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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 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.

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.

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.

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.

A data-assimilating ⅓° regional dynamical ocean model is evaluated on its ability to synthesize components of the Tropical Pacific Ocean Observing System. The four-dimensional variational data assimilation (4DVAR) method adjusts initial conditions and atmospheric forcing for overlapping 4-month model runs, or hindcasts, that are then combined to give an ocean state estimate for the period 2010–13. Consistency within uncertainty with satellite SSH and Argo profiles is achieved. Comparison to independent observations from Tropical Atmosphere Ocean (TAO) moorings shows that for time scales shorter than 100 days, the state estimate improves estimates of TAO temperature relative to an optimally interpolated Argo product. The improvement is greater at time scales shorter than 20 days, although unpredicted variability in the TAO temperatures implies that TAO observations provide significant information in that band. Larger discrepancies between the state estimate and independent observations from Spray gliders deployed near the Galápagos, Palau, and Solomon Islands are attributed to insufficient model resolution to capture the dynamics in strong current regions and near coasts. The sea surface height forecast skill of the model is assessed. Model forecasts using climatological forcing and boundary conditions are more skillful than climatology out to 50 days compared to persistence, which is a more skillful forecast than climatology out to approximately 20 days. Hindcasts using reanalysis products for atmospheric forcing and open boundary conditions are more skillful than climatology for approximately 120 days or longer, with the exact time scale depending on the accuracy of the state estimate used for initializing and on the reanalysis forcing. Estimating the model representational error is a goal of these experiments.

Simulated along-track ocean altimetry data were used to implement the use of a nonlinear dynamic propagator to perform three-dimensional (time and 2D space) interpolation of mesoscale sea surface height (SSH). The method is an inverse approach to processing altimetry data unevenly sampled in time and space into high-level gridded altimetry maps. The inverse approach, similar to the standard objective mapping, contains some correction terms to the innovation vectors to account for nonlinear dynamics. Another key improvement is to solve for the covariance functions through a Green’s function approach. From the Observing System Simulation Experiments carried out to simulate a three-satellite constellation over the Gulf Stream region, the new method can significantly reduce mapping errors and improve the resolving capabilities compared to the standard linear objective analysis such as that used by the AVISO gridding.

Using more than 10 years of Argo temperature and salinity profiles (2004–14), a new optimal interpolation (OI) of the upper ocean in the equatorial Pacific is presented. Following Roemmich and Gilson’s procedures, which were formulated for describing monthly large-scale anomalies, here every 5 days anomaly fields are constructed with improvements in the OI spatial covariance function and by including the time domain. The comparison of Argo maps with independent observations, from the TAO/TRITON array, and with satellite sea surface height (SSH), demonstrates that Argo is able to represent around 70%–80% of the variance at intraseasonal time scales (periods of 20–100 days) and more than 90% of the variance for the seasonal-to-longer-term variability. The RMS difference between Argo and TAO/TRITON temperatures is lower than 1°C and is around 1.5 cm when the Argo steric height is compared to SSH. This study also assesses the efficacy of different observing system components and combinations, such as SSH, TAO/TRITON, and Argo, for estimating subsurface temperature. Salinity investigations demonstrate its critical importance for density near the surface in the western Pacific. Objective error estimates from the OI are used to evaluate different sampling strategies, such as the recent deployment of 41 Argo floats along the Pacific equator. Argo’s high spatial resolution compared with that of the moored array makes it better suited for studying spatial patterns of variability and propagation on intraseasonal and longer periods, but it is less well suited for studying variability on periods shorter than 20 days at point locations. This work is a step toward better utilization of existing datasets, including Argo, and toward redesigning the Tropical Pacific Observing System.

The Inverse Ocean Modeling (IOM) System is a modular system for constructing and running weak-constraint four-dimensional variational data assimilation (W4DVAR) for any linear or nonlinear functionally smooth dynamical model and observing array. The IOM has been applied to four ocean models with widely varying characteristics. The Primitive Equations Z-coordinate-Harmonic Analysis of Tides (PEZ-HAT) and the Regional Ocean Modeling System (ROMS) are three-dimensional, primitive equations models while the Advanced Circulation model in 2D (ADCIRC-2D) and Spectral Element Ocean Model in 2D (SEOM-2D) are shallow-water models belonging to the general finite-element family. These models, in conjunction with the IOM, have been used to investigate a wide variety of scientific phenomena including tidal, mesoscale, and wind-driven circulation. In all cases, the assimilation of data using the IOM provides a better estimate of the ocean state than the model alone.

The sensitivity of the dynamics of a tropical Pacific Massachusetts Institute of Technology (MIT) general circulation model (MITgcm) to the surface forcing fields and to the horizontal resolution is analyzed. During runs covering the period 1992–2002, two different sets of surface forcing boundary conditions are used, obtained 1) from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis project and 2) from the Estimating the Circulation and Climate of the Ocean (ECCO) assimilation consortium. The “ECCO forcing” is the “NCEP forcing” adjusted by a state estimation procedure using the MITgcm with a 1° × 1° global grid and the adjoint method assimilating a multivariate global ocean dataset. The skill of the model is evaluated against ocean observations available in situ and from satellites. The model domain is limited to the tropical Pacific, with open boundaries located along 26°S, 26°N, and in the Indonesian throughflow. To account for large-scale changes of the ocean circulation, the model is nested in the global time-varying ocean state provided by the ECCO consortium on a 1° grid. Increasing the spatial resolution to 1/3° and using the ECCO forcing fields significantly improves many aspects of the circulation but produces overly strong currents in the western model domain. Increasing the resolution to 1/6° does not yield further improvements of model results. Using the ECCO heat and freshwater fluxes in place of NCEP products leads to improved time-mean model skill (i.e., reduced biases) over most of the model domain, underlining the important role of adjusted heat and freshwater fluxes for improving model representations of the tropical Pacific. Combinations of ECCO and NCEP wind forcing fields can improve certain aspects of the model solutions, but neither ECCO nor NCEP winds show clear overall superiority.

A variety of measurements, including acoustic travel times, moored thermistor time series, and hydrographic stations, were made in the Greenland Sea during 1988–89 to study the evolution of the temperature field throughout the year. This region is of intense oceanographic interest because it is one of the few areas in the world where open-ocean convection to great depths has been observed. This paper describes how the various data types were optimally combined using linear, weighted least squaws inverse methods to provide significantly more information about the ocean than can be obtained from any single data type. The application of these methods requires construction of a reference state, a statistical model of ocean temperature variability relative to the reference state, and an analysis of the differing signal-to-noise ratios of each data type. A time-dependent reference state was constructed from all available hydrographic data, reflecting the basic seasonal variability and keeping the pertu...