Using the SWAN Wave Model and Satellite Altimeter Data to Study the Influence of Climate Change at the Coast

This paper describes the development and application of a technique for using satellite altimeter measurements as boundary data to drive the nearshore spectral wave model, SWAN. The aim was to assess the impact in coastal areas of extreme events or changes in offshore climatology and to extend the usefulness of satellite altimetry further inshore.

For the purpose of verifying the technique, three test areas where both bathymetry and some in situ data were available were chosen. The technique could, potentially, be applied to any coastal location where there is bathymetric information although, as the results reported in this paper show, intelligence must be used in adapting the methodology for different sites. It is also necessary to have information on the local wind field from either models or measurements.

The experiments at the three test areas demonstrated that there is not a simple relationship between the offshore wave height climate and the inshore climate in a particular region. Important complicating factors are bathymetry, tidal range and incident wave angle. As was most clearly demonstrated in the Carmarthen Bay test area, bathymetric complexity leads to high spatial variation in the amount of wave energy dissipated close to the coast. In the study of extreme wave events described in this paper the exact value of the local wind field was not found to be critical.

This work was a first trial combining wave climatology derived from satellite altimetry with a third generation coastal wave model so was necessarily experimental. The general trends and patterns of spatial variation obtained are encouraging but there remains significant, unquantifiable uncertainty in the results. Better observations of nearshore waves, improved understanding of the joint probability distribution of water level and waves as well as more knowledge of future climate change would all improve accuracy.     

Global mean sea surface and marine gravity anomaly from multi-satellite altimetry: applications of deflection-geoid and inverse Vening Meinesz formulae

 Global mean sea surface heights (SSHs) and gravity anomalies on a 2^′×2^′ grid were determined from Seasat, Geosat (Exact Repeat Mission and Geodetic Mission), ERS-1 (1.5-year mean of 35-day, and GM), TOPEX/POSEIDON (T/P) (5.6-year mean) and ERS-2 (2-year mean) altimeter data over the region 0^∘–360^∘ longitude and –80^∘–80^∘ latitude. To reduce ocean variabilities and data noises, SSHs from non-repeat missions were filtered by Gaussian filters of various wavelengths. A Levitus oceanic dynamic topography was subtracted from the altimeter-derived SSHs, and the resulting heights were used to compute along-track deflection of the vertical (DOV). Geoidal heights and gravity anomalies were then computed from DOV using the deflection-geoid and inverse Vening Meinesz formulae. The Levitus oceanic dynamic topography was added back to the geoidal heights to obtain a preliminary sea surface grid. The difference between the T/P mean sea surface and the preliminary sea surface was computed on a grid by a minimum curvature method and then was added to the preliminary grid. The comparison of the NCTU01 mean sea surface height (MSSH) with the T/P and the ERS-1 MSSH result in overall root-mean-square (RMS) differences of 5.0 and 3.1 cm in SSH, respectively, and 7.1 and 3.2 μrad in SSH gradient, respectively. The RMS differences between the predicted and shipborne gravity anomalies range from 3.0 to 13.4 mGal in 12 areas of the world's oceans. Received: 26 September 2001 / Accepted: 3 April 2002 Correspondence to: C. Hwang Acknowledgements. This research is partly supported by the National Science Council of ROC, under grants NSC89-2611-M-009-003-OP2 and NSC89-2211-E-009-095. This is a contribution to the IAG Special Study Group 3.186. The Geosat and ERS1/2 data are from NOAA and CERSAT/France, respectively. The T/P data were provided by AVISO. The CLS and GSFC00 MSS models were kindly provided by NASA/GSFC and CLS, respectively. Drs. Levitus, Monterey, and Boyer are thanked for providing the SST model. Dr. T. Gruber and two anonymous reviewers provided very detailed reviews that improved the quality of this paper.     

Quasi-stationary sea surface topography estimation by the multiple input/output method

 Multiple input/multiple output system theory (MIMOST) is briefly presented, and the application of the method to the quasi-stationary sea surface topography (QSST) estimation and the filtering of the input observations are discussed. The repeat character of satellite altimetry missions provides more than one sample of the measured sea surface height (SSH) field, and an approximation of the input signal and error power spectral densities can be determined using this successive information. A case study in the Labrador Sea is considered using SSHs from ERS1 phases C and G, ERS1-GM, ERS2 phase A and TOPEX/POSEIDON altimetric missions in combination with shipborne gravity anomalies. The time period of the observations in this study is from 1993 to 1998. Some comparisons between the techniques used for the power spectral density approximation are carried out and some remarks on the properties of the estimated QSST are presented. Received: 19 October 1999 / Accepted: 23 October 2000     

Ocean tides from T/P, ERS-1, and GEOSAT altimetry

 Aliasing of the diurnal and semi-diurnal tides is a major problem when estimating the ocean tides from satellite altimetry. As a result of aliasing, the tides become correlated and many years of altimeter observations may be needed to seperate them. For the three major satellite altimetry missions to date i.e., GEOSAT, ERS-1, and TOPEX/POSEIDON (T/P), the alias periods as well as the Rayleigh periods over which the tides decorrelate can be identified. Especially in case of GEOSAT and ERS-1, severe correlation problems arise. However, it is shown by means of covariance analyses that the tidal phase advance differences on crossing satellite groundtracks can significantly reduce the correlations among the diurnal and semi-diurnal tides and among these tides and the seasonal cycles of ocean variability. Therefore, it has been attempted to solve a multi-satellite response tidal solution for the diurnal and semi-diurnal bands from a total of 7 years of altimetry. Unfortunately, it could be shown that the GEOSAT and ERS-1 orbit errors are too large to improve a 3-year T/P tidal solution with about 2 years of GEOSAT and 2 years of ERS-1 altimeter observations. However, these results are preliminary and it is expected that more accurate orbits, which have become available recently for ERS-1, and additional altimeter data from ERS-2 and the GEOSAT Follow-On (GFO) should lead to an improved T/P tidal model. Received: 4 May 1999 / Accepted: 24 January 2000     

Operational Altimeter Data Processing for Mesoscale Monitoring

Since 1996, global, near-real-time maps of mesoscale anomalies derived from tandem sampling provided by altimeters aboard the TOPEX/Poseidon and ERS-2 satellites have been posted on web pages hosted at the Colorado Center for Astrodynamics Research. The original, near-real-time processing system was based on a quick-look analysis that referenced the data to a high-resolution gridded mean sea surface available at the time. Recently, state-of-the-art mean sea surfaces have been derived that are based on a more complete record of altimeter observations. An updated mesoscale monitoring system based on a new mean surface is described and shown to provide improved mesoscale monitoring to the successful system implemented in 1996.     

The Role of Multi-Mission ERS Altimetry in the Determination of the Marine Geoid in the Azores

This study concerns the determination of a regional geoid model in the North Atlantic area surrounding the Azores islands by combining multi-mission altimetry from the ERS (European Remote Sensing) satellites and surface gravity data. A high resolution mean sea surface, named AZOMSS99, has been derived using altimeter data from ERS-1 and ERS-2 35-day cycles, spanning a period of about four years, and from ERS-1 geodetic mission. Special attention has been paid to data processing of points around the islands due to land contamination on some of the geophysical corrections. A gravimetric geoid has been computed from all available surface gravity, including land and sea observations acquired during an observation campaign that took place in the Azores in October 1997 in the scope of a European and a Portuguese project. Free air gravity anomalies were derived by altimetric inversion of the mean sea surface heights. These were used to fill the large gaps in the surface gravity and combined solutions were computed using both types of data. The gravimetric and combined solutions have been compared with the mean sea surface and GPS (Global Positioning System)-levelling derived geoid undulations in five islands. It is shown that the inclusion of altimeter data improves geoid accuracy by about one order of magnitude. Combined geoid solutions have been obtained with an accuracy of better than one decimetre.     

Operational Altimeter Data Processing for Mesoscale Monitoring

Since 1996, global, near-real-time maps of mesoscale anomalies derived from tandem sampling provided by altimeters aboard the TOPEX/Poseidon and ERS-2 satellites have been posted on web pages hosted at the Colorado Center for Astrodynamics Research. The original, near-real-time processing system was based on a quick-look analysis that referenced the data to a high-resolution gridded mean sea surface available at the time. Recently, state-of-the-art mean sea surfaces have been derived that are based on a more complete record of altimeter observations. An updated mesoscale monitoring system based on a new mean surface is described and shown to provide improved mesoscale monitoring to the successful system implemented in 1996.     

On the spectral consistency of the altimetric ocean and geoid surface: a one-dimensional example

Geoid models from the new generation of satellite gravity missions, such as GRACE and GOCE, in combination with sea surface from satellite altimetry allow to obtain absolute dynamic ocean topography with rather high spatial resolution and accuracy. However, this implies combination of data with fundamentally different characteristics and different spatial resolutions. Spectral consistency would imply the removal of the short-scale features of the altimetric sea surface height by filtering, to provide altimetric data consistent with the resolution of the geoid field. The goal must be to lose as little as possible from the high precision of the altimetric signal. Using a one-dimensional example we show how the spectrum is changing when a function defined only on a limited domain (ocean in the real case) is extended or not as to cover the complete domain (the whole sphere in the real case). The results depend on the spectral characteristics of the altimetric signal and of the applied filter. Referring to the periodicity condition, as it is requested in the case of Fourier analysis, the action of the two classical filters (Ideal Low Pass and Gauss filter) and of two alternative procedures (wavelets and Slepian) is studied.     

Geoid and high resolution sea surface topography modelling in the mediterranean from gravimetry,altimetry and GOCE data: evaluation by simulation

The determination of local geoid models has traditionally been carried out on land and at sea using gravity anomaly and satellite altimetry data, while it will be aided by the data expected from satellite missions such as those from the Gravity field and steady-state ocean circulation explorer (GOCE). To assess the performance of heterogeneous data combination to local geoid determination, simulated data for the central Mediterranean Sea are analyzed. These data include marine and land gravity anomalies, altimetric sea surface heights, and GOCE observations processed with the space-wise approach. A spectral analysis of the aforementioned data shows their complementary character. GOCE data cover long wavelengths and account for the lack of such information from gravity anomalies. This is exploited for the estimation of local covariance function models, where it is seen that models computed with GOCE data and gravity anomaly empirical covariance functions perform better than models computed without GOCE data. The geoid is estimated by different data combinations and the results show that GOCE data improve the solutions for areas covered poorly with other data types, while also accounting for any long wavelength errors of the adopted reference model that exist even when the ground gravity data are dense. At sea, the altimetric data provide the dominant geoid information. However, the geoid accuracy is sensitive to orbit calibration errors and unmodeled sea surface topography (SST) effects. If such effects are present, the combination of GOCE and gravity anomaly data can improve the geoid accuracy. The present work also presents results from simulations for the recovery of the stationary SST, which show that the combination of geoid heights obtained from a spherical harmonic geopotential model derived from GOCE with satellite altimetry data can provide SST models with some centimeters of error. However, combining data from GOCE with gravity anomalies in a collocation approach can result in the estimation of a higher resolution geoid, more suitable for high resolution mean dynamic SST modeling. Such simulations can be performed toward the development and evaluation of SST recovery methods.     

Impact of tropospheric modelling on GNSS vertical precision: an empirical analysis based on a local active network

The troposphere affects Global Navigation Satellite System (GNSS) signals due to the variability of the refractive index. Tropospheric delay is a function of the satellite elevation angle and the altitude of the GNSS receiver and depends on the atmospheric parameters. If the residual tropospheric delay is not modelled carefully a bias error will occur in the vertical component. In order to analyse the precise altimetric positioning based on a local active network, four scenarios in Southern Spain with different topographical, environmental, and meteorological conditions are presented, considering both favourable and non-favourable conditions. The use of surface meteorological observations allows us to take into account the tropospheric conditions instead of a standard atmosphere, but introduces a residual tropospheric bias which reduces the accuracy of precise GNSS positioning. Thus, with short observation times it is recommended not to estimate troposphere parameters, but to use an a priori model together with the standard atmosphere. The results confirm that it is possible to achieve centimetre-scale vertical accuracy and precision with real time kinematic positioning even with large elevation differences with respect to the nearest reference stations. These numerical results may be taken into consideration for improving the altimetric configuration of the local active network.