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• 1. [Article] Nonstationary Internal Tides Observed Using Dual-Satellite Altimetry

  Dual-satellite crossover data from the Jason-2 and Cryosat-2 altimeter missions are used in a novel approach to quantify stationary and nonstationary tides from time-lagged mean square sea surface height ...

  Citation × Citation Citation Abstract Copy Title: Nonstationary Internal Tides Observed Using Dual-Satellite Altimetry Author: Zaron, Edward D. Year: 2015 Dual-satellite crossover data from the Jason-2 and Cryosat-2 altimeter missions are used in a novel approach to quantify stationary and nonstationary tides from time-lagged mean square sea surface height (SSH) differences, computed for lags from 1 to 1440 h (60 days). The approach is made feasible by removing independent estimates of the stationary tide and mesoscale SSH variance, which greatly reduces the sampling error of the SSH statistics. For the semidiurnal tidal band, the stationary tidal variance is approximately 0.73 cm(2), and the nonstationary variance is about 0.33 cm(2), or 30% of the total. The temporal correlation of the nonstationary tide is examined by complex demodulation and found to be oscillatory with first 0 crossing at 400 h (17 days). Because a significant fraction of the time-variable mesoscale signal is resolved at time scales of roughly 150 h by the present constellation of satellite altimeters, the results suggest that it may be feasible to predict the nonstationary tide from modulations of the resolved mesoscale, thus enhancing the efficacy of tidal corrections for planned wide-swath altimeters such as the Surface Water and Ocean Topography (SWOT) mission. Title: Nonstationary Internal Tides Observed Using Dual-Satellite Altimetry Author: Zaron, Edward D. Year: 2015 Dual-satellite crossover data from the Jason-2 and Cryosat-2 altimeter missions are used in a novel approach to quantify stationary and nonstationary tides from time-lagged mean square sea surface height (SSH) differences, computed for lags from 1 to 1440 h (60 days). The approach is made feasible by removing independent estimates of the stationary tide and mesoscale SSH variance, which greatly reduces the sampling error of the SSH statistics. For the semidiurnal tidal band, the stationary tidal variance is approximately 0.73 cm(2), and the nonstationary variance is about 0.33 cm(2), or 30% of the total. The temporal correlation of the nonstationary tide is examined by complex demodulation and found to be oscillatory with first 0 crossing at 400 h (17 days). Because a significant fraction of the time-variable mesoscale signal is resolved at time scales of roughly 150 h by the present constellation of satellite altimeters, the results suggest that it may be feasible to predict the nonstationary tide from modulations of the resolved mesoscale, thus enhancing the efficacy of tidal corrections for planned wide-swath altimeters such as the Surface Water and Ocean Topography (SWOT) mission. Close

• 2. [Article] Non-Stationary Internal Tides Observed with Satellite Altimetry

  Temporal variability of the internal tide is inferred from a 17-year combined record of Topex/Poseidon and Jason satellite altimeters. A global sampling of along-track sea-surface height wavenumber spectra ...

  Citation × Citation Citation Abstract Copy Title: Non-Stationary Internal Tides Observed with Satellite Altimetry Author: Ray, R. D., Zaron, Edward D. Year: 2011 Temporal variability of the internal tide is inferred from a 17-year combined record of Topex/Poseidon and Jason satellite altimeters. A global sampling of along-track sea-surface height wavenumber spectra finds that non-stationary variance is generally 25% or less of the average variance at wavenumbers characteristic of mode-1 tidal internal waves. With some exceptions the non-stationary variance does not exceed 0.25 cm2. The mode-2 signal, where detectable, contains a larger fraction of non-stationary variance, typically 50% or more. Temporal subsetting of the data reveals interannual variability barely significant compared with tidal estimation error from 3-year records. Comparison of summer vs. winter conditions shows only one region of noteworthy seasonal changes, the northern South China Sea. Implications for the anticipated SWOT altimeter mission are briefly discussed. Title: Non-Stationary Internal Tides Observed with Satellite Altimetry Author: Ray, R. D., Zaron, Edward D. Year: 2011 Temporal variability of the internal tide is inferred from a 17-year combined record of Topex/Poseidon and Jason satellite altimeters. A global sampling of along-track sea-surface height wavenumber spectra finds that non-stationary variance is generally 25% or less of the average variance at wavenumbers characteristic of mode-1 tidal internal waves. With some exceptions the non-stationary variance does not exceed 0.25 cm2. The mode-2 signal, where detectable, contains a larger fraction of non-stationary variance, typically 50% or more. Temporal subsetting of the data reveals interannual variability barely significant compared with tidal estimation error from 3-year records. Comparison of summer vs. winter conditions shows only one region of noteworthy seasonal changes, the northern South China Sea. Implications for the anticipated SWOT altimeter mission are briefly discussed. Close

• 3. [Article] Regional Models of Internal Tides

  Internal tides are ubiquitous in the ocean, and they play an important role in a range of ocean processes, for example, particle dispersal, acoustics, and vertical buoyancy flux. The wavelength of internal ...

  Citation × Citation Citation Abstract Copy Title: Regional Models of Internal Tides Author: Carter, Glenn S., Fringer, Oliver B., Zaron, Edward D. Year: 2012 Internal tides are ubiquitous in the ocean, and they play an important role in a range of ocean processes, for example, particle dispersal, acoustics, and vertical buoyancy flux. The wavelength of internal tides can be as much as 250 km in the open ocean, but as the generation of these tides depends on the angle between the depth-averaged current and the topography, there can be considerable local spatial variability. This range of scales makes it difficult to develop a comprehensive understanding of the processes involved from observations alone. Regional numerical modeling provides a way to study the generation and early propagation of internal tides at high resolution. Here, we review the role that regional internal tide models, primarily hydrostatic models, can play in increasing our understanding. Title: Regional Models of Internal Tides Author: Carter, Glenn S., Fringer, Oliver B., Zaron, Edward D. Year: 2012 Internal tides are ubiquitous in the ocean, and they play an important role in a range of ocean processes, for example, particle dispersal, acoustics, and vertical buoyancy flux. The wavelength of internal tides can be as much as 250 km in the open ocean, but as the generation of these tides depends on the angle between the depth-averaged current and the topography, there can be considerable local spatial variability. This range of scales makes it difficult to develop a comprehensive understanding of the processes involved from observations alone. Regional numerical modeling provides a way to study the generation and early propagation of internal tides at high resolution. Here, we review the role that regional internal tide models, primarily hydrostatic models, can play in increasing our understanding. Close

• 4. [Article] Bottom Topography Mapping via Nonlinear Data Assimilation

  A variational data assimilation method is described for bottom topography mapping in rivers and estuaries using remotely sensed observations of water surface currents. The velocity field and bottom topography ...

  Citation × Citation Citation Abstract Copy Title: Bottom Topography Mapping via Nonlinear Data Assimilation Author: Zaron, Edward D., Pradal, Marie-Aude, Miller, Patrick D., Blumberg, Alan F., Georgas, Nickitas, Li, Wei, Cornuelle, Julia Muccino Year: 2011 A variational data assimilation method is described for bottom topography mapping in rivers and estuaries using remotely sensed observations of water surface currents. The velocity field and bottom topography are related by the vertically integrated momentum and continuity equations, leading to a nonlinear inverse problem for bottom topography, which is solved using a Picard iteration strategy combined with a nonlinear line search. An illustration of the method is shown for Haverstraw Bay, in the Hudson River, where the known bottom topography is well reconstructed. Once the topography has been estimated, currents and water levels may be forecast. The method makes feasible 1) the estimation of bottom topography in regions where in situ data collection may be impossible, dangerous, or expensive, and 2) the calibration of barotropic shallow-water models via control of the bottom topography. Title: Bottom Topography Mapping via Nonlinear Data Assimilation Author: Zaron, Edward D., Pradal, Marie-Aude, Miller, Patrick D., Blumberg, Alan F., Georgas, Nickitas, Li, Wei, Cornuelle, Julia Muccino Year: 2011 A variational data assimilation method is described for bottom topography mapping in rivers and estuaries using remotely sensed observations of water surface currents. The velocity field and bottom topography are related by the vertically integrated momentum and continuity equations, leading to a nonlinear inverse problem for bottom topography, which is solved using a Picard iteration strategy combined with a nonlinear line search. An illustration of the method is shown for Haverstraw Bay, in the Hudson River, where the known bottom topography is well reconstructed. Once the topography has been estimated, currents and water levels may be forecast. The method makes feasible 1) the estimation of bottom topography in regions where in situ data collection may be impossible, dangerous, or expensive, and 2) the calibration of barotropic shallow-water models via control of the bottom topography. Close

• 5. [Article] An Analysis of Secular Change in Tides at Open-Ocean Sites in the Pacific

  Hourly sea level is examined at 25 open-ocean stations in the Pacific Ocean with records longer than 30 yr. A search for trends finds that the amplitude of the dominant semidiurnal tide M2 is increasing ...

  Citation × Citation Citation Abstract Copy Title: An Analysis of Secular Change in Tides at Open-Ocean Sites in the Pacific Author: Zaron, Edward D., Jay, David A. Year: 2014 Hourly sea level is examined at 25 open-ocean stations in the Pacific Ocean with records longer than 30 yr. A search for trends finds that the amplitude of the dominant semidiurnal tide M2 is increasing at 12 of the 13 sites where a statistically significant trend can be identified. It is also found that nontidal variance in the neighborhood of M2 is decreasing at all 12 of the sites where a significant increase in M2 tide is occurring. The trend in amplitude of the dominant diurnal tide K1 is significant at six stations, and it is both increasing (four stations) and decreasing (two stations). The trend in semidiurnal-band variance suggests the hypothesis that increases in M2 could be caused by improvements in time keeping or data processing that would reduce the apparent phase variability of the tide. This possibility is examined and found to be the likely explanation for tidal trends at four stations. Local changes are found to explain the trend at two stations, Johnston Island and Mokuoloe, as diagnosed from correlated changes in nonlinear overtides and site history. Changes in M2 at the equatorial station of Kanton are significant and unexplained by either timing errors or local morphodynamics; although, strong nonlinear overtides are present. Changing tides at five stations in the western Pacific, Malakal, Yap, Saipan, Kapingamarangi, and Pohnpei cannot be explained by the above and suggest a region where a connection between climate and tides may yet be identified. Title: An Analysis of Secular Change in Tides at Open-Ocean Sites in the Pacific Author: Zaron, Edward D., Jay, David A. Year: 2014 Hourly sea level is examined at 25 open-ocean stations in the Pacific Ocean with records longer than 30 yr. A search for trends finds that the amplitude of the dominant semidiurnal tide M2 is increasing at 12 of the 13 sites where a statistically significant trend can be identified. It is also found that nontidal variance in the neighborhood of M2 is decreasing at all 12 of the sites where a significant increase in M2 tide is occurring. The trend in amplitude of the dominant diurnal tide K1 is significant at six stations, and it is both increasing (four stations) and decreasing (two stations). The trend in semidiurnal-band variance suggests the hypothesis that increases in M2 could be caused by improvements in time keeping or data processing that would reduce the apparent phase variability of the tide. This possibility is examined and found to be the likely explanation for tidal trends at four stations. Local changes are found to explain the trend at two stations, Johnston Island and Mokuoloe, as diagnosed from correlated changes in nonlinear overtides and site history. Changes in M2 at the equatorial station of Kanton are significant and unexplained by either timing errors or local morphodynamics; although, strong nonlinear overtides are present. Changing tides at five stations in the western Pacific, Malakal, Yap, Saipan, Kapingamarangi, and Pohnpei cannot be explained by the above and suggest a region where a connection between climate and tides may yet be identified. Close

• 6. [Article] On the Observability of Bottom Topography from Measurements of Tidal Sea Surface Height

  of whether features of the ocean bottom topography can be identified from measurements of water level is investigated using a simplified one-dimensional barotropic model. Because of the nonlinear dependence ...

  Citation × Citation Citation Abstract Copy Title: On the Observability of Bottom Topography from Measurements of Tidal Sea Surface Height Author: Zaron, Edward D. Year: 2016 of whether features of the ocean bottom topography can be identified from measurements of water level is investigated using a simplified one-dimensional barotropic model. Because of the nonlinear dependence of the sea surface height on the water depth, a linearized analysis is performed concerning the identification of a Gaussian bump within two specific depth profiles, (1) a constant depth domain, and, (2) a constant depth domain adjoining a near-resonant continental shelf. Observability is quantified by examining the estimation error in a series of identical-twin experiments varying data density, tide wavelength, assumed (versus actual) topographic correlation scale, and friction. For measurements of sea surface height that resolve the scale of the topographic perturbation, the fractional error in the bottom topography is approximately a factor of 10 larger than the fractional error of the sea surface height. Domain-scale and shelf-scale resonances may lead to inaccurate topography estimates due to a reduction in the effective number of degrees of freedom in the dynamics, and the amplification of nonlinearity. A realizability condition for the variance of the topography error in the limit of zero bottom depth is proposed which is interpreted as a bound on the fractional error of the topography. Appropriately designed spatial covariance models partly ameliorate the negative impact of shelf-scale near-resonance, and highlight the importance of spatial covariance modeling for bottom topography estimation. Title: On the Observability of Bottom Topography from Measurements of Tidal Sea Surface Height Author: Zaron, Edward D. Year: 2016 of whether features of the ocean bottom topography can be identified from measurements of water level is investigated using a simplified one-dimensional barotropic model. Because of the nonlinear dependence of the sea surface height on the water depth, a linearized analysis is performed concerning the identification of a Gaussian bump within two specific depth profiles, (1) a constant depth domain, and, (2) a constant depth domain adjoining a near-resonant continental shelf. Observability is quantified by examining the estimation error in a series of identical-twin experiments varying data density, tide wavelength, assumed (versus actual) topographic correlation scale, and friction. For measurements of sea surface height that resolve the scale of the topographic perturbation, the fractional error in the bottom topography is approximately a factor of 10 larger than the fractional error of the sea surface height. Domain-scale and shelf-scale resonances may lead to inaccurate topography estimates due to a reduction in the effective number of degrees of freedom in the dynamics, and the amplification of nonlinearity. A realizability condition for the variance of the topography error in the limit of zero bottom depth is proposed which is interpreted as a bound on the fractional error of the topography. Appropriately designed spatial covariance models partly ameliorate the negative impact of shelf-scale near-resonance, and highlight the importance of spatial covariance modeling for bottom topography estimation. Close

• 7. [Article] Estimating Open-Ocean Barotropic Tidal Dissipation: The Hawaiian Ridge

  The generalized inverse of a regional model is used to estimate barotropic tidal dissipation along the Hawaiian Ridge. The model, based on the linear shallow-water equations, incorporates parameterizations ...

  Citation × Citation Citation Abstract Copy Title: Estimating Open-Ocean Barotropic Tidal Dissipation: The Hawaiian Ridge Author: Zaron, Edward D., Egbert, Gary D. The generalized inverse of a regional model is used to estimate barotropic tidal dissipation along the Hawaiian Ridge. The model, based on the linear shallow-water equations, incorporates parameterizations for the dissipation of energy via friction in the bottom boundary layer and form drag due to internal waves generated at topographic slopes. Sea surface height data from 364 orbit cycles of the Ocean Topography Experiment (TOPEX)/Poseidon satellite mission are used to perform inversions at eight diurnal and semidiurnal tidal frequencies. It is estimated that the barotropic M2 tide loses energy at a rate of 19 GW, of which 88% is lost within 250 km of the ridge, presumably via conversion to the internal or baroclinic tide. Uncertainty in the assumed model error and wave drag in the forward model suggest that M₂ dissipation values from 18 to 25 GW are consistent with the altimetric observations. Other barotropic tidal constituents are estimated to lose a total of 5.7 GW. The spatial distribution of barotropic dissipation along the ridge is similar to that inferred from three-dimensional primitive equation models, and it is largely insensitive to details of assumed model and data errors. Dissipation at semidiurnal frequencies is most intense at the French Frigate Shoals with lesser, but significant, contributions at other sites. Diurnal tidal dissipation is concentrated to the east of the French Frigate Shoals, at the Gardner Pinnacles. Further work with three-dimensional models will be necessary to determine the fate of the energy that is removed from the barotropic tide. Title: Estimating Open-Ocean Barotropic Tidal Dissipation: The Hawaiian Ridge Author: Zaron, Edward D., Egbert, Gary D. The generalized inverse of a regional model is used to estimate barotropic tidal dissipation along the Hawaiian Ridge. The model, based on the linear shallow-water equations, incorporates parameterizations for the dissipation of energy via friction in the bottom boundary layer and form drag due to internal waves generated at topographic slopes. Sea surface height data from 364 orbit cycles of the Ocean Topography Experiment (TOPEX)/Poseidon satellite mission are used to perform inversions at eight diurnal and semidiurnal tidal frequencies. It is estimated that the barotropic M2 tide loses energy at a rate of 19 GW, of which 88% is lost within 250 km of the ridge, presumably via conversion to the internal or baroclinic tide. Uncertainty in the assumed model error and wave drag in the forward model suggest that M₂ dissipation values from 18 to 25 GW are consistent with the altimetric observations. Other barotropic tidal constituents are estimated to lose a total of 5.7 GW. The spatial distribution of barotropic dissipation along the ridge is similar to that inferred from three-dimensional primitive equation models, and it is largely insensitive to details of assumed model and data errors. Dissipation at semidiurnal frequencies is most intense at the French Frigate Shoals with lesser, but significant, contributions at other sites. Diurnal tidal dissipation is concentrated to the east of the French Frigate Shoals, at the Gardner Pinnacles. Further work with three-dimensional models will be necessary to determine the fate of the energy that is removed from the barotropic tide. Close

• 8. [Article] Initial evaluations of a U.S. Navy Rapidly Relocatable Gulf of Mexico/Caribbean Ocean Forecast System in the Context of the Deepwater Horizon Oil Spill Disaster

  In response to the Deepwater Horizon (DwH) oil spill event in 2010, the Naval Oceanographic Office deployed a nowcast-forecast system covering the Gulf of Mexico and adjacent Caribbean Sea that was designated ...

  Citation × Citation Citation Abstract Copy Title: Initial evaluations of a U.S. Navy Rapidly Relocatable Gulf of Mexico/Caribbean Ocean Forecast System in the Context of the Deepwater Horizon Oil Spill Disaster Author: Zaron, Edward D., Fitzpatrick, Patrick J., Cross, Scott L., Harding, John M., Bub, Frank L., Wiggert, Jerry D., Ko, Dong S., Lau, Yee, Woodward, Katharine, Mooers, Christopher N.K. Year: 2015 In response to the Deepwater Horizon (DwH) oil spill event in 2010, the Naval Oceanographic Office deployed a nowcast-forecast system covering the Gulf of Mexico and adjacent Caribbean Sea that was designated Americas Seas, or AMSEAS, which is documented in this manuscript. The DwH disaster provided a challenge to the application of available ocean-forecast capabilities, and also generated a historically large observational dataset. AMSEAS was evaluated by four complementary efforts, each with somewhat different aims and approaches: a university research consortium within an Integrated Ocean Observing System (IOOS) testbed; a petroleum industry consortium, the Gulf of Mexico 3-D Operational Ocean Forecast System Pilot Prediction Project (GOMEX-PPP); a British Petroleum (BP) funded project at the Northern Gulf Institute in response to the oil spill; and the Navy itself. Validation metrics are presented in these different projects for water temperature and salinity profiles, sea surface wind, sea surface temperature, sea surface height, and volume transport, for different forecast time scales. The validation found certain geographic and time biases/errors, and small but systematic improvements relative to earlier regional and global modeling efforts. On the basis of these positive AMSEAS validation studies, an oil spill transport simulation was conducted using archived AMSEAS nowcasts to examine transport into the estuaries east of the Mississippi River. This effort captured the influences of Hurricane Alex and a non-tropical cyclone off the Louisiana coast, both of which pushed oil into the western Mississippi Sound, illustrating the importance of the atmospheric influence on oil spills such as DwH. Title: Initial evaluations of a U.S. Navy Rapidly Relocatable Gulf of Mexico/Caribbean Ocean Forecast System in the Context of the Deepwater Horizon Oil Spill Disaster Author: Zaron, Edward D., Fitzpatrick, Patrick J., Cross, Scott L., Harding, John M., Bub, Frank L., Wiggert, Jerry D., Ko, Dong S., Lau, Yee, Woodward, Katharine, Mooers, Christopher N.K. Year: 2015 In response to the Deepwater Horizon (DwH) oil spill event in 2010, the Naval Oceanographic Office deployed a nowcast-forecast system covering the Gulf of Mexico and adjacent Caribbean Sea that was designated Americas Seas, or AMSEAS, which is documented in this manuscript. The DwH disaster provided a challenge to the application of available ocean-forecast capabilities, and also generated a historically large observational dataset. AMSEAS was evaluated by four complementary efforts, each with somewhat different aims and approaches: a university research consortium within an Integrated Ocean Observing System (IOOS) testbed; a petroleum industry consortium, the Gulf of Mexico 3-D Operational Ocean Forecast System Pilot Prediction Project (GOMEX-PPP); a British Petroleum (BP) funded project at the Northern Gulf Institute in response to the oil spill; and the Navy itself. Validation metrics are presented in these different projects for water temperature and salinity profiles, sea surface wind, sea surface temperature, sea surface height, and volume transport, for different forecast time scales. The validation found certain geographic and time biases/errors, and small but systematic improvements relative to earlier regional and global modeling efforts. On the basis of these positive AMSEAS validation studies, an oil spill transport simulation was conducted using archived AMSEAS nowcasts to examine transport into the estuaries east of the Mississippi River. This effort captured the influences of Hurricane Alex and a non-tropical cyclone off the Louisiana coast, both of which pushed oil into the western Mississippi Sound, illustrating the importance of the atmospheric influence on oil spills such as DwH. Close

• 9. [Article] Estimating Open-Ocean Barotropic Tidal Dissipation: The Hawaiian Ridge

  The generalized inverse of a regional model is used to estimate barotropic tidal dissipation along the Hawaiian Ridge. The model, based on the linear shallow-water equations, incorporates parameterizations ...

  Citation × Citation Citation Abstract Copy Title: Estimating Open-Ocean Barotropic Tidal Dissipation: The Hawaiian Ridge Author: Zaron, Edward D., Egbert, Gary D. Year: 2006 The generalized inverse of a regional model is used to estimate barotropic tidal dissipation along the Hawaiian Ridge. The model, based on the linear shallow-water equations, incorporates parameterizations for the dissipation of energy via friction in the bottom boundary layer and form drag due to internal waves generated at topographic slopes. Sea surface height data from 364 orbit cycles of the Ocean Topography Experiment (TOPEX)/Poseidon satellite mission are used to perform inversions at eight diurnal and semidiurnal tidal frequencies. It is estimated that the barotropic M2 tide loses energy at a rate of 19 GW, of which 88% is lost within 250 km of the ridge, presumably via conversion to the internal or baroclinic tide. Uncertainty in the assumed model error and wave drag in the forward model suggest that M? dissipation values from 18 to 25 GW are consistent with the altimetric observations. Other barotropic tidal constituents are estimated to lose a total of 5.7 GW. The spatial distribution of barotropic dissipation along the ridge is similar to that inferred from three-dimensional primitive equation models, and it is largely insensitive to details of assumed model and data errors. Dissipation at semidiurnal frequencies is most intense at the French Frigate Shoals with lesser, but significant, contributions at other sites. Diurnal tidal dissipation is concentrated to the east of the French Frigate Shoals, at the Gardner Pinnacles. Further work with three-dimensional models will be necessary to determine the fate of the energy that is removed from the barotropic tide. Title: Estimating Open-Ocean Barotropic Tidal Dissipation: The Hawaiian Ridge Author: Zaron, Edward D., Egbert, Gary D. Year: 2006 The generalized inverse of a regional model is used to estimate barotropic tidal dissipation along the Hawaiian Ridge. The model, based on the linear shallow-water equations, incorporates parameterizations for the dissipation of energy via friction in the bottom boundary layer and form drag due to internal waves generated at topographic slopes. Sea surface height data from 364 orbit cycles of the Ocean Topography Experiment (TOPEX)/Poseidon satellite mission are used to perform inversions at eight diurnal and semidiurnal tidal frequencies. It is estimated that the barotropic M2 tide loses energy at a rate of 19 GW, of which 88% is lost within 250 km of the ridge, presumably via conversion to the internal or baroclinic tide. Uncertainty in the assumed model error and wave drag in the forward model suggest that M? dissipation values from 18 to 25 GW are consistent with the altimetric observations. Other barotropic tidal constituents are estimated to lose a total of 5.7 GW. The spatial distribution of barotropic dissipation along the ridge is similar to that inferred from three-dimensional primitive equation models, and it is largely insensitive to details of assumed model and data errors. Dissipation at semidiurnal frequencies is most intense at the French Frigate Shoals with lesser, but significant, contributions at other sites. Diurnal tidal dissipation is concentrated to the east of the French Frigate Shoals, at the Gardner Pinnacles. Further work with three-dimensional models will be necessary to determine the fate of the energy that is removed from the barotropic tide. Close

• 10. [Article] The time-averaged circulation of the north Pacific Ocean : an analysis based on inverse methods

  The time-averaged velocity field in the North Pacific was estimated in two sets of inverse calculations. The planetary geostrophic equations were the basis for dynamical models of the flow in each case. ...

  Citation × Citation Citation Abstract Copy Title: The time-averaged circulation of the north Pacific Ocean : an analysis based on inverse methods Author: Zaron, Edward D. The time-averaged velocity field in the North Pacific was estimated in two sets of inverse calculations. The planetary geostrophic equations were the basis for dynamical models of the flow in each case. The inverse estimates of the circulation were obtained by minimizing a positive-definite cost function, which measured the inconsistency of the model's predictions against a set of observations comprised of a large, high-quality hydrographic data set, and surface fluxes of heat, fresh water, and momentum. In the first part of this work, four solution methods for the generalized inverse of a linear planetary geostrophic model of the North Pacific are compared. A conjugate gradient solver applied to the equation for the generalized inverse, expressed in terms of a representer expansion, was the most computationally efficient solution method. The other methods, in order of decreasing efficiency, were, a conjugate gradient descent solver (preconditioned with the inverse of the model operators), a direct solver for the representer coefficients, and a second conjugate gradient descent solver (preconditioned so that the diagonal elements of the cost Redacted for Privacy function Hessian were unity). All but the last method were successful at minimizing the penalty function. Inverse estimates of the circulation based on the linear planetary geostrophic model were stable to perturbations in the data, and insensitive to assumptions regarding the model forcing and boundary condition uncertainties. A large calculation, which involved approximately 18,000 observations and 60,000 state variables, indicated that the linear model is remarkably consistent with the observations. The second part of this work describes an attempt to use a nonlinear planetary geostrophic model (which included realistic bottom topography, lateral momentum mixing, out-cropping layers, and air-sea fluxes of heat, freshwater, and momentum) to assimilate the same hydrographic data set as above. Because of the nonlinearity in the model, descent methods (rather than a representer-based method) were used to solve the inverse problem. The nonlinearity of the model and the poor conditioning of the cost function Hessian confounded the minimization process. A solver for the tangent-linearization of the planetary geostrophic system should be used as a preconditioner if calculations of this type are attempted in the future. Title: The time-averaged circulation of the north Pacific Ocean : an analysis based on inverse methods Author: Zaron, Edward D. The time-averaged velocity field in the North Pacific was estimated in two sets of inverse calculations. The planetary geostrophic equations were the basis for dynamical models of the flow in each case. The inverse estimates of the circulation were obtained by minimizing a positive-definite cost function, which measured the inconsistency of the model's predictions against a set of observations comprised of a large, high-quality hydrographic data set, and surface fluxes of heat, fresh water, and momentum. In the first part of this work, four solution methods for the generalized inverse of a linear planetary geostrophic model of the North Pacific are compared. A conjugate gradient solver applied to the equation for the generalized inverse, expressed in terms of a representer expansion, was the most computationally efficient solution method. The other methods, in order of decreasing efficiency, were, a conjugate gradient descent solver (preconditioned with the inverse of the model operators), a direct solver for the representer coefficients, and a second conjugate gradient descent solver (preconditioned so that the diagonal elements of the cost Redacted for Privacy function Hessian were unity). All but the last method were successful at minimizing the penalty function. Inverse estimates of the circulation based on the linear planetary geostrophic model were stable to perturbations in the data, and insensitive to assumptions regarding the model forcing and boundary condition uncertainties. A large calculation, which involved approximately 18,000 observations and 60,000 state variables, indicated that the linear model is remarkably consistent with the observations. The second part of this work describes an attempt to use a nonlinear planetary geostrophic model (which included realistic bottom topography, lateral momentum mixing, out-cropping layers, and air-sea fluxes of heat, freshwater, and momentum) to assimilate the same hydrographic data set as above. Because of the nonlinearity in the model, descent methods (rather than a representer-based method) were used to solve the inverse problem. The nonlinearity of the model and the poor conditioning of the cost function Hessian confounded the minimization process. A solver for the tangent-linearization of the planetary geostrophic system should be used as a preconditioner if calculations of this type are attempted in the future. Close