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24 pages, 6776 KiB  
Article
A 3D Numerical Study on the Tidal Asymmetry, Residual Circulation and Saline Intrusion in the Gironde Estuary (France)
by Damien Pham Van Bang, Ngoc Vinh Phan, Sylvain Guillou and Kim Dan Nguyen
Water 2023, 15(23), 4042; https://doi.org/10.3390/w15234042 - 22 Nov 2023
Cited by 2 | Viewed by 1283
Abstract
A full 3D numerical model is used for studying tidal asymmetry, estuarine circulation, and saline intrusion in the Gironde estuary. The model is calibrated and verified using the data measured during two field surveys in the Gironde estuary. Harmonic analysis of numerical results [...] Read more.
A full 3D numerical model is used for studying tidal asymmetry, estuarine circulation, and saline intrusion in the Gironde estuary. The model is calibrated and verified using the data measured during two field surveys in the Gironde estuary. Harmonic analysis of numerical results is proposed to understand how the superposition of M2, M4 and M6 components generate a complex estuarine circulation and salinity intrusion in the Gironde estuary. The numerical results show that the M6 component plays a significant role as important as the M4 one in modifying the nature of tidal asymmetry, especially in the Gironde upper estuary. In this case, the use of the phase lag between M2 and M4, neglecting M6, to predict the tidal asymmetry nature could produce errors. The effect of asymmetrical tides on saline intrusion and residual circulation is specifically discussed here. Full article
(This article belongs to the Special Issue Estuarine and Coastal Hydrodynamics)
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Figure 1

Figure 1
<p>Location map of the Gironde estuary (France) showing the sampling section (PK: kilometric point, downstream from Bordeaux, [<a href="#B9-water-15-04042" class="html-bibr">9</a>]).</p>
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<p>Bathymetry of the Gironde estuary (the sandbanks are reported in the figure).</p>
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<p>Location of the measure stations in the field surveys from May 1975 (for calibration) and May 1974 (for verification).</p>
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<p>Comparison between computed and measured velocity on surface and on bottom for calibration (mean tide, yearly average discharge ≈ 700 m<sup>3</sup>·s<sup>−1</sup>).</p>
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<p>Comparison between computed and measured values of salinity on surface and on bottom for calibration (mean tide, yearly average discharge ≈ 700 m<sup>3</sup>·s<sup>−1</sup>).</p>
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<p>Comparison between the computed and measured values of velocity on surface and on bottom for verification (spring tide, yearly averaged river discharge ≈ 700 m<sup>3</sup>·s<sup>−1</sup>).</p>
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<p>Comparison between the computed and measured salinity (ppt) on surface and on bottom for verification (spring tide, yearly averaged river discharge ≈ 700 m<sup>3</sup>·s<sup>−1</sup>).</p>
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<p>Isocontours of tidal current amplitude ratios V<sub>M6</sub>/V<sub>M2</sub> (<b>upper</b>) and V<sub>M4</sub>/V<sub>M2</sub> (<b>lower</b>) computed at mid-depth for a yearly averaged river discharge (≈700 m<sup>3</sup>·s<sup>−1</sup>) and for the mean tide in the Gironde estuary.</p>
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<p>Water level-velocity diagrams at the mid-depth at station Richard, Lamena, Pauillac and Marquis for a yearly averaged river discharge (≈700 m<sup>3</sup>·s<sup>−1</sup>) and the mean tide.</p>
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<p>Isocontours of phase lag (<b>a</b>) Δθ<sub>M4</sub> = (2θ<sub>M2</sub> − θ<sub>M4</sub>) and (<b>b</b>) Δθ<sub>M6</sub> = (3θ<sub>M2</sub> − θ<sub>M6</sub>) in the Gironde estuary, computed at mid-depth for a yearly averaged discharge (≈700 m<sup>3</sup>·s<sup>−1</sup>) and for the mean tide. F denotes flood-dominant zones, and E denotes ebb-dominant ones.</p>
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<p>Three-dimensional distribution of turbulent kinetic energy at LW+3 (<b>a</b>) and HW+3 (<b>b</b>) in the navigation channel (discharge ≈ 700 m<sup>3</sup>·s<sup>−1</sup>, mean tide).</p>
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<p>Isohaline maps for different layers (on surface (<b>a</b>), mid-depth (<b>b</b>) and on bottom (<b>c</b>)) at LW, LW+3 (flood tide), HW and HW+3 (ebb tide) (river discharge ≈ 700 m<sup>3</sup>·s<sup>−1</sup>, mean tide).</p>
Full article ">Figure 12 Cont.
<p>Isohaline maps for different layers (on surface (<b>a</b>), mid-depth (<b>b</b>) and on bottom (<b>c</b>)) at LW, LW+3 (flood tide), HW and HW+3 (ebb tide) (river discharge ≈ 700 m<sup>3</sup>·s<sup>−1</sup>, mean tide).</p>
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<p>Three-dimensional distribution of salinity at LW (<b>a</b>), LW+3 (<b>b</b>), HW (<b>c</b>) and HW+3 (<b>d</b>) in the Gironde estuary (river discharge ≈ 700 m<sup>3</sup>·s<sup>−1</sup>, mean tide).</p>
Full article ">Figure 13 Cont.
<p>Three-dimensional distribution of salinity at LW (<b>a</b>), LW+3 (<b>b</b>), HW (<b>c</b>) and HW+3 (<b>d</b>) in the Gironde estuary (river discharge ≈ 700 m<sup>3</sup>·s<sup>−1</sup>, mean tide).</p>
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<p>Five-day Eulerian residual currents on surface (<b>a</b>), at mid-depth (<b>b</b>) and on bottom (<b>c</b>) for a yearly averaged river discharge ≈700 m<sup>3</sup>·s<sup>−1</sup> and mean tide under the effect of sandbanks: (A) Talais, (B) Mets, (C) Trompeloup1 and Trompeloup2. Colour scale shows the intensity in m·s<sup>−1</sup> of residual currents.</p>
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22 pages, 6098 KiB  
Article
Development of a Novel Control Scheme to Achieve the Minimum Unbalance Factor and Real Power Fluctuations under Asymmetrical Faults
by Muhammad Abubakar, Herwig Renner and Robert Schürhuber
Energies 2023, 16(22), 7511; https://doi.org/10.3390/en16227511 - 9 Nov 2023
Cited by 1 | Viewed by 1134
Abstract
The increasing share of converter-based renewable energy sources in the power system has forced the system operators to demand voltage support from the converters in case of faults. In the case of symmetric faults, all the phases have equal voltage support, but in [...] Read more.
The increasing share of converter-based renewable energy sources in the power system has forced the system operators to demand voltage support from the converters in case of faults. In the case of symmetric faults, all the phases have equal voltage support, but in the case of asymmetric faults, selective voltage support is required. The grid codes define the voltage support required in the case of symmetric/asymmetric faults, which is the reactive current injection in the respective sequence proportional to its voltage dip, but studies confirm that it does not result in a minimum unbalance factor in the case of asymmetric faults. The unbalance factor is an indication of the level of imbalance voltage among the phases. Moreover, it also results in fluctuated active power injection in the case of asymmetric faults, which causes dc link voltage fluctuations, and the power reversal may also occur due to such fluctuations, which leads to higher protection costs for the dc link. In order to (1) enhance the uniformity of voltage among different phases in the case of asymmetric faults and (2) minimize the real power fluctuations in such conditions, a novel control scheme is presented in this paper. It optimally distributes the negative sequence current phasor into its active and reactive components to achieve the minimum voltage unbalance factor. It also confirms the minimum real power fluctuations by adjusting the positive and negative sequence current phasors. The proposed scheme also ensures the current limit of the converter. The proposed scheme is developed in Matlab/Simulink and tested under different faulty conditions. The results confirm the better performance of the proposed scheme against the grid code recommendation under different faulty conditions. Full article
(This article belongs to the Section A1: Smart Grids and Microgrids)
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Figure 1
<p>LVRT capability curve.</p>
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<p>Vector representation of unbalanced system and its positive and negative sequence systems.</p>
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<p>VDEAR-N 4110 requirement under asymmetrical faults.</p>
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<p>Layout of test setup, superscript ‘*’ indicates reference quantities.</p>
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<p>Layout of control scheme to provide selective voltage support.</p>
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<p>Layout of SOGI.</p>
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<p>Layout for current limiter.</p>
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<p>Estimation of optimal angle for negative sequence current injection.</p>
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<p>Control layout for estimating the optimum angle for negative sequence current injection.</p>
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<p>Detailed layout of reference current generation block.</p>
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<p>Test setup along with OAI&amp;MRPF control scheme in Simulink.</p>
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<p>Response of different control strategies for SLG fault (<b>a</b>) phase to ground voltage at POC, (<b>b</b>) converter’s line currents, (<b>c</b>) UF and real power output, and (<b>d</b>) negative sequence current angle.</p>
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<p>Response of different control strategies for L-L fault (<b>a</b>) phase to ground voltage at POC, (<b>b</b>) converter’s line currents, (<b>c</b>) UF and real power output, and (<b>d</b>) negative sequence current angle.</p>
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<p>Response of different control strategies for DLG fault (<b>a</b>) phase to ground voltage at POC, (<b>b</b>) converter’s line currents, (<b>c</b>) UF and real power output, and (<b>d</b>) negative sequence current angle.</p>
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17 pages, 3678 KiB  
Article
Simulation of Storm Surge Heights Based on Reconstructed Historical Typhoon Best Tracks Using Expanded Wind Field Information
by Seung-Won Suh
Atmosphere 2023, 14(9), 1461; https://doi.org/10.3390/atmos14091461 - 20 Sep 2023
Viewed by 1577
Abstract
A numerical model integrating tides, waves, and surges can accurately evaluate the surge height (SH) risks of tropical cyclones. Furthermore, incorporating the external forces exerted by the storm’s wind field can help to accurately reproduce the SH. However, the lack of long-term typhoon [...] Read more.
A numerical model integrating tides, waves, and surges can accurately evaluate the surge height (SH) risks of tropical cyclones. Furthermore, incorporating the external forces exerted by the storm’s wind field can help to accurately reproduce the SH. However, the lack of long-term typhoon best track (BT) data degrades the SH evaluations of past events. Moreover, archived BT data (BTD) for older typhoons contain less information than recent typhoon BTD. Thus, herein, the wind field structure, specifically its relationship with the central air pressure, maximum wind speed, and wind radius, are augmented. Wind formulae are formulated with empirically adjusted radii and the maximum gradient wind speed is correlated with the central pressure. Furthermore, the process is expanded to four quadrants through regression analyses using historical asymmetric typhoon advisory data. The final old typhoon BTs are converted to a pseudo automated tropical cyclone forecasting format for consistency. Validation tests of the SH employing recent BT and reconstructed BT (rBT) indicate the importance of the nonlinear interactions of tides, waves, and surges for the macrotidal west and microtidal south coasts of Korea. The expanded wind fields—rBT—based on the historical old BT successfully assess the return periods of the SH. The proposed process effectively increases typhoon population data by incorporating actual storm tracks. Full article
(This article belongs to the Special Issue Sea-Level Rise and Associated Potential Storm Surge Vulnerability)
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Figure 1
<p>Typhoon tracks in the northwestern Pacific are represented by gray lines, whereas those affecting Korea are indicated in red. These tracks are derived from (<b>a</b>) historical data by Regional Specialized Meteorological Center (RSMC) from 1952 and (<b>b</b>) synthetic data by TCRM. The dark blue polygon shows the percentage of typhoon tracks as shown in (<b>c</b>) that entered the Yellow Sea and East China Sea and impacted the west and south coast of Korea. In the historical data (<b>a</b>), these tracks frequently resurface; however, in the synthetic data (<b>b</b>), such tracks are rare and when present, they exhibit a different direction of approach.</p>
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<p>Central pressure distribution with respect to latitude is illustrated using gray dots, representing historical typhoon tracks by RSMC. Conversely, the red dots depict synthetic tracks generated by TCRM.</p>
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<p>Empirical relationships between <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>c</mi> </mrow> </msub> </mrow> </semantics></math> for the historical typhoons [<a href="#B15-atmosphere-14-01461" class="html-bibr">15</a>,<a href="#B25-atmosphere-14-01461" class="html-bibr">25</a>].</p>
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<p>Simulation cases based on synthetically generated wind fields.</p>
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<p>Comparisons of SH for typhoons Bolaven in 2012 and Chaba in 2016 based on several wind structures using BT, rBT with or without tidal conditions at Incheon, Gunsan, Yeosu, and Busan tidal stations.</p>
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17 pages, 5629 KiB  
Article
Implications of a Large River Discharge on the Dynamics of a Tide-Dominated Amazonian Estuary
by Ariane M. M. Silva, Hannah E. Glover, Mariah E. Josten, Vando J. C. Gomes, Andrea S. Ogston and Nils E. Asp
Water 2023, 15(5), 849; https://doi.org/10.3390/w15050849 - 22 Feb 2023
Cited by 3 | Viewed by 3163
Abstract
Estuaries along the Amazonian coast are subjected to both a macrotidal regime and seasonally high fluvial discharge, both of which generate complex circulation. Furthermore, the Amazon River Plume (ARP) influences coastal circulation and suspended sediment concentrations (SSCs). The Gurupi estuary, located south of [...] Read more.
Estuaries along the Amazonian coast are subjected to both a macrotidal regime and seasonally high fluvial discharge, both of which generate complex circulation. Furthermore, the Amazon River Plume (ARP) influences coastal circulation and suspended sediment concentrations (SSCs). The Gurupi estuary, located south of the mouth of the Amazon River, is relatively unstudied. This study evaluates how the Gurupi estuary dynamics respond to seasonal discharge and the varying influence of the ARP using cross-sectional and longitudinal surveys of morphology, hydrodynamics, and sediment transport. The Gurupi was classified as a tide-dominated estuary based on morphology and mean hydrodynamic conditions. However, the estuary was only partially mixed during both the wet and dry seasons. The tides propagated asymmetrically and hypersynchronously, with flood dominance during the dry season and ebb dominance during the rainy season. Seasonal variations of the ARP did not significantly affect the hydrodynamic structure of the lower Gurupi estuary. Estuarine turbidity maxima (ETM) were observed in both seasons, although the increase in fluvial discharge during the wet season attenuated and shifted the ETM seaward. Little sediment was delivered to the estuary by the river, and the SSCs were higher at the mouth in both seasons. Sediment was strongly imported during the dry season by tidal asymmetry. The morphology, hydrodynamics, and sediment dynamics all highlight the importance of considering both fluvial discharge and coastal influences on estuaries along the Amazon coast. Full article
(This article belongs to the Special Issue Hydrodynamics in Coastal Areas)
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<p>The location of (<b>a</b>) South America, (<b>b</b>) the Amazon Coastal Zone, and (<b>c</b>) the Gurupi River estuary, with sampling points.</p>
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<p>Bathymetric profiles showing the morphology of the Gurupi estuary. The red lines show the location of the transect. The green line shows the variation of the cross-sectional area along the estuary. Seasonal bottom morphology changes are not considered.</p>
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<p>Longitudinal variation of salinity and SSC during the rainy (<b>a</b>–<b>c</b>) and dry (<b>d</b>–<b>f</b>) seasons (modified from [<a href="#B18-water-15-00849" class="html-bibr">18</a>]). The dashed line represents the location of the cross-sectional profile with ADCP. Notice that the location of the cross-section profile is the same for both seasons.</p>
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<p>Longitudinal variation of salinity and SSC during the rainy (<b>a</b>–<b>c</b>) and dry (<b>d</b>–<b>f</b>) seasons (modified from [<a href="#B18-water-15-00849" class="html-bibr">18</a>]). The dashed line represents the location of the cross-sectional profile with ADCP. Notice that the location of the cross-section profile is the same for both seasons.</p>
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<p>Hydrodynamics in the cross-sectional area comparing the discharge (red line) and the current velocity (blue line), during the rainy (<b>a</b>) and dry (<b>b</b>) seasons. The black line shows the water level variation.</p>
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<p>Hydrodynamics in the cross-sectional area comparing the salinity and SSC data during the rainy (<b>a</b>) and dry (<b>b</b>) seasons. The blue line shows the salinity level at the water surface (solid line) and bottom (dashed line). The red line shows the SSC data at the water surface (solid line) and at the bottom (dashed line).</p>
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<p>Water (blue line) and sediment (red line) fluxes for the Gurupi estuary during the rainy season (<b>a</b>) and dry season (<b>b</b>).</p>
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<p>Sediment flux decomposition for Gurupi estuary during the rainy (<b>a</b>) and dry (<b>b</b>) seasons. The first column (black) represents the total sediment flux (F). <span class="html-italic">F<sub>R</sub></span>, <span class="html-italic">F<sub>E</sub></span>, and <span class="html-italic">F<sub>T</sub></span> represent river flux, estuarine exchange, and tidal residual flux, respectively.</p>
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<p>Water level oscillation along the Gurupi estuary. Panels (<b>a</b>,<b>b</b>) show the oscillation during rainy and dry seasons, respectively. Panels (<b>c</b>,<b>d</b>) show the longitudinal variation of tidal range and tidal phase duration during rainy and dry seasons.</p>
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<p>The Gurupi estuary in estuarine parameter space (diagram following the classification of [<a href="#B15-water-15-00849" class="html-bibr">15</a>]). The blue point represents the rainy season and the red point represents the dry season.</p>
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<p>Correlation of relative tidal prism and fluvial discharge of the Gurupi estuary based on the seasonal variations of fluvial discharge, in comparison to the Caeté and Urumajó estuaries (data from [<a href="#B18-water-15-00849" class="html-bibr">18</a>]). The red circles represent the dry season, the blue circles represent the rainy season and the black circles represent the mean river discharge values. River discharge is represented in a logarithmic scale.</p>
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17 pages, 6613 KiB  
Article
Applicability Study of a Global Numerical Weather Prediction Model MPAS to Storm Surges and Waves in the South Coast of Korea
by Jin-Hee Yuk, Ji-Sun Kang and Hunjoo Myung
Atmosphere 2022, 13(4), 591; https://doi.org/10.3390/atmos13040591 - 6 Apr 2022
Cited by 5 | Viewed by 2485
Abstract
The south coast of Korea is vulnerable to coastal disasters, such as storm surges, high waves, wave overtopping, and coastal flooding caused by typhoons. It is imperative to predict such disastrous events accurately in advance, which requires accurate meteorological forcing for coastal ocean [...] Read more.
The south coast of Korea is vulnerable to coastal disasters, such as storm surges, high waves, wave overtopping, and coastal flooding caused by typhoons. It is imperative to predict such disastrous events accurately in advance, which requires accurate meteorological forcing for coastal ocean modeling. In this study, to acquire accurate meteorological data as important forcing variables for the prediction of storm surges and waves, we examined the forecast performance and applicability of a next-generation global weather/climate prediction model, the Model for Prediction Across Scales (MPAS). We compared the modeled surface pressure and wind with observations on the south coast of Korea for three typhoons that damaged Korea in 2020—Bavi, Maysak, and Haishen—and investigated the accuracy of these observations with the MPAS prediction. Those meteorological forcing variables were then used in the tightly coupled tide-surge-wave model, Advanced CIRCulation (ADCIRC) and the Simulating Waves Nearshore (SWAN) for the simulation of a typhoon-induced storm surge and wave. We also performed the hindcast of the wave and storm surges using a parametric tropical cyclone model, the best-track-based Generalized Asymmetric Holland Model (GAHM) embedded in ADCIRC+SWAN, to better understand the forecast performance and applicability of MPAS. We compared the forecast results of the typhoon-induced wave and storm surges with their hindcast in terms of the time-series and statistical indices for both significant wave height and storm surge height and found that wave and storm surge prediction forced by MPAS forecast provides a comparable accuracy with the hindcast. Comparable results of MPAS forcing with that of hindcast using best track information are encouraging because ADCIRC+SWAN forced by MPAS forecast with an at most four-day lead time still provides a reasonable prediction of wave and storm surges. Full article
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<p>Typhoon tracks of Bavi, Maysak, and Haishen and the locations of wave observation buoys (blue stars). Here, time information of tracks is formatted as date/hour in UTC.</p>
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<p>ADCIRC+SWAN grids: (<b>a</b>) model domain area and grids; (<b>b</b>) tide observation stations marked with black circles.</p>
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<p>MPAS meshes used in this study: (<b>a</b>) global view of variable resolution (60–15 km), where the gray zone over East Asia and the northeast Pacific region has a finer resolution of 15 km; (<b>b</b>) high resolution meshes over Korea where there are 17,129 cells within the plot; (<b>c</b>) coarse resolution meshes over Florida where there are only 1309 cells in the plot; (<b>d</b>) transient resolution meshes over northern Australia where there are 2925 cells in the plot. Shadings of (<b>b</b>–<b>d</b>) indicate the 36 h forecast of mean sea-level pressure valid at 12UTC on 2 September 2020.</p>
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<p>Ten meter wind (arrows) and surface pressure fields (shadings) simulated by MPAS, and the typhoon best track of JTWC (thick blue lines). (<b>a</b>,<b>c</b>,<b>e</b>) the forecast result from 00 UTC on 1 September for typhoon Maysak, (<b>b</b>,<b>d</b>,<b>f</b>) that from 00 UTC on 5 September for typhoon Haishen.</p>
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<p>Comparison of the MPAS forecast with the observations (Ulsan, Geojedo, and Tongyeong) for the case of Maysak in 2020. (<b>a</b>,<b>d</b>,<b>g</b>) surface pressure (hPa); (<b>b</b>,<b>e</b>,<b>h</b>) wind speed (m/s); (<b>c</b>,<b>f</b>,<b>i</b>) wind direction (degree). Here, the <span class="html-italic">x</span>-axis indicates the time with the date of the simulation period, and the interval of observation data is one hour.</p>
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<p>Comparison of the MPAS forecast with the observations (Ulsan, Geojedo, and Tongyeong) for the case of Haishen in 2020. (<b>a</b>,<b>d</b>,<b>g</b>) surface pressure (hPa); (<b>b</b>,<b>e</b>,<b>h</b>) wind speed (m/s); (<b>c</b>,<b>f</b>,<b>i</b>) wind direction (degree). Here, the <span class="html-italic">x</span>-axis indicates the time with the date of the simulation period, and the interval of observation data is one hour.</p>
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<p>Comparison of the MPAS forecast and the hindcast with the moored buoy observations (Ulsan, Geojedo, and Tongyeong) of significant wave height for typhoons Maysak (<b>a</b>,<b>c</b>,<b>e</b>) and Haishen (<b>b</b>,<b>d</b>,<b>f</b>). Here, the <span class="html-italic">x</span>-axis indicates the time with the date of the simulation period, and the interval of observation data is one hour.</p>
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<p>Comparison of the MPAS forecast and the hindcast with the tide observation stations (Busan, Busan_New_Port, and Gadeokdo) of storm surge height for typhoons Maysak (<b>a</b>,<b>c</b>,<b>e</b>) and Haishen (<b>b</b>,<b>d</b>,<b>f</b>). Here, the <span class="html-italic">x</span>-axis indicates the time with the date of the simulation period, and the interval of observation data is one hour.</p>
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24 pages, 15652 KiB  
Article
Numerical Study of Topographic Effects on Wind-Driven Coastal Upwelling on the Scotian Shelf
by Shiliang Shan and Jinyu Sheng
J. Mar. Sci. Eng. 2022, 10(4), 497; https://doi.org/10.3390/jmse10040497 - 3 Apr 2022
Cited by 8 | Viewed by 2660
Abstract
Wind-driven coastal upwelling can cause a sudden drop in sea surface temperatures (SSTs) of up to more than 8 °C on the inner Scotian Shelf (ScS) in the summer months. Three major coastal upwelling events on the ScS in the summer of 2012 [...] Read more.
Wind-driven coastal upwelling can cause a sudden drop in sea surface temperatures (SSTs) of up to more than 8 °C on the inner Scotian Shelf (ScS) in the summer months. Three major coastal upwelling events on the ScS in the summer of 2012 are analyzed using in-situ SST observations and satellite remote sensing SST data. A spatial correlation analysis of satellite SST data shows an asymmetric distribution in the along-shore direction with smaller correlation coefficients in the downstream area than in the upstream area over the inner ScS during upwelling events. A regression analysis indicates that the wind impulse plays a major role in generating the SST cooling during the initial response stage of upwelling events. A nested-grid ocean circulation model (DalCoast-CSS) is used to examine the effect of irregular coastline and rugged bathymetry on the spatial and temporal variability of wind-driven upwelling over the inner ScS. The model has four submodels downscaling from the eastern Canadian Shelf to the central ScS. The model external forcing includes tides, winds, river discharges, and net heat flux at the sea surface. A comparison of model results with the satellite SST data reveals a satisfactory performance of the model in reproducing the development of coastal upwelling on the ScS. Model results demonstrate that the irregular coastline and rugged bathymetry play important roles in influencing the temporal and spatial evolution of the upwelling plume over the inner ScS. The irregular coastline (e.g., cape) is responsible for the relatively warm SSTs in two downstream inlets (i.e., St. Margarets Bay and Mahone Bay) and adjacent coastal waters. The rugged bathymetry (e.g., submerged bank) influences the spatial extent of filaments through the advection process. Full article
(This article belongs to the Special Issue Numerical Modelling of Atmospheres and Oceans)
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<p>Major bathymetric features of the Scotian Shelf and adjacent northwest Atlantic Ocean (<b>a–d</b>). In (<b>c</b>,<b>d</b>), the black solid circle indicates the position of a buoy in Halifax Harbour (HHb). Land is masked by the tan color. The 50 m, 100 m, and 200 m isobaths are shown by the gray contours. Unit in color bar is m. The Gulf of Maine (GoM), Scotian Shelf (ScS), Gulf of St. Lawrence (GSL) are labelled in (<b>b</b>). LaHave Basin (LB), LaHave Bank (LK), Emerald Basin (EB), Emerald Bank (EK) and Scotian Gulf (SG) are labelled in (<b>c</b>). The four panels represent the four submodels of the nested-grid ocean circulation model used in this study. The following geographical names are used in the discussion of coastal upwelling and labelled in (<b>c</b>,<b>d</b>): Mahone Bay (M), St.Margarets Bay (S), Halifax Harbour (HFX), Cape Sambro and Sambro Ledges.</p>
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<p>(<b>a</b>) Hourly time series of in-situ SSTs (blue) in 2012 and the fitted seasonal cycle (black) at location HHb outside Halifax Harbour. MODIS SSTs at location HHb are plotted as red “+”. (<b>b</b>) Time series of daily mean SST anomalies calculated by subtracting the seasonal cycle from the observed hourly SSTs in 2012.</p>
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<p>Satellite remote sensing data of sea surface temperature (SST) and chlorophyll concentration over the central Scotian Shelf and adjacent deep ocean waters on (<b>a</b>,<b>b</b>) 22 July and (<b>c</b>,<b>d</b>) 1 September, 2012. In (<b>a</b>,<b>c</b>), unit in color bar is °C. In (<b>b</b>,<b>d</b>), unit in color bar is mg m<sup>-3</sup>. SSTs were extracted from the Ocean Color Website (<a href="http://oceancolor.gsfc.nasa.gov" target="_blank">http://oceancolor.gsfc.nasa.gov</a> (accessed on 22 March 2022)). Chlorophyll concentrations were extracted from the dataset provided by the Ocean Color Climate Change Initiative project (<a href="http://www.oceancolour.org" target="_blank">http://www.oceancolour.org</a> (accessed on 22 March 2022)). The position marked by “◦” indicates the location of the Halifax Harbour buoy (HHb). The 18.5 °C isotherm is shown by magenta contours. The 100 m and 200 m isobaths are marked by the black and gray contours, respectively. White areas indicate missing remote sensing data due to cloud coverage and land contamination.</p>
Full article ">Figure 4
<p>Distributions of spatial correlation coefficients of MODIS SSTs over the central Scotian Shelf in relation to the SST at location HHb in (<b>a</b>) summer and (<b>b</b>) winter. MODIS SSTs from 2002 to 2014 were used in the calculation. The position marked by “◦” indicates the location of HHb. The 100 m and 200 m isobaths are marked by the black and gray contours, respectively. The small-scale bathymetric features of Cape Sambro (CS) and Sambro Ledges (SL) are labelled in (<b>a</b>). Mahone Bay (M) and St. Margarets Bay (S) are also marked in (<b>a</b>).</p>
Full article ">Figure 5
<p>(<b>a</b>) Daily mean wind stress (black arrows) and the magnitude of wind stress (gray line), (<b>b</b>) along-shore (65°T, red line) and cross-shore (blue line) components of wind stress, and (<b>c</b>) wind impulse (kg m<sup>−1</sup> s<sup>−1</sup>, red line) and SST anomaly (°C, black line) in July, August and September 2012 at location HHb. In (<b>c</b>), the gray vertical bars indicate the initial response periods of three major upwelling events. The time-mean wind impulse in July, August, and September 2012 is ~1.4 kg m<sup>−1</sup> s<sup>−1</sup> as shown by the horizontal black line in (<b>c</b>).</p>
Full article ">Figure 6
<p>Scatterplot between wind impulse anomaly and SST anomaly in July, August, and September 2012 at location HHb. The wind impulse anomaly is calculated by subtracting the time-mean wind impulse from the daily wind impulse. The time-mean wind impulse is ~1.4 kg m<sup>−1</sup> s<sup>−1</sup> as shown by the horizontal black line in <a href="#jmse-10-00497-f005" class="html-fig">Figure 5</a>c. The values during the initial response periods (gray vertical bars in <a href="#jmse-10-00497-f005" class="html-fig">Figure 5</a>c) are shown in red solid circles. The correlation coefficient (R) is equal to −0.86 for the solid circles. The linear regression lines are shown.</p>
Full article ">Figure 7
<p>Daily mean time series of (<b>a</b>) observed (red) and simulated (blue) SSTs and (<b>b</b>) seasonal SST anomalies at location HHb in 2012. The simulated results are produced by submodel L3. The monthly-mean climatology derived from the 14-year (2000–2013) hourly observations is also shown in (<b>a</b>). The seasonal SST anomalies are calculated by subtracting the corresponding seasonal cycle from daily SSTs in (<b>b</b>).</p>
Full article ">Figure 8
<p>(<b>a</b>,<b>c</b>) Observed and (<b>b</b>,<b>d</b>) simulated instantaneous SSTs over the central Scotian Shelf on 13 July and 1 September 2012. Unit in color bar is °C. The instantaneous wind stress vectors used in the model are plotted as black arrows (<b>b</b>,<b>d</b>). In each panel, the light gray line indicates the glider track. The blue portion on the glider track highlights the path during the corresponding day. The position marked by “◦” indicates the location of HHb. The 100 m and 200 m isobaths are shown by the black and dark gray contours, respectively. White areas in (<b>a</b>) and (<b>c</b>) represent missing remote sensing data due to cloud coverage and land contamination.</p>
Full article ">Figure 9
<p>Vertical distributions of (<b>a-1,a-2</b>) temperature (°C), (<b>b-1,b-2</b>) salinity (unitless), and (<b>c-1,c-2</b>) potential density (kg m<sup>−3</sup>) along a cross-shelf transect from (<b>a-1,b-1,c-1</b>) glider observations and (<b>a-2,b-2,c-2</b> ) results produced by submodel L3 in July 2012. The glider tracks are shown in <a href="#jmse-10-00497-f008" class="html-fig">Figure 8</a>.</p>
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<p>Same as <a href="#jmse-10-00497-f009" class="html-fig">Figure 9</a>, but for September 2012.</p>
Full article ">Figure 11
<p>Distributions of simulated SSTs over the central Scotian Shelf at 00:00 on selected days in July 2012 (<b>a-l</b>). Unit in color bar is °C. The instantaneous reanalysis wind stress vectors used to drive the nested-grid model are plotted as black arrows. The position marked by “◦” indicates the location of HHb. The 100 m and 200 m isobaths are marked by the black and gray contours, respectively.</p>
Full article ">Figure 12
<p>Horizontal distributions of SSTs in three additional numerical experiments by using constant wind (<span class="html-italic">Upwind</span>, <b>a-,b-,c-,d-1</b>), straight coastline (<span class="html-italic">UPline</span> <b>a-,b-,c-,d-2</b>), and smoothed topography (<span class="html-italic">UPtopo</span> <b>a-,b-,c-,d-3</b>). Unit in color bar is °C. The model results on day 3, 5, 10, and 30 are shown. The constant wind stress vectors used in the model are plotted in (<b>a-1</b>, black arrows). A, B and C in (<b>a-1</b>) indicate three filaments. The 50 m isobath is marked by the magenta contours. The 100, 150 and 200 m isobaths are marked by colored contours from dark to light gray. The area marked by the blue box in (<b>a-3</b>) is used to examine the temporal variability of area-averaged SSTs over St. Margarets Bay, Mahone Bay, and adjacent coastal waters in the following discussion.</p>
Full article ">Figure 13
<p>Near-surface (1.5 m) currents in three additional numerical experiments by using constant wind stress (<span class="html-italic">UPwind</span> <b>a-,b-,c-,d-1</b>), straight coastline (<span class="html-italic">UPline</span> <b>a-,b-,c-,d-2</b>), and smoothed topography (<span class="html-italic">UPtopo</span> <b>a-,b-,c-,d-3</b>). The daily-mean currents on day 3, 5, 10, and 30 are shown. The upwelling plume is indicated by the 12 and 15 °C isotherms (red contours) in (<b>a</b>,<b>b</b>) and (<b>c</b>,<b>d</b>), respectively. The 50 m isobath is marked by the magenta contours. The 100, 150, and 200 m isobaths are marked by colored contours from dark to light gray.</p>
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<p>Same as <a href="#jmse-10-00497-f013" class="html-fig">Figure 13</a>, but for currents at the depth of ~50 m.</p>
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<p>Time series of an area-averaged SST in St. Margarets Bay, Mahone Bay and adjacent coastal waters in three additional numerical experiments by using constant wind stress (<span class="html-italic">UPwind</span>), straight coastline (<span class="html-italic">UPline</span>), and smoothed topography (<span class="html-italic">UPtopo</span>). The averaging area is marked by the blue box in <a href="#jmse-10-00497-f012" class="html-fig">Figure 12</a>(a-3).</p>
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18 pages, 9142 KiB  
Article
SNR-Based Water Height Retrieval in Rivers: Application to High Amplitude Asymmetric Tides in the Garonne River
by Pierre Zeiger, Frédéric Frappart, José Darrozes, Nicolas Roussel, Philippe Bonneton, Natalie Bonneton and Guillaume Detandt
Remote Sens. 2021, 13(9), 1856; https://doi.org/10.3390/rs13091856 - 10 May 2021
Cited by 14 | Viewed by 3141
Abstract
Signal-to-noise ratio (SNR) time series acquired by a geodetic antenna were analyzed to retrieve water heights during asymmetric tides on a narrow river using the Interference Pattern Technique (IPT) from Global Navigation Satellite System Reflectometry (GNSS-R). The dynamic SNR method was selected because [...] Read more.
Signal-to-noise ratio (SNR) time series acquired by a geodetic antenna were analyzed to retrieve water heights during asymmetric tides on a narrow river using the Interference Pattern Technique (IPT) from Global Navigation Satellite System Reflectometry (GNSS-R). The dynamic SNR method was selected because the elevation rate of the reflecting surface during rising tides is high in the Garonne River with macro tidal conditions. A new process was developed to filter out the noise introduced by the environmental conditions on the reflected signal due to the narrowness of the river compared to the size of the Fresnel areas, the presence of vegetation on the river banks, and the presence of boats causing multiple reflections. This process involved the removal of multipeaks in the Lomb-Scargle Periodogram (LSP) output and an iterative least square estimation (LSE) of the output heights. Evaluation of the results was performed against pressure-derived water heights. The best results were obtained using all GNSS bands (L1, L2, and L5) simultaneously: R = 0.99, ubRMSD = 0.31 m. We showed that the quality of the retrieved heights was consistent, whatever the vertical velocity of the reflecting surface, and was highly dependent on the number of satellites visible. The sampling period of our solution was 1 min with a 5-min moving window, and no tide models or fit were used in the inversion process. This highlights the potential of the dynamic SNR method to detect and monitor extreme events with GNSS-R, including those affecting inland waters such as flash floods. Full article
(This article belongs to the Special Issue Radar Based Water Level Estimation)
Show Figures

Figure 1

Figure 1
<p>Location of the study area. (<b>a</b>) Location of Podensac on the Garonne River; (<b>b</b>) the Gironde/Garonne/Dordogne estuary in southwest France; (<b>c</b>) drone image of the Garonne River taken by V. Marie (EPOC), showing the first waves of the tidal bore, its direction of propagation, and the platform location; (<b>d</b>) photo of the Garonne River from the platform with the GNSS antenna installed. The narrowness of the river and the vegetation on riverbanks are visible in both images.</p>
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<p>1-Hz resampled pressure water level time series of the Garonne River at Podensac. (<b>a</b>) During the GNSS-R SNR acquisition with red rectangle indicating tidal bores; (<b>b</b>) during four consecutive tide periods. These figures are representative of the entire pressure water level time series and do not show the tidal oscillations over a longer period, as the acquisition was performed during spring tides only when both the tidal range is maximum and tidal bores can form.</p>
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<p>Flowchart of the dynamic SNR method with our improvements adapted from [<a href="#B29-remotesensing-13-01856" class="html-bibr">29</a>]. (<b>a</b>) Processing chain with the addition of a two-step filtering of the dominant frequencies (in orange); (<b>b</b>,<b>c</b>) respective examples of a single-peak output and a multipeak output from LSP for the same satellite track (G01). Red line materializes the level of filtering which depends on parameter <span class="html-italic">k</span> (here <span class="html-italic">k</span> = 0.6), and <math display="inline"><semantics> <mover accent="true"> <mi>f</mi> <mo>˜</mo> </mover> </semantics></math> ~100 Hz.</p>
Full article ">Figure 4
<p>Dominant frequencies extracted from GPS (green) and GLONASS (orange) satellites using the LSP, and river heights inverted with the dynamic SNR method (blue) compared to pressure water levels (red). (<b>a</b>,<b>b</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <mover accent="true"> <mi>f</mi> <mo>˜</mo> </mover> </mrow> </semantics></math> and <span class="html-italic">h</span> from raw LSP output respectively; (<b>c</b>) frequencies filtered out after multipeak rejection with parameter <span class="html-italic">k</span> = 0.6 and iterative LSE; (<b>d</b>) concordant time series of water levels estimated with iterative LSE. Grey areas are masks due to tidal bore occurrence (17 h) and data gaps (21–22 h).</p>
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<p>Final results using the adapted dynamic SNR inversion. (<b>a</b>) Comparison of <span class="html-italic">h</span> calculated using L1 only (orange), L2 only (green), and L1 + L2 + L5 (blue) frequencies for GPS and GLONASS satellites with pressure water levels (red); (<b>b</b>) output <math display="inline"><semantics> <mover accent="true"> <mi>h</mi> <mo>˙</mo> </mover> </semantics></math> with L1 + L2 + L5 bands; (<b>c</b>) number of GPS and GLONASS satellites for the calculation of <span class="html-italic">h</span> and <math display="inline"><semantics> <mover accent="true"> <mi>h</mi> <mo>˙</mo> </mover> </semantics></math>. The value of <math display="inline"><semantics> <mover accent="true"> <mi>h</mi> <mo>˙</mo> </mover> </semantics></math> was derived from the relative antenna height <span class="html-italic">h</span>, thus it was negative during rising tides as the relative antenna height decreased.</p>
Full article ">Figure 6
<p>Statistical results depending on the number of satellites and the vertical velocity. (<b>a</b>) R and ubRMSD computed according to the number of satellites for the inversion of <span class="html-italic">h</span> and <math display="inline"><semantics> <mover accent="true"> <mi>h</mi> <mo>˙</mo> </mover> </semantics></math>; (<b>b</b>) Idem according to the vertical velocity class (intervals computed with range 1 × 10<sup>−4</sup> m.s<sup>−1</sup>).</p>
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34 pages, 11340 KiB  
Article
An Optimized-Parameter Spectral Clustering Approach to Coherent Structure Detection in Geophysical Flows
by Margaux Filippi, Irina I. Rypina, Alireza Hadjighasem and Thomas Peacock
Fluids 2021, 6(1), 39; https://doi.org/10.3390/fluids6010039 - 12 Jan 2021
Cited by 15 | Viewed by 4397
Abstract
In Lagrangian dynamics, the detection of coherent clusters can help understand the organization of transport by identifying regions with coherent trajectory patterns. Many clustering algorithms, however, rely on user-input parameters, requiring a priori knowledge about the flow and making the outcome subjective. Building [...] Read more.
In Lagrangian dynamics, the detection of coherent clusters can help understand the organization of transport by identifying regions with coherent trajectory patterns. Many clustering algorithms, however, rely on user-input parameters, requiring a priori knowledge about the flow and making the outcome subjective. Building on the conventional spectral clustering method of Hadjighasem et al. (2016), a new optimized-parameter spectral clustering approach is developed that automatically identifies optimal parameters within pre-defined ranges. A noise-based metric for quantifying the coherence of the resulting coherent clusters is also introduced. The optimized-parameter spectral clustering is applied to two benchmark analytical flows, the Bickley Jet and the asymmetric Duffing oscillator, and to a realistic, numerically generated oceanic coastal flow. In the latter case, the identified model-based clusters are tested using observed trajectories of real drifters. In all examples, our approach succeeded in performing the partition of the domain into coherent clusters with minimal inter-cluster similarity and maximum intra-cluster similarity. For the coastal flow, the resulting coherent clusters are qualitatively similar over the same phase of the tide on different days and even different years, whereas coherent clusters for the opposite tidal phase are qualitatively different. Full article
(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)
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Figure 1

Figure 1
<p>Example spectral clustering results for the Bickley Jet with parameters identical to those from HA16. The originally chosen value was <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>3.0</mn> </mrow> </semantics></math> in panel (<b>b</b>). Three other values of <span class="html-italic">r</span> yielded a higher eigengap, however, as seen in panels (<b>a</b>,<b>c</b>,<b>d</b>). Moreover, to follow the rule of thumb of 5–10% sparsification, <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>4.5</mn> </mrow> </semantics></math> in panel (<b>d</b>) should be chosen instead. This value fails to detect the individual vortices, instead grouping them in pairs. It does, however, detect the meandering jet as an individual coherent structure. Looking at the maximum eigengap, the value of <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>1.5</mn> </mrow> </semantics></math> in panel (<b>c</b>) should be chosen.</p>
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<p>(<b>a</b>) Poincaré map for the periodic Bickley Jet flow, computed over 1000 perturbation periods. (<b>b</b>) Forward- and (<b>c</b>) Backward-FTLE field, computed over 30 peturbation periods.</p>
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<p>Coherent clusters color-coded by their coherence metrics resulting from the optimized-parameter spectral clustering for the Bickley Jet flow. The initial (<math display="inline"><semantics> <msub> <mi>t</mi> <mn>0</mn> </msub> </semantics></math>—<b>left</b>) and final (<math display="inline"><semantics> <msub> <mi>t</mi> <mi>f</mi> </msub> </semantics></math>—<b>right</b>) positions are shown.</p>
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<p>The asymmetric Duffing oscillator. (<b>a</b>) Poincaré map with 20 periods of perturbation T<math display="inline"><semantics> <msub> <mrow/> <mrow> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mi>t</mi> </mrow> </msub> </semantics></math>. (<b>b</b>) Forward- and (<b>c</b>) Backward- FTLE for 10T<math display="inline"><semantics> <msub> <mrow/> <mrow> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mi>t</mi> </mrow> </msub> </semantics></math>.</p>
Full article ">Figure 5
<p>Coherent clusters, color-coded by their coherence metrics, resulting from the optimized-parameter spectral clustering for the asymmetric Duffing oscillator flow. The initial (<math display="inline"><semantics> <msub> <mi>t</mi> <mn>0</mn> </msub> </semantics></math>—<b>left</b>) and final (<math display="inline"><semantics> <msub> <mi>t</mi> <mi>f</mi> </msub> </semantics></math>—<b>right</b>) positions are shown. For comparison, black curves show the FTLE ridges in forward-time at <math display="inline"><semantics> <msub> <mi>t</mi> <mn>0</mn> </msub> </semantics></math> and in backward time at <math display="inline"><semantics> <msub> <mi>t</mi> <mi>f</mi> </msub> </semantics></math>. The spectral clustering was done for 30T<math display="inline"><semantics> <msub> <mrow/> <mrow> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mi>t</mi> </mrow> </msub> </semantics></math>; FTLE ridges were computed for 10T<math display="inline"><semantics> <msub> <mrow/> <mrow> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mi>t</mi> </mrow> </msub> </semantics></math>.</p>
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<p>Bathymetry of the 200-m resolution model domains around Martha’s Vineyard, extending south towards the continental shelf break. Depths in meters. Data from MSEAS. Large island is Martha’s Vineyard; small island near 70.82W and 41.25N is No Man’s Land.</p>
Full article ">Figure 7
<p>LCS, numerical tracers and experimental drifter positions at the start (15:51 UTC) and end (21:51 UTC) of the 2017 experiment on August 14. (<b>a</b>) Forward and (<b>b</b>) backward FTLE. (<b>c</b>,<b>d</b>) Spectral clusters with coherence metric. The drifters in c-d are color-coded according to the cluster to which they belong, with red crosses if their final positions were outside of their initial cluster.</p>
Full article ">Figure 8
<p>LCS, numerical tracers and experimental drifter positions at the start (16:00 UTC) and end (22:00 UTC) of the 2018 experiment on August 7. (<b>a</b>) Forward and (<b>b</b>) backward FTLE. (<b>c</b>,<b>d</b>) Spectral clusters with coherence metric. The drifters are color-coded according to the cluster to which they belong, with red crosses if their final positions were outside their initial cluster.</p>
Full article ">Figure 9
<p>LCS, numerical tracers and drifter positions at the start (20:00 UTC) and end (02:00 UTC) of the 2018 experiment on August 7–8. (<b>a</b>) Forward and (<b>b</b>) backward FTLE. (<b>c</b>,<b>d</b>) Spectral clusters with coherence metric. The drifters are color-coded according to the cluster to which they belong, with red crosses if their final positions were outside their initial cluster.</p>
Full article ">Figure 10
<p>LCS, numerical tracers and drifter positions at the start (04:00 UTC) and end (10:00 UTC) of the 2018 experiment on August 8. (<b>a</b>) Forward and (<b>b</b>) backward FTLE. (<b>c</b>,<b>d</b>) Spectral clusters with coherence metric. The drifters are color-coded according to the cluster to which they belong, with red crosses if their final positions were outside their initial cluster.</p>
Full article ">Figure A1
<p>(<b>a</b>) Step 1 of the spectral clustering protocol for the Bickley Jet example: normalized eigengap as a function of <span class="html-italic">r</span> with the average distance function. (<b>b</b>) Step 2 of the spectral clustering protocol for the Bickley Jet: sweep of offset coefficients <math display="inline"><semantics> <msup> <mn>10</mn> <mi>n</mi> </msup> </semantics></math> for the gap ratio peaks in (<b>a</b>) at <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>0.90</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>1.25</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>2.00</mn> </mrow> </semantics></math> with the average distance function.</p>
Full article ">Figure A2
<p>Steps 1 and 2 of the spectral clustering protocol for the asymmetric Duffing oscillator. (<b>a</b>) Sweep of <span class="html-italic">r</span> parameters with offset coefficient <math display="inline"><semantics> <msup> <mn>10</mn> <mn>7</mn> </msup> </semantics></math> for the average distance function. (<b>b</b>) Sweep of offset coefficients <math display="inline"><semantics> <msup> <mn>10</mn> <mi>n</mi> </msup> </semantics></math> for average distance function and the normalized eigengap peak at <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p>
Full article ">Figure A3
<p>Steps 1 and 2 of the spectral clustering protocol for the 2017 No Man’s Land experiment for the 15:51–21:51 window. (<b>a</b>) Sweep of <span class="html-italic">r</span> parameters with offset coefficient <math display="inline"><semantics> <msup> <mn>10</mn> <mn>7</mn> </msup> </semantics></math> for the average distance function. (<b>b</b>) Sweep of offset coefficients <math display="inline"><semantics> <msup> <mn>10</mn> <mi>n</mi> </msup> </semantics></math> for average distance function and the normalized eigengap peaks in (<b>a</b>).</p>
Full article ">Figure A4
<p>Steps 1 and 2 of the spectral clustering protocol for the 2018 No Man’s Land 16:00–22:00 experiment. (<b>a</b>) Sweep of <span class="html-italic">r</span> parameters with offset coefficient <math display="inline"><semantics> <msup> <mn>10</mn> <mn>7</mn> </msup> </semantics></math> for the average distance function. (<b>b</b>) Sweep of offset coefficients <math display="inline"><semantics> <msup> <mn>10</mn> <mi>n</mi> </msup> </semantics></math> for average distance function and the normalized eigengap peaks from (<b>a</b>).</p>
Full article ">Figure A5
<p>Steps 1 and 2 of the spectral clustering protocol for the 2018 No Man’s Land 20:00–02:00 experiment. (<b>a</b>) Sweep of <span class="html-italic">r</span> parameters with offset coefficient <math display="inline"><semantics> <msup> <mn>10</mn> <mn>7</mn> </msup> </semantics></math> for the average distance function. (<b>b</b>) Sweep of offset coefficients <math display="inline"><semantics> <msup> <mn>10</mn> <mi>n</mi> </msup> </semantics></math> for average distance function and the normalized eigengap peaks from (<b>a</b>).</p>
Full article ">Figure A6
<p>Steps 1 and 2 of the spectral clustering protocol for the 2018 No Man’s Land 04:00–10:00 experiment. (<b>a</b>) Sweep of <span class="html-italic">r</span> parameters with offset coefficient <math display="inline"><semantics> <msup> <mn>10</mn> <mn>7</mn> </msup> </semantics></math> for the average distance function. (<b>b</b>) Sweep of offset coefficients <math display="inline"><semantics> <msup> <mn>10</mn> <mi>n</mi> </msup> </semantics></math> for average distance function and the normalized eigengap peaks from (<b>a</b>).</p>
Full article ">Figure A7
<p>Poincaré map for a second example of the asymmetric Duffing oscillator with 100 periods of perturbation T<math display="inline"><semantics> <msub> <mrow/> <mrow> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mi>t</mi> </mrow> </msub> </semantics></math>.</p>
Full article ">Figure A8
<p>Step 1 of the spectral clustering protocol for the asymmetric Duffing oscillator shown in <a href="#fluids-06-00039-f0A7" class="html-fig">Figure A7</a>: sweep of <span class="html-italic">r</span> parameters with offset coefficient <math display="inline"><semantics> <msup> <mn>10</mn> <mn>7</mn> </msup> </semantics></math> for the average distance function.</p>
Full article ">Figure A9
<p>Step 3 of the spectral clustering protocol for the asymmetric Duffing oscillator shown in <a href="#fluids-06-00039-f0A7" class="html-fig">Figure A7</a> for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>1.125</mn> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math> and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>3.75</mn> </mrow> </semantics></math>. All individual clusters are color-coded by their coherence metrics.</p>
Full article ">Figure A10
<p>Comparison between real and simulated drifter trajectories for the 2017 No Man’s Land experiment. The trajectories of CODE drifters are plotted with thick lines. The corresponding numerical trajectories, simulated with the same initial conditions as their corresponding CODE drifter, are plotted with thin lines.</p>
Full article ">Figure A11
<p>Comparison between real and simulated drifter trajectories for the 2018 No Man’s Land experiment between 16:00 and 22:00 UTC. The trajectories of CODE drifters are plotted with thick lines. The corresponding numerical trajectories, simulated with the same initial conditions as their corresponding CODE drifter, are plotted with thin lines.</p>
Full article ">Figure A12
<p>Comparison between real and simulated drifter trajectories for the 2018 No Man’s Land experiment between 20:00 and 02:00 UTC. The trajectories of CODE drifters are plotted with thick lines. The corresponding numerical trajectories, simulated with the same initial conditions as their corresponding CODE drifter, are plotted with thin lines.</p>
Full article ">Figure A13
<p>Comparison between real and simulated drifter trajectories for the 2018 No Man’s Land experiment between 04:00 and 10:00 UTC. The trajectories of CODE drifters are plotted with thick lines. The corresponding numerical trajectories, simulated with the same initial conditions as their corresponding CODE drifter, are plotted with thin lines.</p>
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Article
Riverbed Micromorphology of the Yangtze River Estuary, China
by Shuaihu Wu, Heqin Cheng, Y. Jun Xu, Jiufa Li, Shuwei Zheng and Wei Xu
Water 2016, 8(5), 190; https://doi.org/10.3390/w8050190 - 6 May 2016
Cited by 17 | Viewed by 7342
Abstract
Dunes are present in nearly all fluvial channels and are vital in understanding sediment transport, deposition, and flow conditions during floods of rivers and estuaries. This information is pertinent for helping developing management practices to reduce risks in river transportation and engineering. Although [...] Read more.
Dunes are present in nearly all fluvial channels and are vital in understanding sediment transport, deposition, and flow conditions during floods of rivers and estuaries. This information is pertinent for helping developing management practices to reduce risks in river transportation and engineering. Although a few recent studies have investigated the micromorphology of a portion of the Yangtze River estuary in China, our understanding of dune development in this large estuary is incomplete. It is also poorly understood how the development and characteristics of these dunes have been associated with human activities in the upper reach of the Yangtze River and two large-scale engineering projects in the estuarine zone. This study analyzed the feature in micromorphology of the entire Yangtze River estuary bed over the past three years and assessed the morphological response of the dunes to recent human activities. In 2012, 2014, and 2015, multi-beam bathymetric measurements were conducted on the channel surface of the Yangtze River estuary. The images were analyzed to characterize the subaqueous dunes and detect their changes over time. Bottom sediment samples were collected for grain size analysis to assess the physical properties of the dunes. We found that dunes in the Yangtze River estuary can be classified in four major classes: very large dunes, large dunes, medium dunes, and small dunes. Large dunes were predominant, amounting to 51.5%. There was a large area of dunes developed in the middle and upper reaches of the Yangtze River estuary and in the Hengsha Passage. A small area of dunes was observed for the first time in the turbidity maximum zone of the Yangtze River estuary. These dunes varied from 0.12 to 3.12 m in height with a wide range of wavelength from 2.83 to 127.89 m, yielding a range in height to wavelength of 0.003–0.136. Sharp leeside slope angles suggest that the steep slopes of asymmetrical dunes in the middle and upper reaches, and the turbidity maximum zone of the Yangtze River estuary face predominantly towards tides because of the ebb-dominated currents. Sharp windward slope angles in the lower reach of the North Passage show the influence of flood-dominated currents on dunes. It is likely that the scale of dunes will increase in the future in the South Channel because of a sharp decline of sediment discharge caused by recent human activities. Full article
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Figure 1
<p>Geographical location of the study area—the Yangtze River estuary in China, with the Changxing Island, Hengsha Island, the North and South Channels and Passages, and the Jiuduansha Shoal wetland.</p>
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<p>Field measurement routes and locations of the turbidity maximum zone in the Yangtze River estuary, China.</p>
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<p>Subaqueous dunes in the turbidity maximum zone of the Yangtze River estuary, including (<b>A</b>) the dunes in the mouth bar area of the North Channel; (<b>B</b>) the dunes in the middle reach of the North Passage; (<b>C</b>) the dunes in the lower reach of the North Passage; and (<b>D</b>) the dunes in the south side of Jiangyanansha of the upper reach of the South Passage.</p>
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<p>Types of sea-bottom sediment in the Yangtze River estuary in the recent years.</p>
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<p>Thickness of deposition or erosion in the North Channel from 2007 to 2013 (negative values indicate net erosion; while positive values indicate net accretion).</p>
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<p>Thickness of deposition or erosion in the South Passage from 2002 to 2013 (negative values indicate net erosion; while positive values indicate net accretion).</p>
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<p>Change of the annual flow volume and suspended sediment yield in recent years at the Datong station on the Yangtze River estuary.</p>
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