We describe a simple technique for fitting spectra that is applicable to any problem of adjusting a theoretical spectral form to fit observations. All one needs is a functional form for the theoretical spectrum, and an estimate for the instrumental noise spectrum. The method, based on direct application of the Maximum Likelihood approach, has several advantages over other fitting techniques: 1. It is unbiased in comparison with other least-squares or cost function-based approaches. 2. It is insensitive to dips and wiggles in the spectrum. This is because the range of wavenumbers used in the fit does not vary, and the built-in noise model forces the routine to ignore the spectrum as it gets down towards the noise level. 3. Error bars. There is a theoretical estimate for the variance of the fitted parameters, based on how broad or narrow the likelihood function is in the vicinity of its peak. 4. We calculate statistical quantities that indicate how well the observed spectrum fits the theoretical form. This is extremely useful in automating analysis software, to get the computer to automatically flag "bad" fits. The method is demonstrated using data from SCAMP (Self-Contained Autonomous Microstructure Profiler), a free-falling temperature microstructure profiler. Maximum Likelihood fits to the Batchelor spectrum are compared to the SCAMP-generated fits and other least-squares techniques, and also tested against pseudo-data generated by Monte-Carlo techniques. Pseudo-code outlines for the spectral fit routines are given.

No abstract

No abstract

The fact that ocean currents must flow parallel to the coast leads to the dynamics of coastal sea level being quite different from the dynamics in the open ocean. The coastal influence of open-ocean dynamics (dynamics associated with forcing which occurs in deep water, beyond the continental slope) therefore involves a handover between the predominantly geostrophic dynamics of the interior ocean and the ageostrophic dynamics which must occur at the coast. An understanding of how this handover occurs can be obtained by considering the combined role of coastal trapped waves and bottom friction. We here review understanding of coastal trapped waves, which propagate cyclonically around ocean basins along the continental shelf and slope, at speeds which are fast compared to those of baroclinic planetary waves and currents in the open ocean (excluding the large-scale barotropic mode). We show that this results in coastal sea-level signals on western boundaries which, compared to the nearby open-ocean signals, are spatially smoothed, reduced in amplitude, and displaced along the coast in the direction of propagation of coastal trapped waves. The open-ocean influence on eastern boundaries is limited to signals propagating polewards from the equatorial waveguide (although a large-scale diffusive influence may also play a role). This body of work is based on linearised equations, but we also discuss the nonlinear case. We suggest that a proper consideration of nonlinear terms may be very important on western boundaries, as the competition between advection by western boundary currents and a counter-propagating influence of coastal trapped waves has the potential to lead to sharp gradients in coastal sea level where the two effects come into balance.

[1] Skewness of sea level variability for the world's oceans is calculated using gridded altimeter data for the period 1993-2001. Many well-known ocean features can be identified in the skewness map, including the Gulf Stream, Kuroshio Extension, Brazil-Malvinas Confluence, and the Agulhas Retroflection. It is shown, through an idealized example and results from a quasi-geostrophic model, that sea level skewness can be used to identify the mean path of unstable ocean jets and also regions dominated by eddies with a preferred sense of rotation. These ideas are confirmed with a more detailed analysis of the skewness fields for the northwest Atlantic and Agulhas Retroflection region. Finally, it is argued that sea level skewness, like variance, is a potentially powerful diagnostic for testing the realism of high-resolution ocean circulation models.

[1] The Madden-Julian Oscillation (MJO) is the dominant mode of atmospheric variability in the tropical atmosphere on intraseasonal time scales (i.e., weeks to seasons). This study examines the connection between the MJO and global sea level measured by altimeters over the last 17 years. We first identify regions exhibiting a significant (both statistical and practical) relationship between sea level and the MJO. The first region consists of the equatorial Pacific and western coastal zones of North and South America. Consistent with previous studies, we identify wind-driven equatorially trapped Kelvin waves that propagate eastward along the equatorial Pacific and then transform into coastal trapped waves that propagate poleward along the western coasts of North and South America. The second region includes the shallow waters of the Gulf of Carpentaria (off Australia's north coast) and the adjacent Arafura and Timor seas. Setup by onshore winds is shown to be the dominant physical process. Finally, the northeastern Indian Ocean is shown to be a complex region involving a combination of equatorially trapped Kelvin waves, coastal trapped waves, and westward-propagating Rossby waves exhibiting characteristics of both local and remote forcing. The implications of the results for deep and coastal ocean forecasting are discussed.

[1] A 40 year hindcast of storm surges in the northwest Atlantic and adjacent shelf seas is performed using a 2-D nonlinear barotropic ocean model forced by realistic 6 hourly winds and air pressures. This hindcast is used to generate spatial maps of the return level of storm surges and also to estimate the return period of extreme total sea levels. The accuracy of the hindcast is assessed in two ways. First, the standard deviation of the difference between the observed residuals (total sea level minus tide) and the hindcast is calculated at 24 tide gauge locations. A typical error standard deviation is 8 cm. Second, the 40 year return level of observed residuals is compared to that of the hindcast surges. The predicted 40 year return levels are typically within 10 cm of observed return levels at the 24 observation locations. A spatial map of the 40 year return level of surges is presented for the northwest Atlantic. It identifies the regions exposed to the largest surges. Total sea levels are reconstructed using (1) the hindcast surges and (2) tides and higher-frequency variability predicted from short, observed sea level records. An extremal analysis of the reconstructed total sea levels shows that their 40 year return levels are in good agreement (within about 10 cm) with the levels calculated from multidecadal observed sea level records. This means that given a short record anywhere within the model domain, or results from a good tidal model, 40 year return levels can be estimated.

Monthly sea-levels from an extensive array of North Atlantic tide gauges (26-50"N) are examined. The spatial scale of the sea-level variations, and the reasons for them, are discussed; one application of such a study is clearly in the design of a tide gauge network for monitoring eustatic changes of sea-level.The spatial scale of the sea-level changes is large. There is a coherent sealevel signal which can be traced along the eastern boundary of the North Atlantic from Newlyn (50"N) to Tenerife (28"N). There are also two distinct groupings of tide gauges along the western boundary, separated by Cape Hatteras.The contribution of local air pressure and wind stress is quantified at each gauge through multiple regression techniques and the gains are then interpreted in terms of recent theoretical and numerical modelling studies. For example, the gains suggest that the wind-forced boundary current along the Nova Scotian shelf is trapped to within about 16 km of the coast.The influence of local meteorology cannot account for the large-scale modes of variability. The coherent signal along the eastern boundary is correlated with changes in the Sverdrup transport of the North Atlantic and hence the large-scale wind field. The two modes on the western boundary appear to be related to baroclinic boundary current variations.The Newlyn sea-level record is finally 'corrected' for some of the above effects to illustrate the utility of such a residual series in the identification of eustatic changes and vertical crustal movement.