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- Author or Editor: Bruce D. Cornuelle x
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Acoustic Float Tracking with the Kalman SmootherAbstract
Acoustically tracked subsurface floats provide insights into ocean complexity and were first deployed over 60 years ago. A standard tracking method uses a least squares algorithm to estimate float trajectories based on acoustic ranging from moored sound sources. However, infrequent or imperfect data challenge such estimates, and least squares algorithms are vulnerable to non-Gaussian errors. Acoustic tracking is currently the only feasible strategy for recovering float positions in the sea ice region, a focus of this study. Acoustic records recovered from underice floats frequently lack continuous sound source coverage. This is because environmental factors such as surface sound channels and rough sea ice attenuate acoustic signals, while operational considerations make polar sound sources expensive and difficult to deploy. Here we present a Kalman smoother approach that, by including some estimates of float behavior, extends tracking to situations with more challenging datasets. The Kalman smoother constructs dynamically constrained, error-minimized float tracks and variance ellipses using all possible position data. This algorithm outperforms the least squares approach and a Kalman filter in numerical experiments. The Kalman smoother is applied to previously tracked floats from the southeast Pacific (DIMES experiment), and the results are compared with existing trajectories constructed using the least squares algorithm. The Kalman smoother is also used to reconstruct the trajectories of a set of previously untracked, acoustically enabled Argo floats in the Weddell Sea.
Abstract
Acoustically tracked subsurface floats provide insights into ocean complexity and were first deployed over 60 years ago. A standard tracking method uses a least squares algorithm to estimate float trajectories based on acoustic ranging from moored sound sources. However, infrequent or imperfect data challenge such estimates, and least squares algorithms are vulnerable to non-Gaussian errors. Acoustic tracking is currently the only feasible strategy for recovering float positions in the sea ice region, a focus of this study. Acoustic records recovered from underice floats frequently lack continuous sound source coverage. This is because environmental factors such as surface sound channels and rough sea ice attenuate acoustic signals, while operational considerations make polar sound sources expensive and difficult to deploy. Here we present a Kalman smoother approach that, by including some estimates of float behavior, extends tracking to situations with more challenging datasets. The Kalman smoother constructs dynamically constrained, error-minimized float tracks and variance ellipses using all possible position data. This algorithm outperforms the least squares approach and a Kalman filter in numerical experiments. The Kalman smoother is applied to previously tracked floats from the southeast Pacific (DIMES experiment), and the results are compared with existing trajectories constructed using the least squares algorithm. The Kalman smoother is also used to reconstruct the trajectories of a set of previously untracked, acoustically enabled Argo floats in the Weddell Sea.
State Estimates and Forecasts of the Eddy Field in the Subtropical Countercurrent in the Northern Philippine SeaAbstract
A strongly nonlinear eddy field is present in and around the subtropical countercurrent in the northern Philippine Sea (NPS). A regional implementation of the Massachusetts Institute of Technology General Circulation Model–Estimating the Circulation and Climate of the Ocean four-dimensional variational assimilation (MITgcm-ECCO 4DVAR) system is found to be able to produce a series of 2-month-long dynamically consistent optimized state estimates between April 2010 and April 2011 for the eddy-rich NPS region. The assimilation provides a stringent dynamical test of the model, showing that a free run of the model forced using adjusted controls remains consistent with the observations for 2 months. The 4DVAR iterative optimization reduced the total cost function for the observations and controls by 40%–50% from the reference solution, initialized using the Hybrid Coordinate Ocean Model 1/12° global daily analysis, achieving residuals approximately equal to the assumed uncertainties for the assimilated observations. The state estimates are assessed by comparing with assimilated and withheld observations and also by comparing 1-month model forecasts with future data. The state estimates and forecasts were more skillful than model persistence and the reference solutions. Finally, the continuous state estimates were used to detect and track the eddies, analyze their structure, and quantify their vertically integrated meridional heat and salt transports.
Abstract
A strongly nonlinear eddy field is present in and around the subtropical countercurrent in the northern Philippine Sea (NPS). A regional implementation of the Massachusetts Institute of Technology General Circulation Model–Estimating the Circulation and Climate of the Ocean four-dimensional variational assimilation (MITgcm-ECCO 4DVAR) system is found to be able to produce a series of 2-month-long dynamically consistent optimized state estimates between April 2010 and April 2011 for the eddy-rich NPS region. The assimilation provides a stringent dynamical test of the model, showing that a free run of the model forced using adjusted controls remains consistent with the observations for 2 months. The 4DVAR iterative optimization reduced the total cost function for the observations and controls by 40%–50% from the reference solution, initialized using the Hybrid Coordinate Ocean Model 1/12° global daily analysis, achieving residuals approximately equal to the assumed uncertainties for the assimilated observations. The state estimates are assessed by comparing with assimilated and withheld observations and also by comparing 1-month model forecasts with future data. The state estimates and forecasts were more skillful than model persistence and the reference solutions. Finally, the continuous state estimates were used to detect and track the eddies, analyze their structure, and quantify their vertically integrated meridional heat and salt transports.
Abstract
The 2010–11 North Pacific Acoustic Laboratory (NPAL) Philippine Sea experiment measured travel times between six acoustic transceiver moorings in a 660-km diameter ocean acoustic tomography array in the northern Philippine Sea (NPS). The travel-time series compare favorably with travel times computed for a yearlong series of state estimates produced for this region using the Massachusetts Institute of Technology General Circulation Model–Estimating the Circulation and Climate of the Ocean four-dimensional variational (MITgcm-ECCO 4DVAR) assimilation system constrained by satellite sea surface height and sea surface temperature observations and by Argo temperature and salinity profiles. Fluctuations in the computed travel times largely match the fluctuations in the measurements caused by the intense mesoscale eddy field in the NPS, providing a powerful test of the observations and state estimates. The computed travel times tend to be shorter than the measured travel times, however, reflecting a warm bias in the state estimates. After processing the travel times to remove tidal signals and extract the low-frequency variability, the differences between the measured and computed travel times were used in addition to SSH, SST, and Argo temperature and salinity observations to further constrain the model and generate improved state estimates. The assimilation of the travel times reduced the misfit between the measured and computed travel times, while not increasing the misfits with the other assimilated observations. The state estimates that used the travel times are more consistent with temperature measurements from an independent oceanographic mooring than the state estimates that did not incorporate the travel times.
Abstract
The 2010–11 North Pacific Acoustic Laboratory (NPAL) Philippine Sea experiment measured travel times between six acoustic transceiver moorings in a 660-km diameter ocean acoustic tomography array in the northern Philippine Sea (NPS). The travel-time series compare favorably with travel times computed for a yearlong series of state estimates produced for this region using the Massachusetts Institute of Technology General Circulation Model–Estimating the Circulation and Climate of the Ocean four-dimensional variational (MITgcm-ECCO 4DVAR) assimilation system constrained by satellite sea surface height and sea surface temperature observations and by Argo temperature and salinity profiles. Fluctuations in the computed travel times largely match the fluctuations in the measurements caused by the intense mesoscale eddy field in the NPS, providing a powerful test of the observations and state estimates. The computed travel times tend to be shorter than the measured travel times, however, reflecting a warm bias in the state estimates. After processing the travel times to remove tidal signals and extract the low-frequency variability, the differences between the measured and computed travel times were used in addition to SSH, SST, and Argo temperature and salinity observations to further constrain the model and generate improved state estimates. The assimilation of the travel times reduced the misfit between the measured and computed travel times, while not increasing the misfits with the other assimilated observations. The state estimates that used the travel times are more consistent with temperature measurements from an independent oceanographic mooring than the state estimates that did not incorporate the travel times.
Harmonic Analysis of Non-Phase-Locked Tides with Red Noise Using the red_tide PackageAbstract
A novel tidal analysis package (red_tide) has been developed to characterize low-amplitude non-phase-locked tidal energy and dominant tidal peaks in noisy, irregularly sampled, or gap-prone time series. We recover tidal information by expanding conventional harmonic analysis to include prior information and assumptions about the statistics of a process, such as the assumption of a spectrally colored background, treated as nontidal noise. This is implemented using Bayesian maximum posterior estimation and assuming Gaussian prior distributions. We utilize a hierarchy of test cases, including synthetic data and observations, to evaluate this method and its relevance to analysis of data with a tidal component and an energetic nontidal background. Analysis of synthetic test cases shows that the methodology provides robust tidal estimates. When the background energy spectrum is nearly spectrally white, red_tide results replicate results from ordinary least squares (OLS) commonly used in other tidal packages. When background spectra are red (a spectral slope of −2 or steeper), red_tide’s estimates represent a measurable improvement over OLS. The approach highlights the presence of tidal variability and low-amplitude constituents in observations by allowing arbitrarily configurable fitted frequencies and prior statistics that constrain solutions. These techniques have been implemented in MATLAB in order to analyze tidal data with non-phase-locked components and an energetic background that pose challenges to the commonly used OLS approach.
Abstract
A novel tidal analysis package (red_tide) has been developed to characterize low-amplitude non-phase-locked tidal energy and dominant tidal peaks in noisy, irregularly sampled, or gap-prone time series. We recover tidal information by expanding conventional harmonic analysis to include prior information and assumptions about the statistics of a process, such as the assumption of a spectrally colored background, treated as nontidal noise. This is implemented using Bayesian maximum posterior estimation and assuming Gaussian prior distributions. We utilize a hierarchy of test cases, including synthetic data and observations, to evaluate this method and its relevance to analysis of data with a tidal component and an energetic nontidal background. Analysis of synthetic test cases shows that the methodology provides robust tidal estimates. When the background energy spectrum is nearly spectrally white, red_tide results replicate results from ordinary least squares (OLS) commonly used in other tidal packages. When background spectra are red (a spectral slope of −2 or steeper), red_tide’s estimates represent a measurable improvement over OLS. The approach highlights the presence of tidal variability and low-amplitude constituents in observations by allowing arbitrarily configurable fitted frequencies and prior statistics that constrain solutions. These techniques have been implemented in MATLAB in order to analyze tidal data with non-phase-locked components and an energetic background that pose challenges to the commonly used OLS approach.
A Noninterpolated Estimate of Horizontal Spatial Covariance from Nonorthogonally and Irregularly Sampled Scalar VelocitiesAbstract
This paper presents a least squares method to estimate the horizontal (isotropic or anisotropic) spatial covariance of two-dimensional orthogonal vector components, without introducing an intervening mapping step and biases, from the spatial covariance of the nonorthogonally and irregularly sampled raw scalar velocities. The field is assumed to be locally homogeneous in space and sampled in an ensemble so the unknown spatial covariance is a function of spatial lag only. The transformation between the irregular grid on which nonorthogonal scalar projections of the vector are sampled and the regular orthogonal grid on which they will be mapped is created using the geometry of the problem. The spatial covariance of the orthogonal velocity components of the field is parameterized by either the energy (power) spectrum in the wavenumber domain or the lagged covariance in the spatial domain. The energy spectrum is constrained to be nonnegative definite as part of the solution of the inverse problem. This approach is applied to three example sets of data, using nonorthogonally and irregularly sampled radial velocity data obtained from 1) a simple spectral model, 2) a regional numerical model, and 3) an array of high-frequency radars. In tests where the true covariance is known, the proposed direct approaches fitting to parameterizations of the nonorthogonally and irregularly sampled raw data in the wavenumber domain and spatial domain outperform methods that map the data to a regular grid before estimating the covariance.
Abstract
This paper presents a least squares method to estimate the horizontal (isotropic or anisotropic) spatial covariance of two-dimensional orthogonal vector components, without introducing an intervening mapping step and biases, from the spatial covariance of the nonorthogonally and irregularly sampled raw scalar velocities. The field is assumed to be locally homogeneous in space and sampled in an ensemble so the unknown spatial covariance is a function of spatial lag only. The transformation between the irregular grid on which nonorthogonal scalar projections of the vector are sampled and the regular orthogonal grid on which they will be mapped is created using the geometry of the problem. The spatial covariance of the orthogonal velocity components of the field is parameterized by either the energy (power) spectrum in the wavenumber domain or the lagged covariance in the spatial domain. The energy spectrum is constrained to be nonnegative definite as part of the solution of the inverse problem. This approach is applied to three example sets of data, using nonorthogonally and irregularly sampled radial velocity data obtained from 1) a simple spectral model, 2) a regional numerical model, and 3) an array of high-frequency radars. In tests where the true covariance is known, the proposed direct approaches fitting to parameterizations of the nonorthogonally and irregularly sampled raw data in the wavenumber domain and spatial domain outperform methods that map the data to a regular grid before estimating the covariance.
Assimilating Global Wave Model Predictions and Deep-Water Wave Observations in Nearshore Swell PredictionsAbstract
Nearshore wave predictions with high resolution in space and time are needed for boating safety, to assess flood risk, and to support nearshore processes research. This study presents methods for improving regional nearshore predictions of swell-band wave energy (0.04–0.09 Hz) by assimilating local buoy observations into a linear wave propagation model with a priori guidance from global WAVEWATCH III (WW3) model predictions. Linear wave propagation, including depth-induced refraction and shoaling, and travel time lags, is modeled with self-adjoint backward ray tracing techniques. The Bayesian assimilation yields smooth, high-resolution offshore wave directional spectra that are consistent with WW3, and with offshore and local buoy observations. Case studies in the Southern California Bight (SCB) confirm that the nearshore predictions at independent (nonassimilated) buoy sites are improved by assimilation compared with predictions driven with WW3 or with a single offshore buoy. These assimilation techniques, valid in regions and frequency bands where wave energy propagation is mostly linear, use significantly less computational resources than nonlinear models and variational methods, and could be a useful component of a larger regional assimilation program. Where buoy locations have historically been selected to meet local needs, these methods can aid in the design of regional buoy arrays by quantifying the regional skill improvement for a given buoy observation and identifying both high-value and redundant observations. Assimilation techniques also identify likely forward model error in the Santa Barbara Channel, where permanent observations or model corrections are needed.
Abstract
Nearshore wave predictions with high resolution in space and time are needed for boating safety, to assess flood risk, and to support nearshore processes research. This study presents methods for improving regional nearshore predictions of swell-band wave energy (0.04–0.09 Hz) by assimilating local buoy observations into a linear wave propagation model with a priori guidance from global WAVEWATCH III (WW3) model predictions. Linear wave propagation, including depth-induced refraction and shoaling, and travel time lags, is modeled with self-adjoint backward ray tracing techniques. The Bayesian assimilation yields smooth, high-resolution offshore wave directional spectra that are consistent with WW3, and with offshore and local buoy observations. Case studies in the Southern California Bight (SCB) confirm that the nearshore predictions at independent (nonassimilated) buoy sites are improved by assimilation compared with predictions driven with WW3 or with a single offshore buoy. These assimilation techniques, valid in regions and frequency bands where wave energy propagation is mostly linear, use significantly less computational resources than nonlinear models and variational methods, and could be a useful component of a larger regional assimilation program. Where buoy locations have historically been selected to meet local needs, these methods can aid in the design of regional buoy arrays by quantifying the regional skill improvement for a given buoy observation and identifying both high-value and redundant observations. Assimilation techniques also identify likely forward model error in the Santa Barbara Channel, where permanent observations or model corrections are needed.
Optimizing the Biogeochemical Argo Float DistributionAbstract
The core Argo array has operated with the design goal of uniform spatial distribution of 3° in latitude and longitude. Recent studies have acknowledged that spatial and temporal scales of variability in some parts of the ocean are not resolved by 3° sampling and have recommended increased core Argo density in the equatorial region, boundary currents, and marginal seas with an integrated vision of other Argo variants. Biogeochemical (BGC) Argo floats currently observe the ocean from a collection of pilot arrays, but recently funded proposals will transition these pilot arrays to a global array. The current BGC Argo implementation plan recommends uniform spatial distribution of BGC Argo floats. For the first time, we estimate the effectiveness of the existing BGC Argo array to resolve the anomaly from the mean using a subset of modeled, full-depth BGC fields. We also study the effectiveness of uniformly distributed BGC Argo arrays with varying float densities at observing the ocean. Then, using previous Argo trajectories, we estimate the Argo array’s future distribution and quantify how well it observes the ocean. Finally, using a novel technique for sequentially identifying the best deployment locations, we suggest the optimal array distribution for BGC Argo floats to minimize objective mapping uncertainty in a subset of BGC fields and to best constrain BGC temporal variability.
Abstract
The core Argo array has operated with the design goal of uniform spatial distribution of 3° in latitude and longitude. Recent studies have acknowledged that spatial and temporal scales of variability in some parts of the ocean are not resolved by 3° sampling and have recommended increased core Argo density in the equatorial region, boundary currents, and marginal seas with an integrated vision of other Argo variants. Biogeochemical (BGC) Argo floats currently observe the ocean from a collection of pilot arrays, but recently funded proposals will transition these pilot arrays to a global array. The current BGC Argo implementation plan recommends uniform spatial distribution of BGC Argo floats. For the first time, we estimate the effectiveness of the existing BGC Argo array to resolve the anomaly from the mean using a subset of modeled, full-depth BGC fields. We also study the effectiveness of uniformly distributed BGC Argo arrays with varying float densities at observing the ocean. Then, using previous Argo trajectories, we estimate the Argo array’s future distribution and quantify how well it observes the ocean. Finally, using a novel technique for sequentially identifying the best deployment locations, we suggest the optimal array distribution for BGC Argo floats to minimize objective mapping uncertainty in a subset of BGC fields and to best constrain BGC temporal variability.
