**4. A new sea level record from satellite radar altimetry for climate studies**

Several radar altimetry missions have been in operation since the first launch in 1973 (see **Figure 1**). The TOPEX/Poseidon and Jason series (with the addition of the just launched Sentinel-6) is the reference mission for long-term sea level studies, as it is ensured the continuity in the same orbit [29]. However, a single altimeter only provides measurement along a track from open ocean closer to coast. There is always a trade-off between temporal sampling and ground-track spatial coverage.

*Coastal Sea Level Trends from a Joint Use of Satellite Radar Altimetry, GPS and Tide… DOI: http://dx.doi.org/10.5772/intechopen.98243*

#### **Figure 1.**

now at mature stage in this domain, with the various datasets routinely used for global sea level studies. However, data were normally flagged as bad and therefore rejected in the coastal zone. But the situation rapidly changed in the last ten years for two reasons: (1) the prospect of recovering a valuable long-term sea level data around the global coastline; (2) the improved suitability of the new and future altimeters (like those on CryoSat-2, AltiKa, Sentinel-3, Sentinel-6, Crystal). Therefore, a new domain "coastal altimetry", i.e. the extension of altimetry into the oceanic coastal zone has been emerging, with a community around it developing a set of coastal altimetry techniques in order to get more and better sea level data

*Geodetic Sciences - Theory, Applications and Recent Developments*

The analyses of radar echoes revealed that pulse-limited missions, if reprocessed with dedicated models, could provide reliable range measurements to few km from the coastline. An example is the Adaptive Leading Edge Subwaveform (ALES) retracking algorithm, that has been validated and applied successfully to sea level research, demonstrating the ability to increase the quality and the quantity of sea

In addition, it was noted that geophysical corrections that must be applied to altimeter range data have a significant impact in coastal altimetry and therefore their constant improvement is crucial. There have been noticeable developments to improve the tropospheric delay [20], the tidal sea level where global models have still large errors [21] and the mean sea surface models, suitable for the observation of the coastal sea level [22]. There have been also improvements in procedures to avoid aliasing of major tidal signals and short-period ocean response to meteoro-

The wet tropospheric correction is the major source of uncertainty in altimetry budget error, due to its large spatial and temporal variability: this is reason why a multi-channel passive microwave radiometer is on the same platform as the altimeter. Unfortunately, this estimate gets quickly corrupted as soon as land enters the radiometer footprint, i.e. 20–50 Km from the coast. Alternative corrections have been devised and appear to be successful at least in some particular conditions [24]. A very promising approach was the one attempting to estimate the wet tropospheric path delay from GPS measurements known as GPD (GNSS-derived Path Delay),

The classical data editing used in open ocean was also considered excessively restrictive and revisited with novel editing/re-interpolation approaches (e.g., [26]). The new data from the various reprocessing efforts are now bringing altimetry around the global coastline, with a higher spatial resolution and precision that was previously not available in coastal and shelf sea areas, while constant improvement [18] and validation [27] are still ongoing. The new coastal altimetry datasets open a

differences in trend and variability at various distances from the coast, also nearby

Several radar altimetry missions have been in operation since the first launch in 1973 (see **Figure 1**). The TOPEX/Poseidon and Jason series (with the addition of the just launched Sentinel-6) is the reference mission for long-term sea level studies, as it is ensured the continuity in the same orbit [29]. However, a single altimeter only provides measurement along a track from open ocean closer to coast. There is always a trade-off between temporal sampling and ground-track spatial coverage.

**4. A new sea level record from satellite radar altimetry for climate**

new opportunity to study sea level change from open ocean to coast and

closer to the coast.

tide gauges [28].

**studies**

**98**

level retrievals in coastal areas [19].

logical forcing aliases onto low frequency signals [23].

and its latest version called GPD+ (Plus) [25].

*Main characteristics of satellite altimetry missions operating until now and planned for the future.*

A single altimeter always leaves gaps along the coast between neighboring tracks: tenths to hundred km are not covered, so that the vast majority of the worldwide coast is not sampled. The coverage can be augmented with additional existing altimeters.

Data from the various altimeter missions were used to create several datasets. Examples include RADS [30], X-TRACK [28], etc. that also provide sea level estimates. Since 1992, at least two altimeter satellites have been operating simultaneously, and during some periods, even more than two. Such data can be combined in a single product to provide a consistent long-term sea level data set, globally with sufficient spatial coverage over almost three decades. However, altimeter missions need to be accurately homogenized and cross-calibrated to reduce biases and uncertainties [31].

A satellite-based sea level data set to analyze long-term trends that uses the available historic observations from the various radar altimeters is key requirement for the climate community [32]. A recent reprocessing within the European Space Agency (ESA) Sea Level Climate Change Initiative (SLCCI) has produced a gridded altimetry product with a spatial resolution of 0.25° (which is around 25 km resolution) from 1993 to 2015 [33, 34], thus permitting a more detailed view of sea-level change around the world coastlines.

The sea level Environment Climate Variable (ECV) (at global and regional scales) is now operationally produced by the Copernicus Climate Change Service (C3S) [35] by applying the altimetry processing standards developed in the SLCCI initiative. The C3S product ensures a stable number of two altimeters since the beginning and the reference field used to compute sea level anomalies (SLA) is a homogeneous mean sea surface for all missions. The C3S record is a regional product, gridded at 0.125° in the Mediterranean Sea, starting in 1993 and offering ongoing coverage [36]. Both the SLCCI and the C3S datasets are state-of-the-art products designed to be a reference for climate-related sea level studies.

In the case-study illustrated in the chapter, the SLCCI and C3S datasets are used to assess their maturity as state-of-the-art altimetry datasets in climatological studies. The multi-mission gridded products have not still tuned for last 10 km from the coast, where the amount of valid data might decrease. The ESA CCI + Sea Level

project, started in 2017, is extending the processing to the coastal zone, and an experimental coastal sea level product is going to be released to the public, in six selected regions: Northern Europe, Mediterranean Sea, Western Africa, North Indian Ocean, Southeast Asia and Australia [37]. This product is along-track and combines the enhanced spatial resolution provided by high-rate data (20-Hz), the post-processing strategy of X-TRACK and the advantage of the ALES retracker [38]. The product relies on the GPD+ wet tropospheric correction [39] and the FES2014 tidal corrections [40]. The X-TRACK/ALES SLCCI 20 Hz along-track dataset will be indicated with SLCCI-AT hereinafter.

compared with those from conventional approaches, which are limited to the overlapping periods between altimetry and tide gauges. An extension of the method has been applied to Great Lakes and in open ocean regions, such as Alaskan coast [49]. It has been also extended along the coasts of southern Europe [50] with constraints between pairs of tide gauges based on correlation and overlapping periods. The same method has been extended to open ocean in New Zealand straddles, the Tasman Sea and Pacific Ocean [51]. All studies confirmed the superiority

*Coastal Sea Level Trends from a Joint Use of Satellite Radar Altimetry, GPS and Tide…*

A new variant of the inverse method considers to difference sea level trends between pairs of tide gauge records and pairs of altimetry records [52]. Another study proposed different mathematical and statistical models, which enable simultaneous estimation of absolute and relative sea level trends and VLM at a tide gauge station merging altimetry and tide gauge records without the aid of geological

**6. A revisited linear inverse model to estimate sea level trends**

the successful inversion. The explanation will be provided in this section.

The difference between the absolute sea level rise (ASLR) and the relative sea level rise (RSLR) rates, i.e. the velocities at which the sea level vertical motion is observed by satellite altimeters and TGs, denoted respectively with *g*\_ and *s*\_, is an estimate of the vertical velocity at which the land beneath TGs is moving. Such vertical crustal velocity, as previously stated, is named vertical land motion (VLM) and indicated by *u*\_. A subscript *i* is added to denote that the quantities *g*\_, *s*\_ and *u*\_

Eq. (1) is sufficient to obtain good estimates of the VLM rates at each TG, provided that all the variables in the equation refer to the same period and to coherent geophysical processes and have negligible inherent drifts and errors.

where *u*\_ is the column vector of the unknown VLMs *u*\_ ¼ *u*\_ ð Þ 1, … , *u*\_ *<sup>N</sup>* , and *d* is the column vector whose elements are formed by the right-hand side of Eq. (1): *d* ¼

 . In this picture all the unknown VLMs are mutually independent, and the linear system is easily inverted, offering the solution component by component. However, the solution is affected by large errors, as the period during which Eq. (1) is valid corresponds to the overlap period of TG and satellite altimetry observations, and thus no more back in time than 1992. In fact, the current time span of satellite altimetry data is less than 30 years. Such a short time span hinders the derivation of accurate trends from altimeter-gauge time series, as they are affected by inter-annual and decadal sea level signals, in particular by the 18.6-year lunar nodal tide, leading to uncertainties of the order of 1–2 mm yr�<sup>1</sup> [47, 54, 55]. For this reason, Kuo et al. [48] proposed a more elaborate linear system, in which constraints formed by the differenced time series of TGs over longer time periods (>40 yr) pose strong limits to the magnitude of the final errors thanks to the length

*u*\_ *<sup>i</sup>* ¼ *g*\_*<sup>i</sup>* � *s*\_*<sup>i</sup> i* ¼ 1, … , *N* (1)

*Gu*\_ ¼ *d*; *G* ¼ *IN* (2)

The linear inverse model proposed by Kuo et al. [48, 49], and then by Wöppelmann and Marcos [50], assumes that the absolute sea level change rates are similar at all the tide gauge (TG) sites. This assumption is particularly important for

of the inverse method to the classical direct approach.

information or GPS measurements [53].

*DOI: http://dx.doi.org/10.5772/intechopen.98243*

refer to the *i*-th TG of a group of *N*:

*g*\_ <sup>1</sup> � *s*\_1, … , *g*\_*<sup>N</sup>* � *s*\_*<sup>N</sup>*

**101**

Eq. (1) can be expressed in vector–matrix notation:
