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At least 37 records · Page 2

Tidal–hydrological dynamics of water temperature across freshwater forested wetlands on the northeastern Pacific coast

Abstract Tidal freshwater forests were once extensive across temperate coastlines, but loss and fragmentation have made estimation of their ecosystem functions challenging. We measured water temperature for 2 years in three Sitka spruce tidal forests, a restoration site, and an adjacent emergent marsh on the Columbia River, Washington, United States. We assessed spatial variability of water temperature within sites including the effects of hydrology, differences among bay and tributary tidal forests, and differences between the tidal forests and the mainstem Columbia, the restoration site, and the emergent marsh. The tidal forests nearest to the bay had lower interior water temperatures than their channel confluences by up to 2.5°C (weekly median temperature) and 2.0°C (weekly maximum temperature), with most cooling occurring during the low‐flow months of July–September. Tributary sites had maximum temperatures up to 1.9°C cooler than bay sites and 4.2°C cooler than the mainstem. Temperatures in the two bay sites decreased by −0.16°C/100 m and −0.07°C/100 m, on average. The restoration site had the smallest within‐site temperature gradient. Differences in maximum temperatures were greatest when tidal range was low, while higher tidal ranges were associated with warmer and more variable site interiors relative to their confluences. These results suggest that water temperatures in these tidal forests can provide temperature refugia for cold water biota including salmon.

54 ENVIRONMENTAL SCIENCES↗

Public Reference Data for Megawatt-Scale Hydrogen Electrolysis - Simulated Marine Hydrokinetic Tidal Turbine

The U.S. Department of Energy and National Laboratory of the Rockies (NLR) demonstrate hydrogen electrolysis, hydrogen compression and storage, and variable hydrogen fuel cell power production using megawatt-scale equipment at NLR’s Flatirons Campus as part of the Advanced Research on Integrated Energy Systems (ARIES) initiative. This dataset is part of that effort and is intended for academic, national laboratory, industrial, and other stakeholders to plan, design, and validate models of megawatt-scale hydrogen technologies and diverse energy infrastructure. These data provide a baseline for how existing hydrogen electrolysis technologies perform when coupled with other energy technologies. This dataset contains inputs and outputs from simulations of a floating marine hydrokinetic turbine over approximately half a tidal cycle (~6.6 hours). Inflow conditions were derived from field measurements in Alaska’s Cook Inlet and represent a tidal environment in which the current speed ramps from near 0 m/s to a peak of 3 m/s and back. The original acoustic doppler current profiler dataset is publicly available on the Marine and Hydrokinetic Data Repository. In a full tidal cycle, the flow reverses and the rotor would reorient; this reversal was not modeled. In the Cook Inlet campaign , turbulence intensity was similar in both directions. Two inflow cases are included. In the first case, labeled “raw” in the files, the measured current time series was used directly in the InflowWind module of OpenFAST. Speed and direction were applied as a function of time and elevation, uniformly in the horizontal direction. With full spatial coherence, this approach captures high turbulent variability and results in pronounced power fluctuations, so it is considered a conservative, near-worst-case representation of loading. In the second case, labeled “average” in the files, a 30-minute moving average was applied to extract the slowly varying mean speed. The residual fluctuations about this mean were used to generate spatially varying, full-field turbulence inputs with TurbSim, giving a more physically realistic representation of the inflow across the rotor disk. Two random realizations were used to produce distinct inflow conditions for two OpenFAST simulations representing a two-turbine array. The same turbulence intensity is applied across the full time series, producing larger fluctuations at the start and end, where the mean speed is low. The second case is the more appropriate framework for performance and power assessment but overpredicts turbulence at lower flow speeds and underpredicts it at higher speeds. As the floating platform moves and the rotor changes its x-position, Taylor’s frozen turbulence hypothesis used by InflowWind assumes a constant rather than a time-varying mean velocity, introducing some inaccuracy in the velocity plane sampling. The turbine modeled is the 500-kW Reference Model 1, a horizontal-axis two-bladed hydrokinetic turbine on a four-column floating semisubmersible substructure . Simulations were performed using OpenFAST v4.1 with the Reference Open Source Controller (ROSCO) v2.10. All input files required to reproduce the simulations are included. The electrolyzer is a 1.25-MW proton exchange membrane type MC250 system manufactured by Nel . This unit supports up to 2.5 MW, but NLR has only a single 1.25-MW stack. The datasets report hydrogen balance-of-plant and system data, all captured at 1 Hz, including hydrogen mass production measured with an Emerson Coriolis flow meter. The system controls hydrogen production by varying direct current applied to the stack, from a maximum of 3,000 A to a minimum safe operating current of 300 A, or 10%. Because the current–voltage characteristic changes as the stack ages and efficiency degrades, the actual minimum safe operating power changes over time. The simulated tidal turbine time series data was translated from power (kilowatts) to current (amperes) using a curve fit with calibration data and sent to the electrolyzer power supply at 1-Hz. Each zip file represents a single tidal electrolysis experiment and is named: {technology}_{inflow method}_{number of 500 kW tidal turbines connected} For instance, “tidal-500kW-RM1_average_2.zip” is a 6-hour experiment using the 500-kW tidal reference model, scaled by 2x (1-MW) to better match the electrolyzer maximum of 1.25MW, fed with the 30-minute moving average current case. Each zip folder contains the following files: A .csv file of raw data. An .xlsx file explaining all the fields in the raw data. A .png plot showing the time series of hydrogen production in kilograms per hour, electrolysis power consumption, and input wave power. A .csv file combines all tidal profiles as "combined_tidal_experiments.csv." A separate experiment, “characterization_200.zip,” shows the MC250 electrolyzer steady-state response with 30-minute load steps over 5 hours and is accessible with this entry.

08 HYDROGEN↗

Australian tidal currents – assessment of a barotropic model (COMPAS v1.3.0 rev6631) with an unstructured grid

While the variations of tidal range are large and fairly well known across Australia (less than 1 m near Perth but more than 14 m in King Sound), the properties of the tidal currents are not. We describe a new regional model of Australian tides and assess it against a validation dataset comprising tidal height and velocity constituents at 615 tide gauge sites and 95 current meter sites. The model is a barotropic implementation of COMPAS, an unstructured-grid primitive-equation model that is forced at the open boundaries by TPXO9v1. The mean absolute error (MAE) of the modelled M2 height amplitude is 8.8 cm, or 12 % of the 73 cm mean observed amplitude. The MAE of phase (10°), however, is significant, so the M2 mean magnitude of vector error (MMVE, 18.2 cm) is significantly greater. The root sum square over the eight major constituents is 26 % of the observed amplitude. We conclude that while the model has skill at height in all regions, there is definitely room for improvement (especially at some specific locations). For the M2 major axis velocity amplitude, the MAE across the 95 current meter sites, where the observed amplitude ranges from 0.1 to 156 cm s −1 , is 6.9 cm s −1 , or 22 % of the 31.7 cm s −1 observed mean. This nationwide average result is encouraging, but it conceals a very large regional variation. Relative errors of the tidal current amplitudes on the narrow shelves of New South Wales (NSW) and Western Australia exceed 100 %, but tidal currents are weak and negligible there compared to non-tidal currents, so the tidal errors are of little practical significance. Looking nationwide, we show that the model has predictive value for much of the 79 % of Australia's shelf seas where tides are a major component of the total velocity variability. In descending order this includes the Bass Strait, the Kimberley to Arnhem Land, and southern Great Barrier Reef regions. There is limited observational evidence to confirm that the model is also valuable for currents in other regions across northern Australia. We plan to commence publishing “unofficial” tidal current predictions for chosen regions in the near future based on both our COMPAS model and the validation dataset we have assembled.

Tidal currents↗

A review of tidal energy—Resource, feedbacks, and environmental interactions

The ocean contains a variety of renewable energy resources, little of which has been exploited. Here, we review both tidal range and tidal stream energy, with a focus on the resource, feedbacks, and environmental interactions. The review covers a wide range of timescales of relevance to tidal energy, from fortnightly (spring-neap) and semi-diurnal variability, down to array, and device-scale turbulence. When simulating the regional tidal energy resource, and to assess environmental impacts, it is necessary to account for feedbacks between the tidal array and the resource itself. We critically review various methods for simulating energy extraction, from insights gained through theoretical studies of “tidal fences” in idealized channels, to realistic three-dimensional model studies with complex geometry and arrays of turbines represented by momentum sinks and additional turbulence due to the presence of rotors and support structures. We discuss how variability can be reduced by developing multiple (aggregated) sites with a consideration of the enhanced phase diversity offered by exploiting less energetic tidal currents. This leads to future research questions that have not yet been explored in depth at first-generation tidal sites in relatively sheltered channels (e.g., the interaction of waves with currents). Such enhanced understanding of real sea conditions, including the effects of wind and waves, leads to our other identified primary future research direction—reduced uncertainties in turbulence predictions, including the development of realistic models that simulate the interaction between ambient turbulence and the turbulence resulting from multiple wakes, and changes to system-wide hydrodynamics, water quality, and sedimentation.

Environmental impacts↗

The Roles of Tidal Marshes in the Estuarine Biochemical Processes: A Numerical Modeling Study

Observations suggest that the existence of tidal marsh can alter the oxygen and nutrient dynamics in adjacent water bodies, but assessing the impacts of large tidal marshes on an estuary is challenging. In this study, we use a modeling approach to investigate the roles of tidal marshes on the estuarine biochemical processes. The marsh model, which simulates the ecological functions of marshes at seasonal and annual time-scales, is embedded inside an unstructured-grid three-dimensional hydrodynamic and eutrophication model (SCHISM-ICM). This modeling system simulates the growth and metabolism of the tidal marshes and links biological processes to nutrient dynamics in the water column and sediment. This model dynamically simulates nutrient recycling and physical transport of the materials between marshes and open water through wetting-drying processes. This coupled model system is validated and successfully applied to the York River Estuary. Model results suggest that tidal marshes influence the local diurnal dissolved oxygen (DO) cycle by exporting dissolved organic carbon and high sediment oxygen demand in the marsh system through the tidal exchange. The high deposition rates of organics and diurnal DO cycle enhance the sediment release of phosphorus. On the other hand, marshes tend to decrease dissolved inorganic nitrogen in the water column by settling particulate nutrients and enhancing the denitrification process. The study demonstrates that tidal marshes exert substantial impacts on the estuarine biochemical processes. The developed tidal marsh model enhances eutrophication modeling and advances the understanding of the feedback effects between marsh biogeochemistry and estuarine eutrophication processes on a systemic scale.

54 ENVIRONMENTAL SCIENCES↗

A giant umbrella-like stellar stream around the tidal ring galaxy NGC 922

Tidal ring galaxies (TRGs) are rarely observed in the local universe due to their intrinsically transient nature. The tidal ring structures are the result of strong interactions between gas-rich stellar disks and smaller galactic systems, and do not last longer than ~500 Myr. Therefore, these are perfect scenarios in which to look for the debris of recently accreted dwarf galactic systems. Our goal is to study the low surface brightness stellar structures around the TRG NGC 922 and to revise the hypothesis of its formation in light of these new data. We present new deep images of the TRG NGC 922 and its surroundings from the DESI Legacy survey data and from our observations with an amateur telescope. These observations are compared with results from high-resolution N-body simulations that were designed to reproduce an alternative formation scenario for this peculiar galaxy. Our new observations unveil that the low surface brightness stellar tidal structures around NGC 922 are much more complex than reported in previous works. In particular, the formerly detected tidal spike-like structure at the north-east of the central galaxy disk is not connected with the dwarf companion galaxy PGC 3080368, which has been suggested as the intruder triggering the ring formation of NGC 922. The deep images reveal that this tidal structure mainly has a fainter giant umbrella-like shape, and thus it was formed from the tidal disruption of a different satellite. Using the broad-band g, r, and z DESI LS images, we measured the photometric properties of this stellar stream, estimating a total absolute magnitude in the r band of M r = -17.0 ± 0.03 mag and a total stellar mass for the stream of between 6.9 and 8.5×10 8 M ⊙ . We performed a set of N-body simulations to reproduce the observed NGC922-intruder interaction, suggesting a new scenario for the formation of its tidal ring from the infall of a gas-rich satellite around 150 Myr ago. Finally, our deep images also reveal a tidal shell around the dwarf galaxy PGC 3080368, a possible fossil of a recent merger with a smaller satellite, which may suggest it is in its first infall towards NGC 922.

79 ASTRONOMY AND ASTROPHYSICS↗

Tidal capture of stars by a massive black hole

The processes leading to tidal capture of stars by a massive black hole and the consequences of these processes in a dense stellar cluster are discussed in detail. When the amplitude of a tide and the subsequent oscillations are sufficiently large, the energy deposited in a star after periastron passage and formation of a bound orbit cannot be estimated directly using the linear theory of oscillations of a spherical star, but rather numerical estimates must be used. The evolution of a star after tidal capture is discussed. The maximum ratio R of the cross-section for tidal capture to that for tidal disruption is about 3 for real systems. For the case of a stellar system with an empty capture loss cone, even in the case when the impact parameter for tidal capture only slightly exceeds the impact parameter for direct tidal disruption, tidal capture would be much more important than tidal disruption.

Novikov, I. D.↗

Tidal regime of intact planetoid capture model for the Earth-Moon system: Does it relate to the archean sedimentary rock record?

Regardless of one's favorite model for the origin of the Earth-Moon system (fission, coformation, tidal capture, giant-impact) the early history of lunar orbital evolution would produce significant thermal and earth and ocean tidal effects on the primitive earth. Three of the above lunar origin models (fission, coformation, giant-impact) feature a circular orbit which undergoes a progressive increase in orbital radius from the time of origin to the present time. In contrast, a tidal capture model places the moon in an elliptical orbit undergoing progressive circularization from the time of capture (for model purposes about 3.9 billion years ago) for at least a few 10(exp 8) years following the capture event. Once the orbit is circularized, the subsequent tidal history for a tidal capture scenario is similar to that for other models of lunar origin and features a progressive increase in orbital radius to the current state of the lunar orbit. This elliptical orbit phase, if it occurred, should have left a distinctive signature in the terrestrial and lunar rock records. Depositional events would be associated terrestrial shorelines characterized by abnormally high, but progressively decreasing, ocean tidal amplitudes and ranges associated with such an orbital evolution. Several rock units in the age range 3.6-2.5 billion years before present are reported to have a major tidal component. Examples are the Warrawoona, Fortescue, and Hamersley Groups of Western Australia and the Pangola and Witwatersand Supergroups of South Africa. Detailed study of the features of these tidal sequences may be helpful in deciphering the style of lunar orbital evolution during the Archean Eon.

Malcuit, Robert J.↗

Aliased tidal errors in TOPEX/POSEIDON sea surface height data

Alias periods and wavelengths for the M(sub 2, S(sub 2), N(sub 2), K(sub 1), O(sub 1), and P(sub 1) tidal constituents are calculated for TOPEX/POSEIDON. Alias wavelenghts calculated in previous studies are shown to be in error, and a correct method is presented. With the exception of the K(sub 1) constituent, all of these tidal aliases for TOPEX/POSEIDON have periods shorter than 90 days and are likely to be confounded with long-period sea surface height signals associated with real ocean processes. In particular, the correspondence between the periods and wavelengths of the M(sub 2) alias and annual baroclinic Rossby waves that plagued Geosat sea surface height data is avoided. The potential for aliasing residual tidal errors in smoothed estimates of sea surface height is calculated for the six tidal constituents. The potential for aliasing the lunar tidal constituents M(sub 2), N(sub 2) and O(sub 1) fluctuates with latitude and is different for estimates made at the crossovers of ascending and descending ground tracks than for estimates at points midway between crossovers. The potential for aliasing the solar tidal constituents S(sub 2), K(sub 1) and P(sub 1) varies smoothly with latitude. S(sub 2) is strongly aliased for latitudes within 50 degress of the equator, while K(sub 1) and P(sub 1) are only weakly aliased in that range. A weighted least squares method for estimating and removing residual tidal errors from TOPEX/POSEIDON sea surface height data is presented. A clear understanding of the nature of aliased tidal error in TOPEX/POSEIDON data aids the unambiguous identification of real propagating sea surface height signals. Unequivocal evidence of annual period, westward propagating waves in the North Atlantic is presented.

Schlax, Michael G.↗

Topographic enhancement of tidal motion in the western Barents Sea

A high-resolution numerical lattice is used to study a topographically trapped motion around islands and shallow banks of the western Barents Sea caused both by the semidiurnal and diurnal tidal waves. Observations and model computations in the vicinity of Bear Island show well-developed trapped motion with distinctive tidal oscillatory motion. Numerical investigations demonstrate that one source of the trapped motion is tidal current rectification over shallow topgraphy. Tidal motion supports residual currents of the order of 8 cm/s around Bear Island and shallow Spitsbergenbanken. The structures of enhanced tidal currents for the semidiurnal components are generated in the shallow areas due to topographic amplification. In the diurnal band of oscillations the maximum current is associated with the shelf wave occurrence. Residual currents due to diurnal tides occur at both the shallow areas and the shelf slope in regions of maximum topographic gradients. Surface manifestation of the diurnal current enhancement is the local maximum of tidal amplitude at the shelf break of the order of 5 to 10 cm. Tidal current enhancement and tidally generated residual currents in the Bear Island and Spitsbergenabanken regions cause an increased generation of ice leads, ridges and, trapped motion of the ice floes.

Kowalik, Z.↗

Tidal Energy Available for Deep Ocean Mixing: Bounds from Altimetry Data

Maintenance of the large-scale thermohaline circulation has long presented a problem to oceanographers. Observed mixing rates in the pelagic ocean are an order of magnitude too small to balance the rate at which dense bottom water is created at high latitudes. Recent observational and theoretical work suggests that much of this mixing may occur in hot spots near areas of rough topography (e.g., mid-ocean ridges and island arcs). Barotropic tidal currents provide a very plausible source of energy to maintain these mixing processes. Topex/Poseidon (T/P) satellite altimetry data have made precise mapping of open ocean tidal elevations possible for the first time. We can thus obtain empirical, spatially localized, estimates of barotropic tidal dissipation. These provide an upper bound on the amount of tidal energy that is dissipated in the deep ocean, and hence is available for deep mixing. We will present and compare maps of open ocean tidal energy flux divergence, and estimates of tidal energy flux into shallow seas, derived from T/P altimetry data using both formal data assimilation methods and empirical approaches. With the data assimilation methods we can place formal error bars on the fluxes. Our results show that 20-25% of tidal energy dissipation occurs outside of the shallow seas, the traditional sink for tidal energy. This suggests that up to 1 TW of energy may be available from the tides (lunar and solar) for mixing the deep ocean. The dissipation indeed appears to be concentrated over areas of rough topography.

Egbert, Gary D.↗

Tidal Energy Available for Deep Ocean Mixing: Bounds from Altimetry Data

Maintenance of the large-scale thermohaline circulation has long presented an interesting problem. Observed mixing rates in the pelagic ocean are an order of magnitude too small to balance the rate at which dense bottom water is created at high latitudes. Recent observational and theoretical work suggests that much of this mixing may occur in hot spots near areas of rough topography (e.g., mid-ocean ridges and island arcs). Barotropic tidal currents provide a very plausible source of energy to maintain these mixing processes. Topex/Poseidon satellite altimetry data have made precise mapping of open ocean tidal elevations possible for the first time. We can thus obtain empirical, spatially localized, estimates of barotropic tidal dissipation. These provide an upper bound on the amount of tidal energy that is dissipated in the deep ocean, and hence is available for deep mixing. We will present and compare maps of open ocean tidal energy flux divergence, and estimates of tidal energy flux into shallow seas, derived from T/P altimetry data using both formal data assimilation methods and empirical approaches. With the data assimilation methods we can place formal error bars on the fluxes. Our results show that 20-25% of tidal energy dissipation occurs outside of the shallow seas, the traditional sink for tidal energy. This suggests that up to 1 TW of energy may be available from the tides (lunar and solar) for mixing the deep ocean. The dissipation indeed appears to be concentrated over areas of rough topography.

Ray, Richard D.↗

Tidal Energy Available for Deep Ocean Mixing: Bounds From Altimetry Data

Maintenance of the large-scale thermohaline circulation has long presented a problem to oceanographers. Observed mixing rates in the pelagic ocean are an order of magnitude too small to balance the rate at which dense bottom water is created at high latitudes. Recent observational and theoretical work suggests that much of this mixing may occur in hot spots near areas of rough topography (e.g., mid-ocean ridges and island arcs). Barotropic tidal currents provide a very plausible source of energy to maintain these mixing processes. Topex/Poseidon satellite altimetry data have made precise mapping of open ocean tidal elevations possible for the first time. We can thus obtain empirical, spatially localized, estimates of barotropic tidal dissipation. These provide an upper bound on the amount of tidal energy that is dissipated in the deep ocean, and hence is available for deep mixing. We will present and compare maps of open ocean tidal energy flux divergence, and estimates of tidal energy flux into shallow seas, derived from T/P altimetry data using both formal data assimilation methods and empirical approaches. With the data assimilation methods we can place formal error bars on the fluxes. Our results show that 20-25% of tidal energy dissipation occurs outside of the shallow seas, the traditional sink for tidal energy. This suggests that up to 1 TW of energy may be available from the tides (lunar and solar) for mixing the deep ocean. The dissipation indeed appears to be concentrated over areas of rough topography.

Egbert, Gary D.↗

Hydrokinetic tidal energy resource assessment following international electrotechnical commission guidelines

Marine renewable energy can be used as a viable energy source to alleviate the impact of the climate crisis and have a carbon-free electricity sector in the future. Especially the energetic tidal streams are an attractive source of clean energy due to the periodic occurrence of high tidal flows daily. However, before any deployment of tidal turbine farms, it is essential to perform a resource assessment depending on the scope and scale of the project. Here, the International Electrotechnical Commission has developed a technical standard for assessing the tidal stream resource "IEC 62600-201 TS" to aid in this effort: determine a particular site's feasibility and perform the project layout design. In this study, we implemented and validated a high-resolution three-dimensional numerical model and provided results following the IEC TS for a project layout design in a highly energetic tidal channel, Tacoma Narrows of Puget Sound, in the State of Washington, USA. Implementation of the guidelines has helped adequately identify the undisturbed theoretical and technical resources with less bias, where the latter included energy extraction from the flow field arranging a hypothetical tidal energy converter (TEC) array. Also, following the standard, we carefully assessed the changes to channel flow properties from TECs, such as the kinetic energy flux and annual energy production (AEP), to provide the detailed information required for a larger project layout design. Ultimately, this work has shown the important role of IEC TS in tidal stream resource assessment, which can simultaneously act as a benchmark for other studies worldwide.

13 HYDRO ENERGY↗

Tidal Resource Gaps Analysis Technical Report

The tidal resource gaps project was created to address a growing body of evidence that models underpredict tidal current speeds compared to measurements at a number of the top-ranking tidal energy sites. In response, this project compared opportunistic tidal power density measurements from 16 tidal energy hot spot sites with estimates from resource assessment data to identify discrepancies. To improve the accuracy of resource estimates from model data, updated data from eight improved model simulations were obtained. Model improvements included grid refinement, domain coupling, and the use of unstructured or nested grids. New resource estimates were calculated from the updated models, and these data were used to update the tidal hot spots-a list of promising tidal energy sites around the United States.

16 TIDAL AND WAVE POWER↗

Identifying priority ecosystem services in tidal wetland restoration

Classification systems can be an important tool for identifying and quantifying the importance of relationships, assessing spatial patterns in a standardized way, and forecasting alternative decision scenarios to characterize the potential benefits (e.g., ecosystem services) from ecosystem restoration that improve human health and well-being. We present a top-down approach that systematically leverages ecosystem services classification systems to identify potential services relevant for ecosystem restoration decisions. We demonstrate this approach using the U.S. Environmental Protection Agency’s National Ecosystem Service Classification System Plus (NESCS Plus) to identify those ecosystem services that are relevant to restoration of tidal wetlands. We selected tidal wetland management documents from federal agencies, state agencies, wetland conservation organizations, and land stewards across three regions of the continental United States (northern Gulf of Mexico, Mid-Atlantic, and Pacific Northwest) to examine regional and organizational differences in identified potential benefits of tidal wetland restoration activities and the potential user groups who may benefit. We used an automated document analysis to quantify the frequencies at which different wetland types were mentioned in the management documents along with their associated beneficiary groups and the ecological end products (EEPs) those beneficiaries care about, as defined by NESCS Plus. Results showed that a top combination across all three regions, all four organizations, and all four tidal wetland types was the EEP naturalness paired with the beneficiary people who care (existence). Overall, the Mid-Atlantic region and the land steward organizations mentioned ecosystem services more than the others, and EEPs were mentioned in combination with tidal wetlands as a high-level, more general category than the other more specific tidal wetland types. Certain regional and organizations differences were statistically significant. Those results may be useful in identifying ecosystem services-related goals for tidal wetland restoration. This approach for identifying and comparing ecosystem service priorities is broadly transferrable to other ecosystems or decision-making contexts.

54 ENVIRONMENTAL SCIENCES↗

Tidal Friction in the Earth-Moon System and Laplace Planes: Darwin Redux

The dynamical evolution of the Earth-Moon system due to tidal friction is treated here. George H. Darwin used Laplace planes (also called proper planes) in his study of tidal evolution. The Laplace plane approach is adapted here to the formalisms of W.M. Kaula and P. Goldreich. Like Darwin, the approach assumes a three-body problem: Earth, Moon, and Sun, where the Moon and Sun are point-masses. The tidal potential is written in terms of the Laplace plane angles. The resulting secular equations of motion can be easily integrated numerically assuming the Moon is in a circular orbit about the Earth and the Earth is in a circular orbit about the Sun. For Earth-Moon distances greater than ∼10 Earth radii, the Earth's approximate tidal response can be characterized with a single parameter, which is a ratio: a Love number times the sine of a lag angle divided by another such product. For low parameter values it can be shown that Darwin's low-viscosity molten Earth, M. Ross's and G. Schubert's model of an Earth near melting, and Goldreich's equal tidal lag angles must all give similar histories. For higher parameter values, as perhaps has been the case at times with the ocean tides, the Earth's obliquity may have decreased slightly instead of increased once the Moon's orbit evolved further than 50 Earth radii from the Earth, with possible implications for climate. This is contrast to the other tidal friction models mentioned, which have the obliquity always increasing with time. As for the Moon, its orbit is presently tilted to its Laplace plane by 5.2deg. The equations do not allow the Moon to evolve out of its Laplace plane by tidal friction alone, so that if it was originally in its Laplace plane, the tilt arose with the addition of other mechanisms, such as resonance passages.

Darwin Redux↗

Dark Energy Camera photometry reveals extra-tidal stars around the Milky Way globular cluster NGC 6864 (M75)

ABSTRACT Globular clusters are prone to lose stars while moving around the Milky Way. These stars escape the clusters and are distributed throughout extended envelopes or tidal tails. However, such extra-tidal structures are not observed in all globular clusters, and yet there are no structural or dynamical parameters that can predict their presence or absence. NGC 6864 is an outer halo globular cluster with reported no observed tidal tails. We used Dark Energy Camera photometry reaching ∼4 mag underneath its main-sequence turnoff to confidently detect an extra-tidal envelope, and stellar debris spread across the cluster outskirts. These features emerged once robust field star filtering techniques were applied to the fainter end of the observed cluster main sequence. NGC 6864 is associated to the Gaia-Enceladus dwarf galaxy, among others 28 globular clusters. Up-to-date, nearly 64${{\ \rm per\,cent}}$ of them have been targeted looking for tidal tails and most of them have been confirmed to exhibit tidal tails. Thus, the present outcomes allow us to speculate on the possibility that Gaia-Enceladus globular clusters share a common pattern of mass loss by tidal disruption.

Piatti, Andrés E. (ORCID:0000000286790589)↗