Tidal Corrections Research Articles

4SM: A Novel Self-Calibrated Algebraic Ratio Method for Satellite-Derived Bathymetry and Water Column Correction.

All empirical water column correction methods have consistently been reported to require existing depth sounding data for the purpose of calibrating a simple depth retrieval model; they yield poor results over very bright or very dark bottoms. In contrast, we set out to (i) use only the relative radiance data in the image along with published data, and several new assumptions; (ii) in order to specify and operate the simplified radiative transfer equation (RTE); (iii) for the purpose of retrieving both the satellite derived bathymetry (SDB) and the water column corrected spectral reflectance over shallow seabeds. Sea truth regressions show that SDB depths retrieved by the method only need tide correction. Therefore it shall be demonstrated that, under such new assumptions, there is no need for (i) formal atmospheric correction; (ii) conversion of relative radiance into calibrated reflectance; or (iii) existing depth sounding data, to specify the simplified RTE and produce both SDB and spectral water column corrected radiance ready for bottom typing. Moreover, the use of the panchromatic band for that purpose is introduced. Altogether, we named this process the Self-Calibrated Supervised Spectral Shallow-sea Modeler (4SM). This approach requires a trained practitioner, though, to produce its results within hours of downloading the raw image. The ideal raw image should be a “near-nadir” view, exhibit homogeneous atmosphere and water column, include some coverage of optically deep waters and bare land, and lend itself to quality removal of haze, atmospheric adjacency effect, and sun/sky glint.

Determination of a Section of Woji Riverbed Depths for Safe Navigation

The depths of the oceans, seas, rivers, etc. and charting the shape and topography of the ocean floor are only determined though bathymetric processes. And mariners primarily depend on water depths beneath their vessels for safe navigation. Bathymetry also goes a long way to enhance the identification of possible features on the seabed such as elevation changes, rock outcrop, wreckages, sunken vessels, pipeline, or any other obstructions that could cause hazard to navigation. This study employs the bathymetric principles to determine river-bed depths of a section of the Woji River for the purpose of creating a two-dimensional view of the underlying sub-surface and a threedimensional model of the river-bed, to enhance safe navigation. Data acquisition was done using satellite imagery from Google Earth, total tide prediction data, sounding depths using Midas echo sounder and GPS data. Data processing performed on observed bathymetric data include spike removal, tidal correction on instantaneous depths. The processed depths were analysed and presented in form of profile view, graphs, and charts. A flow and sedimentation simulation was carried out using ArcGIS 10.3, to show the nature of the river. The tidal data aided in sounding reduction, and river average depth of 6.022m was obtained. The levelling mis-closure was 0.001m and the average variation in echo sounder calibration was 0.08m. Based on the acquired and output data, the produced chart revealed sedimentation effect on the convex coastline, uneven riverbed topography possibly due to sand excavation, which could pose serious danger to the safety of navigation. Based on these results, the use of Sub-Bottom Profiler and a Multi-Beam Echo Sounder (MBES) is therefore recommended in order to improve the quality of data obtained.

A crossover adjustment for improving sea surface height mapping from in-situ high rate ship-borne GNSS data using PPP technique

Ship-borne global navigation satellite system (GNSS) technique can overcome the weakness of satellite altimetry and tide gauge in measuring sea surface heights (SSHs) over coastal seas. Ship-borne GNSS technique can be used to calibrate SSHs determined by the satellite altimetry and tide gauge. The ship-borne GNSS data are processed with the single-epoch precise point positioning (PPP) method to estimate SSHs which are filtered by the Gaussian filter to weaken and/or remove effects of sea wind and wave field. Tidal corrections are also taken into consideration to improve SSHs. One crossover adjustment method is put forward to calculate the bias and drift along the ship route and assess the accuracy of SSHs. We processed the in-situ ship-borne GPS data over the offshore sea around Keelung to compute precisely SSHs with the single-epoch PPP. Statistical results of SSH differences of crossover points indicate that the root mean squares error of SSHs determined by the ship-borne GPS is up to level of 12.9cm over the offshore sea ~30km far away to land.

Using CryoSat‐2 altimeter data to evaluate M2 internal tides observed from multisatellite altimetry

AbstractThis paper evaluates M2 internal tides observed from multisatellite altimetry (MultiSat20yr) using CryoSat‐2 altimeter data. MultiSat20yr is constructed using 20 years of sea surface height measurements made by multiple satellite altimeters from 1992 to 2012. Here it is demonstrated that M2 internal tides can also be extracted using 4 years of CryoSat‐2 data from 2011 to 2014 (CryoSat4yr) by the same plane wave fit method. MultiSat20yr and CryoSat4yr are in good agreement in the central North Pacific, although they are from satellite data of different sampling patterns (1998 versus 10,688 tracks) and different observational periods (20 versus 4 years). Further comparisons are carried out for three isolated wave components. MultiSat20yr and CryoSat4yr agree very well for both Hawaiian components, suggesting that the Hawaiian Ridge is a relatively stable generation site. In contrast, the Aleutian Ridge is a relatively unstable source in that the M2 amplitudes in MultiSat20yr and CryoSat4yr are very different. With respect to MultiSat20yr, the M2 internal tide in 2011–2014 propagates slower (faster) to the south (north) of Hawaii, respectively, suggesting that the internal tide's propagation speed is subject to significant interannual variability. This feature is supported by M2 internal tides observed using multisatellite altimeter data in 2005 (MultiSat2005) and Argo measured upper ocean temperature profiles. MultiSat20yr is used to correct M2 internal tides in the CryoSat‐2 data. Significant and efficient variance reduction suggests that MultiSat20yr is a reliable internal tide model. A phase‐adjusted MultiSat20yr is built to account for the interannual variations, and it works better in internal tide correction.

Assessment of SARAL-ALTIKA Tidal Corrections in the Coastal Oceans Around India

ABSTRACTThe present tidal correction of sea level records of Satellite with ARgoes and ALtimeter (SARAL) is based on the finite element solution (FES) of global tide model FES2012 tidal solution. In this study, we examined the validity of the tidal corrections in the coastal oceans around India using tide gauge measurements and a regional tidal model. Our regional model is based on the barotropic version of the Princeton Ocean Model that is forced by the time-varying tidal levels at the open ocean end based on the global FES99 tidal solution. Tide charts prepared from the simulated tidal levels are very similar to the FES tidal solutions. Comparison with the tide gauge measurement shows close agreement with the regional tidal solutions. On the other hand, the agreement with the FES tide models differ significantly in the Gulf of Khambhat and the Gulf of Kutch on the northwest, and in the Hooghly estuary on the northeast continental shelf. However, the agreement is exceptional in other parts of the study domain. These tidal solutions are used in the SARAL-ALTIKA X-track data to assess the FES tidal correction and to draw some inferences associated with the coastal processes. It is revealed that these corrections are reasonably accurate for the coastal oceans around India except the aforementioned converging channels.

Middle and long-term prediction of UT1-UTC based on combination of Gray Model and Autoregressive Integrated Moving Average

UT1-UTC is an important part of the Earth Orientation Parameters (EOP). The high-precision predictions of UT1-UTC play a key role in practical applications of deep space exploration, spacecraft tracking and satellite navigation and positioning. In this paper, a new prediction method with combination of Gray Model (GM(1,1)) and Autoregressive Integrated Moving Average (ARIMA) is developed. The main idea is as following. Firstly, the UT1-UTC data are preprocessed by removing the leap second and Earth’s zonal harmonic tidal to get UT1R-TAI data. Periodic terms are estimated and removed by the least square to get UT2R-TAI. Then the linear terms of UT2R-TAI data are modeled by the GM(1,1), and the residual terms are modeled by the ARIMA. Finally, the UT2R-TAI prediction can be performed based on the combined model of GM(1,1) and ARIMA, and the UT1-UTC predictions are obtained by adding the corresponding periodic terms, leap second correction and the Earth’s zonal harmonic tidal correction. The results show that the proposed model can be used to predict UT1-UTC effectively with higher middle and long-term (from 32 to 360days) accuracy than those of LS+AR, LS+MAR and WLS+MAR.

Quantitative Behaviour Characteristics Analysis of GPS Buoy in Rip Current Generation

ABSTRACT Song, D.S; Kim, G.Y., and Lee, J.L., 2016. Quantitative behaviour characteristics analysis of GPS buoy in rip current generation. In: Vila-Concejo, A.; Bruce, E.; Kennedy, D.M., and McCarroll, R.J. (eds.), Proceedings of the 14th International Coastal Symposium (Sydney, Australia). Journal of Coastal Research, Special Issue, No. 75, pp. 1242 - 1246. Coconut Creek (Florida), ISSN 0749-0208. GPS buoys have been used to acquire sea level change data, current measurements and other oceanic variables in sea for the purposes of vertical datum determination, tide correction, radar altimeter calibration, ocean environment and marine pollution monitoring. The occurrence of rip currents in the Haeundae beach, which is one of the most famous beaches in South Korea, has been threatening beach-goer security in summer season annually. Therefore, we adopted a GPS buoy system for an experiment which is to investigate rip current velocity; it is sporadic and may quickly upsurge within minutes due to larger arrivi...

Analysis of Sun/Moon gravitational redshift tests with the STE-QUEST space mission

The Space-Time Explorer and Quantum Equivalence principle Space Test (STE-QUEST) space mission will perform tests of the gravitational redshift in the field of the Sun and the Moon to high precision by frequency comparisons of clocks attached to the ground and separated by intercontinental distances. In the absence of Einstein equivalence principle (EP) violation, the redshift is zero up to small tidal corrections, as the Earth is freely falling in the field of the Sun and Moon. Such tests are thus null tests, allowing us to bound possible violations of the EP. Here we analyze the Sun/Moon redshift tests using a generic EP-violating theoretical framework, with clocks minimally modelled as two-level atoms. We present a complete derivation of the redshift (including both general relativity (GR) and non-GR terms) in a realistic experiment such as the one envisaged for STE-QUEST. We point out and correct an error in previous formalisms linked to the atom’s recoil not being properly taken into account.

Influence of ITRS/GCRS implementation for astrodynamics: Coordinate transformations

Converting between the Geocentric Celestial Reference System (GCRS) and International Terrestrial Reference System (ITRS) is necessary for many applications in astrodynamics, such as orbit determination and analyzing geoscience data from satellite missions. The implementation of this frame transformation and the manner in which the Earth orientation parameters (EOPs) are used have a notable impact on station coordinates and satellite positions. After briefly reviewing the various theories and their mathematical description, we investigate the impact of EOP interpolation methods, ocean tide corrections, precession–nutation simplifications, and Julian date handling on the ITRS/GCRS coordinate transformation. Estimates of the impact on position concern a range of altitudes, from the Earth’s surface to geosynchronous orbit (GEO), and apply to a wide array of astrodynamics applications. We demonstrate that EOP interpolation methods and ocean tide corrections impact the ITRS/GCRS transformation between 5cm and 20cm on the surface of the Earth and at the Global Positioning System (GPS) altitude, respectively. We conclude with a summary of recommendations on EOP usage and bias–precession–nutation model implementations for achieving a wide range of transformation accuracies at several altitudes. This comprehensive set of recommendations allows astrodynamicists, flight software engineers, and Earth scientists to make informed decisions when choosing the best implementation for their application, balancing accuracy and computational complexity.

Nonstationary Internal Tides Observed Using Dual-Satellite Altimetry

AbstractDual-satellite crossover data from the Jason-2 and Cryosat-2 altimeter missions are used in a novel approach to quantify stationary and nonstationary tides from time-lagged mean square sea surface height (SSH) differences, computed for lags from 1 to 1440 h (60 days). The approach is made feasible by removing independent estimates of the stationary tide and mesoscale SSH variance, which greatly reduces the sampling error of the SSH statistics. For the semidiurnal tidal band, the stationary tidal variance is approximately 0.73 cm2, and the nonstationary variance is about 0.33 cm2, or 30% of the total. The temporal correlation of the nonstationary tide is examined by complex demodulation and found to be oscillatory with first 0 crossing at 400 h (17 days). Because a significant fraction of the time-variable mesoscale signal is resolved at time scales of roughly 150 h by the present constellation of satellite altimeters, the results suggest that it may be feasible to predict the nonstationary tide from modulations of the resolved mesoscale, thus enhancing the efficacy of tidal corrections for planned wide-swath altimeters such as the Surface Water and Ocean Topography (SWOT) mission.

Corrections for Tidal Residuals Due to Insufficient Representation Using a Single Station in Shallow Water Multibeam Bathymetric Data

Tidal correction is important for shallow water multibeam sonar to ensure vertical accuracy to International Hydrographic Organization Order 1 standards. The number and distribution of tidal control stations have important influences on tidal zoning and reduction. In many cases, tidal residuals will be unavoidable because of tidal representative errors, particularly when using a single tidal station. Tidal residuals cause depth discrepancies in overlapping areas between the two neighboring swaths. They are different from other vertical error sources. For a multibeam survey project, the distance between the tidal control station on the shore and the survey site or the area surveyed in a single day is relatively short. Therefore, the tidal characteristics between them are usually equal. The tidal curve at each bathymetric point in the small area can be recovered by the observed tide at a single station nearby and synchronous multibeam bathymetric data. After other errors have been considered and corrected, the tidal parameters—that is, the time difference of tide, the ratio of tidal ranges, and the direction of tidal wave propagation—can be estimated with the depth discrepancies and the tidal data from a single station using the least squares method. Then, the tidal residuals can be calculated based on the estimated tidal parameters. The quality of final bathymetry can be improved by the corrections as verified by a field test.

The pole tide and its effect on GRACE time‐variable gravity measurements: Implications for estimates of surface mass variations

AbstractGravity Recovery and Climate Experiment (GRACE) provides monthly solutions for the Earth's gravity field in the form of spherical harmonic coefficients. These can be used to infer changes in mass at the Earth's surface. The pole tide (the response of the Earth and oceans to polar motion) causes gravity signals dominated by harmonics of degree 2, order 1. If the pole tide is not removed from GRACE data, it affects the coefficients of those harmonics (C21, S21) and introduces errors when using those coefficients to determine surface mass variations. The pole tide is partially removed by GRACE processing centers before solving for the gravity field. But long‐period pole tide signals are not usually included in the GRACE pole tide correction, and so those signals are still present in the GRACE coefficients. We discuss this issue from the standpoint of somebody who uses the GRACE gravity fields to infer changes in surface mass. We arrive at a recommendation for an optimal GRACE pole tide correction. We describe how to modify the C21, S21 coefficients provided by the processing centers, so that they conform with our recommendation. We discuss the size of the pole tide contributions to C21, S21, compared to those of the direct load‐induced contributions. As an example, we show how an incompletely removed pole tide can impact GRACE results for the trend in ocean mass. We consider the impact of mantle anelasticity on long‐period pole tide corrections and conclude that it is unlikely to affect those corrections by more than 20%.

GravProcess: An easy-to-use MATLAB software to process campaign gravity data and evaluate the associated uncertainties

We present GravProcess, a set of MATLAB routines to process gravity data from complex campaign surveys and calculate the associated gravity field. Data reduction, analysis, and representation are done using the MATLAB Graphical User Interface Tool, which can be installed on most systems and platforms. Data processing is divided into several steps: (1) Integration of gravity data, station location, and gravity line connection input files; (2) Gravity data reduction applying solid-Earth tide and instrumental drift corrections and, depending on the required processing level, air pressure and oceanic tidal corrections; (3) Automatic network adjustment and alignment to absolute base stations; (4) Free air and terrain corrections to calculate gravity values and anomalies, and to estimate the associated errors. The final step is dedicated to post-processing and includes graphical representations of data and an output text file, which can be used by Geographic Information System software. An example of this processing chain applied to a recent survey in northern Morocco is given and compared with previous available results.

Stacking global GPS verticals and horizontals to solve for the fortnightly and monthly body tides: Implications for mantle anelasticity

AbstractThe availability of long‐term position measurements from permanent GPS stations distributed around the Earth makes it feasible to extract small, globally coherent, long‐period geophysical signals from the data. Using 11 years of daily vertical and horizontal positions from over 600 permanent GPS stations worldwide, we solve for the amplitude and phase of the fortnightly and monthly body tides by stacking the surface displacements against spherical harmonics and isolating the fortnightly and monthly signals in the stacks. We use our solutions to help constrain the Earth's anelastic properties, which are not well understood within the tidal frequency band. Our error estimates include the effects of the following: (1) random noise across the fortnightly and monthly tidal bands; (2) fortnightly and monthly ocean tide model errors; (3) errors in the diurnal and semidiurnal ocean tide models that alias into the fortnightly and monthly frequency bands; (4) errors in the solid Earth Green's functions used to compute ocean tidal loading corrections; and (5) leakage from GPS draconitic signals at periods close to the fortnightly and monthly frequencies. The mantle anelasticity coefficients we infer from our solutions are consistent with a ωα frequency dependence of mantle Q with α in the range 0.1–0.3.

Zero drift and solid Earth tide extracted from relative gravimetric data with principal component analysis

Zero drift and solid Earth tide corrections to static relative gravimetric data cannot be ignored. In this paper, a new principal component analysis (PCA) algorithm is presented to extract the zero drift and the solid Earth tide, as signals, from static relative gravimetric data assuming that the components contained in the relative gravimetric data are uncorrelated. Static relative gravity observations from Aug. 15 to Aug. 23, 2014 are used as statistical variables to separate the signal and noise with PCA to obtain desired signals. The results of the linear drift extracted by PCA are consistent with those calculated by the least squares linear fitting, and the differences only reach to 10−2 μGal/day order of magnitude. Furthermore, PCA is used to estimate the solid Earth tide from the relative gravimetric data corrected by the zero drift. The statistical results are consistent with the results derived from the solid Earth tide correction provided by the internal software of the CG-5 gravimeter (SCINTREX Limited Ontario Canada). The statistical results of the differences between the two methods are both less than 8 μGal, and the RMSs for 9 days are all less than 5 μGal.

Predicting Tidal Heights for New Locations Using 25 h of in situ Sea Level Observations plus Reference Site Records: A Complete Tidal Species Modulation with Tidal Constant Corrections

AbstractA hybrid technique for predicting tides for new locations, based on as little as 25 h of concurrent temporary and reference site sea level observations, plus up to a year of reference records, is evaluated using 2-yr South Korean and New Zealand case studies. Comparisons are made between the existing prediction methods of conventional standard harmonic analysis and prediction (CSHAP) and tidal species modulation with tidal constant corrections (TSM+TCC). Building on these approaches, a new procedure is developed to produce a complete tidal species modulation (CTSM) equivalent of CSHAP, with the added inclusion of nodal factors and angles, astronomical arguments, and tidal species tidal constant correction terms (+TCC), to generate results for temporary sites. The CTSM+TCC approach described here overcomes the record length limitations of traditional standard harmonic-based prediction methods, making the technique more useful to diverse coastal and hydrographic researchers.The CTSM+TCC method is refined using yearlong input and comparative data from contrasting hydrographic settings, revealing spring periods, specific months, and conditions devoid of nontidal residual extremes (e.g., storms) as the most appropriate sample periods for collecting temporary site data in order to maximize prediction accuracy. CTSM+TCC represents a viable alternative to tidal prediction methods using multiconstituent inferences, for those wishing to make predictions for new sites based on established conventional tidal prediction software, with the added benefits of efficient input data collection and no need for a decision process regarding multiconstituent inference calculations. CTSM+TCC could, without compromising accuracy, support the spatial and temporal proliferation of tidal predictions across coastal oceans, where fieldwork funds and instruments currently hinder predictions for new locations.

Estimation of Shoreline Change Using High Resolution Images

The development of imaging systems is nowadays established as one of the most powerful and reliable tools for monitoring shoreline changes. Video-based technology is now becoming an increasingly popular method for monitoring beach fundamentally because it can be used to build a database of frequent, long-term and spatially extensive observations of shoreline changes. It covers timescales from seconds to years and spatial scales from meters to kilometers and possible for monitoring beach morphology as well as dominant factors governing evolution in the nearshore area. In this study presents preliminary results on studying seasonal shoreline change in Gwangan beach, Busan, Korea using high resolution image analysis technique with tide correction, error analysis and mapping accuracy. It is necessary to know at least 6 controlled points in UTM system from GPS devices to calculate parameters for image analysis. For the scope of video monitoring, GCP (Ground Control Point) was measured. In this study we have developed a program from relationship between image coordinate and several real point with coordinate and image corresponding to the position of image point to analysis and interpret shoreline changes. After automatic detection the coastal line via the color spectrum, wave dynamics parameters are also determined. From shoreline change as above mentioned, it is easy to determine the daily sand volume changes. The results of research indicate that the monitoring technique on shoreline changes is very significant and it obviously illustrates a good and appropriate tendency and general picture on seasonal changes of shoreline. This study on shoreline change will be use an important role in calibration and verification for numerical model in order to forecast the long-term evolution of coastal changes.

Implementation of Tidal Constituent Interpolation Method for the Israeli Coastline

Many ship-borne geodetic surveys at sea, such as Global Navigation Satellite System (GNSS)-based sea surface height (SSH) observation, acoustic profiling of the bottom, and others, deal with a dynamic topography which undergoes several changes during the survey campaign (e.g., changes in tide, salinity and currents). Those changes affect the measurements and may causes for some variations in the results. There are several methods for tidal variations correction, being the most dominant phenomena, such as tidal zoning, tidal constituent interpolation or ocean tidal models. In this study, we have implemented the tidal constituent interpolation method for the Israeli coastline in order to assess its quality and determine whether it is suitable for use in this particular region. This paper depicts the interpolation method, discusses some difficulties in the implementation for the Israeli coast and presents results from exemplary processing. In addition, we compare the results to those obtained using global and regional tidal models.

Can recreational echosounder-chartplotter systems be used to perform accurate nearshore bathymetric surveys?

This work intends to determine if low-cost surveying techniques based on recreational echosounders can be used to perform nearshore bathymetry for analysing evolution of coastal sectors. For that purpose, two hydrographic surveying techniques were compared, i.e. (1) a real-time kinematic differential global positioning system (RTK-DGPS) synchronised with a single beam echosounder with real-time tidal elevation correction and (2) a low-cost recreational echosounder-chartplotter system using Global Navigation Satellite Systems (GNSS) with real-time European Geostationary Navigation Overlay Service (EGNOS) augmentation services and depth values post-processed using measured sea level. Two bathymetric data sets were obtained, one by each method, for the same area and survey lines at an ebb tidal delta (Tavira Inlet, Ria Formosa Portugal). Vertical differences were determined assuming no morphological variations between surveys. Results showed that depth elevation differences between bathymetric surfaces were of 0.10 ± 0.16 m, slightly higher but within the same order of the error attributable to the used interpolator (0.00 ± 0.11 m, triangular surface fitting). The differences between surveys performed with two different equipment sets and using different methodologies for correcting water elevations are very small both quantitative and qualitatively. Those differences can be diminished by improving the tidal level correction and uncertainties associated to different tidal slopes throughout the survey area. Pitch/roll corrections performed with low-cost GPS receivers would be also a valuable addition to the accuracy and precision of the method. It is then concluded that navigation with EGNOS augmentation services and sounding devices ten times cheaper than combined RTK-DGPS with single beam echosounders allow to measure and monitor accurately the nearshore bathymetry.

AN ASSESSMENT OF VIDEO-BASED BATHYMETRY ESTIMATION IN A MACRO TIDAL ENVIRONMENT

This paper investigates the utility of video systems for estimating coastal bathymetry in a highly energetic and strongly macro-tidal environment using a linear wave theory inversion approach (cBathy). cBathy has been improved recently (Holman, et al. 2013), introducing a non-linear fit procedure of a phase structure over an area around a point of interest and a Kalman filter. cBathy has been extensively tested in micro/meso tidal environments but never in a macro tidal environment. Now the model is put to the test for the first time in these tidal conditions at Porthtowan, Cornwall in the United Kingdom. The combination of the macro-tidal range and energetic waves means that the accuracy of cBathy is compromised. A novel solution for macro tidal areas is presented in this paper where the pixels lose their fixed position and float around based on the corresponding tidal elevation. cBathy and the modified code are subsequently compared to topographical RTK-GPS measurements covering the inter-tidal area during spring tide. Depending on the tide and waves, the accuracy of the depth estimates varies, but during spring tide (6-7 metre tidal range) the results with the tidal correction are improved significantly. A reduction in RMS-error of 25% for the inter-tidal zone can be found in the most extreme cases.