Multivariate Data Assimilation at a Partially Mixed Estuary
1. Introduction
Having synoptic bathymetry coverage is imperative for coastal management and maritime logistics, and numerical models used for decision-making rely on accurate coastal bathymetry. The highly dynamic nature of nearshore environments and the combination of hydrodynamic forcing and sediment transport necessitates continuous monitoring of the ever-changing bathymetry, with inherent logistical challenges. Year-round, frequent in situ bathymetric surveys are generally impractical. On the other hand, the abundance of remote sensing options including drifters (Thomson 2012), satellite imagery (Horstmann et al. 2015; Ardhuin et al. 2018), X-band radar (Holman and Haller 2013; Honegger et al. 2020), and using marine animals via biologging (Roquet et al. 2017; Chung et al. 2021) opens an opportunity for inverse modeling to retrieve bathymetry. The inversion skill will, however, depend on the coverage of observations within the model domain (which may differ for different observation types), and the sensitivity of the observed variables to the underlying bathymetry. As shown by Moghimi et al. (2016), ocean-estuary observations are often heterogeneous and/or are limited in coverage (e.g., observations of wave height are usually limited to the outer wave-exposed estuary), and a mixture of different observation types may be necessary to obtain accurate bathymetry inversion over the full model domain. Given the increasing number and diversity of coastal observational data, a critical inquiry arises as to the usefulness of such data for mapping coastal bathymetry, determining the necessary amount, and evaluating the accuracy of the mapping compared to traditional surveying techniques.
The present work combines observations of surface currents and wave statistics (significant wave height and surface gravity wavenumbers) to estimate bathymetry (e.g., Zaron 2017a). In recent years, there have been numerous inversion approaches developed and tested in various coastal domains (i.e., rivers, nearshore, estuaries). Zaron et al. (2011) employed a weak-constraint variational technique to calculate bathymetry from surface currents in Haverstraw Bay, Hudson River, New York, which allows for model forcing errors. Similarly, Almeida et al. (2018) adopted a strong-constraint variational technique based on an analytical derivation of the pertinent adjoint equations for nonlinear shallow water flow to invert surface currents over a 95 km section of the Columbia River at Hanford, Washington. The inversion of river bathymetry has also been done using ensemble-based inversion techniques using surface drifters on the Snohomish River, Washington, and the Kootenai River, Idaho (Wilson and Özkan-Haller 2012; Landon et al. 2014). Honnorat et al. (2009) formulated a novel Lagrangian variational approach to estimate the bathymetry of surface drifter trajectories in the 2D shallow water equations. Similarly, Khan and Kevlahan (2021) described a variational inverse method that estimates bathymetry from surface gravity waves in a nonlinear shallow water equation model. Various approaches have been applied to estimate shallow water bathymetry from video recordings, including Kalman filters (Holman et al. 2013), wave mode decomposition (Gawehn et al. 2021), and a combination of both methods (Simarro and Calvete 2022). Ge et al. (2020) developed a wave dispersion–based inverse method for getting bathymetry from shallow/intermediate water surface gravity waves. Santos et al. (2022) combined video imagery and numerical modeling to estimate bathymetry at Figueira de Foz Inlet at the Portuguese coast for intermediate and shallow depths using an analytical wavelet approach. Khan and Kevlahan (2022) introduced an application of inverse methods to shallow coastal domains and used their variational code to conduct adjoint sensitivity analysis. Ensemble methods have also been used for bathymetry inversion in the surfzone by Wilson et al. (2010, 2014), in New River Inlet (a well-mixed estuary), North Carolina, by Moghimi et al. (2016) and a partially mixed estuary by Ardag and Wilson (2022). And on a larger coastal scale, Zaron (2017b) used a variational method to invert tidal observations in the Sea of Okhotsk, for bathymetry and bottom roughness estimations. Importantly, with some exceptions the majority of these past studies on coastal bathymetry inversion have focused on a single observation type, for example, inverting the surface gravity wave dispersion relationship. However, as noted previously, estuaries are a highly heterogeneous environment and in practice a mixture of observation types is often required to estimate bathymetry across the full model domain Moghimi et al. (2016).
Ardag and Wilson (2022) demonstrated the potential for estimating bathymetry at a partially mixed estuary, the mouth of the Columbia River (MCR) by using surface current velocities based upon an iterative ensemble approach initialized from a generic first-guess bathymetry. They used twin tests (i.e., synthetic observations obtained from the same numerical model used for inversion), hence neglecting the potential impacts of observation error and model error on the inversion. Both surface and depth-averaged currents were tested successfully inside the MCR for bathymetry inversion. The present work tests the inverse modeling setup of Ardag and Wilson (2022) for inversion of observed (non-twin-test) currents, as well as other field observation types, obtained in the MCR domain during field experiments in 2013/14.
The MCR was the focus of the Riverine and Estuarine Transport and Data Assimilation and Remote sensing for Littoral Applications experiments (RIVET II and DARLA; supported by the ONR), where an extensive data collection effort spanning May and June of 2013 took place. Various types of surface and subsurface observations were collected, in situ and remotely. From this rich dataset, surface current estimations u and υ, significant wave height Hs observations from the Surface Wave Instrument Float with Tracking (SWIFT) drifters (Thomson 2012; Zippel and Thomson 2017), and surface gravity wavenumber k = (kx, ky) observations from synthetic aperture radar (SAR) imagery from RIVET-II were utilized in our study.
The Cormorant Oceanography Project is built upon the success of using cormorants, benthic feeding marine birds, as meteorological and oceanographic sampling platforms in a 2013 pilot study as part of the Inlet and River Mouth Dynamics at the MCR. The goal of the project is to develop autonomous oceanographic and meteorological sensing methods utilizing tags attached to cormorants (Orben et al. 2021). Following the successful 2013 pilot experiment, more birds were tagged in 2014 at the MCR which then allowed our team to estimate surface currents u and υ, following previous studies (Yoda et al. 2014; Sánchez-Román et al. 2019; Harcourt et al. 2019).
The present work assimilates spatially and temporally distributed field observations to achieve an accurate estimate of bathymetry, and thereby improve the accuracy of coastal model outputs, such as predictions of estuarine salinity and temperature. We are using a previously validated model setup (Akan et al. 2017) to simulate two years of MCR circulation and produce corresponding model state covariances. These covariance matrices are then used to solve a least squares inversion to recover bathymetry h(x, y) from observations of surface currents u and υ, significant wave height Hs, and surface gravity wavenumbers k. It will be shown that, as expected (e.g., Moghimi et al. 2016), observation type and location have significant impact on the inversion skill, which is demonstrated by a series of inversion experiments utilizing different combinations of multivariate observations. Finally, the inversions are found to improve overall model skill with respect to unassimilated control observations of estuary salinity and temperature.
The paper is organized as follows: section 2 describes the bathymetry inversion methodology, the characteristics of the study area, and the data sources for the observed variables employed in this study, section 3 displays the results from inverting different variables individually and inverting these variables concurrently, and section 4 is dedicated to a discussion on the advantages of using current methodology and an overall summary of the findings.
2. Methodology
a. Study site and data sources
The Columbia River is a macrotidal estuary, with a high river discharge reaching up to 12 000 m3 during spring freshet (Bottom et al. 2005), and high wave energy as it is directly exposed to the Pacific Ocean. It was the subject of a comprehensive field effort in 2013, called RIVET-II, involving multiple types of in situ and remote sensing observations. Table 1 shows the RIVET II data sources employed in our study, which includes data from SWIFT drifters (Zippel and Thomson 2017) and SAR. The latter (SAR) data were used previously in a variational bathymetry inversion study that exploits the wave dispersion relationship (Harper 2020). Surface currents were collected in 2013 and 2014 as part of a field experiment by the Cormorant Oceanography Project (Peck-Richardson et al. 2018, 2023; Orben et al. 2021). Table 1 displays the time frame of the data (east–west and north–south surface current estimations u and υ) used in this study.
Observed surface variables and their time frames used in this study. LLS indicates linear least squares; see section 2a(4) for details
1) Bathymetry
MCR bathymetry data were obtained by the U.S. Army Corps of Engineers (USACE) as part of their work to maintain and monitor the MCR for navigational purposes (USACE 2019). The data are focused on two navigational channels (where the deepest part of the channel at the mouth reach down to around 40 m just outside of Jetty A, Fig. 1) which are maintained by USACE through annual dredging campaigns during summer. Echo sounder surveys are conducted throughout the year to monitor changes in the bottom profile at the Columbia River estuary, Oregon. Survey data collected from multiple spots and varying times were combined along the Columbia River estuary to obtain nonsynoptic bathymetric coverages for 2013 and 2014. We used USACE survey data starting from 1 January until 15 July for both 2013 and 2014 to define the most up-to-date bathymetric conditions coinciding with the data sampling periods in this study.
Combination of USACE 2014 surveys (reference bathymetry for our tests). Three different regions—outside, mouth, and inside—are displayed over the survey plot, which will be utilized for the statistical comparisons.
Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0101.1
The differences between the 2013 and 2014 USACE surveys are displayed in Fig. 2; the survey data are combined by averaging data over a rectangular grid with a horizontal resolution of 250 m. Figure 2a shows the difference between the USACE bathymetry surveys in 2013 and 2014, and a cross-channel transect (black solid line), which will also be used for bathymetry inversion in the upcoming sections. The location of the East Sand Island is also highlighted in Fig. 2, which is the location where cormorants were captured for tagging [see section 2a(4)]. Note that, as shown in Fig. 2b, bottom profiles in the northern navigational channel had minimal change from 2013 to 2014. Given the small degree of interannual changes in bathymetry in the target region, it was decided to assume a constant bathymetry for 2013/14 (i.e., using 2013 bathymetry) and thus pool observational data from the two consecutive years in the inverse modeling study, which simplified the study and allowed for a greater degree of intercomparison between inversion data types.
(a) Difference between the 2013 and 2014 USACE MCR surveys and the location of the cross-channel transect; location of the East Sand Island is marked with the arrow. (b) Transect comparison to spotlight the changes in the navigational channel shape between 2013 and 2014.
Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0101.1
2) SWIFT drifters
SWIFT drifters are free-floating compact buoys equipped with GPS loggers, acoustic Doppler current profilers (ADCP), and cameras, capable of measuring various oceanographic quantities throughout the water column (Thomson 2012; Zippel and Thomson 2017). Multiple SWIFT deployments were made at the MCR between May and September 2013 as part of the RIVET-II experiment. To see the distribution of drifters over the MCR during the full field campaign, see Fig. 1 in Zippel and Thomson (2017). We utilized surface currents, u and υ, and significant wave height Hs from this dataset. Surface currents were calculated based on the displacement between successive GPS signals (5 min apart) as drifters are passively advected with the mean flow. The Hs information was obtained by first converting velocity spectra to surface elevation spectra E(f) (Zippel and Thomson 2017) and then using the definition
Comparisons between SWIFT drifter observations and model results with accurate (measured) bathymetry for (a) u, (b) υ, and (c) Hs. Statistical comparisons are given in upper left for each variable type and error bars indicate the observation errors calculated for Hs.
Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0101.1
3) SAR
Data were collected from a satellite with COSMO-SkyMed (CSM) sensors, and processed to obtain SAR backscatter imagery over a 400 m × 400 m grid over the MCR. Two SAR bursts captured at 0200 and 1300 UTC 3 June 2013 are tiled onto a 128 × 128 grid, with a slightly different grid orientation and domain specific to each overflight. SAR backscatter intensity is sensitive to surface gravity waves based on their effects on modulating surface water roughness at the relevant radar scattering wavelengths (Horstmann et al. 2015; Shao et al. 2020). As such, the SAR intensity images contain spatial information on wavelength and direction. To extract wave information from the SAR imagery, a 2D fast Fourier transform (FFT) was applied to each image tile (grid point) n to obtain spectral estimates Sn(k, θ) (where the notation is meant to denote a two-element observation of k and θ at grid point n), and the spectral-peak wavenumber and direction was then extracted.
In order for the SAR wavenumber data to be useful for bathymetry inversion, it is necessary to assign a temporal frequency f to the extracted wavenumber/direction pairs, such that the wave dispersion relationship [Eq. (2)] can be inverted for h. For the present study, wave buoy information showed the waves were strictly narrow banded such that it was possible to assign a single peak wave frequency to all data in a given SAR collection. To extract this wave frequency, the SAR data were assigned approximate depth and current values based on the prior bathymetry, and a least squares fit was used to determine a wave frequency that fitted the set of approximate (k, h) pair. This stage of processing returned fp of 0.1175 and 0.115 Hz for the two SAR observations from 3 June. Figure 4 compares the reference model k outputs and both SAR observations from 3 June with the new assigned frequency information (reference model indicates the verified model setup described in section 2b). The figure displays reasonable agreement (RMSE = 0.01 m−1) between the two.
Comparison between the SAR observations from 3 Jun and the reference model results for the same time period.
Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0101.1
A shortcoming of the present f-assignment method is the assumption of narrowbanded waves. An extension to cases with multiple coexisting wave trains would be possible following Harper (2020). Their approach used buoy information to determine a list of candidate wave trains each with a distinct frequency and direction (as measured at the buoy location). A heuristic method was then developed to cluster the SAR data into wave trains based on their detected wave direction, and one of the buoy wave trains was then assigned to each cluster. Both the present approach and the related one by Harper (2020) are successful in part due to the typical wave climate for this region, which is a mixture of narrowbanded, low-frequency Pacific Ocean swell waves combined with broadbanded higher-frequency wind waves.
The difference caused by this transformation is demonstrated in Fig. 5. Figure 5a shows the SAR observation location marked over the USACE 2014 survey, positioned close to the south jetty, which is the shallow part of the mouth. Figures 5b and 5c show the distribution of the h (depth) versus k side-by-side with h versus k−2, respectively, for ensemble model outputs (black dots), observations (or truth, blue asterisks), prior model output (magenta asterisks), linear regression fit to the ensemble results (black dashed lines), and wave dispersion relationship for prior model f over varying depths (magenta solid line). This behavior was observed with other SAR wavenumber observation points located over the shallow part of the mouth. To emphasize the effect of the transformation, only one observation point is displayed in Fig. 5. This reveals that depending on the water depth and the wave characteristics, Eq. (2) can be linear or nonlinear. Hence, using k−2 which has a linear relationship with depth is a better fit for our methodology and as a result of this transformation, bathymetry inversion results were improved as will be shown in section 3.
(a) Single observation location from 3 Jun 2013 over USACE 2014 survey. (b) Model and observed k and their corresponding depths for ensemble model outputs (black dots), observations (or truth, blue asterisks), prior model output (magenta asterisks), linear regression fit to the ensemble results (black dashed lines), and wave dispersion relationship for prior model f over varying depths (magenta solid line). (c) As in (b), but for depth vs k−2 comparisons.
Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0101.1
4) Biologging
Two species, Brandt’s cormorants, Urile penicillatus (n = 18), and double crested cormorants, Nannopterum auritum (n = 24), were fitted with GPS dataloggers (<41 g, GPS-TDlog; Earth and Ocean Technologies) at the nesting colony on East Sand Island (46.2628°N, 123.9875°W) within the Columbia River estuary (highlighted in Fig. 2). GPS devices were programmed to record locations at 1 or 2 Hz following each foraging dive; however, when birds were submerged (>0.5 m) GPS fixes were not attempted to conserve battery power (Peck-Richardson et al. 2018; Orben et al. 2021). After diving activity ceased for >2 min the GPS switched modes and recorded locations at 15 min intervals. This programming allowed for high-resolution GPS fixes when birds were resting at the surface between dives.
GPS fixes during surface intervals between dives, during the first two minutes after the previous dive, were used to estimate surface currents. Individual fixes i were converted to horizontal displacement [xi(ti), yi(ti)] from the location of the surfacing from the previous dive, where ti is the time of the ith GPS fix since surfacing. Rough estimates of speed and acceleration were computed based on centered differencing of neighboring displacements. These estimates were used to exclude periods of time of obvious bird behavior (e.g., flying or paddling at the surface). Periods were excluded when speed exceeded 3.1 m s−1 or acceleration exceeded 0.5 m s−2. Segments where speed and acceleration fell below these thresholds for three or more consecutive GPS fixes were considered surface drifts, and for these surface drifts velocity and corresponding error metrics were computed using a linear regression versus time.
The velocities the birds encounter are on different time and spatial scales compared to the model. For example, the bird might be drifting with a small-scale eddy or front that is not resolved by the model. To better match the temporal and spatial scales of bird surface velocity estimates to those of the numerical model and to minimize the influence of potential bird behavior, individual surface velocity estimates were grouped and averaged in temporal (15 and 60 min) and spatial (100, 250, and 500 m) windows. After comparing reference model versus observations data assimilation we decided to use a temporal scale of 15 min and spatial scale of 250 m for bathymetry inversion. This is spatially close to our model grid (200 m) and same as our ocean-wave coupling time step, which is every 15 min. The grid averaging also provided the variances of u and υ to be used in bathymetry inversion. Figure 6 shows the observed variables against the reference model results and their corresponding error metrics and observation error bars. Averaged estimates consisting of multiple signals provided surface velocity estimations with higher skill. A small systematic bias is apparent comparing the model to drifter measurements (Fig. 6). Such a bias is consistent with prior validation studies of the model using mooring data (Akan et al. 2018), but it is unknown whether the bias in the present case is due to the model only, or if it is due partly to observational error. Further validation of the drifter methodology is recommended as a topic for future work.
Comparisons between the biologging observations and the reference model results for (a) u and (b) υ. Statistical comparisons and observation error bars are also included in the plots.
Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0101.1
b. Model setup
A high-resolution (200 m horizontal, 40 vertical layers) nested numerical model, Coupled Ocean–Atmosphere–Wave–Sediment Transport Modeling System (COAWST) (Warner et al. 2010), was used for the MCR simulations. The same model setup has been validated by previous studies for the data collection time frames (Akan et al. 2017; Ardag and Wilson 2022) of the current study (refer to Table 1 for these time periods).
In this work, COAWST was used in both ROMS-only mode (i.e., without considering the effects of surface gravity waves), and ROMS–SWAN coupled mode (i.e., considering the physical feedback between the surface gravity waves and the horizontal current profile) for representing the estuary hydrodynamics. ROMS-only mode was used for 2014, when no wave observations were available for assimilation, as outlined in Table 1. The model assumes a constant bathymetry for 2013/14 [as explained in section 2a(1)], and sediment transport is neglected.
For 2014, initial and boundary conditions for temperature, salinity, subtidal water level, and horizontal momentum conditions were defined using daily averages from the West Coast Operational Modeling System (WCOFS) regional model, whose domain extends from California to Washington with 4-km grid resolution (Kurapov et al. 2011, 2017; Ardag and Wilson 2022). For both 2013 and 2014 model runs, the tidal constituents were inferred from the global model TPXO (Egbert and Erofeeva 2002) and atmospheric fields were imported from North American Mesoscale Forecast System (NAM), and atmospheric bulk fluxes were calculated by using Fairall et al. (1996) as described in Akan et al. (2017). Model freshwater discharge and water temperature were based on data taken from the Beaver Army Terminal gauging station (USGS 14246900) located approximately 86 km upstream of the river mouth. The SWAN wave model domain shares the same grid resolution and bathymetry as the ROMS model. The model employs 35 wave frequency components ranging between 0.025 and 0.5 Hz, and 90 directional components covering 360°. The western boundary is forced by hourly wave spectra derived from the National Data Buoy Center (NDBC) buoy 46029 which is located 20 NMs west of the MCR. This is a moored buoy capable of producing hourly two -dimensional energy density spectra E(f, θ). Northern and southern boundaries were created using a 1D spectral transformation along these cross-shore transects. Wind-wave generation was not represented in wave model runs as wind-wave generation was assumed negligible for this domain (Akan et al. 2017). Akan et al. (2017) verified that the model is capable of producing accurate wave heights in the MCR without the need for wind wave generation in the model domain.
c. Bathymetry inversion methodology
The inverse method employed here is that of Wilson et al. (2010), Wilson and Özkan-Haller (2012), Moghimi et al. (2016), and Ardag and Wilson (2022), whose application domains included the surfzone, inlets, rivers, and partially and well-mixed estuaries. Readers are referred to the previous works for in-depth descriptions of the methodology, which uses a state-augmented ensemble parameter estimation approach (Evensen 2009). For consistency with the existing literature, we follow notation from Evensen (2009) and Moghimi et al. (2016).
Study domain and (a) reference, (b) prior model bathymetries, Columbia River estuary. In situ moorings used for model output validation are marked by circles, with data taken from Coastal Margin Observation and Prediction (CMOP) stations Jetty A (6.4 m depth; black circle) and Desdemona (7.3 m depth; red circle). Yellow circle in (a) indicates the subdomain used for Hs vs k inversion tests used in section 3b.
Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0101.1
A novel approach was taken in Ardag and Wilson (2022), by introducing iterations into the inversion scheme, in a similar way as Kalnay and Yang (2010). The initial iteration uses a user-prescribed hf, and obtains an update ha using Eq. (8). Subsequent iterations recenter and resample the ensemble about the ha obtained in the previous iteration [i.e., hf is set equal to the previous iteration’s ha, and a new ensemble of perturbations is drawn from Eq. (7)]. Iterations are repeated until a convergence criterion is reached; Ardag and Wilson (2022) defined this as changes
3. Results
Bathymetry inversions results using a single observation source are displayed first in order to demonstrate the relative effectiveness of different observation types in varying parts of the MCR domain. Afterward, inversion results with combining all the available data sources will be shown.
a. Inversions from individual sources
1) SAR-only inversion
A total of 385 k observations from two 3 June SAR collections were used for the first subset of the bathymetry inversion tests. In Fig. 8, the results are shown for inverting k−2 displaying how accurate bottom features are detected qualitatively.
(a) SAR observation locations are superposed over the 2014 USACE validation survey. (b) Posterior bathymetry result and the three transect locations: out of the MCR (dotted line), along channel (dashed line), and cross channel (solid line). Results are shown for (c) the cross-channel transects, (d) out-of-the-MCR transects, and (e) the along-channel transects. Initial bathymetry (prior) is represented by red lines, USACE bathymetry (truth) by black lines, and the bathymetry inversion result (posterior) by blue lines. Gray background indicates a region in which the validation data have been extrapolated (see text for details).
Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0101.1
In Fig. 8a, SAR observation locations marked by black dots are superposed over the 2014 USACE bathymetry survey (i.e., the validation bathymetry for our tests). Figure 8b shows the posterior bathymetry field, and three transect locations: offshore of the MCR (dotted line), along channel (dashed line), and cross channel (solid line). In Fig. 8 and upcoming similar types of figures, the transect locations were selected to align with areas of data coverage, specifically, places where bathymetry adjustments can be made. For all of the transects, prior (red lines), posterior (blue lines), and truth (black lines) results are illustrated for the different parts of the MCR domain in Fig. 8c through Fig. 8e. Note, the cross-channel transect originating from Jetty A is positioned over a nonsurveyed area of the USACE validation dataset. Hence, data were extrapolated to produce a bottom profile in the nonsurveyed areas according to the reference model grid shown in Fig. 7. The extrapolated zone is displayed as gray background in this figure and in the upcoming cross-channel transects plots.
Figure 8c shows that the south portion of cross channel transect across Jetty A (along-transect distances greater than 1.5 km) received bathymetric corrections where the observations were available, whereas the north part (along-transect distances less than 1.5 km) was in a region with fewer observations hence had smaller corrections. Locations outside the river mouth received the largest corrections as seen in along-channel transect and out of the MCR transects (Figs. 8d and 8e). Notably, three wavenumber observations east of Jetty A produced a nontrivial amount of correction, as shown in Fig. 8e at the along-channel distance 8 km.
2) SWIFT-only inversion
A total of 843 u, 848 υ, and 796 Hs SWIFT observations were employed for these tests. Different numbers for these observations are a result of automated quality-control filtering described in section 2c. In Fig. 9 the results are shown for inverting all of the SWIFT variables combined, in the same way as was done for SAR inversion in Fig. 8. As can be seen from various transects shown in Fig. 9b, the high degree of data coverage resulted in bathymetric corrections all throughout the MCR.
As in Fig. 8, but for SWIFT drifter data.
Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0101.1
Despite the presence of observations inside the river mouth, the MCR navigational channels were not inferred in the posterior bathymetry shown in Fig. 9b, owing to the observation orientation relative to those channels. At the mouth, as the drifters followed the stronger mean tidal flow, they tended to concentrate along the north side of the channel (closer to Jetty A) as exhibited in Fig. 9a, thus limiting the corrections available in the south side of the channel. The resulting data coverage is opposite to what was obtained from SAR, where greater data coverage was available on the south side of the channel. Finally, Figs. 9d and 9e show that the depression feature outside the MCR (marked by the yellow circle in Fig. 7a) was captured accurately; however, its along-channel position was offset by 2 km.
3) Cormorants-only inversion
In this section, 209 pairs of collocated u and υ data were employed. Figure 10a displays the distribution of the surface current estimations distributed along the MCR domain.
As in Fig. 8, but with changes to the location of cross-channel transect. The navigational channels (north and south) are marked for reference along the cross-channel transect.
Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0101.1
Figure 10 shows validations comparable to Figs. 8 and 9, with the exception that the cross-channel transect was moved farther inside the mouth to coincide with an area having more observations along the two navigational channels in the MCR. Figure 10c shows that, using estimated u and υ from the tagged cormorants, it is possible to obtain navigational channel shapes, albeit the estimated channels are wider and not as deep as the truth. From Figs. 10d and 10e, it can be seen that corrections to bathymetry were obtained at and inside the river mouth, but less so outside the mouth where surface currents become decoupled from the impacts of the changes in the bathymetry, in agreement with findings by Ardag and Wilson (2022). In contrast, corrections from SWIFT-drifter data (Fig. 9d) were larger and more accurate outside the river mouth, because in that case Hs observations were included as well as u and υ. Observations of Hs from tagged cormorants is a possible area for future work that would improve the methodology.
b. Comparing Hs versus k
In this section, a comparison of inversions using Hs from SWIFT and k−2 from SAR was conducted to study the differences between the performances of these two surface gravity wave variables. We defined a small region right outside the MCR, indicated by the yellow ellipse in Fig. 7a, and only considered the observations located within these boundaries. SAR data from 3 June and SWIFT data between 1900 UTC 2 June and 2000 UTC 3 June 2013 were chosen, such that the SWIFT and SAR data subsets contained a similar number of observations (25 for SWIFT and 26 for SAR) and were collected during analogous tidal conditions. However, the datasets do differ in terms of their spatial distribution (regular versus irregular) and the range of time represented (snapshot versus random), which are characteristics of the two observational methods.
Table 2 shows the root-mean-square error (RMSE) and squared correlation (r2) for the prior and posterior bathymetries corresponding to inversion of the two subsets of k and Hs data. Corrections done by using k are slightly higher than those by Hs; relative to the initial prior RMSE of 4.83 m, the improvements were 25% and 20%, respectively. However, k inversion has superior r2 for the posterior bathymetry, potentially due to the regular distribution of the k data making it more effective for resolving spatial features in the bathymetry.
Statistical comparisons between k−2 from SAR vs Hs from SWIFT inversions when validated against the USACE survey, within the region marked by the yellow ellipse in Fig. 7a.
c. Multivariate inversion
As shown in Table 1, observations used for this study at the MCR were collected in 2013 and 2014. Our current methodology requires assuming the bathymetry to be static for the period spanned by the assimilated data, which can be justified for the 2013/14 period based on observations shown in Fig. 2. Hence, we were able to combine all data sources from 2013 and 2014 into a single inversion. The multivariate inversion was done iteratively following a similar approach as Ardag and Wilson (2022), with the difference being inclusion of surface gravity wave observations (k and Hs). Figure 11 shows the progression of
Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0101.1
The results of the multivariate assimilation can be seen in Fig. 12. Results from nonconverged iterations are marked as the dashed lines in the transect plots to illustrate the progressive convergence to the solution shown. Figure 12b demonstrates that the estimated bathymetry represents the overall shape of the MCR quite well, with the exception of the south navigational channel inside the mouth where there was a lack of observational data for inversion.
As in Fig. 8, but for multivariate bathymetry inversion. Thin dashed lines in the transect plots indicate the nonconverged results obtained during iterative update steps.
Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0101.1
Additional statistical comparisons are shown in Table 3. For this table, three different regions (outside, mouth, inside) were defined throughout the MCR, considering varying dynamics, as revealed in Fig. 1, and the data availability. The 2014 USACE survey was used for validation. For all three regions, RMSEs are indicated for the prior bathymetries to define a performance benchmark for the inversion experiments (i.e., improvement over the prior RMSE indicates positive skill). Iterations 1 and 3 are shown together to examine the effects of combining multivariate observations and iterations separately. Overall, it can be seen that cormorant-only inversions provided the most accurate results inside and outside the mouth. This is due to the cormorant data providing minimal but accurate corrections, as opposed to larger but distorted corrections by Hs and k. The cormorant-based data were also fortuitously positioned at and around the two navigational channels, as opposed to SWIFT observations which happened to be located in-between the channels for this dataset.
Comparisons of bathymetric improvements in three different regions shown in Fig. 1. Boldface values highlight the lowest RMSE and highest r2 for each region.
d. Improvements to model outputs
For coastal numerical models, having accurate bathymetry is essential in terms of model skill and has direct impact on all types of output variables. Although variables other than bathymetry were not estimated in this study, the estimated bathymetry did result in improvements to the noninverted variables. Statistical validations comparing temperature and salinity observations from the two CMOP stations (Jetty A located at the mouth and Desdemona located inside the mouth) and model outputs with the prior, reference, and posterior bathymetry are shown in Table 4. The validation period spanned 1200 UTC 24 May to 1200 UTC 14 July 2014. The skill when using the reference bathymetry is similar to that found by Akan et al. (2018), which differed mainly in the sources for initial and boundary conditions. Results with the prior bathymetry have had the lowest skill; the prior bathymetry lacks any navigational channels, which significantly modulate the oscillating movement of the salt wedge up and down the estuary. Using the posterior bathymetry, which does contain a representation of the navigational channels among other features, model outputs had a significant improvement.
Comparisons of hydrodynamic outputs at two CMOP stations for multiple model setups with different bathymetry as indicated by row label.
4. Discussion and conclusions
Ardag and Wilson (2022) demonstrated through adjoint sensitivity analysis (i.e., sensitivity of the observations to changes in the bathymetry) and twin-test bathymetry inversion results at the MCR that bottom profile corrections based on surface current estimations mainly occur at the mouth and inside of the estuary. Hence, to obtain an accurate full-domain estimate of bathymetry in such an estuary, u and υ should be supplemented by other types of observations outside the river mouth, such as Hs and k. In the present work, we set out to combine available SAR and SWIFT observations in the MCR domain with the cormorant biologging data, testing the effectiveness of such data types both individually and in combination. Results with individual data types displayed a correction of approximately 5 m (difference between prior and posterior) in various parts of the estuary (inside, mouth, and outside), depending on the source of the dataset.
Cormorants provide a unique, opportunistic alternative to the traditional surveying options and our study showed that the dataset obtained by biologging has potential uses in model validation and bathymetry inversion. One major advantage of using tagged marine birds is the temporally continuous (albeit spatially scattered) data coverage throughout the estuary domain. Overall, Table 3 showed bathymetry inversion with biologging data had the highest skill compared to other data types used in this study.
SWIFT drifters have the benefit of combining accurate measurements of surface velocity and wave height over a relatively broad transect line. The two variable types provide complimentary bathymetry information in wave- versus current-dominated regions over an estuary domain—we were able to obtain significant corrections outside the river mouth by assimilating Hs data, where u and υ are ineffective. The addition of Hs to biologging sensors would be a useful area for future work, as the biologging data tend to be even more spatially extensive owing to the random movement of birds around the estuary over a long period of time. One challenge with using Hs for inversion, however, is the ability to collect data with long enough record length for averaging over random waves and wave groups, a factor which possibly contributed to the lower skill and higher scatter in high Hs (as shown in Fig. 3c).
Data from two SAR images were capable of providing accurate albeit spatially shifted corrections of bathymetric features at and outside of the river mouth. A data transformation from k to k−2 prior to inversion improved the final skill by reducing issues associated with the nonlinear relationship between k and h, particularly in shallower water depths. One challenge with SAR snapshot-derived k is the need to provide an associated wave frequency (f), especially in cases when multiple wave trains are present. Model outputs could be used to help guide the selection of f; however, matching SWAN output E(f, θ) to corresponding observed Sn(k, θ) requires accurate input two-dimensional energy spectra at the model boundaries, wind velocity data over the model domain, and accurate bathymetry (in this case to be determined through inversion). Regarding wave model physics, SWAN model challenges are associated with the wave refraction occurring at the river mouth due to both bathymetry inside the MCR and strong tidal currents generated in the Columbia River estuary (Akan et al. 2017). Representation of the nonlinear wave interactions, especially at the mouth (Ardag and Resio 2019), is also a potential source of model error. These are all factors impacting E(f, θ) output from the model regarding downshifting of f and changes in θ of the wave trains depending on the tidal stage, and these factors also vary spatially within the MCR. New methods for automatic estimation of wave frequency, either from SAR data alone or through combining with model and/or buoy data, would likely improve the model inversions. This is recommended as a topic for future work.
Comparing subset bathymetry inversions using SWIFT Hs versus SAR k−2 observations showed that during similar time frame SAR and SWIFT performed similarly in terms of RMSE. The SAR inversion had a higher correlation with the reference bathymetry, however—its greater spatial resolution allowed SAR inversions to include aspects of the spatially varying bathymetry that increased the correlation value. This signals an advantage of wide regular coverage of surface observations (SAR) versus irregular (SWIFT and biologging). Overall, the various data types assimilated in the present work were highly complementary: SAR provided high-spatial-resolution information outside the river mouth; SWIFT introduced corrections via Hs within and outside the river mouth; SWIFT and cormorant data provided surface velocity data within the river mouth where waves are weaker but currents are stronger.
Bar plots in Fig. 13 illustrate the improvements in RMSE achieved through the incorporation of observations from three different sources at inside, mouth, and outside of the MCR (as defined in Fig. 1), over prior bathymetry. These results are based on the data from Table 3 and the corresponding observation counts at these subdomains are also presented. It can be seen that the majority of the corrections occurred at the mouth, which is in parallel with the bathymetry inversion results obtained by using only u and υ in Ardag and Wilson (2022) for the same area. Inside the mouth, biologging observations outperformed drifters, most likely due to their convenient locations around the channels. Outside the mouth received minimal corrections due to increasing depth and surface dynamics decoupling from the fluctuations of the bathymetry. In terms of number of observations and their impacts, both biologging and SAR observations performed better than drifters, which might be attributed to relatively high scatter at drifter derived wave heights for high Hs compared to the reference model (Fig. 3c). These results align with the sensitivity analysis and modeling highlighted in Ardag and Wilson (2022) and is consistent with the findings of Moghimi et al. (2016).
RMSE improvements against the prior bathymetry (blue bars) for three— different regions; inside, mouth, and outside of the MCR (shown in Fig. 1)—for three different data sources in accordance with Table 3. Observation counts (yellow bars) were also plotted on the same y axis. As OutsideSWIFT observations decreased final bathymetry skill, they were depicted as having no observation impact.
Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0101.1
In summary, it was shown that it is possible to combine multiple types of observed surface variables to estimate bathymetry in the mouth and lower-channel portion of a partially mixed estuary. The method assumes the surrounding regional bathymetry is known, uses an initially featureless channel profile as an initial guess, and makes use of prior information in the form of channel geometry [as encoded in Chh, Eq. (7)]. Inversion tests involving a single observed variable type showed how different observation types provide varying level of corrections at various points throughout the estuary. As a result of the improvements over the prior bathymetry, temperature and salinity skill for the numerical model were improved by ∼40% as validated by two in situ CMOP instruments, showing how bathymetry inversion resulted in an overall improvement to model skill.
Acknowledgments.
This work was supported by the Office of Naval Research (ONR) Grant N00014-19-1-2218. Under Award N00014-13-1-0369, the ONR funded initial work using cormorants as sampling platforms as part of the Inlet and River Mouth Dynamics DRI at the mouth of the Columbia River (MCR), which provided data for this study. Work with birds was approved by the Animal Care and Use Committee of Oregon State University and covered by permits from USGS BBL, USFWS, and ODFW. We gratefully acknowledge Çiğdem Akan and Alexander Kurapov for their contributions to models used in this work, and for valuable discussions. We also acknowledge Chris Wackerman for providing SAR data, and for extensive and valuable discussions. Computational resources for this study were provided by grants from the DoD High Performance Computing Modernization Program at Navy DoD Supercomputing Resource Center and Air Force Research Laboratory. We thank groups, organizations, and individuals that were instrumental in the 2013 and 2014 data collection campaigns: Dan Roby, Ken Collis, Real Time Research, Bird Research NW–Astoria Field Crews, USACE Portland District, BRNW ESI field crews, Yasuko Suzuki, Alexa Piggott, Peter Loschl, Kirsten Bixler, John Mulligan, and Anna Laws.
Data availability statement.
The assimilation code, the initial bathymetry ensemble, and the ensemble of model–data misfits to reproduce our results are available at https://doi.org/10.5281/zenodo.8246681.
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