Gravity,Mean Sea Surface,and Bathymetry Models Comparison in the Canary Islands

In geodetic and oceanographic studies generally, some reference surfaces are needed. These surfaces must represent as much as possible the gravity field of the Earth and the height/bathymetry systems. In the last years, several gravimetric, bathymetric, and mean sea surface models have appeared. Analyzing them it is possible to see that there are significant discrepancies between the models provided by different authors or organizations; there are also differences between the models and data obtained by independent measurements. We present the analysis of such differences and determine the most representative choice of models, in our opinion, for the Canary Islands region.     

Effect of Sea Level Variability on the Estimation of Mean Sea Surface Gradients

It is demonstrated that an along-track mean sea surface (MSS) model estimated with TOPEX altimeter data, including the large 1997-1998 El Niño event, is slightly less accurate than a MSS model calculated from less data where El Niño signals are small. The manner in which true sea level variability corrupts the estimation of MSS gradients is discussed. A model is proposed to reduce the error, based on scaling climate indices such as the Southern Oscillation Index, while accounting for phase shifts using a Hilbert transform. After modeling and removing the seasonal and interannual sea level variations, parameters to a plane MSS model are estimated using TOPEX altimeter data from January 1993 to June 2000. Results indicate an overall improvement over the earlier model based on four years of data, and no apparent degradation due to aliasing of sea level variability.     

TOPEX Constrained Solution of Mean Sea Surface by Joint Processing of TOPEX,ERS-1 and GEOSAT Altimetric Measurements

We present an improved crossover adjustment procedure to determine mean sea surface height using TOPEX, 35-day repeat phase ERS-1, Geosat, and 168-day repeat phase ERS-1 satellite altimeter data. The mean sea surface frame defined by the TOPEX data is imposed as certain constraints in our crossover adjustment procedure rather than held fixed as in some other procedures. The new procedure is discussed in detail. Equations are developed to incorporate the a priori information of Topex data as well as other satellite altimeter data. The numerical computation result shows that the rms crossover discrepancies are reduced by an order of 1 cm when the Topex data is not fixed. Furthermore, the computed mean sea surface is less noisy and more realistic than that computed by the traditional procedure.     

TOPEX Constrained Solution of Mean Sea Surface by Joint Processing of TOPEX, ERS-1 and GEOSAT Altimetric Measurements

We present an improved crossover adjustment procedure to determine mean sea surface height using TOPEX, 35-day repeat phase ERS-1, Geosat, and 168-day repeat phase ERS-1 satellite altimeter data. The mean sea surface frame defined by the TOPEX data is imposed as certain constraints in our crossover adjustment procedure rather than held fixed as in some other procedures. The new procedure is discussed in detail. Equations are developed to incorporate the a priori information of Topex data as well as other satellite altimeter data. The numerical computation result shows that the rms crossover discrepancies are reduced by an order of 1 cm when the Topex data is not fixed. Furthermore, the computed mean sea surface is less noisy and more realistic than that computed by the traditional procedure.     

Using Mean Sea Surface Topography for Determination of Height System Differences across the Baltic Sea

The mean sea surface topography in the Baltic Sea and adjacent waters is reliably known in the Nordic height system NH 60. Using this knowledge we estimate differences between NH 60, based on the Amsterdam zero point, and Russian, Polish, and German height systems along the southeastern coast of the Baltic Sea, based on the Kronstadt zero point. The differences agree within a few centimeters. We also make a simple study of the mean sea level difference between Kronstadt and Amsterdam (which is found to have been approximately 25 cm when sea level was still to be seen there).     

Dependence of Mean Sea Surfaces from Altimeter Data on the Reference Model Used

A mean sea surface model is used as the frame of reference in processing altimeter data. This article focuses on ascertaining the extent to which results depend on the different mean sea surface models used. In particular, we have analyzed the results from the OSU95MSS and the CLS_SHOMv.98.2 models in an area in the North Atlantic Ocean comprising the Canary and Azores Islands. Special attention has been paid to data editing and several criteria were proposed. The amount of detected data is quite small because we used a well corrected data set. However, it was enough to show important relations between the applied criteria and the kind of area. Therefore we analyzed the best way to apply these criteria according to the areas where the points have been found. Singular areas related to several factors have been detected by all the suggested criteria. In particular, rough sea bottom features, dynamic circulation, and amphidromic points of the tidal waves, among others. As a result of this analysis, we have not considered it appropriate to remove all the detected points. Two time-averaged and corrected mean sea surfaces were determined in the test area.     

Dependence of Mean Sea Surfaces from Altimeter Data on the Reference Model Used

A mean sea surface model is used as the frame of reference in processing altimeter data. This article focuses on ascertaining the extent to which results depend on the different mean sea surface models used. In particular, we have analyzed the results from the OSU95MSS and the CLS_SHOMv.98.2 models in an area in the North Atlantic Ocean comprising the Canary and Azores Islands. Special attention has been paid to data editing and several criteria were proposed. The amount of detected data is quite small because we used a well corrected data set. However, it was enough to show important relations between the applied criteria and the kind of area. Therefore we analyzed the best way to apply these criteria according to the areas where the points have been found. Singular areas related to several factors have been detected by all the suggested criteria. In particular, rough sea bottom features, dynamic circulation, and amphidromic points of the tidal waves, among others. As a result of this analysis, we have not considered it appropriate to remove all the detected points. Two time-averaged and corrected mean sea surfaces were determined in the test area.     

Consistency of Geoid Models,Radar Altimetry,and Hydrodynamic Modelling in the North Sea

Radar altimetry, when corrected for tides, atmospheric forcing of the sea surface, and the effects of density variations and mean and time-variable currents, provides an along-track realization of the marine geoid. In this study we investigate whether and how such an ‘altimetric-hydrodynamic’ geoid over the North Sea can serve for validating satellite-gravimetric geoids. Our results indicate that, using ERS-2 and ENVISAT along-track altimetry and water levels from the high-resolution operational circulation model BSHcmod, we do find distinct differences in RMS fits for various state-of-the art satellite-only models (beyond degree 145 for GRACE-only, and beyond degree 185 for GOCE models) and for combined geoid models, very similar as seen in GPS-levelling validations over land areas. We find that, at spectral resolution of up to about 200, an RMS fit as low as about 7 cm can be obtained for the most recent GOCE-derived models such as GOCO05S. This is slightly above what we expect from budgeting individual errors. Key to the validation is a proper treatment of the spectral mismatch between satellite-gravimetric and altimetric-hydrodynamic geoids. Comparison of data fits and error budget suggests that geoid truncation errors residual to EGM2008 (i.e. EGM2008 commission and omission error) may amount up to few cm.     

Constraining Navigation by Matching Swath Bathymetry and Gravity Measurements at Ship Track Crossovers

A method which utilizes the lateral offset information obtained by comparing swath bathymetric data at track crossover points as a further constraint on the navigation is presented. The method, based on generalized least squares inversion theory, derives a new navigational solution that minimizes the overall misfit between the pairs of topography at crossovers while trying to remain smooth and close to the starting model. To achieve a high numerical efficiency during inversions of large matrices, we employed sparse matrix algorithms. The inversion scheme was applied to a set of Sea Beam data collected over the East Pacific Rise near 9° 30' N in early 1988 at the time when the Global Positioning System had limited coverage. The starting model was constructed by taking evenly spaced samples of positions along the tracklines. For each one of the 361 crossovers, we gridded the bathymetric data around the crossover point compared the gridded maps, and calculated the offset and uncertainty associated with this estimation. A suite of inversion solutions were obtained depending on the choice of three free parameters (that is, the a priori model variance, the correlation interval of a priori model, and the trade-off coefficient between fitting the data and remaining close to the a priori model). The best solution was chosen as one that minimizes both the Sea Beam topography and free-air gravity anomaly differences at crossovers. The improvement was significant; the initial rms mismatch between the tracks and free-air gravity anomalies at crossovers was reduced from 610m to 75m and from 2.5mGal to 1.9mGal, respectively.     

Recent Sea Level and Sea Surface Temperature Changes Along the Maldives Coast

Maldives, a South Asian small island nation in the northern part of the Indian Ocean is extremely vulnerable to the impacts of Sea Level Rise (SLR) due to its low altitude from the mean sea level. This artricle attempts to estimate the recent rates of SLR in Maldives during different seasons of the year with the help of existing tidal data recorded in the Maldives coast. Corresponding Sea Surface Temperature (SST) trends, utilizing reliable satellite climatology, have also been obtained. The relationships between the SST and mean sea level have been comprehensively investigated. Results show that recent sea level trends in the Maldives coast are very high. At Male, the capital of the Republic of Maldives, the rising rates of Mean Tidal Level (MTL) are: 8.5, 7.6, and 5.8 mm/year during the postmonsoon (October-December), Premonsoon (March-May) and southwest monsoon (June-September) seasons respectively. At Gan, a station very close to the equator, the increasing rate of MTL is maximum during the period from June to September (which is 6.2 mm/year). These rising trends in MTL along the Maldives coast are certainly alarming for this small developing island nation, which is hardly one meter above the mean sea level. Thus there is a need for careful monitoring of future sea level changes in the Maldives coast. The trends presented are based on the available time-series of MTL for the Maldives coast, which are rather short. These trends need not necessarily reflect the long-term scenario. SST in the Maldives coast has also registered significant increasing trend during the period from June to September. There are large seasonal variations in the SST trends at Gan but SST and MTL trends at Male are consistently increasing during all the seasons and the rising rates are very high. The interannual mode of variation is prominent both in SST as well as MTL. Annual profile of MTL along the Maldives coast is bimodal, having two maxima during April and July. The April Mode is by far the dominant one. The SST appears to be the main factor governing the sea level variations along the Maldives coast. The influence of SST and sea level is more near the equatorial region (i.e., at Gan). There is lag of about two months for the maximum influence of SST on the sea level. The correlation coefficient between the smoothed SST and mean tidal level at Gan with lag of two months is as high as ~ +0.8, which is highly significant. The corresponding correlation coefficients at Male with the lags of one and two months are +0.5 and +0.3, respectively. Thus, the important finding of the present work for the Maldives coast is the dominance of SST factor in sea level variation, especially near the region close to the equator.     

On the Influence of Sea Surface Height Variability on Satellite Altimeter Derived Gravity

The effect of sea surface height (SSH) variability is one of the primary factors that limit the accuracy and resolution of altimeter-derived gravity values. We propose a method to estimate the influence of variation of the sea surface height on the accuracy of satellite-derived gravity by simulation technique, with a case study around Indonesian waters. Wederived an Indonesian marine gravity map using the Geosat-geodetic mission (GM). Since most of the area studied is located around coastal and shallow areas, the measurement of SSH of this area is less accurate. To obtain a distribution of SSH variability over the study area, Topex/Poseidon (T/P) data were first processed and assessed. Processing 52 cycles of the Topex/Poseidon data, the root mean square (RMS) of SSH variability for each cycle was found to vary from 1 to 179 cm. Further, for the purpose of estimating the accuracy of altimeter-derived gravity, we derived several levels of Gaussian noise, computed simulation data by adding the Gaussian noise to Geosat data, and determined simulated gravity maps. Based on the distribution of RMS values from T/P data and standard deviation (STD) differences between the simulated and the original gravity maps, we estimated the accuracy of the gravity map. Around Indonesian waters, the accuracy of the gravity map influenced by SSH variation was estimated to be within the range 0.8~93 mgal.     

On the Influence of Sea Surface Height Variability on Satellite Altimeter Derived Gravity

The effect of sea surface height (SSH) variability is one of the primary factors that limit the accuracy and resolution of altimeter-derived gravity values. We propose a method to estimate the influence of variation of the sea surface height on the accuracy of satellite-derived gravity by simulation technique, with a case study around Indonesian waters. Wederived an Indonesian marine gravity map using the Geosat-geodetic mission (GM). Since most of the area studied is located around coastal and shallow areas, the measurement of SSH of this area is less accurate. To obtain a distribution of SSH variability over the study area, Topex/Poseidon (T/P) data were first processed and assessed. Processing 52 cycles of the Topex/Poseidon data, the root mean square (RMS) of SSH variability for each cycle was found to vary from 1 to 179 cm. Further, for the purpose of estimating the accuracy of altimeter-derived gravity, we derived several levels of Gaussian noise, computed simulation data by adding the Gaussian noise to Geosat data, and determined simulated gravity maps. Based on the distribution of RMS values from T/P data and standard deviation (STD) differences between the simulated and the original gravity maps, we estimated the accuracy of the gravity map. Around Indonesian waters, the accuracy of the gravity map influenced by SSH variation was estimated to be within the range 0.8~93 mgal.     

Comparison of Multimission Altimetric Sea-Surface Heights with Tide Gauge Observations in the Southern Baltic Sea

One possible technique to validate the observations of altimeter missions is the comparison with sea-surface heights measured by tide gauges. In our investigation, we compared observations of the two tide gauge stations, Sassnitz and Warnemünde, which are located at the southern coast of the Baltic Sea, with sea-surface heights obtained from the altimeter missions Geosat, ERS-1, ERS-2, and TOPEX/Poseidon. For this purpose, the compared sea-surface heights were related to a common reference system and extrapolated to a common location. GPS observations, leveling data, regional geoid information, sea-surface topography, and postglacial rebound were included in the analysis. Considering the uncertainties of all model components, a more reliable estimation of the error budget (source, type, and magnitude of the errors) was performed. The obtained absolute altimeter biases are (-243 - 32) mm for Geosat, (467 - 19) mm for ERS-1, (76 - 19) mm for ERS-2, and (13 - 18) mm for TOPEX.     

Recent Sea Level and Sea Surface Temperature Changes Along the Maldives Coast

Maldives, a South Asian small island nation in the northern part of the Indian Ocean is extremely vulnerable to the impacts of Sea Level Rise (SLR) due to its low altitude from the mean sea level. This artricle attempts to estimate the recent rates of SLR in Maldives during different seasons of the year with the help of existing tidal data recorded in the Maldives coast. Corresponding Sea Surface Temperature (SST) trends, utilizing reliable satellite climatology, have also been obtained. The relationships between the SST and mean sea level have been comprehensively investigated. Results show that recent sea level trends in the Maldives coast are very high. At Male, the capital of the Republic of Maldives, the rising rates of Mean Tidal Level (MTL) are: 8.5, 7.6, and 5.8 mm/year during the postmonsoon (October-December), Premonsoon (March-May) and southwest monsoon (June-September) seasons respectively. At Gan, a station very close to the equator, the increasing rate of MTL is maximum during the period from June to September (which is 6.2 mm/year). These rising trends in MTL along the Maldives coast are certainly alarming for this small developing island nation, which is hardly one meter above the mean sea level. Thus there is a need for careful monitoring of future sea level changes in the Maldives coast. The trends presented are based on the available time-series of MTL for the Maldives coast, which are rather short. These trends need not necessarily reflect the long-term scenario. SST in the Maldives coast has also registered significant increasing trend during the period from June to September. There are large seasonal variations in the SST trends at Gan but SST and MTL trends at Male are consistently increasing during all the seasons and the rising rates are very high. The interannual mode of variation is prominent both in SST as well as MTL. Annual profile of MTL along the Maldives coast is bimodal, having two maxima during April and July. The April Mode is by far the dominant one. The SST appears to be the main factor governing the sea level variations along the Maldives coast. The influence of SST and sea level is more near the equatorial region (i.e., at Gan). There is lag of about two months for the maximum influence of SST on the sea level. The correlation coefficient between the smoothed SST and mean tidal level at Gan with lag of two months is as high as ~ +0.8, which is highly significant. The corresponding correlation coefficients at Male with the lags of one and two months are +0.5 and +0.3, respectively. Thus, the important finding of the present work for the Maldives coast is the dominance of SST factor in sea level variation, especially near the region close to the equator.     

Comparison of Satellite Altimetric Gravity and Global Geopotential Models with Shipborne Gravity in the Red Sea

The determination of high-resolution geoid for marine regions requires the integration of gravity data provided by different sources, e.g. global geopotential models, satellite altimetry, and shipborne gravimetric observations. Shipborne gravity data, acquired over a long time, comprises the short-wavelengths gravitation signal. This paper aims to produce a consistent gravity field over the Red Sea region to be used for geoid modelling. Both, the leave-one-out cross-validation and Kriging prediction techniques were chosen to ensure that the observed shipborne gravity data are consistent as well as free of gross-errors. A confidence level equivalent to 95.4% was decided to filter the observed shipborne data, while the cross-validation algorithm was repeatedly applied until the standard deviation of the residuals between the observed and estimated values are less than 1.5 mGal, which led to the elimination of about 17.7% of the shipborne gravity dataset. A comparison between the shipborne gravity data with DTU13 and SSv23.1 satellite altimetry-derived gravity models is done and reported. The corresponding results revealed that altimetry models almost have identical data content when compared one another, where the DTU13 gave better results with a mean and standard deviation of ?2.40 and 8.71 mGal, respectively. A statistical comparison has been made between different global geopotential models (GGMs) and shipborne gravity data. The Spectral Enhancement Method was applied to overcome the existing spectral gap between the GGMs and shipborne gravity data. EGM2008 manifested the best results with differences characterised with a mean of 1.35 mGal and a standard deviation of 11.11 mGal. Finally, the least-squares collocation (LSC) was implemented to combine the shipborne gravity data with DTU13 in order to create a unique and consistent gravity field over the Red Sea with no data voids. The combined data were independently tested using a total number of 95 randomly chosen shipborne gravity stations. The comparison between the extracted shipborne gravity data and DTU13 altimetry anomalies before and after applying the LSC revealed that a significant improvement is procurable from the combined dataset, in which the mean and standard deviation of the differences dropped from ?3.60 and 9.31 mGal to ?0.39 and 2.04 mGal, respectively.     

Distribution of Organic Matter, Iron, Mangenese in SurfaceSediments in the Nansha Islands Sea Area, South China Sea

Concentrations of organic matter, iron and manganese in the deep sea surface sediments in the Nansha Islands sea area, South China Sea are measured, Horizontal and vertical distributions of iron and manganese are discussed. The vertical distribution of iron and manganese in the sediments results from reduction, diffusion, and redeposition of manganese (or iron) oxide and hydroxide in the sediment. There are the maxima of iron and manganese in solid phase in the top of the sediment, which is caused by the penetration of O2 and the upward flux of Mn^2 ( or Fe^2 ). Manganese bacteria play a very important role in the cycle of solid-phase iron and manganese in the ocean environment. Manganese bacteria oxidize Mn^2 ( or Fe^2 ) in dissolved state to Mn^4 ( or Fe^3 ) in oxidized state under the aerobic condition, whereas they reduce iron and manganese in anaerobic conditions.     

Sea Level Variations and Geomorphological Changes in the Coastal Belt of Pakistan

The UNEP in its regional seas program in 1989 has included Pakistan in a group of countries which are vulnerable to the impact of rising sea level. If the present trend of sea level rise (SLR) at Karachi continues, in the next 50 years the sea level rise along the Pakistan Coast will be 50 mm (5 cm). Since the rising rates of sea level at Karachi are within the global range of 1-2 mm/year, the trends may be treated as eustatic SLR. Historical air temperature and sea surface temperature (SST) data of Karachi also show an increasing pattern and an increasing trend of about 0.67°C has been registered in the air temperature over the last 35 years, whereas the mean SST in the coastal waters of Karachi has also registered an increasing trend of about 0.3°C in a decade. Sindh coastal zone is more vulnerable to sea level rise than Baluchistan coast, as uplifting of the coast by about 1-2 mm/year due to subduction of Indian Ocean plate is a characteristic of Baluchistan coast. Within the Indus deltaic creek system, the area nearby Karachi is more vulnerable to coastal erosion and accretion than the other deltaic region, mainly due to human activities together with natural phenomena such as wave action, strong tidal currents, and rise in sea level. Therefore, The present article deals mainly with the study of dynamical processes such as erosion and accretion associated with sea level variations along the Karachi coast and surrounding Indus deltaic coastline. The probable beach erosion in a decade along the sandy beaches of Karachi has been estimated. The estimates show that 1.1 mm/year rise in sea level causes a horizontal beach loss of 110 mm per year. Therefore, coast eroded with rise in sea level at Karachi and surrounding sandy beaches would be 1.1 m during a period of next 10 years. The northwestern part of Indus delta, especially the Gizri and Phitti creeks and surrounding islands, are most unstable. Historical satellite images are used to analyze the complex pattern of sediment movements, the change in shape of coastline, and associated erosion and accretion patterns in Bundal and Buddo Islands. The significant changes in land erosion and accretion areas at Bundal and Buddo Islands are evident and appear prominently in the images. A very high rate of accretion of sediments in the northwestern part of Buddo Island has been noticed. In the southwest monsoon season the wave breaking direction in both these islands is such that the movement of littoral drift is towards west. Erosion is also taking place in the northeastern and southern part of Bundal Island. The erosion in the south is probably due to strong wave activities and in the northeast is due to strong tidal currents and seawater intrusion. Accretion takes place at the northwest and western parts of Bundal Island. By using the slope of Indus delta, sea encroachment and the land area inundation with rising sea level of 1 m and 2 m have also been estimated.     

Sea Level Variations and Geomorphological Changes in the Coastal Belt of Pakistan

The UNEP in its regional seas program in 1989 has included Pakistan in a group of countries which are vulnerable to the impact of rising sea level. If the present trend of sea level rise (SLR) at Karachi continues, in the next 50 years the sea level rise along the Pakistan Coast will be 50 mm (5 cm). Since the rising rates of sea level at Karachi are within the global range of 1-2 mm/year, the trends may be treated as eustatic SLR. Historical air temperature and sea surface temperature (SST) data of Karachi also show an increasing pattern and an increasing trend of about 0.67°C has been registered in the air temperature over the last 35 years, whereas the mean SST in the coastal waters of Karachi has also registered an increasing trend of about 0.3°C in a decade. Sindh coastal zone is more vulnerable to sea level rise than Baluchistan coast, as uplifting of the coast by about 1-2 mm/year due to subduction of Indian Ocean plate is a characteristic of Baluchistan coast. Within the Indus deltaic creek system, the area nearby Karachi is more vulnerable to coastal erosion and accretion than the other deltaic region, mainly due to human activities together with natural phenomena such as wave action, strong tidal currents, and rise in sea level. Therefore, The present article deals mainly with the study of dynamical processes such as erosion and accretion associated with sea level variations along the Karachi coast and surrounding Indus deltaic coastline. The probable beach erosion in a decade along the sandy beaches of Karachi has been estimated. The estimates show that 1.1 mm/year rise in sea level causes a horizontal beach loss of 110 mm per year. Therefore, coast eroded with rise in sea level at Karachi and surrounding sandy beaches would be 1.1 m during a period of next 10 years. The northwestern part of Indus delta, especially the Gizri and Phitti creeks and surrounding islands, are most unstable. Historical satellite images are used to analyze the complex pattern of sediment movements, the change in shape of coastline, and associated erosion and accretion patterns in Bundal and Buddo Islands. The significant changes in land erosion and accretion areas at Bundal and Buddo Islands are evident and appear prominently in the images. A very high rate of accretion of sediments in the northwestern part of Buddo Island has been noticed. In the southwest monsoon season the wave breaking direction in both these islands is such that the movement of littoral drift is towards west. Erosion is also taking place in the northeastern and southern part of Bundal Island. The erosion in the south is probably due to strong wave activities and in the northeast is due to strong tidal currents and seawater intrusion. Accretion takes place at the northwest and western parts of Bundal Island. By using the slope of Indus delta, sea encroachment and the land area inundation with rising sea level of 1 m and 2 m have also been estimated.