, perform worse than the survey and cBKF-T when using significant wave height bias and percent RMSE as skill statistic measures. The threshold minimizes the effects of cBathy’s overestimation of depths during storms and breaking waves. When waves are smallest (during the summer months of this study), all of the simulations performed with similar skill (suggesting that these errors were inherent to the wave model or 21

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other inputs). Wave model results over the cBKF-T boundary condition as a whole outperformed the original cBKF boundary condition, which suggests that any negatives that could come from restricting the bathymetric update rate, are outweighed by positives of limiting the depth overestimations that occur during large breaking waves. As camera equipment continues to become less expensive and data storage and transfer costs are reduced, utilization of cBathy for bathymetry using the cBKF-T estimation methods is more feasible for routine project deployment. These data could be collected with low cost (semi) permanent camera stations deployed at project sites or on mobile platforms (e.g., small unmanned aerial vehicles or drones), supplemented by regional scale background bathymetry surrounding the site. In addition, this study also provided an opportunity to evaluate the scales of errors that are introduced when bathymetry is held static over the course of a year’s modeling period. Overall, these results suggest that remotely sensed bathymetry is a viable bathymetric data source to provide boundary conditions for nearshore wave models.

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Appendix: Statistics To evaluate the performance of the nearshore wave height simulations over the various bathymetry boundaries, model skill as compared to the observation data is presented. The statistics used to provide insight into the model skill are defined here. The first skill statistic used is residual error: Residual A1(8)

R = imod ― jobs

where imod and jobs are the individual time-matched model output and field observation, respectively. The residual is the difference between the model and observations. Bias

b

A2(9)

1  imod  jobs N

The bias represents an assessment of the overall mean of the model error. Root-Mean-Square Error (RMSE) RMSE =

∑(i

mod

A3(10)

― jobs)2

RMSE assesses the scatter in the model error. Normalized Root-Mean-Square Error (NRMSE)

NRMSE 

 (i  j j mod

obs 2

A4(11)

)2

obs

NRMSE assesses the scatter in the model error, normalized by the magnitude of the observation. This is otherwise known as percent root-mean-square error. APPENDIX B: STWAVE model The wave model used in this analysis is STWAVE (Massey et al., 2011; Smith, 2007), a steady-state, phase-averaged spectral wave model for wave generation, propagation, transformation, and dissipation. STWAVE solves a steady-state conservation of spectral wave action along a back-traced wave ray: ∂ CCgcos (α)E(ω, α) = ∂xi ω

(Cg)i

S

∑ω

B1

where E is the wave energy density divided by (w g), w is the density of water, g is gravitation acceleration, C is wave celerity, Cg is wave group celerity, ω is angular frequency, α is wave angle, Sis the energy source and sink terms, x is the cross-shore coordinate and i is tensor notation for the x and y crossshore/alongshore coordinates. STWAVE assumptions include: mild bottom slope and negligible wave reflection, steady-state waves and winds (forcing conditions varying more slowly than the time required for waves to transit the grid), and linear refraction and shoaling. STWAVE has the capability to include currents, but currents are not applied in these simulations. Wave breaking is based on the Miche-type criterion (Miche, 1951; Smith et 23

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al., 1997). STWAVE input includes a bathymetry grid, offshore wave forcing, and wind forcing over the grid.

ACKNOWLEDGEMENTS: The authors would like to thank the FRF team members Jason Pipes, Brian Scarborough, Mark Priesser, Rob Mitchell, Dan Freer, Kent Hathaway, Mike Forte, and Patrick Dickhudt for support and maintenance of the instrumentation and data collections; Mary Bryant for her assistance with the model setup; and Rob Holman and John Stanley at Oregon State University for the support and maintenance of the Argus video imagery system. This work was completed as part of CHL's Coastal Model Test Bed and was funded by the US Army Corps of Engineer's Coastal Ocean Data Systems and Coastal Field Data Collection programs.

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- A video-based depth inversion algorithm, cBathy, was evaluated as a temporally varying bottom boundary condition relative to frequently surveyed and static bathymetry for nearshore wave modeling at an open coast beach in Duck, NC. - Remotely sensed bottom boundary estimates were improved by only including estimates when offshore wave heights were below 1.2 m, reducing over-estimations of depth at large wave heights. - Nearshore wave height predictions from STWAVE were compared to field observations over 11 months and model runs over the remotely sensed and frequently surveyed bathymetry had similar skill. - During storm events, the modified cBathy boundary condition reduced over-estimations of wave height predictions compared to the original cBathy boundary condition.