Comparative Evaluation of Volumetric Current Measurements in a Tidally Dominated Coastal Setting: A Virtual Field Experiment

Trevor Harrison University of Washington, Seattle, Washington

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Kristen M. Thyng Texas A&M University, College Station, Texas

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Brian Polagye University of Washington, Seattle, Washington

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Abstract

High-resolution, four-dimensional mapping of currents in tidally dominated coastal settings can be conducted with a range of instrumentation. Here, we assess four approaches to data collection: an X-band radar, a stationary (bottom mounted) acoustic Doppler current profiler (ADCP), a mobile (vessel based) ADCP, and a swarm of Lagrangian floats. Using the output from a hydrodynamic simulation, a virtual field campaign was performed at 24 locations in Admiralty Inlet, Puget Sound, Washington, during spring and neap tidal exchanges. A reconstruction of the volumetric currents was generated for each platform every 15 min and evaluated against the true currents to assess accuracy over a horizontal extent of 400 m × 500 m at 5 m resolution and vertically through the entire water column (20–80 m) at 2 m resolution. Results demonstrate that, for this survey extent and resolution, a vessel-based ADCP survey is most accurate, followed closely by the float swarm. The overall performance hierarchy persists over most locations and times. Thus, if mapping currents at high resolution (<10 m) and short time scales (<1 day) is the primary scientific objective, vessel-based ADCP surveys are likely the best option. For longer-duration surveys, a combined deployment with a stationary ADCP and X-band radar system is the best choice. Last, if in situ measurements of scalar properties (e.g., salinity, temperature, dissolved oxygen) are also desired, float swarms can simultaneously sample these while surveying currents with accuracy comparable to mobile ADCPs.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Trevor Harrison, twharr@uw.edu

Abstract

High-resolution, four-dimensional mapping of currents in tidally dominated coastal settings can be conducted with a range of instrumentation. Here, we assess four approaches to data collection: an X-band radar, a stationary (bottom mounted) acoustic Doppler current profiler (ADCP), a mobile (vessel based) ADCP, and a swarm of Lagrangian floats. Using the output from a hydrodynamic simulation, a virtual field campaign was performed at 24 locations in Admiralty Inlet, Puget Sound, Washington, during spring and neap tidal exchanges. A reconstruction of the volumetric currents was generated for each platform every 15 min and evaluated against the true currents to assess accuracy over a horizontal extent of 400 m × 500 m at 5 m resolution and vertically through the entire water column (20–80 m) at 2 m resolution. Results demonstrate that, for this survey extent and resolution, a vessel-based ADCP survey is most accurate, followed closely by the float swarm. The overall performance hierarchy persists over most locations and times. Thus, if mapping currents at high resolution (<10 m) and short time scales (<1 day) is the primary scientific objective, vessel-based ADCP surveys are likely the best option. For longer-duration surveys, a combined deployment with a stationary ADCP and X-band radar system is the best choice. Last, if in situ measurements of scalar properties (e.g., salinity, temperature, dissolved oxygen) are also desired, float swarms can simultaneously sample these while surveying currents with accuracy comparable to mobile ADCPs.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Trevor Harrison, twharr@uw.edu

1. Introduction

Comprehensive mapping of water currents in energetic, coastal environments is challenging due to the combined forcing of tides, winds, waves, as well as the mixing of fresh- and saltwater, all of which vary in space and time. Yet a four-dimensional understanding is essential for multiple applications: currents affect navigation of surface and underwater vehicles (Kruger et al. 2007), they control transport of pollutants and nutrients (Paerl 2006; Panchang et al. 1997), they drive sediment transport (Allen et al. 1980), and they determine the feasibility of renewable power generation (Polagye and Thomson 2013).

Here, we perform a virtual experiment to evaluate the performance of four measurement platforms for volumetric current mapping: a stationary acoustic Doppler current profiler (ADCP), a vessel-based mobile ADCP survey, an X-band surface radar, and an underwater float swarm. While these measurement platforms are used throughout the coastal ocean, their relative performance has not been benchmarked in energetic tidal environments. The platforms are evaluated using the output of a numerical simulation of Admiralty Inlet, Puget Sound, Washington (Thyng 2012a; Thyng et al. 2013). Specifically, volumetric flow-field reconstructions with a small spatial range O(1) km and high-resolution O(10) m are generated by all platforms every 15 min over an ebb–flood tidal cycle O(10) h during neap and spring conditions. While observational requirements will vary with use case, this type of short-term, high-resolution measurement is relevant to model validation efforts such as renewable energy resource characterization (Adcock et al. 2015) and rip current identification (Castelle et al. 2016). We first examine the accuracy of all platforms at one location in Admiralty Inlet over a single ebb–flood cycle to identify sources of reconstruction error. We then compare results across locations and neap-spring cycles to assess general performance. In the discussion, we provide commentary on how the virtual results may extend to real surveys and larger surveys. We also include a qualitative comparison of platform operational constraints, as well as an examination of the particular strengths of hybrid stationary ADCP/radar surveys and of float swarms. We begin by briefly reviewing each of the measurement techniques.

a. ADCPs

ADCPs are widely employed to measure currents, using sound to remotely profile three-dimensional water velocity. ADCPs are available from multiple manufacturers and can operate in water depths shallower than 10 m to ocean scale (2000 m), with trade-offs between range, resolution, and measurement uncertainty (González-Castro and Muste 2007; Teledyne RD Instruments 2019). When deployed on stationary platforms such as bottom landers or moored buoys, they provide good temporal resolution (up to 16 Hz), but limited spatial coverage. Mobile surveys expand spatial coverage when deployed from surface vessels (Geyer and Signell 1990; Willcox et al. 2001), autonomous surface vehicles (ASVs) (Brown et al. 2011; Codiga 2015), autonomous underwater vehicles (AUVs) (An et al. 2001; Brown et al. 2011; Mullison et al. 2011; Todd et al. 2017), and drifting platforms (Guerra and Thomson 2016; Shcherbina et al. 2018). Correcting for vessel motion can be accomplished through ground tracking, integration with the ships navigation system, and motion tracking on board the instrument (Velasco and Nylund 2019; Heitsenrether et al. 2018; Muste et al. 2004; Fong and Monismith 2004). For a mobile survey, increased spatial coverage comes at the cost of “blurring” in the volumetric current reconstruction due to the temporal evolution of hydrodynamics during a survey (Matthews 1997). Thus, survey times are limited by the local period of temporal stationarity, which can be as short as five minutes in tidal channels (McCaffrey et al. 2015; Thomson et al. 2012). In vessel-mounted, ASV, and AUV applications, survey strategies generally involve variations on repeated transects (Cáceres et al. 2003; Epler et al. 2010; Geyer and Signell 1990; Shay et al. 2003), though station keeping methods that emulate repeated short-term stationary deployments have also been used to improve signal-to-noise ratios (Brown et al. 2011; Palodichuk et al. 2013). ADCP current measurements rely on an assumption of flow homogeneity across diverging sensing beams (e.g., at 80 m distance from instrument, beams with 20° angle from normal measure points 50 m apart). In flows with strong, sharp gradients, this assumption can be violated, thus increasing measurement uncertainty (Theriault 1986), though modern instruments flag measurements with poor correlation between beams. Early narrowband ADCPs also suffered from appreciable O(10%) full scale range Doppler noise, requiring averaging over multiple pings for acceptable accuracy (Geyer and Signell 1990). However, technological improvements in broadband processing have decreased Doppler noise to near-negligible magnitudes relative to mean current speeds in energetic tidal channels (Guerra and Thomson 2017). Finally, ADCPs cannot accurately survey near boundaries (surface or seabed) due to acoustic reflections (Teledyne RD Instruments 2019).

b. X-band radar

X-band radar images backscatter off capillary waves on the sea surface. Young et al. (1985) developed the algorithm to estimate water currents from a time series of similar radar measurements. The algorithm has been subsequently improved (Gangeskar 2002; Senet et al. 2001, 2008) and remains an area of active research (Bell et al. 2012; Campana et al. 2017; Huang et al. 2016; Lund et al. 2015, 2018; Shen et al. 2015). Horizontal surface currents are estimated from the difference between the distribution of measured wavenumbers and the distribution predicted by an ideal wave-dispersion relation (Bell et al. 2012; Lund et al. 2018; Swinkels et al. 2012; Young et al. 1985). The resulting data product is a map of horizontal surface currents over the imaged region. While a wide range of radar frequency bands [HF (Paduan and Washburn 2013), VHF (Sentchev and Yaremchuk 2007), etc.] have been utilized in wave field and current monitoring, we restrict our attention to X-band technologies, as the range and resolution are most comparable to the other survey methods. X-band radars are typically deployed on shore, though recent vessel-based deployments with motion compensation have proved successful (Lund et al. 2015, 2018). The primary advantage of shore-based radar is the capacity for large spatial coverage O(10) km2 over extended time-periods. However, because the method relies on wave–current interactions, there is inherent depth averaging in the estimated current field and limited subsurface resolution. Recently, vertical gradients in horizontal currents have been estimated from the wavenumber dependency of current-induced Doppler shift (Campana et al. 2017; Lund et al. 2015). However, fetch-limited coastal environments may not produce the spectrum of wavelengths necessary for these methods. In all cases, the accuracy of the current estimates depends on meteorological and wave conditions: wave height greater than 0.5 m, wind speed greater than 1 m s−1 (Miros AS 2019; Rutter 2019), and alignment of wind and waves within 45° (Friedman 2014), any of which may be intermittent in coastal waters. Additionally, all processing algorithms involve horizontal spatial averaging and must balance spatial resolution against measurement noise, with resulting output resolutions of 70 to 250 m. Last, typical X-band radar data products do not include any direct estimate of vertical velocity.

c. Float swarms

Oceanographic floats are in situ mobile sensing platforms that drift with the water currents. The most notable example is the worldwide Argo float array, with over 3800 floats currently deployed (Riser et al. 2016). These floats adjust their buoyancy to move up and down in the water column and send data back to shore via satellite when at the surface. Recent efforts have extended float sensing to coastal environments to measure internal waves (Jaffe et al. 2017), larval transport (Jaffe et al. 2017), circulation (Schwithal and Roman 2009), turbulence (D’Asaro et al. 1996), and biological abundance (Roman et al. 2011). The transition from ocean to coastal environments has spurred advancements in buoyancy control for larger density gradients and underwater tracking for sustained, high-resolution position measurements (Jaffe et al. 2017). While promising, floats have a number of weaknesses. First, due to their limited actuation, they may quickly leave the area of interest and the intervention (recovery and redeployment) necessary to sustain persistent sensing is labor intensive. Second, strong density gradients at freshwater–saltwater interfaces complicate control of buoyancy engines used for vertical actuation and self-ballasting (D’Asaro 2003; Schwithal and Roman 2009; McGilvray and Roman 2010). Third, when submerged, float position must be estimated. Most localization techniques rely on short acoustic messages from beacons with known locations [e.g., drifting GPS-localized buoys (Jaffe et al. 2017) or ultrashort baseline (USBL) (Raggi 2019)], and therefore accuracy is impacted by the quality of the acoustic environment. Nonacoustic methods include visual odometry (Casagrande 2013) and terrain-based localization (Raggi 2019) and are impacted by water clarity and knowledge of bathymetry, respectively. Whatever the method chosen, there will be associated limitations on accuracy, sample rate, and range of float position estimates.

2. Methods

a. Simulation domain

To compare platform performance, the virtual measurement campaign was conducted within a numerical simulation of Admiralty Inlet, Puget Sound. Puget Sound is a fjord estuary in which nearly the entire tidal prism is exchanged through Admiralty Inlet (Mofjed and Larsen 1984), leading to tidal currents in excess of 3.5 m s−1 (Polagye and Thomson 2013). Tides are mixed semidiurnal and have unbalanced ebb–flood cycles. Irregular coastline features, such as Admiralty Head, produce local flow acceleration and eddies. In additional to strong horizontal currents, two sills, at the northern and southern ends of Admiralty Inlet, cause strong upwelling and downwelling. The combination of vertical and horizontal gradients in water currents, as well as their temporal evolution, provides a complicated and energetic setting to evaluate platform performance.

We used the output from a high-resolution model of Admiralty Inlet (Thyng 2012a; Thyng et al. 2013), which is a subdomain of the Model of the Salish Sea (MoSSea; Sutherland et al. 2011). MoSSea is implemented in the Regional Ocean Modeling System (ROMS), a three-dimensional, free surface, hydrostatic model with structured horizontal coordinates and terrain-following vertical coordinates (Haidvogel et al. 2008; Shchepetkin and McWilliams 2005). For the subdomain, open boundary forcing information comes from MoSSea model. The Flather boundary condition is used for barotropic velocities and Chapman boundary condition for the free surface. Radiation and nudging were used for both the baroclinic velocity field and scalar quantities (i.e., salinity, density, and temperature). All walls were treated as no-slip and quadratic bottom stress with used with CD = 3 × 10−3, matching Sutherland et al. (2011). The subdomain has a uniform horizontal grid with 65 m resolution and 20 vertical terrain-following layers that stretch proportionally to the local water depth at each horizontal location. The model output consists of velocity components Ux, Uy, Uz aligned with east, north, up coordinates, respectively, as well as salinity, density, and temperature. Output temporal resolution is 15 min. Further specifics of the simulation are given in Thyng (2012a) and output data are available from Thyng (2012b). While the magnitude of the modeled tidal currents within the Admiralty Inlet subdomain are known to be underestimated relative to field observations, the model adequately reproduces general circulation patterns (Thyng 2012a; Thyng et al. 2013).

Within the subdomain, 24 locations were chosen for analysis (black points, Fig. 1), representing areas with strong spatial gradients (e.g., nearshore at Bush Point, Admiralty Inlet, and Point Wilson, Fig. 1, B, A, P, respectively), as well as midchannel locations with more homogenous flow. We evaluated platform performance during two tidal exchanges during September 2016 (arbitrary selection), for one strong, spring and one weak, neap tidal exchange (Fig. 2).

Fig. 1.
Fig. 1.

Virtual study site: (a) Admiralty Inlet. Color indicates local depth in meters, relative to mean sea level. Black circles indicate analysis locations. The black squares on land indicate X-band radar locations (N) North; (P) Point Wilson; (A) Admiralty Head; (M) Marrowstone Island; (B) Bush Point; (S) South. Location ID letter prefix indicates the corresponding radar location used for comparison with other platforms. (b) MoSSea model domain (Sutherland et al. 2011), with the Admiralty Inlet subdomain outlined in red. (c),(d) Horizontal currents at 15 m depth during peak spring ebb and flood tides, respectively.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0131.1

Fig. 2.
Fig. 2.

Time series of water surface level (ζ) at location A6. The two tidal cycles used in the analysis, a strong, spring exchange and weak, neap exchange, are indicated in gray.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0131.1

The virtual field experiment required interpolating the model output at arbitrary positions and times. Using MATLAB (MathWorks), terrain-following vertical layers were mapped to Cartesian coordinates based on local depth. Spatial linear interpolation functions, Gi = f(x, y, z), were then constructed for all model data outputs at each time step i to estimate quantities at any position. For the remainder of the paper, all reference to “sampling” the site model refers to querying these interpolation functions, rather than the discrete model output. Evaluation periods were constrained to a 15 min time interval to align with the model output time step and approximate period of statistical stationarity at this location (McCaffrey et al. 2015). For temporal interpolation to intermediate times within an evaluation period, we first compute spatial information at the two bounding model output time steps (i.e., Gi, Gi+1) and linearly interpolate between them.

Table 1 presents an overview of the raw data, sampling method, and processing for each platform. Figure 3 depicts the platform deployment stencil. The location of the stationary ADCP serves as the reference for deployment layout and determines nominal site parameters of depth Dnom (relative to the mean sea level) and velocity Unom (horizontal velocity at 2 m depth). For a given tidal exchange (ebb or flood), the deployment layout was aligned relative to the flow direction during peak currents, and remained constant through the exchange. Details of sampling and deployment are provided for each platform in sections 2ce and the underlying code is available from Harrison et al. (2019).

Table 1.

Summary of samples and processing for each platform.

Table 1.
Fig. 3.
Fig. 3.

Deployment stencil. At each location indicated in Fig. 1, the platforms were deployed accordingly. Horizontal spatial position is referenced relative to the stationary ADCP. Mobile ADCP survey and floats were aligned according to the nominal surface velocity Unom defined for each peak ebb and flood cycle. For the mobile ADCP, solid lines indicate transects (sampling) and dashed lines indicate transits (not sampling). For floats, the first float (“1”) is deployed furthest upstream and final float (“30”) aligned with the boundary of the mobile ADCP survey. For the radar, the light green box indicates the area of spatial averaging for the output point ×, with smaller light green dots indicating the raw samples. The larger light green dots indicate radar output points.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0131.1

b. Performance evaluation

Platform performance was evaluated in terms of “sample accuracy” (i.e., how accurately each platform estimated the currents at a position in space and time) and “volumetric reconstruction accuracy” (i.e., how accurately the volumetric currents could be reconstructed from the platform measurements).

1) Sample accuracy

The sampling accuracy of each platform was evaluated by comparing measured values to the true values at sample locations. As a reminder, “true” values are those interpolated directly from the original Admiralty Inlet model data. For radar and static ADCP surveys, sample error was taken as the difference between the measured and the true time-mean value at the sample location over the survey interval (15 min). For mobile ADCP and floats, sample error was computed as the difference between the instantaneous measured and true values at the sample location. Additionally for these two platforms, “time blurring” error (Willcox et al. 2001) was calculated as the difference between the instantaneous measured value and the time mean over the survey interval at the sample location.

2) Volumetric reconstruction accuracy

The accuracy of each reconstruction was assessed by comparing the measured field to the true field over the survey volume shown in Fig. 4, defined by the rectangle bounding the mobile ADCP survey in the horizontal plane (~400 m × 500 m) and by the water depth in the vertical. A regular grid of query points with 5 m × 5 m × 2 m resolution was generated throughout the survey volume. The true field, U, was defined as the ROMS model output spatially interpolated over this evaluation grid and time averaged over the survey interval. This oversampling of the ROMS model output improves the visual interpretation of reconstruction errors. The measured field, U˜, was generated for each platform as detailed in sections 2c and 2d. To facilitate interpretation, we present these fields as horizontal current magnitude |UH| and direction θH. Local reconstruction error Ek is calculated as the difference between the measured and true field at evaluation point k,
Ek=U˜kUk.
Examining spatial distributions of reconstruction errors over a horizontal plane provides a qualitative understanding of how site dynamics and sampling techniques interact. However, a more compact representation is necessary for quantitative comparisons between multiple locations and tidal exchanges. For this purpose, we use the median absolute deviation (MAD) to characterize reconstruction accuracy. This is evaluated over the grid for each survey interval as
MAD=median(|Ek|).
Fig. 4.
Fig. 4.

Evaluation geometry. The survey volume (indicated by dashed lines) is defined horizontally by the extent of the mobile ADCP survey (orange, transits omitted for clarity) and vertically by the water depth. The gray horizontal plane at 15 m depth is used to compare reconstruction accuracy in section 3a. The gray vertical cross-stream plane aligned with the stationary ADCP location (red) is used to evaluate salinity field reconstruction accuracy in section 4f. As in Fig. 3, water flow direction is indicated by the blue arrow.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0131.1

c. ADCP measurements

ADCPs estimate three-dimensional current speed by measuring the beamwise velocity of acoustic scatterers (e.g., zooplankton, sediment, bubbles) via the Doppler shift of a transmitted pulse, or “ping” (Teledyne RD Instruments 2019). Time gating differentiates the distances of returned signals from the instrument. With multiple, divergent beams, an assumption of spatial homogeneity of the measured field, and knowledge of the instrument position relative to the global reference frame, beam velocities are transformed to absolute water velocity. These samples are assigned a nominal position along a vertical profile extending away from the instrument.

ADCP: Model implementation

To capture the sampling error associated with ADCP beam spread in an heterogeneous current field, we followed the method of Richmond et al. (2015). A stencil of instrument-relative sample points was constructed based on the specified instrument range (100 m), bin size (1 m), blanking distance (1 m), and beam angle (20°), and transformed to absolute coordinates according to the instrument position, heading, and orientation (upward looking or downward looking). The ROMS site model (section 2a) was sampled at each along-beam bin location, projected into the beam direction, and these along-beam velocities were then used to estimate the absolute Cartesian velocity. We neglect Doppler noise here, but discuss its implications in section 4b. For bottom-mounted, upward-looking ADCPs, samples near the sea surface (within 6% of local water depth) were discarded. For vessel-mounted, downward-looking ADCPs, equivalent samples near the bottom were discarded.

(i) Stationary platform
A bottom-mounted, upward-looking ADCP was implemented as the representative stationary deployment configuration (red circle, Fig. 3). The ADCP was elevated 1 m from the sea floor, consistent with a typical bottom package. A single, time-average profile was generated for each 15-min survey interval. To extrapolate the profile over the survey volume, we assumed a constant velocity profile shape, but scale magnitude as
Ulocal=UADCPDnomDlocal,
where Dlocal is the local water depth. Velocity direction was assumed horizontally invariant over the survey volume. This “continuity” extrapolation is naïve, but a reasonable starting point for a previously unsurveyed location, and, as discussed in section 3a, yields relatively low MAD values.
(ii) Mobile platform

The mobile ADCP survey was modeled as a downward-looking ADCP submerged to a depth of 1 m below a small vessel. The survey path followed a “lawn mower” pattern (orange track, Fig. 3) and was constrained to a synoptic, round-trip time of 15 min. The path consisted of four 400 m survey transects oriented perpendicular to the horizontal current and centered on the stationary ADCP. Vessel speed was 2 m s−1 along transects, sufficient to maintain vessel controllability in high currents while minimizing overground and relative flow velocities, both of which are potential sources of measurement error (Epler et al. 2010; Goddijn-Murphy et al. 2013). Along each transect, a profile was sampled every 1 m of horizontal distance, corresponding to a 2 Hz sample rate. Maximum sample rates of ADCPs appropriate for our site depths are 8 Hz, thus the rate used here corresponds to a four-sample averaging to further justify omission of Doppler-noise effects. Vessel speed increased to 10 m s−1 between transects, resulting in a transect separation distance of approximately 125 m. We optimistically assumed the vessel had sufficient propulsion to overcome surface currents and that bottom-tracking and ship-motion compensation algorithms (Teledyne RD Instruments 2019; Fong and Monismith 2004; Muste et al. 2004; Heitsenrether et al. 2018; Velasco and Nylund 2019) were able to mitigate impacts of vessel heave, pitch, or roll on data quality. The data output from the mobile ADCP survey was a profile of three-dimensional velocity at each sample (i.e., ping) location along the transects. All samples within a survey interval were used to construct a linear interpolation function for comparison with the true field.

d. X-band radar

The raw data output from an X-band radar consists of a series of digitized images of radar backscatter from capillary waves. Every antenna revolution (2–4 s period), a 360° image is produced, with range and resolution determined by power, settings, and deployment geometry. Data processing requires a time series of O(100) images, so in practice, a current field estimate can be produced every 4–7 min. All modern data-reduction techniques utilize a three-dimensional fast Fourier transform over a spatial window through a number of time frames to estimate the wave field and currents. The process generates a single, spatially averaged current estimate for each window. Larger spatial windows improve the signal-to-noise ratio, while smaller windows reduce inhomogeneity within the analyzed wave field and better resolve gradients. While the analysis window can be shifted by an arbitrarily small amount, movements smaller than the window size act to smooth the output grid, rather than increase underlying resolution, at the cost of increased computation time (Friedman 2014). Balancing these factors, window sizes range from 70 m (J. Culina 2019, personal communication) to 750 m (Campana et al. 2017), with 0%–50% overlap. Further, real wave fields contain a spectrum of wavelengths, where longer wavelengths penetrate deeper and interact differently with the underlying currents (Lund et al. 2015).

X-band radar: Model implementation

Fully resolving a realistic water-wave climate, simulating the radar-signal interaction, and implementing a typical data-reduction technique was well beyond the scope of this paper. Instead, we restricted our effort to generating a velocity field representative of those produced by X-band radar data, while specifically accounting for the depth averaging inherent in wave–current interactions and horizontal spatial averaging inherent in radar postprocessing. We assumed the radar to have a range of 4 km radar with no degradation of accuracy within that range. Consequently, six onshore locations (black squares, Fig. 1) provided coverage for all survey locations. The data output was a 150 m resolution grid of current estimates within the sensed region of a given radar (larger light green dots, Fig. 3). To account for spatial averaging inherent in data processing, each output point was generated by oversampling the true field on a 50 m grid within a 300 m square spatial window (light green rectangle and points, Fig. 3) centered on the output point and averaging the result. Wave–current interactions were approximated by depth averaging currents from the top 5 m of the water column (corresponding to a surface wave with a 10 m wavelength). For the purposes of evaluating sample accuracy, measurements were assigned to a nominal depth of 2.5 m below the surface (i.e., midpoint of the 5 m depth average). For volumetric reconstruction of horizontal velocity, we assumed 1/7th power-law velocity profile (Sellar et al. 2018), decaying from the estimated near-surface current to 0 m s−1 at the seabed. Direction was assumed constant with depth. One current field estimation was generated every survey interval (15 min).

e. Float swarm

Underwater floats function as trackable water parcels with vertical control achieved via buoyancy manipulation (D’Asaro 2003; McGilvray and Roman 2010). Floats are small (<1 m) relative to spatial variations in mean currents, and when adjusted to be neutrally buoyant, float transport can be considered Lagrangian (i.e., float velocity is equal to the local water velocity) (D’Asaro 2003; D’Asaro et al. 1996; Davis 1991).

Float swarm: Model implementation

The float swarm was composed of 30 individual floats (dark green dots, Fig. 3). This number was chosen semiarbitrarily as a balance between deployment/recovery logistics and volumetric sampling density. As a relatively nascent approach for sampling in coastal waters, there remain technological challenges associated with buoyancy control and localization (D’Asaro 2003; Jaffe et al. 2017; McGilvray and Roman 2010). Because underwater localization remains an area undergoing rapid evolution (Tan et al. 2011; Li et al. 2016; Luo et al. 2018) and our focus is interplatform comparison, we did not define a specific localization method and instead optimistically assumed that underwater tracking could provide absolute position of the floats every 5 s. We discuss implications of position uncertainty in section 4b and operational challenges in section 4d.

We simulated a simple float deployment procedure employed by Jaffe et al. (2017): a vessel-running cross stream with floats sequentially placed in the water. As shown in Fig. 3, the vessel path was angled such that all floats entered the survey volume at roughly the same time. The deployment line ran 500 m cross stream (extending 50 m to either side of the mobile transects). We assumed floats could be dropped over the side at an interval of 5 s, requiring 145 s to deploy all 30 floats and vessel speed of 3.8 m s−1. The floats were set to one of five depth settings (5%, 20%, 40%, 60%, 90% of nominal site depth), repeated sequentially along the deployment line. On deployment, a float would dive at a rate of 0.4 m s−1 (a reasonable balance between buoyancy actuation and drag) until reaching target depth, then adopt Lagrangian behavior under the assumption that control action maintains neutral buoyancy. In the event that a float impacted the seabed (e.g., advection by downwelling), the float track was discontinued. In fast currents, floats leave the survey volume during the 15-min survey interval, while in relatively slow currents, floats only traverse part of the survey volume. To compare this sampling approach to other platforms, a new float swarm was deployed every 15 min. This optimistically assumes a sufficient supply of floats and vessels such that deployment can occur concurrent with recovery.

The raw data output from the swarm are float positions every 5 s. Velocity was computed by differentiating position (third-order polynomial spline). As with the mobile ADCP survey, all samples collected within each survey interval were considered a single snapshot of the field and used to compute a linear interpolation function for comparison to the true field. Velocities during diving and resurfacing were not included in the reconstruction. No extrapolation was made to evaluation points outside the convex volume bounding float samples and excluded evaluation points were not included in calculation of reconstruction statistics (i.e., MAD assessed only over the volume surveyed, not necessarily the entire survey volume).

3. Results

a. Volumetric current reconstruction at a single location

Figure 5 depicts the time series of the horizontal velocity magnitude reconstruction accuracy (MAD) during the spring tidal cycle for each type of measurement platform at a midchannel location between Admiralty Head and Point Wilson (Fig. 1, Site A6), as well as snapshots of the vertical and horizontal spatial variations of currents and reconstruction errors throughout the tidal cycle.

Fig. 5.
Fig. 5.

Volumetric current reconstruction midchannel between Admiralty Head and Point Wilson (Fig. 1, Site A6) during the spring tidal cycle. (a) Time series of the median horizontal current magnitude and interquartile range (IQR) and the corresponding MAD for each platform, as evaluated over the entire survey volume. (b) Magnification of the vertical axis in (a), dropping current and radar data series for easier comparison of stationary ADCP, mobile ADCP, and floats. (c)–(h) Snapshots of the field and reconstructions at the indicated time. (c) Current profile (median and IQR) and platform errors [Eq. (1)] at the static ADCP location. (d)–(g) Reconstruction errors over a horizontal plane at 15 m depth. (h) Current anomaly, U − median(U) on the same plane. The dashed line across the vertical profiles in (c) indicates the horizontal plane. For floats in (e), light gray regions indicate unmeasured portions of the survey volume due to insufficient float coverage.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0131.1

The mobile ADCP survey produces the lowest reconstruction error throughout the tidal cycle (Figs. 5a,b). From the snapshots (Figs. 5c,d), we observe the effects of nonsynoptic measurements (i.e., time blurring). When the flow is accelerating (hour 3, strengthening ebb), the reconstruction underestimates the mean field over the upstream half of the survey area (instantaneously sampled velocity is less than the time mean over the survey interval) and overestimates it for the downstream half. During peak ebb (hour 5), there is minimal field acceleration, and the error is negligible over the domain.

The float swarm has a MAD comparable to the mobile ADCP survey (Figs. 5a,b), though artifacts of linear interpolation from sparse sampling can be observed in all float snapshots (Fig. 5e). The floats have three primary limitations. First, during weak currents (less than 0.6 m s−1), they do not traverse the entire survey volume (e.g., during slack tide, Fig. 5e, hour 2 and hour 8). Second, as for the mobile ADCP, there is nonsynoptic measurement error (e.g., underestimate at hour 3, overestimate at hour 7). This is because the floats pass through the domain in much less than the 15-min survey interval during periods of high currents, and thus measure a slower speed than the interval time mean when the flow is accelerating and a faster speed when the flow is decelerating. Third, the float measurements are spatially sparse. For example, float sampling cannot resolve the vertical gradient over the upper 20 m of the water column at hour 10, leading to systematic overestimate of current speed (Fig. 5e). However, the flow is also accelerating during this period, which means that the nonsynoptic error concurrently underestimates current speed. This is an example of how these limitations can combine to produce unexpected patterns in reconstruction errors.

Despite the simplistic horizontal extrapolation scheme, the stationary ADCP performs moderately well through much of the tidal cycle (Figs. 5a,b). Reconstruction errors (Figs. 5a,b) are correlated with the horizontal current anomaly (Fig. 5h). Because the vertical profile is relatively consistent within the survey volume (the vertical profile IQR is frequently not discernible from the median, Fig. 5c), the single profile is representative.

Conversely, the radar performance correlates directly to time variation in the vertical profile. When the current profile is well represented by the assumed power law (Fig. 5g, hours 5, 7, 12, and 14), the reconstruction error is similar to the other platforms (Fig. 5a). However, reconstruction error increases sharply when the vertical structure deviates from this approximation (e.g., hours 9 and 10).

b. Sources of error

Reconstruction error is a combination of the sampling error for individual measurements and errors from interpolation and extrapolation in space and time. Table 2 shows that, for all devices, error contributions from sampling are an order of magnitude smaller than those from reconstruction interpolation and extrapolation.

Table 2.

RMS sample, time-blurring, and reconstruction error (MAD) computed over time series in Fig. 5a for each measurement platform.

Table 2.

For both the float swarm and the mobile ADCP, instantaneous sample error is negligibly small relative to the interpolation errors. For the floats, the small sample errors are expected, as the only source of error is the differentiation of position to estimate velocity. For both ADCPs, sample error results from nonuniform flow across the beams; however, the stationary ADCP exhibits higher sample error than the mobile ADCP. This makes sense, since beam spreading for the bottom-mounted, upward-looking platform is greatest near the surface where currents are strongest, while for the downward-looking platform at the surface, beam spreading is greatest where currents are smallest. Sample error is highest for the radar, appropriate as it averages over a much larger volume of water than the other platforms.

Additionally, reconstruction error for both the mobile ADCP and floats appears predominantly attributable to time blurring, as shown by the comparison of reconstruction error (MAD) to field acceleration (Fig. 6). For the mobile ADCP, the spatial interpolation implemented in the reconstruction mitigates the time-blurring error, as the transect sampling scheme causes upstream (early) samples to be spatially averaged with downstream (late) samples. In contrast, float measurements are all sequentially “downstream” in both space and time and thus interpolation exacerbates the time-blurring error, increasing the reconstruction error.

Fig. 6.
Fig. 6.

Comparison of mobile ADCP (orange) and float (green) errors to field acceleration over time for Site A6. For platforms, solid lines are median time-blurred sample error and dotted lines are the reconstruction error, as defined in 2b. The solid blue line is the field acceleration.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0131.1

c. Performance trends across locations

Moving away from the single survey location discussed in sections 3a and 3b, we now consider platform performance across all 24 representative locations in the Admiralty Inlet subdomain. Figure 7 shows the time-distribution of platform performance (MAD) at each location (i.e., each platform time series in Fig. 5 is reduced to the statistical distributions shown for site A6 in Fig. 7). These distributions include data from both the spring and neap tidal cycles, with no noteworthy differences in performance between spring and neap. Across locations, there is minimal variation in performance of the mobile ADCP or floats. Stationary ADCP and radar exhibit greater variability, which is expected since the appropriateness of the simple extrapolations in the horizontal and vertical directions change with location. Figure 8 reduces these data further, categorizing the overall performance of each platform in an energetic coastal setting by the distribution of time-median reconstruction errors over all locations. This is evaluated for horizontal velocity, horizontal direction, and vertical velocity. Overall, relative platform performance is consistent across velocity components and locations in the Admiralty Inlet subdomain.

Fig. 7.
Fig. 7.

Temporal distribution of horizontal velocity reconstruction accuracy (MAD) at all locations. Location IDs correspond to the positions in the site map (Fig. 1). Note the axes scale for stationary ADCP and radar are double that for floats and mobile ADCP, as indicated by the shading. For each distribution, the white bar denotes the median, the thick bar denotes the interquartile range (IQR), and whiskers extend from Q25 − 1.5 × IQR to Q25 + 1.5 × IQR. All values outside that range are considered outliers and denoted by points. For each platform, the median and IQR computed over the median values (white bars) from all locations are included for reference.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0131.1

Fig. 8.
Fig. 8.

Generalized performance trends over the domain. Each distribution is composed of the temporal median from each of the 24 locations (i.e., distribution of the white bars in Fig. 7). Note the difference in units for horizontal (cm s−1) and vertical (mm s−1) currents. Distribution statistics are the same as described in Fig. 7.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0131.1

4. Discussion

a. General trends in reconstruction accuracy

When interpreting results, we remind the reader that the conclusions drawn are specific to the spatial and temporal range and resolution of the simulated survey: in this case, mean currents measured at 15 min intervals during the span of a tidal cycle (12 h) over a horizontal range of <1 km with 5 m resolution and vertical ranges <100 m with 2 m resolution. We expect the trends observed here will hold for surveys at similar orders of magnitude and discuss implications for considerably different scale in section 4c. For this virtual survey, there are consistent trends in volumetric reconstruction accuracy: mobile ADCP performs best, followed closely by the float swarm and the stationary ADCP, and finally X-band radar. Relative performance varies in time (Fig. 5), with stationary ADCP and floats sometimes matching performance of the mobile ADCP, and the radar sometimes outperforming the stationary ADCP. While these distributions do vary moderately by location (Fig. 7), this variation is small relative to the overall differences between platforms. Further, the performance trend is consistent across all velocity components (Fig. 8). The performance trends are correlated with the number of samples obtained by each platform within the survey volume. This demonstrates that the accuracy of volumetric reconstruction depends primarily on sample distributions and appropriateness of the interpolation/extrapolation scheme, rather than the individual sample accuracy. This is consistent with the magnitude of the sample, time-blurring, and reconstruction errors shown in Table 2. The mobile ADCP and floats directly sample throughout the survey volume and, accordingly, perform better than the X-band radar and stationary ADCP, which require assumptions about the vertical and horizontal structure, respectively. The stationary ADCP is able to estimate volumetric currents with surprising accuracy when combined with a simple horizontal extrapolation. During periods with strong mean-flow acceleration, the stationary ADCP can even outperform a mobile ADCP survey, as it is unaffected by time blurring. The relative performance difference between the radar and stationary ADCP is consistent with velocity gradients in the survey volumes, which are more significant in the vertical than horizontal directions.

We emphasize that these results are indicators of relative rather than absolute platform performance for several reasons. First, the MoSSea model is known to underestimate peak velocities in this region by as much as 1 m s−1 and has correspondingly weaker spatial gradients (Thyng 2012a). Second, the reconstruction errors are specific to the interpolation and extrapolation methods, and the simple strategies used here are likely a conservative estimate of the absolute accuracy that could be obtained with more sophisticated methods. For example, temporal de-meaning (Goddijn-Murphy et al. 2013; Sellar et al. 2018; Vennell 1994) or model-based data assimilation strategies [e.g., EOF (Toner et al. 2001), 4DVar (Bannister 2017)] would likely reduce reconstruction errors across platforms.

b. Extension to real surveys

We expect the overall performance trends observed here to extend to real surveys. However, the relative differences will be altered by sources of error omitted from our platform models and environmental phenomena not captured in the site model.

1) Impact of omitted platform sample errors

Our sample errors are significantly smaller than those reported for experimental measurements using some of these platforms. For mobile ADCPs, Guerra and Thomson (2017) report single-ping noise of 0.027 m s−1, which is an order of magnitude larger than errors arising from the inhomogeneity across beams that is resolved by our implementation. For floats, Jaffe et al. (2017) estimate localization accuracy of ±1 m horizontal with an update interval of 12 s, corresponding to velocity uncertainty of ±0.08 m s−1, two orders of magnitude larger than sample errors from differentiation of position to obtain velocity. For both of these platforms, real sample error appears to be of similar magnitude to the reconstruction error estimated here. X-band radar measurements have recently been validated against surface drifters, with measurement differences of approximately 0.04 m s−1 (Lund et al. 2018). As with the mobile ADCP and floats, these differences are an order of magnitude larger than errors arising from the spatial averaging in our implementation.

To explore how increased sample error for the mobile ADCP and floats would impact reconstruction accuracy, we reconsidered the simulation at site A6, modifying the float localization to include ±1 m standard deviation white noise on horizontal position, and the mobile ADCP to have ±0.03 m s−1 standard deviation white noise in horizontal velocity. With the additional noise, the root-mean-square reconstruction error (MAD) for the mobile ADCP increases to 0.024 m s−1 and, for the float swarm, increases to 0.053 m s−1. This amounts to increases of 15% and 30%, respectively, relative to the errors reported in Table 2 arising from the more optimistic approach. Therefore, we expect the relative performance differences between mobile ADCP, floats, and stationary will likely decrease for real surveys, but maintain the hierarchy described in section 3c.

2) Impact of additional environmental phenomena

Next, we consider the implications of dynamics not resolved in the Admiralty Inlet subdomain. The site model does not resolve flow gradients at horizontal scales less than 65 m, vertical scales less than 3–5 m, and temporal scales less than 15 min (i.e., velocity perturbations from turbulence or wave orbital velocities are not explicitly resolved). Because the radar and stationary ADCP obtain a time-averaged measurement, we do not expect their ability to reconstruct mean currents to be affected by waves or turbulence (with the caveat that X-band radar measurements require sufficient waves for operation). The impact of turbulence on the mobile ADCP and floats is more subtle. For both platforms, small-scale isotropic turbulence (1 s to 1 min) will increase sample error in a similar manner as the elevated sample noise scenarios. In contrast, larger, coherent turbulent features with time scales on the order of 1 to 15 min can substantially bias float measurements. For example, if some floats are caught within a coherent gust (e.g., an eddy) that propagates through the domain, they may observe currents that depart substantially from the time-mean value of that area. Without repeated sampling within the statistically stationary period, it is impossible to separate temporal variability from spatial gradients. Mobile ADCPs face similar challenges, though these are mitigated by the ability to maintain a survey transect through large-scale flow features. Therefore, for locations with relatively large coherent turbulent features, we expect reconstruction error to increase moderately for floats and, to a lesser extent, mobile ADCPs.

Wave effects will vary with site. In some locations, wave conditions may be strong enough to modify the overall mean flow field (Hashemi et al. 2015; Wolf and Prandle 1999) and sampling from all platforms should be avoided in waves if measurements of purely tidal currents are paramount. In moderate sea states when the velocity field can be treated as a linear superposition of wave orbital velocities and tidal currents, estimates of tidal currents can be obtained using processing specific to each platform and to the relative magnitude of wave and current contributions. For tidal channels like Admiralty Inlet, which are protected from swell, the wave field will be fetch-limited with relatively short wavelengths and waves would be unlikely to significantly bias sampling of energetic mean currents over the water column. However, in locations with greater exposure to high-amplitude swell, such as Pentland Firth, United Kingdom, or locations with lower mean currents, wave orbital velocities may be comparable to tidal currents. Time averaging samples will filter wave contributions for radar and stationary ADCP measurements, but more sophisticated processing would be necessary to parse these contributions in mobile ADCP and float surveys. Finally, while the site model also lacks wind-driven currents and Stokes drift, we do not expect these phenomena to noticeably alter the results, as they also decay exponentially with depth and their velocities (0.01–0.1 m s−1) are an order of magnitude smaller than mean currents over most of the tidal cycle at the study location.

c. Extension to larger survey areas

With regards to spatial coverage, the results presented are constrained to a mobile ADCP survey to a track that could be repeated in 15 min, resulting in a relatively small 400 m × 500 m area. While quantitative analysis of generalized survey strategies is beyond the scope of the present work, some qualitative discussion is possible. For the mobile ADCP survey, expanding coverage will reduce horizontal resolution and increase time blurring in accelerating flows (Willcox et al. 2001). For floats, coverage depends on the deployment distribution and the currents. Adjustments to the deployment distribution based either on a priori knowledge or real-time observations of trajectories could improve accuracy and/or coverage. For the static ADCP, the success of the horizontal extrapolation implies that locations throughout Admiralty Inlet (as modeled) are largely horizontally homogeneous over spatial scales <250 m. As the extrapolation scheme is applied over larger survey areas or to locations with stronger horizontal gradients, accuracy is expected to diminish. Conversely, X-band radar provides an order of magnitude greater spatial coverage than the other platforms, with accuracy expected to remain largely constant over a larger survey area.

d. Operational constraints

Thus far, our evaluation has solely considered the relative accuracy of the platforms, yet the choice of sensing platform must also weigh operational constraints: costs, spatial coverage, duration, and operational logistics. These are summarized in Table 3. Logistically, a radar system is the simplest platform to deploy, supervise, and recover because it is land based and is only restricted by availability of a vantage point and electrical power. Deployment and recovery of bottom-mounted ADCPs is also relatively straightforward, requiring a vessel with sufficient lifting capacity and favorable surface conditions during a slack tide. Bottom platforms must have sufficient ballast to remain stationary when exposed to strong tidal currents or wave orbital velocities in locations with high-amplitude swell, and be trawl resistant in locations with active fishing. Mobile ADCP surveys require a ship with sufficient propulsion to maintain maneuverability in strong tidal currents and moderate wave conditions, though even then, consistent repetition of survey tracks can be difficult (Epler et al. 2010). Floats are logistically much more challenging, requiring deployment and recovery once per survey interval. Logistical effort and cost will scale with the number of floats and their spatial distribution at recovery. Because of this, such operations may be better suited to autonomous, robotic systems than human crews. However, float swarms may be able to use the depth and time variance of currents (Smith and Dunbabin 2011) to increase persistence and reduce logistical effort devoted to deployment and recovery. Finally, most float localization schemes use active acoustics, which require additional infrastructure, supervision, and specific environmental conditions (e.g., ambient noise at localization frequencies) to ensure optimal data quality.

Table 3.

Operational considerations for survey platforms.

Table 3.

e. Combining stationary ADCP and X-band radar

Both stationary ADCP and X-band radar provide long-duration datasets, but suffer from required extrapolations in the horizontal and vertical directions, respectively. As they provide complementary vertical and horizontal data, a logical solution is to deploy the platforms simultaneously. To evaluate the potential benefits for dual-platform deployments, we used the ADCP-measured vertical profile structure over the survey domain, scaled by the magnitude of the radar-measured local surface current relative to the surface current at the ADCP. The combined method was evaluated for all locations. As shown in Fig. 9a, combining stationary ADCP with X-band radar results in a median MAD over all locations of 0.029 m s−1, a moderate improvement over the stationary ADCP in isolation (0.039 m s−1) and a dramatic improvement over the X-band radar (0.121 m s−1). While the combined method outperforms floats (0.032 m s−1), the mobile ADCP (0.014 m s−1) remains the optimal method. Figures 9b–d depicts example cases of combined performance for the spring tidal cycle (currents as depicted in Fig. 5a) relative to the simpler stationary ADCP and radar methods, with mobile ADCP included for reference. Over all locations and for the vast majority of the time, the combined method is either equal to or better than the lesser of ADCP and radar reconstructions errors, as is demonstrated in Fig. 9b. However, combining the platforms does not always improve the results, as can be observed in Fig. 9c from hours 9–14, suggesting a particularly complicated flow, with strong variations in the horizontal and vertical. Finally, Fig. 9d depicts a case when the site variance is largely vertical: the radar reconstruction suffers from the power-law extrapolation while the stationary ADCP performs nearly as well as the mobile ADCP. This site also demonstrates the most common way in which the combined method performs worse than either isolated platform: at hours 9–10, the radar error dominates the reconstruction, suggesting that the horizontal variance at the surface, as captured by the radar, is different than the variance throughout the water column. While the mobile ADCP still consistently performs better than the combined method, the dual deployment of stationary ADCP and X band generally increases accuracy and has a clear persistence benefit over either floats and mobile ADCPs.

Fig. 9.
Fig. 9.

Combined stationary ADCP and radar deployment. (a) Distribution of horizontal velocity reconstruction accuracy (MAD) at all locations. Distribution statistics are as described in Fig. 7. (b)–(d) Time series of MAD for combined method as compared to radar, stationary ADCP, and mobile ADCP at locations A2, A5, and B4. Floats excluded for clarity.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0131.1

f. Float swarm physical sampling

While floats are unable to reconstruct velocity with as high an accuracy as the mobile ADCP and are only suited to short-term deployments, they have one distinct advantage over the other platforms: they can simultaneously sample physical properties that cannot be remotely sensed at depth, such as temperature, salinity, and dissolved oxygen. To demonstrate this capacity, we applied the same methods to sample and reconstruct salinity, another output from the site model, under an assumption of negligible sample error in this quantity. Figure 10 shows the salinity reconstruction accuracy of the float swarm through site A6 during the neap tidal cycle (condition with highest stratification). As would be expected, depth-averaged salinity increases during the flood tide, as water from the Pacific Ocean enters the domain from the northwest, and decreases during ebb when brackish water exits Puget Sound. The floats accurately capture this signal, with reconstruction errors an order of magnitude smaller than the range over the time series. The one notable exception is around slack tide, when poor coverage biases the volumetric reconstruction at hours 6 and 7. As for the velocity fields, interpolation artifacts caused by sparse sampling are evident in all reconstructions (Fig. 10c), but suggest an ability to volumetrically resolve gradients in scalar water properties to an extent that is not currently feasible.

Fig. 10.
Fig. 10.

Reconstruction error of salinity field. (a) Time series of the true salinity (solid purple), the float measured salinity (dashed purple), and magnitude of the horizontal water currents (solid blue) over the weak-neap exchange (all are median values evaluated over the survey volume). (b),(c) Snapshots of the cross-stream vertical plane (Fig. 4) centered on the stationary ADCP location, with the dark gray region indicating the seafloor. Thus, floats in streamwise currents move into the page. Salinity anomaly in (b) is the spatially demeaned field at the indicated time step. Reconstruction error in (c) is the difference between the measured and true salinity field at all evaluation points in the survey volume. For the reconstruction, light gray regions indicate unmeasured portions of the survey volume due to insufficient float coverage.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0131.1

5. Conclusions

This study evaluates the ability of four sensing platforms—stationary ADCP, mobile ADCP, X-band radar, and a float swarm—to volumetrically characterize four-dimensional currents over a survey volume with a horizontal extent of 400 m× 500 m. For this virtual survey, mobile ADCP surveys perform best, followed closely by float swarms, and then, more distantly, stationary ADCPs and X-band radar. X-band radar does, however, provide significantly greater coverage than any other platform and has a low incremental cost for relatively long survey durations. Radar accuracy can be significantly improved by simultaneously deploying a stationary ADCP to provide information about the vertical velocity structure, overcoming the primary limitations of both platforms. While a mobile ADCP is likely the best choice for surveying currents at these scales [range O(1) km, resolution O(10) m], floats can simultaneously gather cotemporal scalar quantities, such as temperature, salinity, and dissolved oxygen. Even though this study is specific to a tidally dominated environment, accurate volumetric reconstructions in any environment require measurements that adequately sample horizontal and vertical gradients.

Acknowledgments

Thanks to Alexandra Simpson from Oregon State University for guidance on X-band radar systems. Joe Culina provided valuable details on X-band window processing. Thanks also to Emma Cotter for helpful discussion and thoughtful comments. We additionally thank our three anonymous reviewers for their thorough and constructive feedback. All color maps used here came from the cmocean library (Thyng et al. 2016). Funding: This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant DGE-1762114 and U.S. Department of Defense Naval Facilities Engineering Command.

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