Cross-track Distance Research Articles

The DTU21 global mean sea surface and first evaluation

Abstract. A new mean sea surface (MSS) from the Technical University of Denmark (DTU) called DTU21MSS for referencing sea-level anomalies from satellite altimetry is introduced in this paper, and a suite of evaluations are performed. One of the reasons for updating the existing mean sea surface is the fact that during the last 6 years, nearly 3 times as many data have been made available by space agencies, resulting in more than 15 years of altimetry from long-repeat orbits (LROs) or geodetic missions. This includes the two interleaved long-repeat cycles of Jason-2 with a systematic cross-track distance as low as 4 km. A new processing chain with updated filtering and editing has been implemented for the DTU21MSS. This way, the DTU21MSS has been computed from 2 Hz altimetry in contrast to the former DTU15MSS and DTU18MSS which were computed from 1 Hz altimetry. The new DTU21MSS is computed over the same 20-year averaging time from 1 January 1993 to 31 December 2012 with a well-specified central time of 1 January 2003 and is available from https://doi.org/10.11583/DTU.19383221.v1 (Andersen, 2022). Cryosat-2 employs synthetic aperture radar (SAR) and SAR interferometric (SARin) modes in a large part of the Arctic Ocean due to the presence of sea ice. For SAR- and SARin-mode data we applied the SAMOSA+ physical retracking to make it compatible with the physical retracker used for conventional low-resolution-mode data in other parts of the ocean.

Sustainable navigation approach: Efficacy assessment of the constant radius turn technique in calculating wheel over point using a ship simulator

Changing a ship’s course while manoeuvring on a planned track is challenging as the ship may deviate from its intended course line, particularly when a late course alteration is made. Therefore, a wheel over point must be precisely established as an indicator to initiate course alteration. The study examines the Constant Radius Turn technique’s accuracy, where it is frequently used to calculate and determine the wheel over point. Even though mariners on board the ship have been widely using the technique, there is a lack of evidence in the scholarly literature to verify its effectiveness. In this study, simulations were carried out using a ship simulator to obtain the cross-track distance data for a ship’s manoeuvrability in various navigation regions consist of harbour and confined water, coastal navigation, and open water navigation. The results were then compared to the cross-track limits for each region, which led to the discovery that constant radius turn is an excellent method for identifying wheel over points in coastal and open water navigation, but it is not suitable for use in harbours and confined water areas.

Timeliness of Correcting Baseline Error in Wide-Swath Altimeter Based on Reference Topography Data

The baseline error is a primary error source of the wide-swath altimeter, directly related to the cross-track distance, and can lead to serious height errors at the swath’s outer edge. Cross-calibration using discrepancies with reference data can effectively estimate and correct the baseline error. However, building a reference surface that accurately describes the sea surface at the observation time is necessary to use this cross-correction method. The dynamic ocean environments where the sea surface structure changes over time are challenging. This paper proposes a method for constructing reference topography data (RTD) based on multi-source data products to correct the baseline error of the wide-swath altimeter. The effectiveness of the proposed method is evaluated using HYCOM ocean model data to assess the timeliness of the baseline error correction. The results demonstrate that using RTD at the observation time of the wide-swath altimeter can significantly correct the baseline error. The RMSE of the corrected sea surface height (SSH) in different regions is typically between 1~2 cm, except in some regions with strong currents where the RMSE is approximately 3~4 cm. However, the time interval between the RTD and the observation time of the wide-swath altimeter can affect the accuracy of the baseline error correction. The timeliness of this correction is influenced by the variability of SSH in different regions. In regions with relatively slow SSH changes near the equator, the effective time based on HYRTD and MORTD can basically reach more than 7 days. In regions where the SSH changes more rapidly, the correction result may no longer be reliable in only 1~3 days.

ELECTRONIC CHARTS: DEVELOPMENT OF THE MULTIPURPOSE MODEL FOR CROSS TRACK LIMIT DETERMINATION

According to the requirements of the International Convention for the Safety of Life at Sea (SOLAS-74) vessels must be equipped with Electronic Chart Display and Information System (ECDIS). This equipment is designed to improve safety of navigation and definitely has a number of indisputable advantages over the paper charts navigation. At the same time use of ECDIS requires navigators to have a sufficient level of competency for professional operation. Inadequate setting of safety parameters as well as incorrect interpretation of information from the display can lead to an accident. The determination of cross track limit (XTL) value as one of the route safety parameters in ECDIS is considered in the paper. Some companies navigational procedures are studied; it has been found out that companies have individual requirements regarding XTL value and they can vary. The issue of XTL value determination was recently studied and the authors of the previous research had proposed their own method of XTL calculation. This method is analysed in the paper and it has been concluded that this method is applicable for determining minimum XTL value, however in order to find the optimal value it is necessary to consider ship particulars and characteristics of a specific waterway as well as company requirements for under-keel clearance. The model structure, which integrates this information, is proposed in the paper, and the previously proposed method is used within the model. The model developed by the author is flexible: the input values can be adjusted, which allows to assess the safety of any size ship passage through any waterway. The incorporation of bottom contour information into the model through a piecewise function enables to assess the under-keel clearance for any values of XTL and to determine dangerous values of cross-track distance in particular conditions. The main disadvantage of the model is a necessity to define the piecewise function which adequately corresponds with the actual depth distribution in the waterway analysed, which restricts the application of this model to natural waterways with a difficult terrain of the bottom. It should be noted that with particular input values some «borderline cases» can take place, when the safety of passage is doubtful. In order to solve these uncertainties, the model can be later upgraded by including experts’ opinions with the use of fuzzy logic methods.

Statistical trajectory-distance metric for nautical route clustering analysis using cross-track distance

ABSTRACTThis study presents a novel statistical trajectory-distance metric specialized for nautical route clustering analysis. Based on the dynamic time warping (DTW) metric, one of the most used metrics for trajectory-distance, the statistical trajectory-distance metric was defined by replacing the distance term in DTW with a linear combination of the Jensen–Shannon divergence and Wasserstein distance. Each waypoint from a nautical route was modelled as a discrete and asymmetric binomial normal distribution defined by the cross-track distance (XTD) of the waypoint. The model was then used to compute the statistical distance between waypoints. Nautical route clustering was performed using density-based spatial clustering of applications with noise and the statistical trajectory-distance metric. The nautical route for the clustering analysis, including the XTD information, was extracted from automatic identification system data from the southern sea of the Korean Peninsula. The clustering results were evaluated by comparing them with the results of other popular trajectory-distance metrics. The proposed method was more effective compared to other trajectory-distance when the trajectories pass on both sides of a small island, which is frequent case in coastal route clustering.

Super-Resolving Ocean Dynamics from Space with Computer Vision Algorithms

Surface ocean dynamics play a key role in the Earth system, contributing to regulate its climate and affecting the marine ecosystem functioning. Dynamical processes occur and interact in the upper ocean at multiple scales, down to, or even less than, few kilometres. These scales are not adequately resolved by present observing systems, and, in the last decades, global monitoring of surface currents has been based on the application of geostrophic balance to absolute dynamic topography maps obtained through the statistical interpolation of along-track satellite altimeter data. Due to the cross-track distance and repetitiveness of satellite acquisitions, the effective resolution of interpolated data is limited to several tens of kilometres. At the kilometre scale, sea surface temperature pattern evolution is dominated by advection, providing indirect information on upper ocean currents. Computer vision techniques are perfect candidates to infer this dynamical information from the combination of altimeter data, surface temperature images and observing-system geometry. Here, we exploit one class of image processing techniques, super-resolution, to develop an original neural-network architecture specifically designed to improve absolute dynamic topography reconstruction. Our model is first trained on synthetic observations built from a numerical general-circulation model and then tested on real satellite products. Provided concurrent clear-sky thermal observations are available, it proves able to compensate for altimeter sampling/interpolation limitations by learning from primitive equation data. The algorithm can be adapted to learn directly from future surface topography, and eventual surface currents, high-resolution satellite observations.

A Comparison Study between Advance Transfer Technique and Advance Transfer Mathematical Model Using Bulk Carrier Ship: Cross-track Distance Validation by Percentage Change and Mann Whitney U Test

A Comparison Study between Advance Transfer Technique and Advance Transfer Mathematical Model Using Bulk Carrier Ship: Cross-track Distance Validation by Percentage Change and Mann Whitney U Test

Development of WOP mathematical model for efficient course alteration: LNG tanker manoeuvring analysis and Mann-Whitney U test

Route monitoring is essential for the safety of the ship during navigation. It includes navigating in a straight line and carrying out course alteration. Wheel over point (WOP) is a marking made on the charted courses to warn the navigation officer that course alteration of the ship needs to be initiated to avoid overshooting the planned track. Advance transfer technique (ATT) is one of the methods to identify WOP. Apart from presenting a practical review on ATT, this study also identifies two research gaps with regards to the technique. To fill in the research gaps found, an improved advance transfer mathematical model (ATMM) is developed in this study by restructuring the usage of the ship's turning circle. A manoeuvring analysis is then carried out in this study using a ship simulator to collect the data produced by the ATMM and ATT. The data, specifically the cross-track distance (XTD) reduction, are observed and further verified via the Mann Whitney U test using IBM SPSS. The ATMM has resulted in a better track keeping function compared to the ATT. The ATMM can be used as an algorithm in the integrated bridge navigation system to help the navigation officer in making a better course alteration.

Development of WOP Mathematical Model for Optimum Track-Keeping. A Ship Simulation Study Using VLCC, Focusing on Hard Over Rudder Turning Circle with Three Stages of Validation Analysis

Abstract Navigational safety necessitates careful route monitoring, which includes staying on the planned course. For a ship to achieve effective route monitoring while changing course, a wheel over point (WOP) must be precisely calculated and marked on a charted course. The reason is to warn the watchkeeping officer that the ship must make a course alteration to prevent overshooting the intended route. One of the techniques for appraising the WOP is the advance transfer technique (ATT). During a practical review by means of an electronic and paper chart work exercise of the ATT, this study discovered two research gaps related to the technique. Following that, this study created an improved advance transfer mathematical model (ATMM) by restructuring the use of the ship’s turning circle to overcome the limitations discovered. To validate the improvement of the ATMM over the ATT, data were collected by evaluating both methods using a ship simulator and performing a manoeuvring analysis. The data, specifically the reduction in the cross-track distance (XTD), was validated in three verification stages: compliance with XTL, percentage change, and Mann‒Whitney U test using IBM SPSS. In comparison to the ATT, the ATMM produces better results in terms of the course-keeping capability and it can be implemented as an algorithm in an integrated bridge navigation system for autonomous ship navigation safety.

Wheel over point mathematical model

This research proposes an improved mathematical model which can be used to calculate wheel over point (WOP) for a ship's route optimisation. WOP is a marking made on the charted course to demonstrate where the ship must initiate the course alteration to guarantee that it follows the route. The advance transfer technique (ATT) was used to determine WOP. Through practical exercise, two gaps were identified in ATT. From there, an improved mathematical model, namely ATMM, were developed. A preliminary manoeuvring analysis was then carried out in this study using a ship simulator for ATMM and the existing ATT. Then, the cross-track distance produced by both methods were compared to verify the difference. It was found that the ATMM produced better result in maintaining a ship on its course. This research's mathematical model is expected to be used onboard ship and used in the Electronic Chart Display and Information System to aid navigator in making more effective course alteration.

Fuel-Efficient Cross-Track Distance Establishment in Satellite Formations

Satellite formation establishment may consume considerable fuel if cross-track distance (CTD) is a mission requirement. This work proposes a strategy for significantly reducing the required fuel. Instead of direct out-of-plane maneuvers, it is suggested to use in-plane maneuvers, while using the nodal precession caused by the perturbation. The CTD dynamics are analyzed, and representative formation geometries are considered. Analytical expressions for the CTD and related establishment timing are derived for the case of impulsive thrust. For most cases, the expected CTD establishment duration is reasonable, and the fuel saving with the -assisted CTD establishment strategy is considerable. For the case of -assisted CTD establishment with continuous thrust, optimal control methods are used. The proposed strategy is proven to be optimal for two cases: limited and unlimited thrust magnitude. Finally, the cases of -assisted CTD establishment with impulsive and with continuous thrust are compared. It is shown that continuous thrust is preferable in terms of fuel, for similar CTD establishment durations.

The second-order effect of Earth\u2019s rotation on Cryosat-2 fully focused SAR processing

We investigated the sensitivity of fully focused SAR (FF-SAR) processing of Cryosat-2 altimeter data to Earth rotation. Earth’s rotation causes scatterers at varying cross-track locations to have a different relative velocity with respect to the satellite. This second-order effect of Earth rotation on the phase is currently not corrected for in FF-SAR processing of altimetry data. The difference is largest near the poles, where the satellite flies parallel to the equator. Not correcting for the second-order effect yields a parabolic shape in the counter-rotated phase, which increases with the cross-track distance. Its effect is, however, limited by the time-in-view of the scatterer, which is shorter at the edge of the altimeter footprint, and therefore destructive interference will not occur when using Cryosat-2 data. For Cryosat-2, the only expected effect is a reduction in power and along-track resolution in the waveform tail and in the grating lobes. If the FF-SAR processor focuses on one point, and there is a bright scatterer at another, then there is a residual parabolic phase, whose sign and shape depend on the cross-track distance and whether the signal is left or right of the chosen focal point. In theory, if the viewed scene only has few bright coherent scatterers, then it might be possible to determine the cross-track position of each. In practice, however, natural targets are rarely coherent over the integration time.

Gender Differences in Eating Disorder Risk among NCAA Division I Cross Country and Track Student-Athletes.

Purpose This study compared gender differences in eating disorder risk among NCAA Division I cross country and track distance running student-athletes. Methods Six hundred thirty-eight male and female student-athletes competing at distances of 800m or greater completed the Eating Disorder Screen for Primary Care (ESP). Scores on the ESP were used as the risk of eating disorders. Results Females screened positive at higher rates for risk of eating disorders than males on the ESP at a cutoff of 2 (sensitivity 90-100%, specificity 71%) with rates of 45.95% ± 3.03 and 13.66% ± 1.80, respectively. Females were also screened positive at higher rates than males at a stricter cutoff of 3 (sensitivity 81%, specificity 92%), with rates of 21.69% ± 2.50 compared to 4.64% ± 1.10, respectively. Conclusion This study highlights that, among distance runners, both males and females are at risk of eating disorders, with females being at higher risk. It also emphasizes the need for screening for risk of eating disorders in this population.

Extreme values of relative distances for spacecraft in elliptic displaced orbits

This paper provides a framework to obtain a semi-analytical approximation of extreme values of relative distances between two spacecraft that cover elliptic displaced orbits. The relative motion is described in the rotating reference frame of the chief spacecraft and is parameterized with a new set of displaced orbital elements. The extreme values of the radial, along-track and cross-track distance are analytically evaluated (as roots of suitable algebraic equations) both for quasi-periodic orbits in the incommensurable case, and for periodic orbits in the 1:1 commensurable case. In particular, in the 1:1 commensurable case a Fourier series expansion is used to obtain a time-explicit expression of the relative motion. Finally, some illustrative examples are presented to validate the correctness of the proposed method.

Global representation of tropical cyclone-induced short-term ocean thermal changes using Argo data

Abstract. Argo floats are used to examine tropical cyclone (TC) induced ocean thermal changes on the global scale by comparing temperature profiles before and after TC passage. We present a footprint method that analyzes cross-track thermal responses along all storm tracks during the period 2004–2012. We combine the results into composite representations of the vertical structure of the average thermal response for two different categories: tropical storms/tropical depressions (TS/TD) and hurricanes. The two footprint composites are functions of three variables: cross-track distance, water depth and time relative to TC passage. We find that this footprint strategy captures the major features of the upper-ocean thermal response to TCs on timescales up to 20 days when compared against previous case study results using in situ measurements. On the global scale, TCs are responsible for 1.87 PW (11.05 W m−2) of heat transfer annually from the global ocean to the atmosphere during storm passage (0–3 days). Of this total, 1.05 ± 0.20 PW (4.80 ± 0.85 W m−2) is caused by TS/TD and 0.82 ± 0.21 PW (6.25 ± 1.5 W m−2) is caused by hurricanes. Our findings indicate that ocean heat loss by TCs may be a substantial missing piece of the global ocean heat budget. Changes in ocean heat content (OHC) after storm passage are estimated by analyzing the temperature anomalies during wake recovery following storm events (4–20 days after storm passage) relative to pre-storm conditions. Results indicate the global ocean experiences a 0.75 ± 0.25 PW (5.98 ± 2.1 W m−2) heat gain annually for hurricanes. In contrast, under TS/TD conditions, the ocean experiences 0.41 ± 0.21 PW (1.90 ± 0.96 W m−2) ocean heat loss, suggesting the overall oceanic thermal response is particularly sensitive to the intensity of the event. The ocean heat uptake caused by all storms during the restorative stage is 0.34 PW.

Results of the TanDEM-X Baseline Calibration

The TanDEM-X mission based on two satellites provides a radar interferometer in space with the goal to derive a global Digital Elevation Model (DEM) with never achieved quality for a global coverage: a global DEM with a relative height accuracy of 2 m and 10 m absolute. In order to achieve this mission goal, the radial and cross-track distance between both satellites, the so called baseline has to be known with high accuracy. Only then, systematic baseline errors can be detected and compensated for, i.e., an accurate calibration of the global DEM can be ensured. The paper describes the procedure and the results of calibrating the baseline, verifying the outstanding accuracy of this calibration procedure.

Evaluation of Aerial Remote Sensing Techniques for Vegetation Management in Power-Line Corridors

This paper presents an evaluation of airborne sensors for use in vegetation management in power-line corridors. Three integral stages in the management process are addressed, including the detection of trees, relative positioning with respect to the nearest power line, and vegetation height estimation. Image data, including multispectral and high resolution, are analyzed along with LiDAR data captured from fixed-wing aircraft. Ground truth data are then used to establish the accuracy and reliability of each sensor, thus providing a quantitative comparison of sensor options. Tree detection was achieved through crown delineation using a pulse-coupled neural network and morphologic reconstruction applied to multispectral imagery. Through testing, it was shown to achieve a detection rate of 96%, while the accuracy in segmenting groups of trees and single trees correctly was shown to be 75%. Relative positioning using LiDAR achieved root-mean-square-error (rmse) values of 1.4 and 2.1 m for cross-track distance and along-track position, respectively, while direct georeferencing achieved rmse of 3.1 m in both instances. The estimation of pole and tree heights measured with LiDAR had rmse values of 0.4 and 0.9 m, respectively, while stereo matching achieved 1.5 and 2.9 m. Overall, a small number of poles were missed with detection rates of 98% and 95% for LiDAR and stereo matching.

A Neural Network Technique for Improving the Accuracy of Scatterometer Winds in Rainy Conditions

We exhibit a technique for improving wind accuracy in Ku-band ocean wind scatterometers in the presence of rain. The technique is autonomous in that it only makes use of measurements made by the scatterometer itself, so that no colocation of an external data set (e.g., rain radiometers) is required to perform the correction. The only inputs to the technique are the normalized radar cross-section measurements for each wind vector cell, the cross-track distance of the cell as a proxy for measurement geometry, and the nominal retrieved wind vector for the cell without rain correction. This last input is used to avoid modifying winds not contaminated by rain. The technique was applied to QuikSCAT data for the month of January 2008, resulting in a marked improvement to rainy data. For data that were determined to be rain contaminated by the Jet Propulsion Laboratory rain flag, the rms speed error with respect to National Data Buoy Center buoy winds improved from 8.9 to 3.5 m/s for colocations within 25 km. The rms speed error in rain also improved when compared with the European Centre Medium-Range Weather Forecast winds from 7 to 3 m/s. Data that were not flagged as rain contaminated were not significantly changed, despite the fact that the technique does not make use of the rain flag. The technique was able to distinguish between rain-contaminated wind cells and rain-free wind cells and to substantially improve the wind speed accuracy of the former using QuikSCAT data alone without recourse to any external information about the extent of the rain.

Numerical investigation of an oceanic resonant regime induced by hurricane winds

The oceanic mixed layer (OML) response to an idealized hurricane with different propagation speeds is investigated using a two-layer reduced gravity ocean model. First, the model performances are examined with respect to available observations relative to Hurricane Frances (2004). Then, 11 idealized simulations are performed with a Holland (Mon Weather Rev 108(8):1212–1218, 1980) symmetric wind profile as surface forcing with storm propagation speeds ranging from 2 to 12 m s−1. By varying this parameter, the phasing between atmospheric and oceanic scales is modified. Consequently, it leads to different momentum exchanges between the hurricane and the OML and to various oceanic responses. The present study determines how OML momentum and heat budgets depend on this parameter. The kinetic energy flux due to surface wind stress is found to strongly depend on the propagation speed and on the cross-track distance from the hurricane center. A resonant regime between surface winds and near-inertial currents is clearly identified. This regime maximizes locally the energy flux into the OML. For fast-moving hurricanes (>6 m s−1), the ratio of kinetic energy converted into turbulence depends only on the wind stress energy input. For slow-moving hurricanes (<6 m s−1), the upwelling induced by current divergence enhances this conversion by shallowing the OML depth. Regarding the thermodynamic response, two regimes are identified with respect to the propagation speed. For slow-moving hurricanes, the upwelling combined with a sharp temperature gradient at the OML base formed in the leading part of the storm maximizes the oceanic heat loss. For fast propagation speeds, the resonance mechanism sets up the cold wake on the right side of the hurricane track. These results suggest that the propagation speed is a parameter as important as the surface wind speed to accurately describe the oceanic response to a moving hurricane.

Great Circle v Rhumb Line Cross Track Distance at Mid-Longitude – The Final Answer

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