Improvement in the Determination of the Marine Geoid by Estimating the Bathymetry from Altimetry and Depth Soundings

Abstract

The contribution of bathymetry to the estimation of gravity field related quantities is investigated in an extended test area in the Mediterranean Sea. The region is located southwest of the island of Crete, Greece, bounded between 33^? ≤ ? ≤ 35^? and 15^? ≤ λ ≤ 25^?. Gravity anomalies from the KMS99 gravity field and shipborne depth soundings are used with a priori statistical characteristics of depths in a least-squares collocation procedure to estimate a new bathymetry model. Two different global bathymetry models, namely JGP95E and Sandwell and Smith V8, are used to derive the depth a priori statistical information, while the estimated model is compared against both the global ones and the shipborne depth soundings to assess whether there is an improvement. Various marine geoid models are estimated using ERS1 and GEOSAT Geodetic Mission altimetry and shipborne gravity data. In that process, the effect of the bathymetry is computed using both the estimated and the original depths through a residual terrain modeling reduction. The TOPEX/Poseidon Sea Surface Heights, known for their high accuracy and precision, and the GEOMED solution for the geoid in the Mediterranean are used as control for the validation of the new geoid models and to assess the improvement that the estimated depths offer to geoid modeling. The results show that the newly estimated bathymetry agrees better (by about 30 to 300 m) with the shipborne depth soundings and provides smoother residual geoid heights and gravity anomalies (by about 8–20%) than those from global models. Finally, the achieved accuracy in geoid modeling ranges between 6 and 10 cm (1σ).     

Improvement in the Determination of the Marine Geoid by Estimating the Bathymetry from Altimetry and Depth Soundings

The contribution of bathymetry to the estimation of gravity field related quantities is investigated in an extended test area in the Mediterranean Sea. The region is located southwest of the island of Crete, Greece, bounded between 33^ˆ ≤ ϕ ≤ 35^ˆ and 15^ˆ ≤ λ ≤ 25^ˆ. Gravity anomalies from the KMS99 gravity field and shipborne depth soundings are used with a priori statistical characteristics of depths in a least-squares collocation procedure to estimate a new bathymetry model. Two different global bathymetry models, namely JGP95E and Sandwell and Smith V8, are used to derive the depth a priori statistical information, while the estimated model is compared against both the global ones and the shipborne depth soundings to assess whether there is an improvement. Various marine geoid models are estimated using ERS1 and GEOSAT Geodetic Mission altimetry and shipborne gravity data. In that process, the effect of the bathymetry is computed using both the estimated and the original depths through a residual terrain modeling reduction. The TOPEX/Poseidon Sea Surface Heights, known for their high accuracy and precision, and the GEOMED solution for the geoid in the Mediterranean are used as control for the validation of the new geoid models and to assess the improvement that the estimated depths offer to geoid modeling. The results show that the newly estimated bathymetry agrees better (by about 30 to 300 m) with the shipborne depth soundings and provides smoother residual geoid heights and gravity anomalies (by about 8-20%) than those from global models. Finally, the achieved accuracy in geoid modeling ranges between 6 and 10 cm (1σ).     

Geoid Validation on the Baltic Sea Using Ship-borne GNSS Data

Abstract

We studied geoid validation using ship-borne global navigation satellite systems (GNSS) on the Baltic Sea. We obtained geoid heights by combining GNSS–inertial measurement unit observations, tide gauge data, and a physical sea model. We used two different geoid models available for the area. The ship route was divided into lines and the lines were processed separately. The GNSS results were reduced to the sea surface using attitude and draft parameters available from the vessel during the campaign. For these lines, the residual errors between ellipsoidal height versus geoid height and absolute dynamic topography varied between 0 and 15?cm, grand mean being 2?cm. The mean standard deviations of the original time series were approximately 11?cm and reduced to below 5?cm for the time series filtered with 10?min moving average. We showed that it is possible to recover geoid heights from the GNSS observations at sea and validate existing geoid models in a well-controlled area.     

基于最小二乘支持向量机的声速空间变化模型构建

建立声速空间变化模型是解决声速剖面代表性误差的有效方法。在对不同声速剖面进行标准化处理的基础上,通过声速训练样本及核函数的选取,提出并实现了一种基于最小二乘支持向量机算法的声速空间变化模型构建方法。为了检验该方法的有效性,选取实测的声速剖面数据进行验证,结果表明该方法能有效地构建声速空间变化模型,从而消除或最大限度地削弱声速剖面代表性误差。     

Reduction of geoid gradient error in ocean variability from satellite altimetry

Altimeter measurements of sea‐level variability have errors due to the altimeter not repeatedly sampling the same point on the ocean surface. The errors are proportional to the local slope of the mean sea surface. Accurate removal of geoid error is essential if altimeter data are to be used to study the relationship between geostrophic turbulence and bathymetry. The error can be reduced by using an accurate model of the mean surface. We use the multiyear TOPEX altimeter data set to develop a model for the mean sea surface along the TOPEX/POSEIDON ground track by estimating the coefficients of a local plane centered on every 2 km x 7 km bin sampled by the altimeter. We have evaluated the ability of this model. compared against two global mean sea‐surface models, to reduce the error associated with steep gradients. The two global models are the Center for Space Research 1995 model and the Ohio State University 1995 model. The three models show similar variability over the oceans, and none shows the large residual errors that can be seen in collinear analysis near some seamounts and trenches. The standard deviation of the variability using the plane model, however, is consistently smaller in low‐variability, high‐geoid‐gradient areas, indicating a slightly better performance than the two global models.     

Hydrographic Vertical Separation Surfaces (HyVSEPs) for the Tidal Waters of Canada

Since the advent of Global Navigation Satellite Systems, it has been possible to perform hydrographic survey reductions through the ellipsoid, which has the potential to simplify operations and improve bathymetric products. This technique requires a spatially continuous separation surface connecting chart datum (CD) to a geodetic ellipsoid. The Canadian Hydrographic Service (CHS), with support from the Canadian Geodetic Survey, has developed a new suite of such surfaces, termed Hydrographic Vertical Separations Surfaces, or HyVSEPs, for CD and seven tidal levels. They capture the spatial variability of the tidal datum and levels between tide gauges and offshore using semiempirical models coupling observations at tide stations with relative sea-level rise estimates, dynamic ocean model solutions, satellite altimetry, and a geoid model. HyVSEPs are available for all tidal waters of Canada, covering over seven million square kilometers of ocean and more than 200,000 kilometers of shoreline. This document provides an overview of the CHS's modeling approach, tools, methods, and procedures.

The HyVSEP for CD defines the new hydrographic datum for the tidal waters of Canada. HyVSEPs for other tidal levels are fundamental for coastal studies, climate change adaptation and the definition of the Canadian shoreline and offshore boundaries. HyVSEPs for inland waters are not discussed.     

Forecasting seasonal to multi-year shoreline change

This contribution details a simple empirical model for forecasting shoreline positions at seasonal to interannual time-scales. The one-dimensional (1-D) model is a simplification of a 2-D behavioural-template model proposed by Davidson and Turner (2009). The new model is calibrated and tested using five-years of weekly video-derived shoreline data from the Gold Coast, Australia. The modelling approach first utilises a least-squares methodology to calibrate the empirical model coefficients using the first half of the dataset of observed shoreline movement in response to known forcing by waves. The model is then verified by comparison of hindcast shoreline positions to the second half of the observed shoreline dataset. One thousand synthetic time-series of wave height and period are generated that encapsulate the statistical characteristics of the modelled wave field, retaining the observed seasonal variability and sequencing characteristics. The calibrated model is used in conjunction with the simulated wave time-series to perform Monte Carlo forecasting of the resulting shoreline positions. The ensemble-mean of the 1000 individual five-year shoreline simulations is compared to the unseen shoreline time-series. A simple linear trend forecast of the shoreline position was used as a baseline for assessing the performance of the model. The model performance relative to this baseline prediction was quantified by several objective methods, including cross-correlation (r), root mean square (RMS) error analysis and Brier Skill tests. Importantly, these tests involved no prior knowledge of either the wave forcing or shoreline response. The new forecast model was found to significantly improve shoreline predictions relative to the simple linear trend model, capturing well both the trend and seasonal shoreline variabilities observed at this site. Brier Skill Scores (BSS) indicate that the model forecasts based on unseen data were rated as ‘excellent’ (BSS = 0.83), and root mean square errors were less than 7 m (≈ 14% of the observed variability). The standard deviations of the 1000 individual simulations from ensemble-averaged ‘mean’ forecast were found to provide a useful means of predicting the higher-frequency (individual storm) shoreline variability, with 98% of the observed shoreline data falling within two standard deviations of the forecast position.     

Validation of Marine Geoid Models by Profile-wise GNSS Measurements on Ice Surface

Ship-board global navigation satellite system (GNSS) measurements are widely used to determine sea surface heights, marine geoid validation, and/or satellite altimetry calibration. However, the use of a vessel could be complicated near coastal areas due to shallow water. Therefore, in the area of sea ice formation, GNSS measurements on the ice surface could be a viable alternative to vessel-borne surveys. Importantly, the ice-covered water is not affected by short-term winds, which otherwise could have systematic influence on the instantaneous sea surface topography. This study tackles methodology and validation of marine geoid models by profile-wise GNSS measurements on ice in an archipelago of the Baltic Sea. The GNSS measurements were carried out on the three ice roads with total length 48 kilometers. The along-route standard deviation between the gravimetric geoid model and profile-wise GNSS heights remained within ±2.1 centimeters.     

Adjustment and filtering of seasat altimetry with the least squares response technique

The least squares response technique has been applied to SEASAT altimetry data for the adjustment and filtering of individual profiles without the use of standard crossover analyses. Based on a multichannel input-single output model, the technique allows a straightforward multi-correlation of the altimetry information with different types of forcing inputs. In addition, it can account for other known constituents such as datum biases, linear trends, periodic constituents of known periods and arbitrarily defined user-specified functions. In this paper, results of this approach are compared with geoid profiles computed from standard geopotential models such as GEM-10B which show a consistently good agreement with rms differences found at the level of the errors at long wavelengths of the geoid model used.     

Sea Level Change Analysis and Models Identification Based on Short Tidal Gauge Measurements in Alexandria,Egypt

Sea level change analysis and models identification are important factors used for coastal engineering applications. Moreover, sea level change modeling is used widely to evaluate and study shoreline and climate changes. This study intends to analyze and model Alexandria, Egypt sea level change by investigating yearly tide gauge data collected in a short duration (2008–2011). The time-frequency method was used to evaluate the meteorological noise frequencies. Two models were used to predict the time series data: Neural Network Autoregressive Moving Average (NNARMA) and Adaptive Neuro-Fuzzy Inference System (ANFIS). The time-frequency analysis and models identification results showed that no extreme events were detected for Alexandria point during the monitoring period. Therefore, the NNARMA and ANFIS models can be used to identify the sea level change. The estimates of the models were compared with the three different statistics, determination coefficient, root mean square errors, and auto-correlation function. Comparison of these results revealed that the NNARMA model performs better than the ANFIS model for the study area.     

Beach morphology and shoreline evolution: Monitoring and modelling medium-term responses (Portuguese NW coast study site)

Numerical models for shoreline evolution have been used for coastal management planning for several decades. The model calibration is a start point to project shoreline scenarios and in this aim the use of data acquired within the scope of monitoring programmes provides the opportunity to assess the models' capabilities under real condition. This work applies calibration data (retrieved from field surveys) to numerical models to predict medium-term shoreline evolution using, as a case study, a beach stretch named AC, about 3.5 km long and located downdrift of a groin on the northwest Portuguese coast. A smaller stretch AB (2.4 km long), included in the total one, which exhibits a pronounced erosive tendency usually better reproduced in shoreline evolution models, was also analysed. Based on topographic surveys, associated wave climate conditions registered between 2003 and 2008 and typical wave conditions registered over a longer wave climate time period, this work compares the calibration of two different shoreline evolution models, Long-term Configuration (LTC) and GENESIS for this period. Then, considering the 2003 topographic conditions for the models' calibration, the results of both models are discussed with respect to simulation scenarios after 10, 15 and 20 years of evolution. The 10-year evolution projections of the models are also compared to the results of a survey performed in February 2012. For the wave data calibration period (2003–2008), the average shoreline retreat of the analysed coastal stretch was reproduced with small differences (around 1% and 10% for LTC and 15% and 14% for GENESIS, considering stretches AB or AC, respectively), though local differences along the AB coastal stretch represent root mean square errors reaching up to 52% and 88% for GENESIS and LTC, respectively, and were above 118% for both models along the AC coastal stretch.     

Robust LS-SVM regression for ore grade estimation in a seafloor hydrothermal sulphide deposit

Due to the geological complexities of ore body formation and limited borehole sampling, this paper proposes a robust weighted least square support vectormachine (LS-SVM) regression model to solve the ore grade estimation for a seafloor hydrothermal sulphide deposit in Solwara 1, which consists of a large proportion of incomplete samples without ore types and grade values. The standard LS-SVM classification model is applied to identify the ore type for each in complete sample. Then, a weighted K-nearest neighbor (WKNN) algorithm is proposed to interpolate the missing values. Prior to modeling, the particle swarm optimization (PSO) algorithm is used to obtain an appropriate splitting for the training and test data sets so as to eliminate the large discrepancies caused by randomdivision. Coupled simulated annealing (CSA) and grid search using 10-fold cross validation techniques are adopted to determine the optimal tuning parameters in the LS-SVM models. The effectiveness of the proposed model by comparing with other well-known techniques such as inverse distance weight (IDW), ordinary kriging (OK), and back propagation (BP) neural network is demonstrated. The experimental results show that the robust weighted LS-SVM outperforms the othermethods, and has strong predictive and generalization ability.     

基于Stokes边值理论的大地水准面计算模型改化及分析检验

针对源自经典Stokes边值理论的大地水准面计算模型适用性问题,提出了3种实用化的Stokes积分模型分阶段改化方法,分析讨论了数据截断误差和观测噪声对大地水准面计算结果的影响,设计了改化计算模型的数值检验方案,使用超高阶位模型EGM2008作为数值模拟标准场,对3种改化计算模型进行了数值计算实验和精度检核,同时开展了数据观测噪声影响评估检验,得出了一些有参考和实际应用价值的研究结论。在一定条件下,使用改化Stokes方法计算大地水准面可获得1 cm的内符合度。     

A hybrid forecasting model for depth-averaged current velocities of underwater gliders

In this paper, we propose a hybrid forecasting model to improve the forecasting accuracy for depth-averaged current velocities (DACVs) of underwater gliders. The hybrid model is based on a discrete wavelet transform (DWT), a deep belief network (DBN), and a least squares support vector machine (LSSVM). The original DACV series are first decomposed into several high- and one low-frequency subseries by DWT. Then, DBN is used for high-frequency component forecasting, and the LSSVM model is adopted for low-frequency subseries. The effectiveness of the proposed model is verified by two groups of DACV data from sea trials in the South China Sea. Based on four general error criteria, the forecast performance of the proposed model is demonstrated. The comparison models include some well-recognized single models and some related hybrid models. The performance of the proposed model outperformed those of the other methods indicated above.     

Applications of satellite altimetry to oceanography and geophysics

Satellite-borne altimeters have had a profound impact on geodesy, geophysics, and physical oceanography. To first order approximation, profiles of sea surface height are equivalent to the geoid and are highly correlated with seafloor topography for wavelengths less than 1000 km. Using all available Geos-3 and Seasat altimeter data, mean sea surfaces and geoid gradient maps have been computed for the Bering Sea and the South Pacific. When enhanced using hill-shading techniques, these images reveal in graphic detail the surface expression of seamounts, ridges, trenches, and fracture zones. Such maps are invaluable in oceanic regions where bathymetric data are sparse. Superimposed on the static geoid topography is dynamic topography due to ocean circulation. Temporal variability of dynamic height due to oceanic eddies can be determined from time series of repeated altimeter profiles. Maps of sea height variability and eddy kinetic energy derived from Geos-3 and Seasat altimetry in some cases represent improvements over those derived from standard oceanographic observations. Measurement of absolute dynamic height imposes stringent requirements on geoid and orbit accuracies, although existing models and data have been used to derive surprisingly realistic global circulation solutions. Further improvement will only be made when advances are made in geoid modeling and precision orbit determination. In contrast, it appears that use of altimeter data to correct satellite orbits will enable observation of basin-scale sea level variations of the type associated with climatic phenomena.     

Precise Geoid Determination over Hong Kong from Heterogeneous Data Sets using a Hybrid Method

ABSTRACT

This study attempts to develop a methodology to construct a high-precision geoid model (HKGEOID-2016) over Hong Kong. To achieve this objective, a hybrid method is employed in this article. The proposed method involves three steps: the combination of multisource data; the construction of gravimetric geoid model using the remove-restore technique and Molodensky's theory; and the optimal combination of heterogeneous height data, improved by the evaluation of stochastic models through the variance component estimation method and assessment of the parametric model. The accuracy of the constructed geoid is evaluated with independent GNSS/leveling data. Numerical results indicate that external precision of 1.5 cm level is achievable. Furthermore, compared with the former geoid model HKGEOID-2000, the proposed procedure in this study improves the accuracy of the geoid significantly.     

大地水准面高的计算及其在海底地形反演中的应用

为充分挖掘海洋重力数据在反演海底地形中的应用潜力,尝试探索利用大地水准面高反演海底地形的技术途径,并以夏威夷—皇帝海山链拐点所在海区作为反演试验区进行验证。首先采用Belikov列推法计算伴随(缔和)勒让德函数,利用EIGEN-6C4地球重力场模型解算获取了分辨率为1'的大地水准面高格网数值模型;然后通过综合分析反演比例函数和转换函数特点、研究海区大地水准面高与海底地形的相干特性以及大地水准面高本身尺度特征,获得了利用大地水准面高反演海底地形的频段范围;最终以试验海区大地水准面高为数据输入,构建了相应的海底地形模型(BNT模型),并与ETOPO1等海深模型进行比对分析。试验结果表明:BNT模型检核差值在一倍均方差范围检核点数量占比70.60%,相比正态分布更加集中;BNT模型检核精度低于ETOPO1等海深模型;海深模型检核精度随着水深增加不断提升,水深小于1 000 m时,海深模型相对误差出现较大发散现象;计算海域ETOPO1模型精度最高,GEBCO模型和DTU10模型检核精度相当。     

Digital Tide-Coordinated Shoreline

The shoreline is one of the most important features on earth's surface. It is valuable to a diverse user community. But the dynamic nature of the shoreline makes it difficult to be represented in a naturally dynamic style and to be utilized in applications. The officially used shoreline, for example in nautical charts, is the so-called tide-coordinated shoreline. It is also the shoreline that makes the computation of shoreline changes and associated environmental changes meaningful. Mapping of the tide-coordinated shoreline has been very costly. On the other hand, instantaneous shorelines extracted from different data sources may be available. Also, high-resolution satellite and airborne imagery have the capacity of stereo imaging and can be used to extract instantaneous shorelines at a high accuracy and low cost. This article proposes an approach to derivation of digital tidecoordinated shorelines from (a) those instantaneous shorelines and (b) digital coastal surface models and a digital water surface model. Some preliminary study results, analysis, and the potential of the approach are discussed.     

Digital Tide-Coordinated Shoreline

The shoreline is one of the most important features on earth's surface. It is valuable to a diverse user community. But the dynamic nature of the shoreline makes it difficult to be represented in a naturally dynamic style and to be utilized in applications. The officially used shoreline, for example in nautical charts, is the so-called tide-coordinated shoreline. It is also the shoreline that makes the computation of shoreline changes and associated environmental changes meaningful. Mapping of the tide-coordinated shoreline has been very costly. On the other hand, instantaneous shorelines extracted from different data sources may be available. Also, high-resolution satellite and airborne imagery have the capacity of stereo imaging and can be used to extract instantaneous shorelines at a high accuracy and low cost. This article proposes an approach to derivation of digital tidecoordinated shorelines from (a) those instantaneous shorelines and (b) digital coastal surface models and a digital water surface model. Some preliminary study results, analysis, and the potential of the approach are discussed.     

A Practical Indirect Back Analysis Approach for Geomechanical Parameters Identification

Back analysis is a powerful tool to determine geomechanical parameters. In this article, a practical approach that employs the response surface method and MS Excel solver for back analysis is presented. The least square support vector machine (LSSVM)-based response surface is utilized to represent the nonlinear relationship between the geomechanical parameters and the monitored information and Excel solver is used to search the geomechanical parameters based on the monitoring information. We analyze the robustness and search ability of the proposed approach. On the other hand, two numerical cases on a circular tunnel and a slope are used to verify the proposed approach. Results clearly indicate that LSSVM-based response surface is effectively able to be used to identify the geomechanical parameters from the monitoring displacements.