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J. Thomas Farrar

Abstract

Spectral techniques applied to altimetry data are used to examine the dispersion relation and meridional sea level structure of wavelike variability with periods of about 20 to 200 days in the equatorial Pacific Ocean. Zonal wavenumber–frequency power spectra of sea surface height, when averaged over about 7°S–7°N, exhibit spectral peaks near the theoretical dispersion curves of first baroclinic-mode equatorial Kelvin and Rossby waves. There are distinct, statistically significant ridges of power near the first and second meridional-mode Rossby wave dispersion curves. Sea level variability near the theoretical Kelvin wave and first meridional-mode Rossby wave dispersion curves is dominantly (but not perfectly) symmetric about the equator, while variability near the theoretical second meridional-mode Rossby wave dispersion curve is dominantly antisymmetric. These results are qualitatively consistent with expectations from classical or shear-modified theories of equatorial waves.

The meridional structures of these modes resemble the meridional modes of equatorial wave theory, but there are some robust features of the meridional profiles that were not anticipated. The meridional sea level structure in the intraseasonal Kelvin wave band closely resembles the theoretically expected Gaussian profile, but sea level variability coherent with that at the equator is detected as far away as 11.75°S, possibly as a result of the forced nature of these Kelvin waves. Both first and second meridional-mode Rossby waves have larger amplitude in the Northern Hemisphere. The meridional sea level structure of tropical instability waves closely resembles that predicted by Lyman et al. using a model linearized about a realistic equatorial zonal current system.

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J. Thomas Farrar

Abstract

Tropical instability waves are triggered by instabilities of the equatorial current systems, and their sea level signal, with peak amplitude near 5°N, is one of the most prominent features of the dynamic topography of the tropics. Cross-spectral analysis of satellite altimetry observations shows that there is sea level variability in the Pacific Ocean as far north as Hawaii (i.e., 20°N) that is coherent with the sea level variability near 5°N associated with tropical instability waves. Within the uncertainty of the analysis, this off-equatorial variability obeys the dispersion relation for nondivergent, barotropic Rossby waves over a fairly broad range of periods (26–38 days) and zonal wavelengths (9°–23° of longitude) that are associated with tropical instability waves. The dispersion relation and observed wave properties further suggest that the waves are carrying energy away from the instabilities toward the North Pacific subtropical gyre, which, together with the observed coherence of the sea level signal of the barotropic waves with that of the tropical instability waves, suggests that the barotropic Rossby waves are being radiated from the tropical instability waves. The poleward transport of kinetic energy and westward momentum by these barotropic Rossby waves may influence the circulation in the subtropics.

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Theodore S. Durland
and
J. Thomas Farrar

Abstract

Longuet-Higgins in 1964 first pointed out that the Rossby wave energy flux as defined by the pressure work is not the same as that defined by the group velocity. The two definitions provide answers that differ by a nondivergent vector. Longuet-Higgins suggested that the problem arose from ambiguity in the definition of energy flux, which only impacts the energy equation through its divergence. Numerous authors have addressed this issue from various perspectives, and we offer one more approach that we feel is more succinct than previous ones, both mathematically and conceptually. We follow the work described by Cai and Huang in 2013 in concluding that there is no need to invoke the ambiguity offered by Longuet-Higgins. By working directly from the shallow-water equations (as opposed to the more involved quasigeostrophic treatment of Cai and Huang), we provide a concise derivation of the nondivergent pressure work and demonstrate that the two energy flux definitions are equivalent when only the divergent part of the pressure work is considered. The difference vector comes from the nondivergent part of the geostrophic pressure work, and the familiar westward component of the Rossby wave group velocity comes from the divergent part of the geostrophic pressure work. In a broadband wave field, the expression for energy flux in terms of a single group velocity is no longer meaningful, but the expression for energy flux in terms of the divergent pressure work is still valid.

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Theodore S. Durland
and
J. Thomas Farrar

Abstract

The theoretical resonant excitation of equatorial inertia–gravity waves and mixed Rossby–gravity waves is examined. Contrary to occasionally published expectations, solutions show that winds that are broadband in both zonal wavenumber and frequency do not in general produce peaks in the wavenumber–frequency spectrum of sea surface height (SSH) at wavenumbers associated with vanishing zonal group velocity.

Excitation of total wave energy in inertia–gravity modes by broadband zonal winds is virtually wavenumber independent when the meridional structure of the winds does not impose a bias toward negative or positive zonal wavenumbers. With increasing wavenumber magnitude |k|, inertia–gravity waves asymptote toward zonally propagating pure gravity waves, in which the magnitude of meridional velocity υ becomes progressively smaller relative to the magnitude of zonal velocity u and pressure p. When the total wave energy is independent of wavenumber, this effect produces a peak in |υ|2 near the wavenumber where group velocity vanishes, but a trough in |p|2 (or SSH variance). Another consequence of the shift toward pure gravity wave structure is that broadband meridional winds excite inertia–gravity modes progressively less efficiently as |k| increases and υ becomes less important to the wave structure. Broadband meridional winds produce a low-wavenumber peak in total wave energy leading to a subtle elevation of |p|2 at low wavenumbers, but this is due entirely to the decrease in the forcing efficiency of meridional winds with increasing |k|, rather than to the vanishing of the group velocity. Physical conditions that might alter the above conclusions are discussed.

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J. Thomas Farrar
and
Theodore S. Durland

Abstract

In the 1970s and 1980s, there was considerable interest in near-equatorial variability at periods of days to weeks associated with oceanic equatorial inertia–gravity waves and mixed Rossby–gravity waves. At that time, the measurements available for studying these waves were much more limited than today: most of the available observations were from scattered island tide gauges and a handful of short mooring records. More than a decade of the extensive modern data record from the Tropical Atmosphere Ocean (TAO)/Triangle Trans-Ocean Buoy Network (TRITON) mooring array in the Pacific Ocean is used to reexamine the internal-wave climate in the equatorial Pacific, with a focus on interpretation of the zonal-wavenumber/frequency spectrum of surface dynamic height relative to 500 decibars at periods of 3–15 days and zonal wavelengths exceeding 30° of longitude. To facilitate interpretation of the dynamic height spectrum and identification of equatorial wave modes, the spectrum is decomposed into separate spectra associated with dynamic height fluctuations that are symmetric or antisymmetric about the equator. Many equatorial-wave meridional modes can be identified, for both the first and second baroclinic mode. Zonal-wavenumber/frequency spectra of the zonal and meridional wind stress components are also examined. The observed wind stress spectra are used with linear theory of forced equatorial waves to provide a tentative explanation for the zonal-wavenumber extent of the spectral peaks seen in dynamic height. Examination of the cross-equatorial symmetry properties of the wind stress suggests that virtually all of the large-scale equatorial inertia–gravity and mixed Rossby–gravity waves examined may be sensitive to both zonal and meridional wind stress.

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Dudley B. Chelton
,
Roger M. Samelson
, and
J. Thomas Farrar

Abstract

The Ka-band Radar Interferometer (KaRIn) on the Surface Water and Ocean Topography (SWOT) satellite will revolutionize satellite altimetry by measuring sea surface height (SSH) with unprecedented accuracy and resolution across two 50-km swaths separated by a 20-km gap. The original plan to provide an SSH product with a footprint diameter of 1 km has changed to providing two SSH data products with footprint diameters of 0.5 and 2 km. The swath-averaged standard deviations and wavenumber spectra of the uncorrelated measurement errors for these footprints are derived from the SWOT science requirements that are expressed in terms of the wavenumber spectrum of SSH after smoothing with a filter cutoff wavelength of 15 km. The availability of two-dimensional fields of SSH within the measurement swaths will provide the first spaceborne estimates of instantaneous surface velocity and vorticity through the geostrophic equations. The swath-averaged standard deviations of the noise in estimates of velocity and vorticity derived by propagation of the uncorrelated SSH measurement noise through the finite difference approximations of the derivatives are shown to be too large for the SWOT data products to be used directly in most applications, even for the coarsest footprint diameter of 2 km. It is shown from wavenumber spectra and maps constructed from simulated SWOT data that additional smoothing will be required for most applications of SWOT estimates of velocity and vorticity. Equations are presented for the swath-averaged standard deviations and wavenumber spectra of residual noise in SSH and geostrophically computed velocity and vorticity after isotropic two-dimensional smoothing for any user-defined smoother and filter cutoff wavelength of the smoothing.

Open access
Andrew J. Wells
,
Claudia Cenedese
,
J. Thomas Farrar
, and
Christopher J. Zappa

Abstract

The aqueous thermal boundary layer near to the ocean surface, or skin layer, has thickness O(1 mm) and plays an important role in controlling the exchange of heat between the atmosphere and the ocean. Theoretical arguments and experimental measurements are used to investigate the dynamics of the skin layer under the influence of an upwelling flow, which is imposed in addition to free convection below a cooled water surface. Previous theories of straining flow in the skin layer are considered and a simple extension of a surface straining model is posed to describe the combination of turbulence and an upwelling flow. An additional theory is also proposed, conceptually based on the buoyancy-driven instability of a laminar straining flow cooled from above. In all three theories considered two distinct regimes are observed for different values of the Péclet number, which characterizes the ratio of advection to diffusion within the skin layer. For large Péclet numbers, the upwelling flow dominates and increases the free surface temperature, or skin temperature, to follow the scaling expected for a laminar straining flow. For small Péclet numbers, it is shown that any flow that is steady or varies over long time scales produces only a small change in skin temperature by direct straining of the skin layer. Experimental measurements demonstrate that a strong upwelling flow increases the skin temperature and suggest that the mean change in skin temperature with Péclet number is consistent with the theoretical trends for large Péclet number flow. However, all of the models considered consistently underpredict the measured skin temperature, both with and without an upwelling flow, possibly a result of surfactant effects not included in the models.

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Michael Schlundt
,
J. Thomas Farrar
,
Sebastien P. Bigorre
,
Albert J. Plueddemann
, and
Robert A. Weller

Abstract

The comparison of equivalent neutral winds obtained from (i) four WHOI buoys in the subtropics and (ii) scatterometer estimates at those locations reveals a root-mean-square (RMS) difference of 0.56–0.76 m s−1. To investigate this RMS difference, different buoy wind error sources were examined. These buoys are particularly well suited to examine two important sources of buoy wind errors because 1) redundant anemometers and a comparison with numerical flow simulations allow us to quantitatively assess flow distortion errors, and 2) 1-min sampling at the buoys allows us to examine the sensitivity of buoy temporal sampling/averaging in the buoy–scatterometer comparisons. The interanemometer difference varies as a function of wind direction relative to the buoy wind vane and is consistent with the effects of flow distortion expected based on numerical flow simulations. Comparison between the anemometers and scatterometer winds supports the interpretation that the interanemometer disagreement, which can be up to 5% of the wind speed, is due to flow distortion. These insights motivate an empirical correction to the individual anemometer records and subsequent comparison with scatterometer estimates show good agreement.

Open access
Anthony R. Kirincich
,
Steven J. Lentz
,
J. Thomas Farrar
, and
Neil K. Ganju

Abstract

The spatial structure of the tidal and background circulation over the inner shelf south of Martha's Vineyard, Massachusetts, was investigated using observations from a high-resolution, high-frequency coastal radar system, paired with satellite SSTs and in situ ADCP velocities. Maximum tidal velocities for the dominant semidiurnal constituent increased from 5 to 35 cm s−1 over the 20-km-wide domain with phase variations up to 60°. A northeastward jet along the eastern edge and a recirculation region inshore dominated the annually averaged surface currents, along with a separate along-shelf jet offshore. Owing in part to this variable circulation, the spatial structure of seasonal SST anomalies had implications for the local heat balance. Cooling owing to the advective heat flux divergence was large enough to offset more than half of the seasonal heat gain owing to surface heat flux. Tidal stresses were the largest terms in the mean along- and across-shelf momentum equations in the area of the recirculation, with residual wind stress and the Coriolis term dominating to the west and south, respectively. The recirculation was strongest in summer, with mean winds and tidal stresses accounting for much of the differences between summer and winter mean circulation. Despite the complex bathymetry and short along-shelf spatial scales, a simple model of tidal rectification was able to recreate the features of the northeastward jet and match an estimate of the across-shelf structure of sea surface height inferred from the residual of the momentum analysis.

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K. Jossia Joseph
,
Amit Tandon
,
R. Venkatesan
,
J. Thomas Farrar
, and
Robert A. Weller

Abstract

The inception of a moored buoy network in the northern Indian Ocean in 1997 paved the way for systematic collection of long-term time series observations of meteorological and oceanographic parameters. This buoy network was revamped in 2011 with Ocean Moored buoy Network for north Indian Ocean (OMNI) buoys fitted with additional sensors to better quantify the air–sea fluxes. An intercomparison of OMNI buoy measurements with the nearby Woods Hole Oceanographic Institution (WHOI) mooring during the year 2015 revealed an overestimation of downwelling longwave radiation (LWR↓). Analysis of the OMNI and WHOI radiation sensors at a test station at National Institute of Ocean Technology (NIOT) during 2019 revealed that the accurate and stable amplification of the thermopile voltage records along with the customized datalogger in the WHOI system results in better estimations of LWR↓. The offset in NIOT measured LWR↓ is estimated first by segregating the LWR↓ during clear-sky conditions identified using the downwelling shortwave radiation measurements from the same test station, and second, finding the offset by taking the difference with expected theoretical clear-sky LWR↓. The corrected LWR↓ exhibited good agreement with that of collocated WHOI measurements, with a correlation of 0.93. This method is applied to the OMNI field measurements and again compared with the nearby WHOI mooring measurements, exhibiting a better correlation of 0.95. This work has led to the revamping of radiation measurements in OMNI buoys and provides a reliable method to correct past measurements and improve estimation of air–sea fluxes in the Indian Ocean.

Significance Statement

Downwelling longwave radiation (LWR↓) is an important climate variable for calculating air–sea heat exchange and quantifying Earth’s energy budget. An intercomparison of LWR↓ measurements between ocean observing platforms in the north Indian Ocean revealed a systematic offset in National Institute of Ocean Technology (NIOT) Ocean Moored buoy Network for north Indian Ocean (OMNI) buoys. The observed offset limited our capability to accurately estimate air–sea fluxes in the Indian Ocean. The sensor measurements were compared with a standard reference system, which revealed problems in thermopile amplifier as the root cause of the offset. This work led to the development of a reliable method to correct the offset in LWR↓ and revamping of radiation measurements in NIOT-OMNI buoys. The correction is being applied to the past measurements from 12 OMNI buoys over 8 years to improve the estimation of air–sea fluxes in the Indian Ocean.

Open access