Altimeter Surveys, Coastal Tides, and Shelf Circulation
A conventional radar altimeter aboard a satellite is a nadir-looking active microwave sensor. Its signal pulse, transmitted vertically downward, reflects from the ocean surface back to an altimeter antenna. The round-trip time and the propagation speed of the electromagnetic waves are used to compute the range between the antenna and the ocean surface.
From the altimeter-measured range, the instantaneous sea surface relative to a reference surface, such as an ellipsoid, can be determined if a satellite orbit relative to the reference surface is known. With the knowledge of the oceanic geoid, the sea surface topography relative to the geoid due to ocean dynamic circulation including the temporal averages can be obtained. Although the geoid is not well determined yet, repeated observations can provide a measurement of the temporal variability of the sea surface height since the geoid can be treated as time-invariant for oceanographic applications.
Oceanographic applications of satellite altimetry require an accuracy of a few centimeters. This requirement constrains not only the altimeter sensor but also pertinent atmospheric and oceanographic corrections that have to be made, the satellite orbit, and, in some applications, the reference geoid. One-second data are provided to the science community as the Geophysical Data Records (GDR). So far, the accuracy of altimetric sensors has steadily improved to a few centimeters. The atmospheric corrections consist of ionospheric delay and wet and dry tropospheric delays; the oceanographic effects are composed of the sea state bias, inverse barometric response, the elastic ocean tides, solid Earth tides, and pole tides. The radial uncertainty of the orbit has long been one of the largest error sources in satellite altimetry until the TOPEX/Poseidon (T/P) mission. So far, the root mean square accuracy of the orbit used for producing GDRs is better than 1.5 cm. At present, the geoid errors occurring at various spatial scales are one of the largest error sources and the major obstacle to the derivation of the mean current from altimeter data.
Because almost all radar altimeter missions use a repeating orbit, repeat track analysis or collinear analysis becomes a conventional approach for application of altimeter data in physical oceanography. A mean at a location is calculated from data available, and then the mean is removed from the data to produce sea surface height anomalies relative to the mean. Thus, the repeat track analysis eliminates the geoid and its errors, the mean sea surface, and a portion of the orbit error. There are three variants from the standard approach. One is to subtract a selected instantaneous sea surface instead of the mean sea surface; another calculates the along-track slope deviations instead of sea level deviations. For a tidal analysis, collinear differences are usually calculated to bypass the uncertainty associated with the mean sea surface.
While satellite altimeters perform well over the open ocean, the reflected signals in coastal waters have artifacts due to the presence of land within the instrument footprint. To remedy these artifacts, waveform retrackers have been developed, including empirical ones and physically based ones (Gommenginger et al. 2011).
Conventional radar altimeters are pulse-limited. New altimeter sensors have been developed. For example, a delay-Doppler altimeter (also called as synthetic-aperture radar (SAR) altimeter) applies coherent processing to groups of transmitted pulses and thus utilizes the full Doppler bandwidth to make the most efficient use of the power reflected from the ocean surface. The SAR altimetry has high along-track resolution and can measure closer to the coast than the conventional pulse-limited altimeter. Both Cryosat-2 and Sentinel-3 missions operate SAR mode altimeters.
Satellite altimetry produces global measurements of instantaneous sea surface heights relative to a reference surface and is one of the essential tools for monitoring ocean surface conditions and understanding physical oceanographic processes. Altimetric sea surface height measurements are one of the most important data for ocean forecasting. Research using altimetric data has significantly improved global ocean tide models (Stammer et al. 2014) and greatly advanced our understanding of mesoscale circulation variability in the deep ocean (Fu and Cazenave 2001).
In the past decade or so, coastal altimetry has also advanced to a great deal (Vignudelli et al. 2011). Coastal altimetry products have been developed, which provide valid data points within ones of kilometers from the coast. Among those products are the Innovative Processing System Prototype for Coastal and Hydrology Applications (PISTACH, Mercier et al. 2010), the Prototype for Expertise on AltiKa for Coastal, Hydrology and Ice (PEACHI, http://www.aviso.altimetry.fr/en/data/products/sea-surface-height-products/global/experimental-saral-products-peachi.html), the SAR Altimetry Coastal and Open Ocean Performance (SCOOP, http://www.satoc.eu/projects/SCOOP/), and the X-TRACK (Birol et al. 2016). This article reviews advances related to applications of satellite altimetry to coastal tides , storm surges , as well as coastal and shelf circulation.
Coastal tides are mainly forced by adjacent deep-ocean tides which themselves are generated by the tide-generating potential associated with the motion of both the moon and the sun. The tidal waves in coastal seas propagate as trapped Kelvin waves, subject to significant amplifications in magnitude and reductions in wavelength. Shallow water tide constituents are generated due to nonlinear effects.
Several empirical methods can be used to derive tides from altimetric time series. These include but are not limited to harmonic analysis, response analysis, and the inverse method. The first two methods are applied to each geographical location, and the last method considers the spatial correlation as defined by a priori spatial covariance in the tidal signal.
Both harmonic and response analyses are purely temporal analyses, common in the analysis of hourly tide gauge data. The methods are suitable for either coastal seas (Woodworth and Thomas 1990; Han et al. 1996) or deep oceans (Cartwright and Ray 1990), not constrained by large satellite track intervals. However, an assimilative model in which altimetric tidal information is optimally blended with a dynamical model would be a great benefit in providing spatial interpolation and extrapolation of tidal fields (Han et al. 2000; Egbert and Erofeeva 2002).
In the past decade, global tide models have further advanced and their accuracy over the shelf has been significantly improved. The root-sum-square (RSS) errors for the eight major tide constituents at 195 tide gauge stations over the continental shelf are as small as 5 cm (Stammer et al. 2014). At a smaller number (56) of coastal tide gauge stations, the RSS errors for the eight tide constituents are as small as 7 cm. Nowadays, global tide models are still used to correct for satellite altimetry by coastal altimetry users. It is cautioned that global tide model errors can be large in coastal waters. Where possible, coastal altimetry users should use validated local tide models with sufficient accuracy. Accurate, high-resolution coastal tide models are needed for coastal altimetry. More accurate bathymetric information is critical for improving coastal tidal simulations. Coastal tide models need to be smoothly blended with global tide models for widespread use by the altimeter community (Ray et al. 2011).
Storm surge is the main factor that causes extremely high sea level and catastrophic coastal flooding, such as in New Orleans during Hurricane Katrina and in the Philippines during Typhoon Haiyan. Coastal tide gauges have been the main tool for monitoring storm surges. Hydrodynamic models have been used for storm surge forecasting.
In the past decade, there have been studies showing the utility of satellite altimetry for observing storm surges, e.g., in the Gulf of Mexico during Hurricane Katrina (Scharroo et al. 2005), off Newfoundland during Hurricane Igor (Han et al. 2012), off the US eastern coast during Hurricane Sandy (Lillibridge et al. 2013; Chen et al. 2014), in the North Sea during Cyclone Xaver (Fenoglio-Marc et al. 2015), and off the northeastern coast of the Gulf of Mexico (Han et al. 2017). Antony et al. (2014) showed that the multi-mission satellite data significantly enhance the chance of detecting storm surges in the Bay of Bengal. It is opportunistic for an altimeter to capture storm surge, while a constellation of altimeter missions may significantly enhance the chance. Relative to a conventional altimeter, a wide-swath altimeter has much high capacity of capturing storm surges (Turki et al. 2015; Han et al. 2017).
Subinertial Coastal and Shelf Circulation
Another important application of satellite altimetry in physical oceanography is to subinertial variability over a continental shelf and in coastal waters. One of the key components of the geophysical corrections is the removal of oceanic tides.
In coastal seas, tides are often larger than subinertial variability and have horizontal scales of about 100 km owing to the local coastline and bottom topography. During the early years of accurate altimetry, global tidal models were clearly not adequate for shallow waters; for example, the M2 amplitudes and phases in Geosat GDRs are significantly different from both tide gauge and altimeter data over the Scotian Shelf and the Grand Banks (Han et al. 1993) and in the Amazon mouth (Minster et al. 1995). The tide model in T/P GDRs was found not sufficient over the Canadian Pacific shelf (Foreman et al. 1998).
Because the semidiurnal and diurnal constituents are aliased into fluctuations with longer periods, their errors may obscure subinertial fluctuations of interest. For example, the K 1 has an aliasing period of 173 days in the T/P data, close to a semiannual cycle. One way to reduce the tidal correction errors is to use regional tidal models that have higher accuracy (Han et al. 1993; Ray et al. 2011). The separation of the low-frequency variability of interest from the aliased tidal constituents can also be achieved using harmonic analysis. The results may be subject to notable statistical uncertainties, depending on the length of data, magnitudes of tidal errors, and error correlation.
The altimetric data can be used to calculate sea surface slopes and thus to derive geostrophic surface currents . There have been increasingly more applications of satellite altimetry for coastal circulation, such as in the Mediterranean Sea (Bouffard et al. 2011), the Caspian Sea (Kouraev et al. 2011), the Black Seas (Ginzburg et al. 2011), the Barents and White Seas (Lebedev et al. 2011), as well as off the coasts of North America (Emery et al. 2011) and of China (Han and Huang 2008).
The geostrophic currents at depth can be determined when combined with interior density structure. Han and Tang (1999) combined the T/P data with density and wind data to study seasonal variability of current and transport in the Labrador Current. The method was also used to study interannual (Han and Tang 2001) and multiyear variability of the Labrador Current (Han et al. 2010).
The spatial sampling resolution is critical for shelf circulation. Dynamic circulation models are needed for a space-time interpolation to make the best use of the information. The assimilation of altimeter data into numerical models is one of the most promising approaches to study subinertial coastal and shelf circulation. The availability of near-real-time satellite altimetry data is very useful for nowcasts and forecasts of coastal ocean conditions.
Application of satellite altimetry for sea level and currents in coastal waters remains more challenging than in the deep ocean (Han 1995). These challenges are being tackled actively from several fronts. Dynamic features in coastal seas are strongly influenced by the complex coastline and bottom topography and have temporal scales of several days to weeks and spatial scales of ones to tens of kilometers. A conventional satellite altimeter is not good at sampling these small-scale features. Altimeter waveforms are subject to land contamination upon crossing the land-sea boundary; useful data are not available close to the coast. Atmospheric and oceanographic corrections are more uncertain for coastal waters than for the deep ocean. SAR and interferomeric altimeters have been used to improve spatial sampling resolution; waveform retracking algorithms have been applied to alleviate the land contamination associated with conventional altimeters. Special editing techniques such as for wet tropospheric effects and correction models such as for dynamic atmospheric pressure effects have been applied to improve atmospheric and oceanographic corrections.
High temporal and spatial resolutions are very important, particularly in the coastal seas. Unfortunately, fast (more frequent) sampling must be at the expense of large orbit interval (cross-track separation), and a reasonable compromise must be made to best meet mission requirement.
A wide-swath interferometric altimeter provides high-resolution two-dimensional image of sea surface topography within each swath. An appropriately formed constellation of satellite altimeter missions can improve both the spatial and temporal resolutions.
Dynamical models with data assimilation are useful for optimally blending the model dynamics with altimetry. Only dynamical models may be able to effectively derive ocean interior conditions from their sea surface manifestation observed by an altimeter.
This work is partially supported by the Surface Water and Ocean Topography – Canada (SWOT-C) Program, Canadian Space Agency.
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