Sea Surface Height Spectrum Research Articles

Sea Surface Height Variability in the 30–120 km Wavelength Band From Altimetry Along‐Track Observations

AbstractReprocessed altimetry along‐track sea surface height (SSH) observations from multiple missions are analyzed for the SSH variability in the 30–120 km wavelength band. This band of variability is missing in the widely used global multi‐mission mapped SSH data set, known as the Archiving, Validation and Interpretation of Satellite Oceanographic Data SSH product. The SSH variability is derived from along‐track SSH variance spectra after subtracting noise floors, and its global spatial patterns are consistent among the missions and the output of a high‐resolution ocean general circulation model simulation. High SSH variability in the 30–120 km wavelength band is found in the intratropics of all ocean basins (25°S–25°N), the western boundary current outflow regions, and in five regions along the Antarctic Circumpolar Current: Agulhas Retroflection zone, Kerguelen Plateau, Macquarie Ridge, Pacific Antarctic Ridge, and Drake Passage. The average slope of the along‐track SSH spectra in the 30–120 km wavelength band in the intratropics falls between −2.14 and −1.56, consistent with the Garrett‐Munk spectral slope. The spatial patterns of the SSH variability could be used as a metric to evaluate high‐resolution numerical models and to shed light on what to expect from future high‐resolution altimetry missions.

Interactions between barotropic tides and mesoscale processes in deep ocean and shelf regions

The interactions between barotropic tides and mesoscale processes were studied using the results of a numerical model in which tidal forcing was turned on and off. The research area covered part of the East Atlantic Ocean, a steep continental slope, and the European Northwest Shelf. Tides affected the baroclinic fields at much smaller spatial scales than the barotropic tidal scales. Changes in the horizontal patterns of the M2 and M4 tidal constituents provided information about the two-way interactions between barotropic tides and mesoscale processes. The interaction between the atmosphere and ocean measured by the work done by wind was also affected by the barotropic tidal forcing. Tidal forcing intensified the transient processes and resulted in a substantial transformation of the wave number spectra in the transition areas from the deep ocean to the shelf. Tides flattened the sea-surface height spectra down to ~ k−2.5 power law, thus reflecting the large contribution of the processes in the high-frequency range compared to quasi-geostrophic motion. The spectra along sections parallel or normal to the continental slope differ from each other, which indicates that mesoscale turbulence was not isotropic. An analysis of the vorticity spectra showed that the flattening was mostly due to internal tides. Compared with the deep ocean, no substantial scale selectivity was observed on the shelf area. Particle tracking showed that the lengths of the Lagrangian trajectories increased by approximately 40% if the barotropic tidal forcing was activated, which contributed to changed mixing properties. The ratio between the horizontal and vertical scales of motion varied regionally depending on whether barotropic tidal forcing was included. The overall conclusion is that the barotropic tides affect substantially the diapycnal mixing.

Spectral Decomposition Method for Large Sea Surface Generation and Radar Backscatter Modeling

AbstractThis paper analyzes different methods to simulate sea surface waves over a large area rapidly and with low computational complexity. Indeed, for wind speed between 1 and 10 m/s, the area of the sea surfaces must range from 10 to 92,000m2 to account for all the surface roughness scales which can contribute to the scattering process at microwave frequencies. At frequencies higher than 10 GHz, a sampling rate of one tenth of the wavelength can lead to a prohibitive numerical cost. The impact of these approaches on the surface power spectral density and on the monostatic normalized radar cross section is investigated. The proposed methods consist of splitting the full sea surface height spectrum into sub‐spectra of smaller extents. Sub‐sea surfaces are generated and combined from different interpolation and recombination techniques. In this paper, an original closed‐form expression of the resulting sea surface height spectrum is derived to interpret the simulation results. Finally, the efficiency of the methods in terms of accuracy and memory requirement is analyzed by computing the monostatic normalized radar cross section from sea surfaces with the first‐order small slope approximation (SSA1) scattering model.

Scale Transition From Geostrophic Motions to Internal Waves in the Northern South China Sea

AbstractThe eddy‐abundant circulation in the northern South China Sea (NSCS) tends to be dynamically complex due to monsoon forcing, Kuroshio intrusion, and emitted internal waves from the Luzon Strait. This study uses 13‐year shipboard acoustic Doppler current profiler measurements (2004–2016), orbital altimeter data, and high‐resolution model output to perform wave‐vortex decompositions and investigate the scale of transition from dominantly geostrophic flows to internal wave motions in the northern South China Sea. The upper ocean kinetic energy spectra transition on scales exceeds 200 km. This large scale of transition is attributed to the energetic low‐mode internal waves (e.g., internal tides and inertia‐gravity waves). However, inconsistencies in the decomposition reveal that the assumptions of homogeneity and isotropy required for the 1‐D decomposition (Bühler et al., 2014) are sufficiently violated at smaller scales to affect the subdominant member of the decomposition on scales below 100 km. A method for direct quantification of the consequences by degree of violation using bootstrapping of the 2‐D model data is developed and illustrated. Observed and modeled sea surface height spectra flatten at scales smaller than 125 km, which is found in the model to be due to the coherent, semidiurnal internal waves. The large scale of transition between geostrophic and wave motions in the South China Sea is an irreducible uncertainty for altimeter velocities (e.g., the Surface Water and Ocean Topography mission).

Impact of Rain, Swell, and Surface Currents on the Electromagnetic Bias in GNSS-Reflectometry

The assessment of the electromagnetic (EM) bias is required to predict the performance of upcoming global navigation satellite systems-reflectometry (GNSS-R) altimetry systems, and its impact in data assimilation climate studies. In previous studies, the EM bias in bistatic GNSS-R altimetry (L-band) was numerically estimated for a wind-driven sea surface height spectrum, including the time-domain variability. In the present study, spectral models for the rain, swell, and surface currents are used to compute a perturbed wind-driven sea surface height spectrum, from which a perturbed three-dimensional (3-D) time-evolving wind-driven sea surface height is computed. The generated sea surface is then illuminated by a right hand circular polarization (RHCP) L-band EM wave, and the wave scattered from each facet is computed from each facet using the physical optics (PO) method under the Kirchhoff approximation (KA). Finally, the EM bias is computed numerically as the height of each patch times the forward-scattering coefficient, divided by the average of the forward-scattering coefficient. The impact of rain on the EM bias is a moderate decrease (in magnitude) due to the damping of the large gravity waves, which is more significant as the wind speed increases. The impact of swell is a small increase (in magnitude) mostly due to the change of the local incidence angles. The impact of currents can be either a moderate increase or decrease (in magnitude), depending on the sense of the current with respect to the wind, due to a change in the surface roughness.

Numerical Computation of the Electromagnetic Bias in GNSS-R Altimetry

In radar altimetry, the electromagnetic (EM) bias is originated by the smaller reflectivity of wave crests than troughs; thus, the average sea surface height is underestimated. Bias uncertainty is currently the largest factor in altimetry error budgets. The EM bias in a bistatic forward-scattering configuration at L-band, such as in Global Navigation Satellite Systems Reflectometry (GNSS-R) altimetry, remains one of the major sources of uncertainty in the altimetry error budget. In this paper, the EM bias is computed using numerical simulations. To do so, a time-dependent synthetic non-Gaussian sea surface is created using the Pierson–Moskowitz and Elfouhaily sea surface height spectra and spreading function. The sea surface is then discretized in facets and “illuminated” using a right-hand circular polarization GNSS signal, previously recorded by an up-looking antenna connected to a data logger. The waves scattered from each facet are then computed using the physical optics method under the Kirchhoff approximation, and the radar cross section of each facet is computed. The scattered electric fields are “collected” by a down-looking left-hand circular polarization antenna, and the EM bias is computed based on its fundamental definition. The numerical model is validated against Millet's model (a combined model of the weakly non-linear and modulation transfer models) with real data at C- and Ku-bands. Then, the numerical model is applied at L-band, for bistatic configurations, including different azimuth angles and different wind speeds. It is found that the EM bias is almost insensitive to the sea surface spectra selected and increases with increasing wind speed and incidence/scattering angle (up to ∼-20 cm at $\theta_{i,s}=45^{\circ}$ and $U_{10}=12 \mbox{m/s}$ ), and it also exhibits a non-negligible azimuthal dependence, which must be accounted for in the error budgets of upcoming GNSS-R altimetry missions.

The Effects of Altimeter Instrument Noise on the Estimation of the Wavenumber Spectrum of Sea Surface Height

Abstract The wavenumber spectrum of sea surface height (SSH) observed by satellite altimetry was analyzed by Xu and Fu. The spectral shape in the wavelength range of 70–250 km was approximated by a power law, representing a regime governed by geostrophic turbulence theories. The effects of altimeter instrument noise were assumed insignificant at wavelengths longer than 70 km. The authors reexamined the assumption in the study. Using nearly simultaneous observations made by Jason-1 and Jason-2 during their cross-calibration phase, this study found that the white noise level of altimetry measurement was best estimated from the spectral values at wavelengths from 25 to 35 km. After removing a white noise level based on such estimate from the SSH spectrum, the spectral slope values changed significantly over most of the oceans. A key finding is that the spectral slopes are generally steeper than k−2 (k is wavenumber) poleward of the 20° latitudes, where flatter spectral slopes in some regions have previously caused problems for dynamic interpretations. The new results indicate that the spectral slopes in the core regions of the major ocean current systems have values between the original geostrophic turbulence theory and the surface quasigeostrophic theory. The near k−4 spectrum suggests that the sea surface height variability at these wavelengths in the high eddy energy regions might be governed by frontogenesis.

Remote and local forcing of a coastal lagoon: The Virginia Coast Reserve

The effects of local and remote wind forcing of water level heights in the Virginia Coast Reserve (VCR) are examined in order to determine the significant forces governing estuarine motions over subtidal time scales. Recent (1996–2008) data from tide and wind stations in the lagoon, a tide station to the north at Sandy Hook, NJ, and one offshore wind station at the Chesapeake Light Tower are examined. Sea surface height spectrum calculations reveal significant diurnal and semidiurnal tidal effects along with subtidal variations, but a suppressed inertial signal. Sea-surface heights (SSH) with 2–5 day periods at Wachapreague, VA are coherent with those at Sandy Hook and lag them in time, suggesting that southward-propagating continental shelf waves provide subtidal variability within the lagoon. The coherence between lagoon winds and sea surface height, as well as between winds and cross-lagoon sea height gradient, were significant at a relatively small number of frequency and wind direction combinations. The frequencies at which this wind forcing occurs are the tidal and subtidal bands present to the north, so that lagoon winds selectively augment existing SSH signals, but do not generate them. The impact of the wind direction is closely related to the geometry of the lagoon and bounding landmasses. The effect of wind stress is also constrained by geometry in affecting the cross-lagoon water height gradient. Water levels at subtidal frequencies are likely forced by a combination of local wind forcing, remote wind forcing and oceanic forcing modified by the complex topography of the lagoon, shelf, and barrier islands.

Statistical representation of equatorial waves and tropical instability waves in the Pacific Ocean

Sea surface height (SSH), sea surface temperature (SST), and surface currents derived from satellite observations are analyzed to investigate signals of equatorial Kelvin and tropical instability waves (TIWs) in the Pacific Ocean. A wavenumber–frequency spectral analysis of SSH and SST anomalies was performed in order to examine their space and time variability. Significant spectral peaks along the dispersion curves of the first baroclinic mode Rossby and Kelvin waves are found in the SSH spectrum, indicating that the analysis can effectively identify the signals of equatorial waves in the upper ocean. A prominent peak in SSH fields at around 33 days and 1500 km wavelength along the Rossby wave dispersion curve is evident, and a similar peak is also found in SST fields. This upper ocean variability on these space and time scales is shown to be associated with TIWs. The spatial structure of 33-day TIWs is further examined based on an analysis of time series filtered in the frequency-wavenumber domain. The phase relationship between SSH, SST, and surface velocity associated with TIWs is described based on a cross-correlation analysis. Also, the interannual variability of TIW activity is compared with that of ENSO, showing a moderate correlation.