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We perform an out-of-distribution analysis of ~12,000,000 semi-independent 128x128 pixel^2 SST regions, which we define as cutouts, from all nighttime granules in the MODIS R2019 Level-2 public dataset to discover the most complex or extreme phenomena at the ocean surface. Our algorithm (Ulmo) is a probabilistic autoencoder, which combines two deep learning modules: (1) an autoencoder, trained on ~150,000 random cutouts from 2010, to represent any input cutout with a 512-dimensional latent vector akin to a (non-linear) EOF analysis; and (2) a normalizing flow, which maps the autoencoder's latent space distribution onto an isotropic Gaussian manifold. From the latter, we calculate a log-likelihood value for each cutout and define outlier cutouts to be those in the lowest 0.1% of the distribution. These exhibit large gradients and patterns characteristic of a highly dynamic ocean surface, and many are located within larger complexes whose unique dynamics warrant future analysis. Without guidance, Ulmo consistently locates the outliers where the major western boundary currents separate from the continental margin. Buoyed by these results, we begin the process of exploring the fundamental patterns learned by Ulmo, identifying several compelling examples. Future work may find that algorithms like Ulmo hold significant potential/promise to learn and derive other, not-yet-identified behaviors in the ocean from the many archives of satellite-derived SST fields. As important, we see no impediment to applying them to other large, remote-sensing datasets for ocean science (e.g., sea surface height, ocean color)., Comment: 16 pages, 12 figures

A CTD (conductivity, temperature, depth) device measures temperature and salinity versus pressure. This document is the Argo quality control manual for CTD and trajectory data. It describes two levels of quality control: - The first level is the real-time system that performs a set of agreed automatic checks. - The second level of quality control is the delayed-mode system. These quality control procedures are applied to the parameters JULD, LATITUDE, LONGITUDE, PRES, TEMP, PSAL, and CNDC.

Shoreline erosion and storm tide inundation increasingly threaten coastal populations, infrastructure and economies. Hard infrastructure, known as gray infrastructure (e.g. concrete seawalls), has commonly been used to protect coastal communities but is expensive to build, maintain, and deteriorates coastal vegetation. Green infrastructure (e.g. restored or conserved mangrove and marsh ecosystems) delivers nature-based coastal protection but in comparatively lower density coastal areas. Nowadays a more popularized approach to coastal protection is hybrid eco-engineering. In this study, we discuss lessons-learnt on how the hybridization of engineered structures and wetland restoration practices compared with traditional gray and green approaches. We contrast hybrid applications in mangrove and tidal marsh areas in the UK and south-east Asia. The majority (70%) of successful hybrid infrastructure cases were underpinned by understanding of ecological and hydrological changes in response to infrastructure and involved a wide range of stakeholders. In terms of construction and maintenance cost, limited data suggested that hybrid infrastructure may be more cost effective than gray infrastructure, but more expensive than green; however, data were very limited and therefore we suggest the need for further cost-benefit analyses to inform a robust comparison. Development of new technologies should see growing efficacy of future hybrid infrastructure in mitigating coastal flood risks.

The Regional Ocean Modeling System (ROMS), including an ice shelf component, has been applied on a circum-Antarctic domain to derive estimates of ice shelf basal melting. Significant improvements made compared to previous models of this scale are the inclusion of tides and a horizontal spatial resolution of 2 km, which is sufficient to resolve on-shelf heat transport by bathymetric troughs and eddy-scale circulation. We run the model with ocean–atmosphere–sea ice conditions from the year 2007 to represent nominal present-day climate. We force the ocean surface with buoyancy fluxes derived from sea ice concentration observations and wind stress from ERA-Interim atmospheric reanalysis. Boundary conditions are derived from the ECCO2 ocean state estimate; tides are incorporated as sea surface height and barotropic currents at the open boundary. We evaluate model results using satellite-derived estimates of ice shelf melting and established compilations of ocean hydrography. The Whole Antarctic Ocean Model (WAOM v1.0) qualitatively captures the broad scale difference between warm and cold regimes as well as many of the known characteristics of regional ice–ocean interaction. We identify a cold bias for some warm-water ice shelves and a lack of high-salinity shelf water (HSSW) formation. We conclude that further calibration and development of our approach are justified. At its current state, the model is ideal for addressing specific, process-oriented questions, e.g. related to tide-driven ice shelf melting at large scales.

A long simulation over the period 1901–2010 with an eddy-permitting ocean circulation model is used to study the variability of the upper layer circulation in the North Ionian Gyre (NIG) in the Eastern Mediterranean Sea (EMed). The model is driven by the atmospheric forcing from the twentieth century reanalysis data set ERA-20C, ensuring a consistent performance of the model over the entire simulation period. The main modes of variability known in the EMed, in particular the decadal reversals of the NIG upper layer circulation observed since the late 1980s are well reproduced. We find that the simulated NIG upper layer circulation prior to the observational period is characterized by long-lasting cyclonic phases with weak variability during years 1910–1940 and 1960–1985, while in the in-between period (1940–1960) quasi-decadal NIG circulation reversals occur with similar characteristics to those observed in the recent decades. Our simulation indicates that the NIG upper layer circulation is rather prone to the cyclonic mode with occasional kicks to the anticyclonic mode. The coherent variability of the NIG upper layer circulation mode and of the Adriatic Deep Water (AdDW) outflow implies that atmospheric forcing triggering strong AdDW formation is required to kick the NIG into an anticyclonic circulation 1–2 years later. A sensitivity experiment mimicking a cold winter event over the Adriatic Sea supports this hypothesis. Our simulation shows that it is the multi-decadal variability of the salinity in the Adriatic Sea that leads to periods where low salinity prevents strong AdDW formation events. This explains the absence of quasi-decadal NIG reversals during 1910–1940 and 1960–1985.

Eddy saturation describes the nonlinear mechanism in geophysical flows whereby, when average conditions are considered, direct forcing of the zonal flow increases the eddy kinetic energy, while the energy associated with the zonal flow does not increase. We present a minimal baroclinic model that exhibits complete eddy saturation. Starting from Phillips’ classical quasi-geostrophic two-level model on the beta channel of the mid-latitudes, we derive a reduced order model comprising of six ordinary differential equations including parameterised eddies. This model features two physically realisable steady state solutions, one a purely zonal flow and one where, additionally, finite eddy motions are present. As the baroclinic forcing in the form of diabatic heating is increased, the zonal solution loses stability and the eddy solution becomes attracting. After this bifurcation, the zonal components of the solution are independent of the baroclinic forcing, and the excess of heat in the low latitudes is efficiently transported northwards by finite eddies, in the spirit of baroclinic adjustment.

Ice algae play a fundamental role in shaping polar marine ecosystems and biogeochemistry. This role can be investigated by field observations, however the influence of ice algae at the regional and global scales remains unclear due to limited spatial and temporal coverage of observations, and because ice algae are typically not included in current Earth System Models. To address this knowledge gap, we introduce a new model intercomparison project (MIP), referred to here as the Ice Algae Model Intercomparison Project phase 2 (IAMIP2). IAMIP2 is built upon the experience from its previous phase, and expands its scope to global coverage (both Arctic and Antarctic) and centennial timescales (spanning the mid-twentieth century to the end of the twenty-first century). Participating models are three-dimensional regional and global coupled sea ice–ocean models that incorporate sea-ice ecosystem components. These models are driven by the same initial conditions and atmospheric forcing datasets by incorporating and expanding the protocols of the Ocean Model Intercomparison Project, an endorsed MIP of the Coupled Model Intercomparison Project phase 6 (CMIP6). Doing so provides more robust estimates of model bias and uncertainty, and consequently advances the science of polar marine ecosystems and biogeochemistry. A diagnostic protocol is designed to enhance the reusability of the model data products of IAMIP2. Lastly, the limitations and strengths of IAMIP2 are discussed in the context of prospective research outcomes.

Strong, regional sea level trends, mainly related to basin–wide wind stress anomalies, have been observed in the western tropical Pacific over the last three decades. Analyses of regional sea level in the densely populated regions of the neighbouring Australasian Mediterranean Sea (AMS) are hindered by its complex topography and respective studies are sparse. We used a series of global, eddy permitting ocean models, including a high–resolution configuration that resolves the AMS with horizontal resolution, forced by a comprehensive atmospheric forcing product over 1958–2016, to characterize the patterns and magnitude of decadal sea level variability in the AMS. The nature of this variability is elucidated further by sensitivity experiments with interannual variability restricted to either the momentum or buoyancy fluxes, building on an experiment employing a repeated-year forcing without interannual variability in all forcing components. Our results suggest that decadal fluctuations of ENSO account for over 80 % of the variability in all deep basins of the region, except for the central South China Sea (SCS). PDO–related changes are most pronounced in the shallow Arafura and Timor seas and in the central SCS. On average, buoyancy fluxes account for less than 10 % of decadal SSH variability, although this ratio is highly variable over time and can reach values of up to 50 %. In particular, our results suggest that buoyancy flux forcing amplifies the dominant wind stress driven anomalies related to ENSO cycles. Intrinsic variability is mostly negligible except in the SCS, where it accounts for 25 % of the total decadal SSH variability.

The international Thermodynamic Equation of Seawater 2010 (TEOS-10) defined the enthalpy and entropy of seawater, thus enabling the global ocean heat content to be calculated as the volume integral of the product of in situ density, ρ, and potential enthalpy, h0 (with reference sea pressure of 0 dbar). In terms of Conservative Temperature, Θ, ocean heat content is the volume integral of ρcp0Θ, where cp0 is a constant “isobaric heat capacity”. However, many ocean models in the Coupled Model Intercomparison Project Phase 6 (CMIP6) as well as all models that contributed to earlier phases, such as CMIP5, CMIP3, CMIP2, and CMIP1, used EOS-80 (Equation of State – 1980) rather than the updated TEOS-10, so the question arises of how the salinity and temperature variables in these models should be physically interpreted, with a particular focus on comparison to TEOS-10-compliant observations. In this article we address how heat content, surface heat fluxes, and the meridional heat transport are best calculated using output from these models and how these quantities should be compared with those calculated from corresponding observations. We conclude that even though a model uses the EOS-80, which expects potential temperature as its input temperature, the most appropriate interpretation of the model's temperature variable is actually Conservative Temperature. This perhaps unexpected interpretation is needed to ensure that the air–sea heat flux that leaves and arrives in atmosphere and sea ice models is the same as that which arrives in and leaves the ocean model. We also show that the salinity variable carried by present TEOS-10-based models is Preformed Salinity, while the salinity variable of EOS-80-based models is also proportional to Preformed Salinity. These interpretations of the salinity and temperature variables in ocean models are an update on the comprehensive Griffies et al. (2016) paper that discusses the interpretation of many aspects of coupled Earth system models.

In recent years, significant trends toward earlier breakup and later freeze-up of sea ice in Hudson Bay have led to a considerable increase in shipping activity through the Port of Churchill, which is located in western Hudson Bay and is the only deep-water ocean port in the province of Manitoba. Therefore, understanding sea-level variability at the port is an urgent issue crucial for safe navigation and coastal infrastructure. Using tidal gauge data from the port along with an atmospheric reanalysis and Churchill River discharge, we assess environmental factors impacting synoptic to seasonal variability of sea level at Churchill. An atmospheric vorticity index used to describe the wind forcing was found to correlate with sea level at Churchill. Statistical analyses show that, in contrast to earlier studies, local discharge from the Churchill River can only explain up to 5 % of the sea-level variability. The cyclonic wind forcing contributes from 22 % during the ice-covered winter–spring season to 30 % during the ice-free summer–fall season due to cyclone-induced storm surges generated along the coast. Multiple regression analysis revealed that wind forcing and local river discharge combined can explain up to 32 % of the sea-level variability at Churchill. Our analysis further revealed that the seasonal cycle of sea level at Churchill appears to be impacted by the seasonal cycle in atmospheric circulation rather than by the seasonal cycle in local discharge from the Churchill River, particularly post-construction of the Churchill River diversion in 1977. Sea level at Churchill shows positive anomalies for September–November compared to June–August. This seasonal difference was also revealed for the entire Hudson Bay coast using satellite-derived sea-level altimetry. This anomaly was associated with enhanced cyclonic atmospheric circulation during fall, reaching a maximum in November, which forced storm surges along the coast. Complete sea-ice cover during winter impedes momentum transfer from wind stress to the water column, reducing the impact of wind forcing on sea-level variability. Expanding our observations to the bay-wide scale, we confirmed the process of wind-driven sea-level variability with (i) tidal-gauge data from eastern Hudson Bay and (ii) satellite altimetry measurements. Ultimately, we find that cyclonic winds generate sea-level rise along the western and eastern coasts of Hudson Bay at the synoptic and seasonal timescales, suggesting an amplification of the bay-wide cyclonic geostrophic circulation in fall (October–November), when cyclonic vorticity is enhanced, and Hudson Bay is ice-free.

Assessing the risk of tsunami-driven debris has increasingly been recognized as an important design consideration. The recent ASCE/SEI7-16 standard Chapter 6 requires all the areas included within a 22.5° spreading angle from the debris source to consider the debris impact. However, it would be more reasonable to estimate the risks using numerical simulation models. Although a number of simulation models to predict tsunami debris transport have been proposed individually, comparative studies for these simulation models have rarely been conducted. Thus, in the present study, an inter-model comparison for tsunami debris simulation model was performed as a part of the virtual Tsunami Hackathon held in Japan from September 1 to 3 in 2020. The blind benchmarking experiment, which recorded the transport of three container models under a tsunami-like bore, was conducted to generate a unique dataset. Then, four different numerical models were applied to reproduce the experiments. Simulated results demonstrated considerable differences among the simulation models. Essentially, the importance of accurate modelling of a flow field, especially a tsunami front, was confirmed to be important in simulating debris motion. Parametric studies performed in each model and comparisons between different models also confirmed that a drag coefficient and inertia coefficient would influence the simulated debris trajectory and velocity. It was also shown that two-way coupled modelling to express the interaction between debris and a tsunami is important to accurately model the debris motion.

The St. Lawrence Estuary connects the Great Lakes with the Atlantic Ocean. The accepted view, based on summer conditions, is that the estuary's surface layer receives its nutrient supply from vertical mixing processes. This mixing is caused by the estuarine circulation and tides interacting with the topography at the head of the Laurentian Channel. During winter when ice forms, historical process-based studies have been limited in scope. Winter monitoring has been typically confined to vertical profiles of salinity and temperature as well as near-surface water samples collected from a helicopter for nutrient analysis. In 2018, however, the Canadian Coast Guard approved a science team to sample in tandem with its ice-breaking and ship escorting operations. This opportunistic sampling provided the first winter turbulence observations, which covered the largest spatial extent ever measured during any season within the St. Lawrence Estuary and the Gulf of St. Lawrence. The nitrate enrichment from tidal mixing resulted in an upward nitrate flux of about 30 nmol m−2 s−1, comparable to summer values obtained at the same tidal phase. Further downstream, deep nutrient-rich water from the gulf was mixed into the subsurface nutrient-poor layer at a rate more than an order of magnitude smaller than at the head. These fluxes were compared to the nutrient load of the upstream St. Lawrence River. Contrary to previous assumptions, fluvial nitrate inputs are the most significant source of nitrate in the estuary. Nitrate loads from vertical mixing processes would only exceed those from fluvial sources at the end of summer when fluvial inputs reach their annual minimum.

In this study, the Adriatic Sea and Coast (AdriSC) kilometre-scale atmosphere–ocean climate model covering the Adriatic Sea and northern Ionian Sea is presented. The AdriSC ocean results of a 31-year-long (i.e. 1987–2017) climate simulation, derived with the Regional Ocean Modeling System (ROMS) 3 km and 1 km models, are evaluated with respect to a comprehensive collection of remote sensing and in situ observational data. In general, it is found that the AdriSC model is capable of reproducing the observed sea surface properties, daily temperatures and salinities, and the hourly ocean currents with good accuracy. In particular, the AdriSC ROMS 3 km model demonstrates skill in reproducing the main variabilities of the sea surface height and the sea surface temperature, despite a persistent negative bias within the Adriatic Sea. Furthermore, the AdriSC ROMS 1 km model is found to be more capable of reproducing the observed thermohaline and dynamical properties than the AdriSC ROMS 3 km model. For the temperature and salinity, better results are obtained in the deeper parts than in the shallow shelf and coastal parts, particularly for the surface layer of the Adriatic Sea. The AdriSC ROMS 1 km model is also found to perform well in reproducing the seasonal thermohaline properties of the water masses over the entire Adriatic–Ionian domain. The evaluation of the modelled ocean currents revealed better results at locations along the eastern coast and especially the northeastern shelf than in the middle eastern coastal area and the deepest part of the Adriatic Sea. Finally, the AdriSC climate component is found to be a more suitable modelling framework to study the dense water formation and long-term thermohaline circulation of the Adriatic–Ionian basin than the available Mediterranean regional climate models.

The Kitikmeot Sea is a semi-enclosed, east–west waterway in the southern Canadian Arctic Archipelago (CAA). In the present work, the ice conditions, stratification, and circulation of the Kitikmeot...

Regional anomalies of steric sea level are either due to redistribution of heat and freshwater anomalies or due to ocean–atmosphere buoyancy fluxes. Interannual to decadal variability in sea level across the tropical Pacific is mainly due to steric variations driven by wind stress anomalies. The importance of air–sea buoyancy fluxes is less clear. We use a global, eddy-permitting ocean model and a series of sensitivity experiments with quasi-climatological momentum and buoyancy fluxes to identify the contribution of buoyancy fluxes for interannual to decadal sea level variability in the tropical Pacific. We find their contribution on interannual timescales to be strongest in the central tropical Pacific at around a 10∘ latitude in both hemispheres and also relevant in the very east of the tropical domain. Buoyancy-flux-forced anomalies are correlated with variations driven by wind stress changes, but their effect on the prevailing anomalies and the importance of heat and freshwater fluxes vary locally. In the eastern tropical basin, interannual sea level variability is amplified by anomalous heat fluxes, while the importance of freshwater fluxes is small, and neither has any impact on decadal timescales. In the western tropical Pacific, the variability on interannual and decadal timescales is dampened by both heat and freshwater fluxes. The mechanism involves westward-propagating Rossby waves that are triggered during El Niño–Southern Oscillation (ENSO) events by anomalous buoyancy fluxes in the central tropical Pacific and counteract the prevailing sea level anomalies once they reach the western part of the basin.

– Introducing a new method for mapping submerged archaeological landscapes. – Airborne hyperspectral data allows estimation of bottom depth and reflectance for archaeological surveys in shallow waters.

The western Mediterranean Sea area is frequently affected in autumn by heavy precipitation events (HPEs). These severe meteorological episodes, characterized by strong offshore low-level winds and heavy rain in a short period of time, can lead to severe flooding and wave-submersion events. This study aims to progress towards an integrated short-range forecast system via coupled modeling for a better representation of the processes at the air–sea interface. In order to identify and quantify the coupling impacts, coupled ocean–atmosphere–wave simulations were performed for a HPE that occurred between 12 and 14 October 2016 in the south of France. The experiment using the coupled AROME-NEMO-WaveWatchIII system was notably compared to atmosphere-only, coupled atmosphere–wave and ocean–atmosphere simulations. The results showed that the HPE fine-scale forecast is sensitive to both couplings: the interactive coupling with the ocean leads to significant changes in the heat and moisture supply of the HPE that intensify the convective systems, while coupling with a wave model mainly leads to changes in the low-level dynamics, affecting the location of the convergence that triggers convection over the sea. Result analysis of this first case study with the AROME-NEMO-WaveWatchIII system does not clearly show major changes in the forecasts with coupling and highlights some attention points to follow (ocean initialization notably). Nonetheless, it illustrates the higher realism and potential benefits of kilometer-scale coupled numerical weather prediction systems, in particular in the case of severe weather events over the sea and/or in coastal areas, and shows their affordability to confidently progress towards operational coupled forecasts.

Assimilation of weather radar measurements including radar reflectivity and radial wind data has been operational at the Deutscher Wetterdienst, with a diagonal observation error (OE) covariance matrix. For an implementation of a full OE covariance matrix, the statistics of the OE have to be a priori estimated, for which the Desroziers method has been often used. However, the resulted statistics consists of contributions from different error sources and are difficult to interpret. In this work, we use an approach that is based on samples for truncation error in radar observation space to approximate the representation error due to unresolved scales and processes (RE) and compare its statistics with the OE statistics estimated by the Desroziers method. It is found that the statistics of the RE help the understanding of several important features in the variances and correlation length scales of the OE for both reflectivity and radial wind data and the other error sources from the microphysical scheme, radar observation operator and the superobbing technique may also contribute, for instance, to differences among different elevations and observation types. The statistics presented here can serve as a guideline for selecting which observations to assimilate and for assignment of the OE covariance matrix that can be diagonal or full and correlated.

We prove that Hilbert’s Tenth Problem for meromorphic functions and for entire functions in several variables is unsolvable over the language of rings, together with constant symbols for two of the variables and a predicate for a place. This is the first result in the literature, which proves unsolvability of a diophantine problem for the ring of complex analytic functions in a number of variables. The proof rests upon an interplay between analytic geometry, analysis, number theory, and logic.

The paper reports a numerical investigation into the effect of rubble mounds inside perforated caisson breakwaters (PCBs), in which a line-shaped mass source wavemaker is proposed for generating random waves. A series of experiments are employed to validate the numerical model, and good agreements are observed in the comparison of the experimental and numerical results. With the use of the validated numerical model, the numerical investigation is performed, in which the attention is mainly paid to two parameters: the slope angle and porosity of the inner rubble mound. The result shows that, as the slope angle of the inner rubble mound increases, the reflection coefficient is observed to decrease first and then increase, and compared to the experiment, both the positive and negative hydrodynamic pressure acting on the solid rear wall of PCBs is weakened. On the other hand, although a larger inner rubble mound porosity is beneficial to diminish the reflection coefficient, the reduction is not obvious especially when the front wall porosity is small. Furthermore, as the increase of front wall porosity and relative wave absorption chamber length (the ratio of wave absorption chamber length to significant wavelength), the effect of the slope angle and porosity of the inner rubble mound becomes more significant because more waves could enter the wave absorption chamber. The relative wave absorption chamber length considered in the present study ranges from 0.06 to 0.21, and the recommended slope angle is approximately 45 degrees.

Purpose. The research is aimed at developing methods for creating highly productive and highly nutritious pasture agrophytocenoses, adapted to the extreme conditions of the arid zone of the Northern Caspian region. Methods. The paper provides an assessment of the productivity of perennial one-species (Agropyron) and poly-species (Agropyron, Eutoria, Kochia) agrophytocenoses for a five-year period of their vegetation, depending on the timing (autumn, spring) and sowing methods (ordinary, scattered). Results. These phytocenoses, created in the harsh climatic conditions of the semi-desert on light chestnut soils with a low level of fertility (humus – 0.68 %), starting from the first year, formed the yield 2–7 times higher than the natural pasture. According to the results of the study, it was revealed that a significant role in the creation of arid forage phytocenosis was played by the sowing method and species composition, including the scattered sowing method turned out to be more productive (in monospecific – by 57–70 %, in poly-species – by 63–82 %), the yield of the poly-species composition of the phytocenosis, starting from the second year, increased by 1–2 t/ha for all years of the study in comparison with the monospecific composition both on the row and on the spread method of sowing. Scientific novelty. All created agrophytocenoses for all variants had a fodder value 3–10 times higher than the natural pasture, including the presence of different plant species on the pasture increased the collection of fodder units in comparison with a single-species pasture by 1.5–2 times, and the spread method of sowing also increased the provision of pasture fodder with protein by 0.18–0.2 t/ha. Already by the second year of plant development, it was noted that the presence of shrubs and semi-shrubs on the forage lands creates better conditions than the aftermath of the corn crop for snow retention, and, accordingly, contributes to a greater accumulation of moisture in the soil.

The quality of wave measurements is of primary importance for the validation of wave forecasting models, satellite wave calibration and validation, wave physics, offshore operations and design and climate monitoring. Validation of global wave forecasts revealed significant regional differences, which were linked to the different wave buoy systems used by different countries. To fully understand the differences between the wave measurement systems, it is necessary to go beyond investigations of the integral wave parameters height, period and direction, into the frequency spectra and the four directional Fourier parameters that are used to estimate the directional distribution. We here analyse wave data measured from three different sensors (non-directional Datawell Waverider buoy, WaveRadar Rex, Optech laser) operating at the Ekofisk oil production platform located in the central North Sea over a period of several months, with significant wave height ranging from 1 to 10 m. In general, all three sensors provide similar measurements of the integral wave properties and frequency spectra, although there are some significant differences which could impact design and operations, forecast verification and climate monitoring. For example, the radar underestimates energy in frequency bands higher than 8 s by 3–5%, swell (12.5–16 s) by 5–13%, while the laser has 1–2% more energy than the Waverider in the most energetic bands. Lee effects of structures are also estimated. Lower energy at the frequency tail with the radar has an effect on wave periods (they are higher); wave steepness is seen to be reduced by 10% in the wind seas. Goda peakedness and the unidirectional Benjamin-Feir index are also examined for the three sensors.

In this paper, a numerical study is presented to investigate wave force on the connections of main parts of a side-anchored straight floating bridge concept for the Bjørnafjorden fjord crossing. The floating bridge is supported by 18 pontoons, and three groups of mooring lines are employed to restrain the bridge against horizontal loads and increase its transverse stiffness. The created wave forces at the connections of pontoon-column and column-girder of the floating bridge considering the effects of short-crested and long-crested waves, varying wave direction, hydrodynamic interaction between pontoons, and mooring system are analyzed. It is found that short-crested and long-crested waves depending on their direction decrease or increase the wave forces on the joints. Considering that the effect of hydrodynamic interaction between pontoons can increase or reduce the wave forces and moments created in the joints, which means the neglect of the hydrodynamic interaction effects between the pontoons to simplify the modeling of this type of floating bridge, may be unacceptable. Moreover, the results showed that the bridge mooring system does not merely reduce the wave forces and moments at joints along the bridge.

The North River estuary (Massachusetts, USA) is a tidal marsh creek network where tidal dispersion processes dominate the salt balance. A field study using moorings, shipboard measurements, and drone surveys was conducted to characterize and quantify tidal trapping due to tributary creeks. During flood tide, saltwater propagates up the main channel and gets “trapped” in the creeks. The creeks inherit an axial salinity gradient from the time-varying salinity at their boundary with the main channel, but it is stronger than the salinity gradient of the main channel because of relatively weaker currents. The stronger salinity gradient drives a baroclinic circulation that stratifies the creeks, while the main channel remains well-mixed. Because of the creeks’ shorter geometries, tidal currents in the creeks lead those in the main channel; therefore, the creeks never fill with the saltiest water which passes the main channel junction. This velocity phase difference is enhanced by the exchange flow in the creeks, which fast-tracks the fresher surface layer in the creeks back to the main channel. Through ebb tide, the relatively fresh creek outflows introduce a negative salinity anomaly into the main channel, where it is advected downstream by the tide. Using high-resolution measurements, we empirically determine the salinity anomaly in the main channel resulting from its exchange with the creeks to calculate a dispersion rate due to trapping. Our dispersion rate is larger than theoretical estimates that neglect the exchange flow in the creeks. Trapping contributes more than half the landward salt flux in this region.

The structure of locally soluble periodic groups in which every abelian subgroup is locally cyclic was described over 20 years ago. We complete the aforementioned characterization by dealing with the non-periodic case. We also describe the structure of locally finite groups in which all abelian subgroups are locally cyclic.

It is well-known that the notion of limit in the sharp topology of sequences of Colombeau generalized numbers$$\widetilde{\mathbb {R}}$$R~does not generalize classical results. E.g. the sequence$$\frac{1}{n}\not \rightarrow 0$$1n↛0and a sequence$$(x_{n})_{n\in \mathbb {N}}$$(xn)n∈Nconvergesifand only if$$x_{n+1}-x_{n}\rightarrow 0$$xn+1-xn→0. This has several deep consequences, e.g. in the study of series, analytic generalized functions, or sigma-additivity and classical limit theorems in integration of generalized functions. The lacking of these results is also connected to the fact that$$\widetilde{\mathbb {R}}$$R~is necessarily not a complete ordered set, e.g. the set of all the infinitesimals has neither supremum nor infimum. We present a solution of these problems with the introduction of the notions of hypernatural number, hypersequence, close supremum and infimum. In this way, we can generalize all the classical theorems for the hyperlimit of a hypersequence. The paper explores ideas that can be applied to other non-Archimedean settings.

A recently developed energy flux diagnosis scheme, which incorporates a smooth connection between the tropical and subtropical zones, is used in the present study to investigate vertically propagating waves in the tropical Indian Ocean (IO) based on the result of a linear, continuously stratified ocean model driven by climatological wind forcing. This extended diagnosis reveals deep-reaching eastward energy fluxes at the equator which develop four times per year and are associated with equatorial Kelvin waves (KWs) generated by semiannual winds. The authors find that the downward transfer of wave energy is particularly deep in the southern Bay of Bengal (SBoB). This downward flux is attributed to off-equatorial Rossby waves and appears four times per year, maximizing its amplitude during November–December. Southwesterly winds in the Arabian Sea intensify eastward energy flux of KWs at mid-depth, which maximizes in amplitude in August. This is contrastive to KW energy flux at the surface which peaks in May. These mid-depth equatorial KW packets subsequently arrive at the eastern boundary of the IO and are diffracted poleward to produce downward energy flux in November and December detected in the SBoB.

The captured underwater images suffer from color cast and haze effect caused by absorption and scattering. These interdependent phenomena jointly degrade images, resulting in failure of autonomous machines to recognize image contents. Most existing learning-based methods for underwater image enhancement (UIE) treat the degraded process as a whole and ignore the interaction between color correction and dehazing. Thus, they often obtain unnatural results. To this end, we propose a novel joint network to optimize the results of color correction and dehazing in multiple iterations. Firstly, a novel triplet-based color correction module is proposed to obtain color-balanced images with identical distribution of color channels. By means of inherent constraints of the triplet structure, the information of channel with less distortion is utilized to recover the information of other channels. Secondly, a recurrent dehazing module is designed to alleviate haze effect in images, where the Gated Recurrent Unit (GRU) as the memory module optimizes the results in multiple cycles to deal with severe underwater distortions. Finally, an iterative mechanism is proposed to jointly optimize the color correction and dehazing. By learning transform coefficients from dehazing features, color features and basic features of raw images are progressively refined, which maintains color balanced during the dehazing process and further improves clarity of images. Experimental results show that our network is superior to the existing state-of-the-art approaches for UIE and provides improved performance for underwater object detection.

This article presents two interrelated problems-along tracking and cross tracking-in guidance design for curved path following for unmanned surface vehicles. Since these two types of directional tracking are interactively constrained in most research work, an iteration mechanism is first put forward to optimize the path parameter in each closed loop such that along tracking will not affect cross tracking in the subsequent time period. An extended line-of-sight (ELOS) guidance principle is then proposed by varying the look-ahead distance with the cross-track error such that sideslip in cross tracking can be promptly compensated through vehicle heading amendment. Both simulation and experimental results verify the effectiveness of the proposed methods, which perform better than the conventional line-of-sight (LOS) and integral LOS (ILOS) guidance laws.

Recent advances in the utilization of Lie Groups for robotic localization have led to dramatic increases in the accuracy of estimation and uncertainty characterization. One of the novel methods, the Invariant Extended Kalman Filter (InEKF) extends the Extended Kalman Filter (EKF) by leveraging the fact that some error dynamics defined on matrix Lie Groups satisfy a log-linear differential equation. Utilization of these observations result in linearization with minimal approximation error, no dependence on current state estimates, and excellent convergence and accuracy properties. In this letter we show that the primary sensors used for underwater localization, inertial measurement units (IMUs) and doppler velocity logs (DVLs) meet the requirements of the InEKF. Furthermore, we show that singleton measurements, such as depth, can also be used in the InEKF update with minor modifications, thus expanding the set of measurements usable in an InEKF. We compare convergence, accuracy and timing results of the InEKF to a quaternion-based EKF using a Monte Carlo simulation and show notable improvements in long-term localization and much faster convergence with negligible difference in computation time.

In the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $$\mathbf {ZF}$$ ZF , some are shown to be independent of $$\mathbf {ZF}$$ ZF . For independence results, distinct models of $$\mathbf {ZF}$$ ZF and permutation models of $$\mathbf {ZFA}$$ ZFA with transfer theorems of Pincus are applied. New symmetric models of $$\mathbf {ZF}$$ ZF are constructed in each of which the power set of $$\mathbb {R}$$ R is well-orderable, the Continuum Hypothesis is satisfied but a denumerable family of non-empty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube $$[0, 1]^{\mathbb {R}}$$ [ 0 , 1 ] R .

Brittle stars are one of the leading components of the benthic communities in the Kara Sea. The fauna of the Kara Sea brittle stars is represented by 12 species. Ophiocten sericeum (Forbes, 1852), Ophiopleura borealis Danielssen et Koren, 1877, Ophiacantha bidentata (Bruzelius, 1805), and Ophioscolex glacialis Müller et Troschel, 1842 are most widespread within the sea. Based on the available data, distribution maps for each species were constructed. A comparative analysis of the Barents Sea, the Kara Sea and the Laptev Sea fauna was carried out. It was found that during evolution the fauna of Kara Sea brittle stars at the genus level was under balanced influence of autochthonous and allochthons processes; at the species level the autochthonous processes were predominant. The obtained value of the taxonomic uniqueness index characterizes the fauna of the Kara Sea brittle stars as quite isolated at all taxonomic levels. Six biogeographic groups were distinguished in the biogeographic structure of the fauna of the sea, of which the boreal-Arctic and high-boreal-Arctic forms are the most represented. The use of the Jaccard species similarity coefficients and Pearson correlation showed that the greatest similarity at the species level is observed between the Kara and the Laptev seas.

In August 2018, a remarkable polynya was observed off the north coast of Greenland, a perennial ice zone where thick sea ice cover persists. In order to investigate the formation process of this polynya, satellite observations, a coupled ice-ocean model, ocean profiling data, and atmosphere reanalysis data were applied. We found that the thinnest sea ice cover in August since 1978 (mean value of 1.1 m, compared to the average value of 2.8 m during 1978−2017) and the modest southerly wind caused by a positive North Atlantic Oscillation (mean value of 0.82, compared to the climatological value of −0.02) were responsible for the formation and maintenance of this polynya. The opening mechanism of this polynya differs from the one formed in February 2018 in the same area caused by persistent anomalously high wind. Sea ice drift patterns have become more responsive to the atmospheric forcing due to thinning of sea ice cover in this region.

We consider the generalised Hahn sequence space $$h_{d}$$ , where d is an unbounded monotone increasing sequence of positive real numbers, and characterise several classes of bounded linear operators or matrix transformations from $$h_{d}$$ into the spaces of all bounded, convergent and null sequences, and into the space of all abolutely convergent series and $$h_{d}$$ , and also from spaces of all absolutely convergent series, all null, convergent and bounded sequences into $$h_{d}$$ . Furthermore, we establish identities or estimates for the norms of the corresponding bounded linear operators. We also derive identities for the Hausdorff measure of noncompactness for the operators in the above classes with the exception of the final space being the space of all bounded sequences and charcaterise the classes of all corresponding compact operators. Finally, we apply our results to present a Fredholm operator from $$h_{d}$$ into itself given by a tridiagonal matrix.

If we consider a real hypersurface M in a complex projective space we have the covariant derivatives associated to both the Levi-Civita connection and, for any nonnull real number k, to the k-th generalized Tanaka-Webster connection. We also have the Lie derivative and a derivative of Lie type associated to the k-th generalized Tanaka-Webster connection. If we consider the structure Lie operator $$L_{\xi }$$ on M, we can define two tensor fields of type (1,2) on M from $$L_{\xi }$$ associated to the derivatives mentioned above, $$L_{{\xi }_F}^{(k)}$$ and $$L_{{\xi }_T}^{(k)}$$ . Kaimakamis, Panagiotidou and Perez obtained the classifications of real hypersurfaces for which either $$L_{{\xi }_F}^{(k)}$$ or $$L_{{\xi }_T}^{(k)}$$ identically vanish. We generalize such results classifying real hypersurfaces in complex projective space such that $$L_{{\xi }_F}^{(k)}$$ (respectively, $$L_{{\xi }_T}^{(k)}$$ ) is either symmetric or skew symmetric.

Elucidating the mechanisms of fluctuations in fish populations are key to sustainable fisheries management. However, limited data combined with climate variability and fishing further constrain our understanding of fish population dynamics. Fortunately, marine sedimentary archives of fish abundance and environmental changes in the past, may provide new insights into long-term fish population fluctuations. Here, we used 150-year sediment records of the abundance of Japanese anchovy (Engraulis japonicus) scales, phytoplankton, and zooplankton biomarkers, and δ15N data previously reported from the central Yellow Sea (YS). We discussed the linkages of the anchovy abundance to ecosystem structure and sea surface temperatures (SSTs). Principal component analysis (PCA) identified negative effects of strong stratification (higher δ15N) and high abundance of haptophytes (higher alkenone content) on the anchovy stock through our analytical period (~1860–2005 AD). In addition, we found positive relationships between the anchovy abundance and plankton productivity in proxies before the period of intense fishing (1860–1980 AD), indicating bottom-up processes affecting the anchovy stock. However, the bottom-up processes became unclear under excessive fishing. This was possibly due to overfishing becoming a major driver after 1980, thereby altering the cascading of the marine ecosystem towards a different structure. Climate variability seems to indirectly influence the anchovy stock through bottom-up control via a cascading effect from the changes in the North Pacific Gyre Oscillation (NPGO) or the Pacific North American pattern (PNAP). The impacts of these changes on the hydrodynamic features of YS in turn influence the productivity of plankton prey for the anchovy. Collectively, our findings suggest that synergistic effects of climate and fishing on the anchovy need to be paid greater attention. Our results also contribute to an improved understanding of fish population fluctuations in other seas.

Tropical Storm Eta impacted the coast of west-central Florida from 11 November to 12 November 2020 and generated high waves over elevated water levels for over 20 hours. A total of 148 beach and nearshore profiles, spaced about 300 m (984 ft) apart, were surveyed one to two weeks before and one to eight days after the storm to examine the beach changes along four barrier islands, including Sand Key, Treasure Island, Long Key, and Mullet Key. The high storm waves superimposed on elevated water level reached the toe of dunes or seawalls and caused dune erosion and overwash at various places. Throughout most of the coast, the dune, dry beach, and nearshore area was eroded and most of the sediment was deposited on the seaward slope of the nearshore bar, resulting in a roughly conserved sand volume above closure depth. The longshore variation of beach-profile volume loss demonstrates an overall southward decreasing trend, mainly due to a southward decreasing nearshore wave height as controlled by offshore bathymetry and shoreline configurations. The Storm Erosion Index (SEI) developed by Miller and Livermont (2008) captured the longshore variation of beach-profile volume loss reasonably well. The longshore variation of breaking wave height is the dominant factor controlling the longshore changes of SEI and beach erosion. Temporal variation of water level also played a significant role, while beach berm elevation was a minor factor. Although wider beaches tended to experience more volume loss from TS Eta due to the availability of sediment, they were effective in protecting the back beach and dune area from erosion. On the other hand, smaller profile-volume loss from narrow beach did not necessarily relate to less dune/ structure damage. The opposite is often true. Accurate evaluation of a storm’s severity in terms of erosion potential would benefit beach management especially under the circumstance of increasing storm activities due to climate change.

Hurricane Isaias struck the Cape Fear Region of North Carolina around 23:00 EDT on 3 August 2020, making landfall at Ocean Isle Beach as a Category 1 storm with peak wind speeds of 80 mph. An array of nearshore Sofar Spotter wave buoys captured the wave field at two beaches off the coasts of Bald Head Island (south-facing and east-facing beaches) and Masonboro Island. Local variations in significant wave height and peak wave direction were observed along the Lower Cape Fear Region, due to large shoal features impacting the regional wave climate. A cross-shore transect of five pressure sensors was installed at the north end of Masonboro Island 2.5 days prior to landfall to measure storm surge, wave runup, and variation of gravity/ infragravity wave energy across the barrier island. The three fast-sampling wave gauges along the backshore became buried before Hurricane Isaias peak storm surge, and the two gauges on and behind the dune were never inundated. A low-cost (< $250) Storm Surge Observation Camera (SSOC) prototype captured storm surge and coastal erosion at Kure Beach, in conjunction with pre- and post-storm RTK GPS beach profile surveys. Kure Beach experienced more than 1.0 m of vertical erosion of the berm, while Masonboro Island experienced around 0.1 m of accretion across the backshore, despite nearly identical wave and wind forcing conditions at the two beaches separated by ~20 km. Pre-storm berm height and width (higher and wider at Kure Beach), as well as foreshore slope (steeper, 1:9, at Kure Beach), are likely factors influencing significant erosion at Kure Beach, while slight accretion was observed at Masonboro Island.

Storm surges create coastal flooding that can be damaging to life and property. In estuaries with significant river influence (fluvial), it is possible for tides, storm surge, and river discharge to interact and enhance surges relative to the immediate coast. These tide-surge-river interactions were previously identified in a fluvial Maine estuary as higher frequency (>four cycles per day) oscillations to storm surge which were proposed to be incited by enhanced friction and resonance during certain windstorm events (Spicer et al. 2019). The relative contributions to tide-surge-river interaction from atmospheric forcing variables (wind, barometric pressure, and externally generated surge) remains unclear. This work seeks to decompose and analyze a recent windstorm surge event to better isolate the effects of atmospheric forcing on tidesurge- river interaction. Results show total storm surges in the fluvial estuary to be two times larger than at the estuary mouth because of tide-surge-river interaction. Analysis indicated at least 50% of the magnitude of tide-surge-river interactions are created by non-tidal forcing, in the form of wind, enhancing frictional energy in the estuary. The remaining tide-surge-river interaction is likely a result of changes in tidal wave propagation speed due to surge deepening the mean estuary water level.

In this study, we investigated the mechanism of eutrophication and hypoxia in the upper Gulf of Thailand from August 2014 to June 2015 based on field observation data, box model analysis, and the unscaled trophic status index (UNTRIX). Fresh water residence time derived from a simple box model was long (38.61 days) during the transition period between the southwest to northeast monsoon in September 2014. In contrast, fresh water residence time was short (2.63 days) during the late northeast monsoon in February 2015. Long residence time was related to the development of widespread strong hypoxia in near-bottom waters in over half of the gulf during the transition between the southwest and the northeast monsoon, when river discharge was also very large. UNTRIX is used to assess water trophic levels, and is based on water qualities including concentrations of chlorophyll-a (Chl-a), dissolved oxygen (DO), dissolved inorganic nitrogen (DIN), and dissolved inorganic phosphorus (DIP). Hypertrophic and eutrophic conditions were observed at river mouths; their seasonal eutrophication was related to river discharge and circulation. Nutrients were mainly increased by river discharge. Water column stratification and long residence time were required for the development of severe hypoxia in the study area.

Since August 2017, the Kuroshio has taken a large-meander (LM) path, which has forced the Kuroshio extension (KE) to be in its stable state against its wind-forced decadal variability. How such current conditions have impacted the formation and advection of North Pacific subtropical mode water (STMW) over its distribution region was examined using Argo float data during 2005–2020. Out of the whole STMW defined as a low-potential vorticity layer of 16–19.5 ºC, a relatively cold variety of 16–18 ºC, which was formed south of the KE and advected westward and southward, occupied more than 80% of the total volume. The formation rate of the 16–18 ºC variety was low during 2006–2009 in an unstable-KE period and high during 2010–2015 in a stable-KE period, and then dropped drastically in 2016 despite the KE still being in the stable state. After a short unstable-KE period in 2016–2017, the LM-forced, stable-KE period began, but the formation rate of the 16–18 ºC variety has not restored, possibly due to stronger background stratification propagated from the central North Pacific. In addition, the 16–18 ºC variety has had to make a southern detour around the LM, and its westward advection from the formation region south of the KE to the region south of Japan has been significantly decreased, possibly because it is dissipated more strongly over a southern part of the Izu–Ogasawara Ridge. Due to such decline in the formation and advection, the volume of the 16–18 ºC variety and hence that of the whole STMW have gradually decreased since 2016.

Green infrastructure, utilizing coastal ecosystems, provides a nature-based solution to counteract coastal hazards and rising sea level. Coastal forests, a major type of green infrastructure, are r...

Five high-resolution hydrographic sections were conducted at the periphery of an anticyclonic mesoscale eddy north of the Kuroshio Extension (KE) to explore the evolution of submesoscale structure in the subsurface layer associated with mesoscale eddies. The five sections continuously captured patches of low temperature and salinity water originated from the subarctic region with a horizontal scale of 10–20 km and a vertical scale of 100 m in the strain field at the periphery and in the interior of the eddy detected mainly by the surface Okubo-Weiss parameter. Each patch on the same isopycnal constituted a submesoscale filament. A cold and fresh filament in the intermediate layer in and around the eddy was recently ventilated compared with ambient water, suggesting that submesoscale filaments contribute to a rapid water mass transport from the outside to the inside of the eddy, as well as from the subarctic to the KE region. Filaments at the periphery of the eddy were forced by the convergence in the cross-frontal direction. The horizontal tracer gradient of the filaments evolved in the downstream direction, and 10–50% of the evolution was explained by geostrophic forcing. Moreover, the analysis implied that the evolution of the vertical tracer gradient might have been caused by the vertical shear of the horizontal velocity. The resulting patches were expected to contribute to an effective mixing, suggesting the influence of submesoscale filaments on not only the water mass transport but also the transformation in and around mesoscale eddies in the KE region.

The role of coastal blue carbon ecosystems in climate mitigation and adaptation efforts has been recognized. Blue carbon ecosystem functionality is one component of coastal nature-based or green–gr...

This special issue marks the 100th anniversary of the founding of the Liverpool Tidal Institute (LTI), one of a number of important scientific developments in 1919. The preface gives a brief history of how the LTI came about and the roles of its first two Directors, Joseph Proudman and Arthur Doodson. It also gives a short overview of the research on tides at the LTI through the years. Summaries are given of the 26 papers in the special issue. It will be seen that the topics of many of them could be thought of as providing a continuation of the research first undertaken at the LTI. Altogether, they provide an interesting snapshot of work on tides now being made by groups around the world.

With the development of the Internet of Underwater Things (IoUT), underwater acoustic sensor networks (UASNs) have become an enabling system to support real-time and continuous data transmission. Existing scheduling-based medium access control (MAC) protocols ignored the limitations between the generation time and the transmission time of forwarding packets. This results in unavailability of some scheduled slots, and makes packets endure more waiting time on relay nodes and thereafter longer end-to-end delay. To reduce transmission latency, this article develops a novel scheduling-based MAC protocol, which schedules slots in the packet level. All packets to be generated and transmitted in a frame are predicted and scheduled. Considering our defined packet collision constraint and traffic-flow constraint, we formulate the slot scheduling problem in a frame into a combinatorial optimization problem, which ensures that all source packets transmitted in a frame can be delivered to the sink node with the minimum average end-to-end delay within the same frame. To solve this problem, two algorithms are proposed, namely, an optimal packet-level slot scheduling (PLSS) algorithm and a heuristic approximate PLSS (PLSS-A) algorithm. The performances of our proposed protocol using both algorithms are evaluated with different network scales, packet lengths, and offered traffic loads. Numerical results demonstrate that both PLSS and PLSS-A perform well in terms of average end-to-end delay and service fairness, and have an advantage in the network throughput in large-scale networks. Our proposed PLSS MAC protocol is predicted to be promising in large-scale UASNs with demand for real-time and long-term monitoring.

International audience; Since pilots generally avoid intense convective areas, ice crystals icing (ICI) is an aeronautical weather incident that mainly occurs in the anvil of tropical deep convective clouds. Samples of favorable conditions for the occurrence of ICI and data from the High Altitude Ice Crystals (HAIC) 2015 field campaign in French Guiana are investigated and compared with simulations of the French operational mesoscale forecast system Application of Research to Operations at Mesoscales (AROME). To this end, a contextualization of convective systems into convective, stratiform, and cirriform regions is employed for both observations and AROME. General features of the microphysics of deep tropical convective systems are identified. The number concentration of crystals larger than 125 μm and total water content (TWC) are strongly correlated at each temperature level, and both decrease with increasing distance from convective cores. AROME can reproduce the general behavior of the observed microphysics, especially TWC, but seems unable to simulate extreme ICI events. Reasons are sought in the assumptions performed in the microphysical scheme ICE3, and guidelines are proposed to enhance its skills in the context of ICI. In particular, the representation of the snow particle size distribution is adjusted across observations using a generalized gamma shape. This shape is found to outperform the usual Marshall–Palmer and gamma shapes. Additionally, a temperature and snow content dependence of generalized gamma parameters is found. These changes are found to significantly improve the snow concentration diagnostic of ICE3, and these modifications open the way for improvements in the ICE3 scheme

Polyvalent meanings behind naval ram displays were prevalent and ingrained in the Roman world, especially at Octavian’s Campsite Memorial for the Actian War. Naval rams and their display alluded to gender and power discourses within Roman society. These discourses included Roman notions of sex, penetration, domination, phallus size, and ideas of achieved hierarchies of masculinity. Analyzing ram displays through Roman perceptions of gender and sexuality, specifically concerning ancient masculinity, reveals that rams functioned not only as weapons of war but also as metaphorical phalloi that embodied and projected immense power. Octavian’s ram display at Actium was used to effeminize Marc Antony through the successful defeat and figurative castration of his fleet, which was done by cutting off the rams from the bows of the warships. By exhibiting the rams as such, Octavian asserted his own impenetrability and masculine virtue, which simultaneously promoted Antony’s penetrability and lack of masculinity. In choosing the largest rams, Octavian implied that his masculine prowess was invincible. The ram display unveiled Octavian’s phallic dominion over all other Greeks and Romans. As Octavian’s naval ram display was the largest and most impressive of the ancient world, he effectively rendered all previous ram dedications subordinate to his own.

Assume that $${{\mathfrak {H}}}$$ and $${{\mathfrak {K}}}$$ are two real or complex Hilbert spaces, A a linear relation from $${{\mathfrak {H}}}$$ to $${{\mathfrak {K}}}$$ and B a linear relation from $${{\mathfrak {K}}}$$ to $${{\mathfrak {H}}}$$ , respectively. Necessary and sufficient conditions for B to be equal to the adjoint of A are provided. New characterizations for closed, skew–adjoint and selfadjoint linear relations are obtained.

Grazing significantly affects the distribution, growth, and productivity of shrubs. In this study, we evaluated the effects of grazing disturbance on the spatial distribution patterns and interspecific relationships of two desert shrubs, Ammopiptanthus mongolicus and Sarcozygium xanthoxylon. Three types of grazing conditions were considered, including enclosed area (EA), seasonal rotational grazing area (SRGA), and grazing area (GA) (100 m × 100 m), in the West Ordos Nature Reserve of Inner Mongolia, China. The results showed that A. mongolicus and S. xanthoxylon populations were uniformly distributed at a small scale, and the distribution in EA and SRGA became gradually random. In GA, A. mongolicus population showed aggregated distribution but S. xanthoxylon population showed random distribution at a small scale. Moreover, both A. mongolicus and S. xanthoxylon populations at the 5–7 m scale showed random distribution. At the small and intermediate scales, the two species showed positive interspecific relationships of GA. However, no interspecific relationship was noted between the two species in EA and SRGA. A significant positive relationship (P P P P