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     

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.     

Gravity recovery using COSMIC GPS data: application of orbital perturbation theory

 COSMIC is a joint Taiwan–US mission to study the atmosphere using the Global Positioning System (GPS) occultation technique. Improved formulas are developed for the radial, along-track, and cross-track perturbations, which are more accurate than the commonly used order-zero formulas. The formulas are used to simulate gravity recovery using the geodetic GPS data of COSMIC in the operational phase. Results show that the EGM96 model can be improved up to degree 26 using 1 year of COSMIC data. TOPEX/POSEIDON altimeter data are used to derive a temporal gravity variation. COSMIC cannot reproduce this gravity variation perfectly because of data noise and orbital configuration, but the recovered field clearly shows the gravity signature due to mass movement in an El Ni?o. Received: 3 March 2000 / Accepted: 10 November 2000     

Influence of Regional Features on Accuracy in Determining wind Speed Over the Oceans

The influence of regional features on the accuracy of single- and twoparameter algorithms for radioaltimeter determination of the speed of the near-surface wind over the ocean was investigated. The analysis was made using data from contact measurements (NDBC buoys) and the TOPEX/POSEIDON satellite radioaltimeter (wavelength 2.1 cm). It is shown that the nature of the waves, to a considerable degree related to regional conditions, exerts a strong influence on the accuracy in wind speed determination, resulting in an error in wind speed determination of 2-2.5 m/s. A new approach to the wind speed retrieval problem is proposed, making it possible to reduce the retrieval error to a level comparable with the best existing algorithms.     

Seasonal sea level change from TOPEX/Poseidon observation and thermal contribution

Seasonal steric sea-level change due to temperature variation in the mixing layer is assessed using space-measured sea-surface temperature data and historical in situ temperature measurements. The results are compared with TOPEX/Poseidon satellite altimeter measurement at different large spatial scales. It is indicated that thermal effect accounts for much of the observed seasonal variability, especially when averaging over zonal regions. Some regional seasonal patterns of sea-level anomalies in the tropical oceans are well represented by the thermal model prediction. Systematic differences are shown between TOPEX/Poseidon observation and thermal contribution at a 1–2 cm level. The potential causes for these differences are discussed, including water mass exchanges among the atmosphere, land, and oceans, and error sources in the steric result and geophysical corrections applied in TOPEX/Poseidon data. Received: 25 September 1998 / Accepted: 13 July 1999     

Comparison between the harmonic and response methods of tidal analysis using TOPEX/POSEIDON altimetry

Three years of TOPEX/POSEIDON altimeter data have been processed at Delft Institute for Earth-Oriented Space Research (DEOS) to solve the major diurnal and semi-diurnal constituents of the global ocean tide using the two classical methods of tidal analysis, i.e. the harmonic and response analyses. Some experiments with the parameters in the response formalism show that the tidal admittance in both the diurnal and semi-diurnal band can be adequately described with a lag interval of 2 days and a number of lags of three. Results of both methods are evaluated from the differences with the most recent Grenoble hydrodynamic model (FES95.2) and from the fit with the harmonic constants of a globally distributed set of tide gauges. It was found that the solutions of the two methods differ at the millimeter level and are thus fully equivalent, which is confirmed by the tide gauges and the differences with FES95.2. From the comparisons with the Grenoble model it was found that the M ₂ and S ₂ solutions of that model likely contain bathymetric errors which are of the order of 1–2 cm for M ₂ and 0.5 cm for S ₂. Received: 18 December 1996 / Accepted: 12 May 1997     

Seasonality and Latitudinal Variation of Water Vapour and Aerosol Optical Thickness and Their relationship Over Tropical Indian Ocean

Aerosol and water vapour are very important element in the Earth’s climate system which has direct role in the Earth’s radiation budget. In this paper the seasonality, latitudinal distribution and the relationship of aerosol optical thickness (AOD) and water vapour (WV) using MODIS Level 3 monthly data from 2001 to 2008 are analysed. The analysis shows that AOD (0.55 μm) values reach maximum during southwest monsoon and remain minimum during northeast monsoon period. The Equatorial Indian Ocean shows minimum AOD (0.115 to 0.153) throughout the year compared to Arabian Sea (0.208 to 0.613) and Bay of Bengal (0.214 to 0.351). Arabian Sea shows high variation and maximum value of AOD compared to Bay of Bengal and Equatorial Indian Ocean. During southwest monsoon WV over Bay of Bengal was found higher in concentration compared to Arabian Sea and Equitorial Indian Ocean throughout the study period. Comparison between Arabian Sea (2.98 cm to 5.07 cm) and Bay of Bengal (3.49 cm to 5.94 cm) shows that WV concentration is less in Arabian Sea throughout the year. The analysis of correlation between WV and AOD was found to be inconsistent. However, AOD and WV shows a strong positive correlation for whole year (Mean R² =0.90) in the Equitorial Indian Ocean region except in the months of January, February and March. In general, the correlation between WV and AOD is found to be strongly positive for oceanic aerosol (sea salt) in low water vapour condition.     

由ERS-2和TOPEX卫星测高数据推算的海面高异常的主成分分析

利用1995~2003年间的TOPEX/POSEIDON和ERS-2卫星测高数据,尽量采用相同的改正模型对TOPEX和ERS-2卫星测高数据分别进行改正,然后由共线分析法分别推算了全球1°×1°的35 d的海面高异常时间序列,并采用主成分分析法分别对这两个海面高异常时间序列进行了分析。     

Theory of satellite ground-track crossovers

The fundamental geometry of satellite ground tracks and their crossover problem are investigated. For idealized nominal ground tracks, the geometry is governed by a few constant parameters whose variations lead to qualitative changes in the crossover solutions. On the basis that the theory to locate crossovers has not been studied in sufficient detail, such changes are described in regard to the number of crossover solutions in conjunction with their bifurcations. Employing the spinor algebra as a tool for establishing the ground-track crossing condition, numerical methodologies to locate crossovers appearing in general dual-satellite ground-track configurations are also presented. The methodologies are applied to precisely determined orbital ephemerides of the GEOSAT, ERS-1, and TOPEX/POSEIDON altimeter satellites. Received: 19 November 1996 / Accepted: 12 May 1997     

由卫星测高数据观测到的印度洋海啸波高

本文介绍了利用卫星测高资料测定的印度洋地震引起的海啸波高的研究成果 ,以及卫星测高数据在对海啸灾害进行预测的应用价值。通过卫星雷达测高可观测到沿卫星星下点轨迹的相距几公里的点上的海面高 ,还提供了特别有价值的对海啸波的连续观测结果     

Analysis of the bias between TOPEX and GPS vTEC determinations

The TOPEX/Poseidon satellite was jointly developed and deployed by the National Aeronautics and Space Administration (NASA), USA, and the Centre National d’Etudes Spatiales (CNES), France (for details see Chelton et al. In: Fu L-L, Cazenave A (eds) International geophysics series, vol 69, ISBN 0-12-269545-3, Academic Press, CA, pp 1–131, 2001), with the main scientific goal of sea surface height monitoring. The process that ends with the TOPEX main observable (the range between the satellite and the sea surface) involves the measurement of several parameters of the radar pulses reflected by the sea surface and the computation of several other corrections. After several calibration campaigns performed by the Calibration/Validation team of the mission, it was found that TOPEX range determinations were systematically shorter than expected and it was decided to add an empirical correction of +15 mm to the TOPEX range-computation algorithm. As a by-product, TOPEX provides vertical total electron content (vTEC) determinations which have turned out to be a very important data source for the ionospheric research community. Since TOPEX vTEC measurements became available, several comparison studies have detected a constant bias, from +2 to +5 TECu, when TOPEX is compared to other vTEC sources, e.g., Global Positioning System (GPS), Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS), (TOPEX always greater than the others). In this work, we show that miscalibration of the corrections used in the TOPEX processing algorithm can cause the shortening effect of TOPEX ranges and at the same time the constant bias on the TOPEX vTEC values. It is also shown that changes on TOPEX System Biases of less than 10 mm for the Ku-band and between 40 and 70 mm for the C-band, can make both effects disappear. The analyzed hypothesis is supported by theoretical considerations and data analysis available in the specialized literature. On behalf of the authors of the contribution ‘Analysis of the bias between TOPEX and GPS vTEC determinations’, I declare that the paper has not been, nor is in the process of being published in any other publication.     

Comparison of Inherent Optical Properties (IOPs) in Open and Coastal Waters of Arabian Sea Using In-Situ Bio-Optical Data

The two main inherent optical properties (IOPs) namely absorption and back scattering coefficients were estimated using a quasi analytical algorithm (QAA) for open and coastal ocean waters of Arabian Sea. Absorption due to gelbstoff and back scattering due to the particulate matter were calculated using the quasi analytical algorithm for all the in-situ measured reflectance spectra collected in the Arabian Sea. A comparative study was made to study the spectral variability of reflectance spectra in open as well as coastal waters of Arabian Sea. Spectral analysis was made for the absorption and back scattering coefficients calculated using the QAA for both open and coastal waters. The absorption coefficient in the open ocean waters vary from a minimum value of 0.029 to a maximum value of 0.445 and it varies from a minimum value of 0.081 to a maximum value of 4.000 for the coastal waters of Arabian Sea. Absorption due to gelbstoff or the CDOM a_g(λ), calculated for the Arabian Sea waters show a variation of 0.000202 to 0.112437 for open ocean waters and it varies from 0.002848 to 2.8936 for coastal waters of Arabian Sea. Particulate back scattering coefficient for open ocean waters vary from 0.0000307 to 0.006575 whereas b_bp(λ) vary from 0.000167 to 0.026014 for coastal ocean waters. The minimum slope for the open ocean waters is 0.989 and maximum value of 2.147 (average value of 1.7) was observed; whereas a minimum value of 0.046 and a maximum value of 1.201 (average value of 0.6) were observed from the in-situ spectra for coastal waters of Veraval. The slope ‘Y’ estimated from the model is 1.957 for open ocean waters and 0.515 for coastal waters collected in the Arabian Sea.     

On monitoring a vertical datum with satellite altimetry and water-level gauge data on large lakes

Using TOPEX satellite altimetry, water-level-gauge data, and a geoid model, the geopotential, W ₀, of the International Great Lakes Datum of 1985 (IGLD85) is determined. This is compared to an analogous determination using GPS and leveling data in the region. The two sets of data yield generally consistent results at the few-decimeter level and both indicate a tilt of about 33 cm in the computed datum across the region. On the basis of this and other studies, it is conjectured that the source of the tilt is a regional error in G99SSS. Further analysis of the altimetry and water-level data indicate that the geoid model, G99SSS, is in error by up to 20 cm at scales of about 100–150 km. In addition, the analysis of 8 years of altimeter and water-level data shows varying trends (up to 2 mm/yr) in crustal uplift throughout the region, generally consistent with an independent post-glacial rebound (PGR) model, ICE-4G. AcknowledgmentThis research was supported in part by the Ohio Sea Grant Program, grant no. NA86RG0053 (R/CE-5). A. Mainville kindly provided data and information for Canadian stations. The authors are grateful to M. Bursa, M. Poutanen, D. Zilkoski, and an anonymous reviewer for contributing significantly to the improvement of the paper.     

Variability of Altimetric Range Correction Parameters over Indian Tropical Region using JASON-1 & JASON-2 Radar Altimeters

Region-specific atmospheric range correction maps are generated over the Indian tropical region from Jason-1 & Jason-2 radar altimeters data. Seasonal and spatial variability of wet tropospheric correction (WTC), ionospheric correction (IC), dry tropospheric correction (DTC), and sea state bias (SSB) correction are analyzed over the Bay of Bengal and the Arabian Sea. Two year atmospheric range correction data from JASON-1 (2008) & JASON-2 altimeters (2009) has been analyzed where each Jason cycle is exactly 9.9156?days repeat. The monthly and yearly mean variation of the range correction parameters has been studied over the Indian continent. For precise study, four different regions were selected as the Region of Interest in the North & South of the Arabian Sea and Bay of Bengal. WTC, Significant Wave Height (SWH), Wind Speed (WS) and SSB show the higher values during monsoon months. The yearly mean WTC over Indian Tropical region was 26.22?cm in 2008 and 26.20?cm in 2009. SSB Correction values mainly depend on the SWH and wind speed. The yearly mean SSB correction over Indian Tropical region was 6.87?cm in 2008 and 7.02?cm in 2009. DTC values are less during monsoon season and it shows a high value in the month of January. The yearly mean DTC over Indian Tropical region was 230.42?cm in 2008 and 230.43?cm in 2009.The IC values mainly depend on frequency and total electron content (TEC) in the ionosphere which further depends on the solar activity. The yearly mean IC over Indian Tropical region was higher in 2008 (2.98?cm) in comparison to mean IC in 2009 (2.29?cm). This study is useful to understand the variability of atmospheric correction parameters especially over Indian continent.     

A spectral optimally interpolated mean sea surface from satellite radar altimetry

 A technique is presented for the development of a high-precision and high-resolution mean sea surface model utilising radar altimetric sea surface heights extracted from the geodetic phase of the European Space Agency (ESA) ERS-1 mission. The methodology uses a cubic-spline fit of dual ERS-1 and TOPEX crossovers for the minimisation of radial orbit error. Fourier domain processing techniques are used for spectral optimal interpolation of the mean sea surface in order to reduce residual errors within the initial model. The EGM96 gravity field and sea surface topography models are used as reference fields as part of the determination of spectral components required for the optimal interpolation algorithm. A comparison between the final model and 10 cycles of TOPEX sea surface heights shows differences of between 12.3 and 13.8 cm root mean square (RMS). An un-optimally interpolated surface comparison with TOPEX data gave differences of between 15.7 and 16.2 cm RMS. The methodology results in an approximately 10-cm improvement in accuracy. Further improvement will be attained with the inclusion of stacked altimetry from both current and future missions. Received: 22 December 1999 / Accepted: 6 November 2000     

Making the connection between Geosat and TOPEX/Poseidon

We can presently construct two independent time series of sea level, each at a precision of a few centimeters, from Geosat (1985–1988) and TOPEX/Poseidon (1992–1995) collinear altimetry. Both are based on precise satellite orbits computed using a common geopotential model, JGM-2 (Nerem et al. 1994). We have attempted to connect these series using Geosat-T/P crossover differences in order to assess long-term ocean changes between these missions. Unfortunately, the observed result are large-scale sea level differences which appear to be due to a combination of geodetic and geopotential error sources. The most significant geodetic component seems to be a coordinate system bias for Geosat sea level (relative to T/P) of −7 to −9 cm in the y-axis (towards the Eastern Pacific). The Geosat-T/P sea height differences at crossovers (with JGM-2 orbits) probably also contain stationary geopotential-orbit error of about the same magnitude which also distort any oceanographic interpretation of the observed changes. We also found JGM-3 Geosat orbits have not resolved the datum errors evident from the JGM-2 Geosat -T/P results. We conclude that the direct altimetric approach to accurate determination of sea level change using Geosat and T/P data still depends on further improvement in the Geosat orbits, including definition of the geocenter. Received: 11 March 1996; Accepted: 19 September 1996     

Black sea annual and inter-annual water mass variations from space

This study evaluates the performance of two widely used GRACE solutions (CNES/GRGS RL02 and CSR RL04) in deriving annual and inter-annual water mass variations in the Black Sea for the period 2003–2007. It is demonstrated that the GRACE derived water mass variations in the Black Sea are heavily influenced by the leakage of hydrological signals from the surrounding land. After applying the corresponding correction, we found a good agreement with water mass variations derived from steric-corrected satellite altimetry observations. Both GRACE and altimetry show significant annual water mass variations of roughly 7 cm amplitude peaking in May and a semi-annual signal of roughly 3 cm peaking in June and in December. The amplitude of the annual water mass signal varies significantly from year to year and is significantly larger during 2004–2006 than in 2003 and 2007. This is also in agreement with the steric corrected altimetry.     

ANTICYCLONIC EDDIES OVER THE NORTHWESTERN CONTINENTAL SLOPE IN THE BLACK SEA AND TRANSPORT OF CHLOROPHYLL-RICH WATERS INTO ITS ABYSSAL BASIN

A series of infrared NOAA satellite images of the northwestern Black Sea (resolution 1 km) and corresponding maps of chlorophyll “a” (SeaWiFS data, resolution 9 km) are analyzed for the period 1 June-28 August 1998. A major objective was detection of the movement of three synoptic-scale anticyclonic eddies over the continental slope and the entrainment of photopigment-rich coastal waters by them. The study examines the effects of wind direction on the visibility of eddies in the chlorophyll field, and attempts to identify conditions favoring the transport of chlorophyll-rich shelf waters into the sea's abyssal basin.     

卫星测高数据的沿轨迹重力异常反演法及其应用

本文给出了一套基于直角坐标系下的垂线偏差求解重力异常公式 ,并将之发展成为一套新的沿轨迹重力异常求解公式。与其他方法相比 ,本方法无须求解交叠点处沿轨迹和跨轨迹方向的海面高斜率 ,仅需计算沿轨迹方向的海面高斜率 ,因而更为简洁、有效 ,而且分辨率可以更高并可与真正的沿航迹实际船测重力相比较、验证。据此 ,利用 Geosat/GM、ERS-1 /35天及TOPEX/Poseidon三种测高数据 ,反演了南中国海域 (0°～ 2 5°N,1 0 5°～ 1 2 2°E)的 2′× 2′重力异常—— IGG-S。通过与实际船测资料和国际同行提供的重力模型相比 ,IGG-S总体精度达到1 0× 1 0 - 5ms- 2。     

Analysis of some systematic errors affecting altimeter-derived sea surface gradient with application to geoid determination over Taiwan

This paper analyzes several systematic errors affecting sea surface gradients derived from Seasat, Geosat/ERM, Geosat/GM, ERS-1/35d, ERS-1/GM and TOPEX/POSEIDON altimetry. Considering the data noises, the conclusion is: (1) only Seasat needs to correct for the non-geocentricity induced error, (2) only Seasat and Geosat/GM need to correct for the one cycle per revolution error, (3) only Seasat, ERS-1/GM and Geosat/GM need to correct for the tide model error; over shallow waters it is suggested to use a local tide model not solely from altimetry. The effects of the sea surface topography on gravity and geoid computations from altimetry are significant over areas with major oceanographic phenomena. In conclusion, sea surface gradient is a better data type than sea surface height. Sea surface gradients from altimetry, land gravity anomalies, ship gravity anomalies and elevation data were then used to calculate the geoid over Taiwan by least-squares collocation. The inclusion of sea surface gradients improves the geoid prediction by 27% when comparing the GPS-derived and the predicted geoidal heights, and by 30% when comparing the observed and the geoid-derived deflections of the vertical. The predicted geoid along coastal areas is accurate to 2 cm and can help GPS to do the third-order leveling. Received 22 January 1996; Accepted 13 September 1996