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 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

Aliased Tidal Variability in Mesoscale Sea Level Anomaly Maps

Sea level anomaly (SLA) maps are routinely produced by objective analysis of data from the constellation of satellite altimeter missions in operation since 1992. Beginning in 2014, changes in the Data Unification and Altimeter Combination System (DUACS) used to create the SLA maps resulted in improved spatial resolution of mesoscale variability, but it also increased the levels of aliased tidal variability compared to the methodology employed prior to 2014. The present work investigates the magnitude and spatial distribution of these tidal signals, which are typically smaller than 1 cm in the open ocean but can reach tens of centimeters in the coastal ocean. In the open ocean, the signals are caused by a combination of phase-locked and phase-variable baroclinic tides. In the coastal ocean, the signals are a combination of aliased high-frequency nontidal variability and aliased variability caused by erroneous tidal corrections applied to the along-track altimetry prior to objective analysis. Several low-pass and bandpass filters are implemented to reduce the tidal signals in the mapped SLA, and independent tide gauge data are used to provide an objective assessment of the performance of the filters. The filter that attenuates both the small-scale (less than 200 km) and the high-frequency (period shorter than 108 days) components of SLA removes aliased baroclinic tidal variability and improves the accuracy of tidal analysis in the open ocean while also performing acceptably in the coastal ocean

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 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

Data Assimilation in Models with Convective Adjustment

Practical hydrostatic ocean models are often restricted to statically stable configurations by the use of a convective adjustment. A common way to do this is to assign an infinite boat conductivity to the water at a given level if the water column should become statically unstable. This is implemented in the form of a switch. When a statically unstable configuration is detected, it is immediately replaced with a statically stable one in which heat is conserved. In this approach, the model is no longer governed by a smooth set of equations, and usual techniques of variational data assimilation must be modified. In this note, a simple one-dimensional diffusive model is presented. Despite its simplicity, this model captures the essential behavior of the convective adjustment scheme in a widely used ocean general circulation model. Since this simple model can be derived from the more complex general circulation model, it then follows that many of the properties of the constrained system can be observed in this very simple scalar ordinary differential equation with a constraint on the solution. Techniques from the theory of optimal control are used to find solutions of a simple formulation of the variational data assimilation problem in this simple case. The optimal solution involves the solution of a nonlinear problem, even when the unconstrained dynamics are linear. In cases with discontinuous dynamics, one cannot define the adjoint of the linearized system in a straightforward manner. The very simplest variational formulation is shown to have nonunique stationary points and undesirable physical consequences. Modifications that lead to better behaved calculations and more meaningful solutions are presented. Whereas it is likely that the underlying principles from control theory are applicable to practical ocean models, the technique used to solve the simple problem may be applicable only to steady problems. Derivation of suitable techniques for initial value problems will involve a major research effort

Time-Variable Refraction of the Internal Tide at the Hawaiian Ridge

The interaction of the dominant semidiurnal M₂ internal tide with the large-scale subtidal flow is examined in an ocean model by propagating the tide through an ensemble of background fields in a domain centered on the Hawaiian Ridge. The background fields are taken from the Simple Ocean Data Assimilation (SODA) ocean analysis, at 2-month intervals from 1992 through 2001. Tides are computed with the Primitive Equation Z-coordinate Harmonic Analysis of Tides (PEZ-HAT) model by 14-day integrations using SODA initial conditions and M₂ tidal forcing. Variability of the tide is found to occur primarily as the result of propagation through the nonstationary background fields, rather than via generation site variability. Generation of incoherent tidal variability is mapped and shown to occur mostly in association with waves generated at French Frigate Shoals scattering near the Musicians Seamounts to the north of the ridge. The phase-coherent internal tide loses energy at a domain-average rate of 2mWm⁻² by scattering into the non-stationary tide. Because of the interference of waves from multiple generation sites, variability of the internal tide is spatially inhomogeneous and values of the scattering rate 10 times larger occur in localized areas. It is estimated that 20% of the baroclinic tidal energy flux is lost by adiabatic scattering (refraction) within 250 km of the ridge, a value regarded as a lower bound because of the smoothed nature of the SODA fields used in this study

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 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

Can Tidal Perturbations Associated with Sea Level Variations in the Western Pacific Ocean be used to Understand Future Effects of Tidal Evolution?

This study examines connections between mean sea level (MSL) variability and diurnal and semidiurnal tidal constituent variations at 17 open-ocean and 9 continental shelf tide gauges in the western tropical Pacific Ocean, a region showing anomalous rise in MSL over the last 20 years and strong interannual variability. Detrended MSL fluctuations are correlated with detrended tidal amplitude and phase fluctuations, defined as tidal anomaly trends (TATs), to quantify the response of tidal properties to MSL variation. About 20 significant amplitude and phase TATs are found for each of the two strongest tidal constituents, K1 (diurnal) and M2 (semidiurnal). Lesser constituents (O1 and S2) show trends at nearly half of all gauges. Fluctuations in MSL shift amplitudes and phases; both positive and negative responses occur. Changing overtides suggest TATs are influenced by changing shallow water friction over the equatorial Western Pacific and the eastern coast of Australia (especially near the Great Barrier Reef). There is a strong connection between semidiurnal TATs at stations around the Solomon Islands and changes in thermocline depth, overtide generation, and the El Niño Southern Oscillation (ENSO). TATs for O1, K1 and M2 are related to each other in a manner that suggests transfer of energy from M2 to the two diurnals via resonant triad interactions; these cause major tidal variability on sub-decadal time scales, especially for M2. The response of tides to MSL variability is not only spatially complex, it is frequency dependent; therefore, short-term responses may not predict long-term behavior

A Mathematical Model for Outgassing and Contamination

A model for the mathematical description of the processes of outgassing and contamination in a vacuum system is proposed. The underlying assumptions are diffusion in the source, convection and diffusion in the cavity, mass transfer across the source-cavity interface, and a generalization of the Langmuir isotherm for the sorption kinetics on the target. Three approximations are considered where the asymptotic behavior of the model for large time is shown as well as the dependence and sensitivity of the model on some of the parameters. Some numerical examples of the full model are then presented together with a proof of the uniqueness of the solution

Toward Realistic Nonstationarity of Semidiurnal Baroclinic Tides in a Hydrodynamic Model

Semidiurnal baroclinic tide sea surface height (SSH) variance and semidiurnal nonstationary variance fraction (SNVF) are compared between a hydrodynamic model and altimetry for the low‐ to middle‐latitude global ocean. Tidal frequencies are aliased by ∼10‐day altimeter sampling, which makes it impossible to unambiguously identify nonstationary tidal signals from the observations. In order to better understand altimeter sampling artifacts, the model was analyzed using its native hourly outputs and by subsampling it in the same manner as altimeters. Different estimates of the semidiurnal nonstationary and total SSH variance are obtained with the model depending on whether they are identified in the frequency domain or wave number domain and depending on the temporal sampling of the model output. Five sources of ambiguity in the interpretation of the altimetry are identified and briefly discussed. When the model and altimetry are analyzed in the same manner, they display qualitatively similar spatial patterns of semidiurnal baroclinic tides. The SNVF typically correlates above 80% at all latitudes between the different analysis methods and above 60% between the model and altimetry. The choice of analysis methodology was found to have a profound effect on estimates of the semidiurnal baroclinic SSH variance with the wave number domain methodology underestimating the semidiurnal nonstationary and total SSH variances by 68% and 66%, respectively. These results produce a SNVF estimate from altimetry that is biased low by a factor of 0.92. This bias is primarily a consequence of the ambiguity in the separation of tidal and mesoscale signals in the wave number domain.Key PointsHydrodynamic models incorporating mesoscale dynamics and tides are beginning to resolve stationary and nonstationary baroclinic tidesThe ratio of nonstationary to total semidiurnal variance computed from altimetry and HyCOM simulations agrees at low and middle latitudesComparisons of analysis methodologies show that total and nonstationary semidiurnal variances are underestimated in altimetry on averagePeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152034/1/jgrc23624_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152034/2/jgrc23624.pd