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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Offshore Breaking of Impact Tsunami: Van Dorn was Right

Tsunami generated by the impacts of asteroids and comets into the Earth s oceans are widely recognized as a potentially catastrophic hazard to the Earth s population (e.g. Chapman and Morrison 1994, Nature, 367, 33; Hills et al. 1994, in Hazards Due to Comets and Asteroids, (ed. T. Gehrels), 779; Atkinson et al. 2000, Report of the UK Task Force on Potentially Hazardous NEOs; Ward and Asphaug 2000, Icarus, 145, 64). A peculiarity of ocean impacts is the potential global effects of an impact that would otherwise be of only regional or local importance should it occur on land. This is, of course, due to the ability of waves to propagate globally, as seen by the terrible effects of the recent earthquake off the coast of Sumatra. The overall process of an impact tsunami is complex and falls into several distinct phases: 1) initial impact of the bolide into the ocean and formation of a transient cavity in the water, 2) collapse of the cavity and propagation of large waves from the impact center outward over deep water (typically several km in depth), 3) initial effects on wave amplitude as shallower water of the continental slope is reached ("wave shoaling"), possible breaking of waves in relatively shallow water (less than 100 m depth), on continental shelves, and 5) final contact of waves with the shore and their progression onto dry land ("run-up" and "run-in"). Here we report on numerical calculations (and semi-analytic theory) covering phases 3 and 4.

Korycansky, D. G.↗
DOE OSTI2022

Quantification of Off-Channel Inundated Habitat for Pacific Chinook Salmon ( Oncorhynchus tshawytscha ) along the Sacramento River, California, Using Remote Sensing Imagery

Off-channel areas are one of the most impacted aquatic habitats by humans globally, as extensive agricultural and urban development has limited them to roughly 10% of historical extent. This is also true for California’s Sacramento River Valley, where historically frequent widespread inundation has been reduced to a few off-channel water bodies along the mid-Sacramento River. This remaining shallow-water habitat provides crucial ecological benefits to multiple avian and fish species, but especially to floodplain-adapted species such as Chinook salmon (Oncorhynchus tshawytscha). Characterizing spatiotemporal off-channel dynamics, including inundation extent and residence time, is fundamental to better understanding the intrinsic value of such habitats and their potential to support recovery actions. Remote sensing techniques have been increasingly used to map surface water at regional and local scales, with improved resolutions. As such, this study maps off-channel inundation areas and describes their temporal dynamics by analyzing pixel-based time- series of multiple water indices, modified Normalized Difference Water Index (mNDWI) and the Automated Water Extraction Index (AWEI), generated from LandSat-8 and Sentinel-2 data between 2013–2021. Quantified off-channel area was similar with each water index and method used, but improved performance was associated with Sentinel-2 products and AWEI index to identify wetted areas under lower mainstem discharges. Results indicate an uneven distribution of off-channel habitat in the study area, with limited inundated areas in upstream reaches (<16% of total off-channel area for greater flows). In addition, much less habitat exists for flows under 400 m 3 /s, an important migration cue for endangered winter-run Chinook salmon, limiting juvenile access to areas with enhanced rearing conditions. Off-channel habitat residence times averaged between 7 and 16 days, primarily defined by the rate of receding flows, with rapid flow recession providing marginal off-channel habitat. This study shows reasonable performance of moderate resolution LandSat-8 and Sentinel-2 remote sensing imagery to characterize shallow-water inundated habitat in higher-order rivers, and as a method to inform restoration and native fish recovery efforts.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Observations and seismoacoustic simulations of earthquake-generated infrasound waves in non-epicentral regions

We analysed infrasound waves associated with the Gyeongju earthquake (ML 5.8) that occurred on 2016 September 12, in the southeastern Korean Peninsula. For infrasound wave detection, the Progressive Multichannel Correlation method was applied to the infrasound data set recorded at seven arrays operating in South Korea at epicentral distances ranging from 178 to 472 km. Based on the back-projection method constrained by array-dependent celerity and azimuth deviation models, the source regions were identified in both the epicentral and non-epicentral regions. Remarkably, the non-epicentral secondary sources of this earthquake were located in regions with shallow water depths: (i) the western coastal area in the Yellow Sea and (ii) the shallow ocean basin and bank in the East Sea. The location results obtained from the earthquake could be corroborated through its foreshock (ML 5.1), yielding location results consistent with those of the main shock. The generation of infrasound waves over shallow water depths was fortuitously validated by direct recordings of dominant single-frequency (~0.3 Hz) infrasound waves at close range via temporary sensors near the ocean basin and bank. We interpreted that low-frequency infrasound signals could be generated from interactions among the ocean floor, shallow seawater and atmosphere. We performed numerical simulations of seismoacoustic fields to predict ground motions on the seafloor and acoustic transmission efficiency between the water and air interface. The simulations quantified the energy transfer through different media and clarified our observational results. We found that because this solid Earth‒water‒atmosphere coupled air wave has a relatively low frequency (~0.3 Hz), it can survive propagation over long distances compared with high-frequency infrasound waves generated in inland and mountain regions. In this study, we extend our understanding of water‒atmosphere coupling and the monitoring framework for earthquake-associated non-epicentral infrasound waves, encompassing not only inland ground shaking but also shallow sea regions located far from the epicentre.

Earthquake monitoring and test-ban treaty verifica↗
NASA NTRS1981

Determining solutions of hyperbolic systems from incomplete data

An investigation is conducted regarding first-order hyperbolic systems of partial differential equations, taking into account problems for which complete initial data are not available. Problems of the considered kind arise in geophysical applications where satellites are used to collect data. In global weather prediction, it is possible to derive atmospheric temperature and pressure reasonably well over the whole globe from satellite measurements; obtaining the wind field globally is more difficult. It is pointed out that a simple model of atmospheric flow investigated in numerical weather prediction is governed by the shallow water equations. The effect of the Coriolis term on the linearized shallow-water equations is studied.

Bube, K. P.↗
NASA NTRS2010

The Application of Remotely Sensed Data and Models to Benefit Conservation and Restoration Along the Northern Gulf of Mexico Coast

New data, tools, and capabilities for decision making are significant needs in the northern Gulf of Mexico and other coastal areas. The goal of this project is to support NASA s Earth Science Mission Directorate and its Applied Science Program and the Gulf of Mexico Alliance by producing and providing NASA data and products that will benefit decision making by coastal resource managers and other end users in the Gulf region. Data and research products are being developed to assist coastal resource managers adapt and plan for changing conditions by evaluating how climate changes and urban expansion will impact land cover/land use (LCLU), hydrodynamics, water properties, and shallow water habitats; to identify priority areas for conservation and restoration; and to distribute datasets to end-users and facilitating user interaction with models. The proposed host sites for data products are NOAA s National Coastal Data Development Center Regional Ecosystem Data Management, and Mississippi-Alabama Habitat Database. Tools will be available on the Gulf of Mexico Regional Collaborative website with links to data portals to enable end users to employ models and datasets to develop and evaluate LCLU and climate scenarios of particular interest. These data will benefit the Mobile Bay National Estuary Program in ongoing efforts to protect and restore the Fish River watershed and around Weeks Bay National Estuarine Research Reserve. The usefulness of data products and tools will be demonstrated at an end-user workshop.

Quattrochi, Dale↗
NASA NTRS2001

An Improved Heat Budget Estimation Including Bottom Effects for General Ocean Circulation Models

This paper studies the effects of the underwater light field on heat-budget calculations of general ocean circulation models for shallow waters. The presence of a bottom significantly alters the estimated heat budget in shallow waters, which affects the corresponding thermal stratification and hence modifies the circulation. Based on the data collected during the COBOP field experiment near the Bahamas, we have used a one-dimensional turbulence closure model to show the influence of the bottom reflection and absorption on the sea surface temperature field. The water depth has an almost one-to-one correlation with the temperature rise. Effects of varying the bottom albedo by replacing the sea grass bed with a coral sand bottom, also has an appreciable effect on the heat budget of the shallow regions. We believe that the differences in the heat budget for the shallow areas will have an influence on the local circulation processes and especially on the evaporative and long-wave heat losses for these areas. The ultimate effects on humidity and cloudiness of the region are expected to be significant as well.

Carder, Kendall↗
NASA NTRS1989

Deep circulations under simple classes of stratification

Deep circulations where the motion field is vertically aligned over one or more scale heights are studied under barotropic and equivalent barotropic stratifications. The study uses two-dimensional equations reduced from the three-dimensional primitive equations in spherical geometry. A mapping is established between the full primitive equations and general shallow water behavior and the correspondence between variables describing deep atmospheric motion and those of shallow water behavior is established.

Salby, Murry L.↗
NASA NTRS1973

Utilization of ERTS-1 data to monitor and classify eutrophication of inland lakes

The author has identified the following significant results. Significant findings are: (1) one-acre lakes and one-acre islands are detectable; (2)removal of atmospheric parameters derived from RPMI measurements show test lakes to have reflectances of 3.1 to 5.5% in band 4 and 0.3 to 2.3% in band 5; (3) failure to remove reflectance caused by atmosphere results in errors up to 500% in computing lake reflectance from ERTS-1 data; (4) in band 4, up to seven reflectance levels were observed in test lakes; (5) reflectance patterns have been displayed on a color-coded TV monitor and on computer-generated gray scales; (6) deep and shallow water can be separated by a trained photointerpreter and automatic machine processing, with estimates of water depth possible in some cases; (7) RPMI provides direct spectral signature measurements of lakes and lake features such as algal scums and floating plants; (8) a method is reported for obtaining lake color, as estimated by Forel-Ule standards, from ERTS-1 data; (9) a strong correlation between browner water color, diminishing water transparency; and (10) classifying lake eutrophication by observation of surface scums or macrophytes in shallow water seems straightforward.

Rogers, R. H.↗
NASA NTRS2017

MODIS Retrieval of Aerosol Optical Depth over Turbid Coastal Water

We present a new approach to retrieve Aerosol Optical Depth (AOD) using the Moderate Resolution Imaging Spectroradiometer (MODIS) over the turbid coastal water. This approach supplements the operational Dark Target (DT) aerosol retrieval algorithm that currently does not conduct AOD retrieval in shallow waters that have visible sediments or sea-floor (i.e., Class 2 waters). Over the global coastal water regions in cloud-free conditions, coastal screening leads to approx. 20% unavailability of AOD retrievals. Here, we refine the MODIS DT algorithm by considering that water-leaving radiance at 2.1 microns to be negligible regardless of water turbidity, and therefore the 2.1 microns reflectance at the top of the atmosphere is sensitive to both change of fine-mode and coarse-mode AODs. By assuming that the aerosol single scattering properties over coastal turbid water are similar to those over the adjacent open-ocean pixels, the new algorithm can derive AOD over these shallow waters. The test algorithm yields approx. 18% more MODIS-AERONET collocated pairs for six AERONET stations in the coastal water regions. Furthermore, comparison of the new retrieval with these AERONET observations show that the new AOD retrievals have equivalent or better accuracy than those retrieved by the MODIS operational algorithm's over coastal land and non-turbid coastal water product. Combining the new retrievals with the existing MODIS operational retrievals yields an overall improvement of AOD over those coastal water regions. Most importantly, this refinement extends the spatial and temporal coverage of MODIS AOD retrievals over the coastal regions where 60% of human population resides. This expanded coverage is crucial for better understanding of impact of anthropogenic aerosol particles on coastal air quality and climate.

Retrieval↗
NASA NTRS2019

Scaling Laws for Impact Craters in Water

Tsunami waves from asteroid impacts into water are of concern from asteroids in the 200 m to 1 km diameter range because this spans the range from asteroids that will likely hit the surface and not airburst, but also be small enough that global climate effects will hopefully be minimal. Current estimates of impact tsunamis depend on either hydrocode simulations or on semi-analytical models. Unfortunately there is significant disagreement between these methods. One of the main reasons for the disparity is that the semi-analytical models such as Holsapple (1993) rely on experimental impacts into deep water. However for asteroids in the 200 - 1000 m range even the deep ocean basins can appear as shallow water impacts where the crater formed in the water reaches all the way to the sea floor. Another reason for the disparity arises from the linear interpolation of data across many orders of magnitude difference between Froude number (ratio of kinetic to gravitational energy) used in the laboratory experiments and what would be seen in an asteroid impact. The Gault & Sonett (1982) experiment shot millimeter sized glass spheres into water at 1 to 6 km/s and the Olevson (1969) experiment dropped millimeter sized water drops at a few meters per second. The goal of this work was to fill in the gaps and conduct experiments and simulations at the correct Froude numbers of interest, and in both deep and shallow water, to help resolve the disparity and extend the semi-analytical models.

Robertson, Darrel↗
DOE OSTI2024

Air-coupled tsunamis generated from impacts and airbursts: Our understanding before Hunga-Tonga Hunga-Ha'apai

The effort to prevent or mitigate the effects of an impact on Earth is known as planetary defense. A significant component of planetary defense research involves risk assessment. Much of our understanding of the risk from near-Earth objects comes from the geologic record in the form of impact craters, but not all asteroid impacts are crater-forming events. Small asteroids explode before reaching the surface, generating an airburst, and most impacts into the ocean do not penetrate the water to form a crater in the sea floor. The risk from these non-crater-forming ocean impacts and airbursts is difficult to quantify and represents a significant uncertainty in our assessment of the overall threat. We are currently working to better understand impact scenarios that can generate dangerous tsunamis. One of the suggested mechanisms for the production of asteroid–generated tsunamis is by direct coupling of the pressure wave to the water, analogous to the means by which a moving weather front can generate a meteotsunami. To test this hypothesis, we ran a series of airburst simulations and provided time-resolved pressure and wind profiles to use as source functions for tsunami models. We used the CTH hydrocode to model the various airburst scenarios to compare to the results of other simulations and provide time dependent boundary conditions as input to shallow-water wave propagation codes. The strongest and most destructive meteotsunamis are generated by atmospheric pressure oscillations with amplitudes of only a few hPa1 (mbar), corresponding to changes in sea level of a few cm. The resulting wave is strongest when there is a resonance between the ocean and the atmospheric forcing. A Proudman resonance takes place when the atmospheric disturbance’s translational speed (U) equals the longwave phase speed $\sqrt{gh}$ of shallow water wave. Coupling is strongest when the Froude number (Fr=U/c) is unity. A weather front propagates much slower than the speed of sound, so meteotsunamis are most common and dangerous in shallow bodies of water such as the Mediterranean Sea or Lake Michigan. By contrast, the blast wave from an airburst or crater-forming impact propagates at a speed faster than a tsunami in the deepest ocean, and a Proudman resonance cannot be achieved even though the overpressures are orders of magnitude greater. However, blast wave profiles are N-waves in which a sharp shock wave leading to overpressure is followed by a more gradual rarefaction to a much longer-duration underpressure phase. Even though the blast outruns the water wave it is forcing, the tsunami should continue to be driven by the out-of-resonance gradient associated with the suction phase, which may depend strongly on the details of the airburst or impact scenario. The open question is whether there are any conditions under which such an airburst-driven tsunami can be dangerous enough to contribute to the overall impact risk. We have also identified other potential mechanisms for airburst-generated tsunamis: 1) reaction force at the surface from the plume ejected into space, which carries significant momentum, 2) expanding toroidal vortices at the surface, which travel more slowly than the shock wave and can generate a Proudman resonance in relatively shallow ocean (such as continental shelf), and 3) steam explosion from seawater ablation by a “Type II” (Libyan Desert Glass-type) airburst in which the hot vapor jet descends to the surface. On January 15, 2022, the Hunga-Tonga Hunga-Ha’apai volcano, located approximately 60 km north of Tongatapu, the main island of Tonga, violently erupted with a powerful explosion, culminating the period of volcanic activity that started in December of 2021. This event and resulting tsunamis provided an existence proof for the air pressure wave coupling mechanism we proposed. It also suggests that it can be stronger and more significant over much greater distances than we contemplated, leading to global tsunamis associated with impact events on land as well as in the water. Large atmospheric explosions generate global Lamb waves with larger amplitudes, longer periods, and slower speeds than the local and regional blast waves we modeled prior to that event. This paper reviews our analysis and modeling of airburst-driven tsunamis prior to the 2022 Hunga-Tonga Hunga-Ha’apai tsunami, which was the subject of two presentations at the 2023 Planetary Defense Conference and is the subject of another paper currently in preparation.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1973

Calculations of water depth from ERTS-MSS data

ERTS-1 MSS data taken on October 10, 1972 of the Little Bahama Bank are being used to demonstrate the use of ERTS-1 data for mapping of shallow water features for the purpose of upgrading world navigation charts. Marked reflectance differences occur for the shallow water areas in Bands 4, 5, and 6. Digital processing of two adjacent data tapes within the ERTS frame covering an area of about 40 by 40 miles has been completed. Correlation of depth measurements to 5 meters has been successful. A mathematical model for depth measurements using ratio of voltages in Band 4 and 5 has been successfully developed and is being tested for accuracy. Additional studies for areas near Puerto Rico and in Northern Lake Michigan will be undertaken. Satellite data will also provide geographical evidence for verifying existence or nonexistence of doubtful shoal waters now appearing on world charts and considered to be hazardous to shipping.

Polcyn, F. C.↗
NASA NTRS1995

Mean Sea Level Derived from Altimetry and Wind-Driven Numerical Models in the Indian Ocean

Wind-driven model skill in simulating sea level variations in the Indian Ocean depends on our knowledge of the mean ocean dynamic topography. This is demonstrated by running the nonlinear or linear version of a shallow-water model driven by observed winds over Geosat and TOPEX periods. Geosat variations are assimilated in the nonlinear shallow-water model with the objective of obtaining topography data.

numerical models Indian ocean mean sea level remot↗
NASA NTRS1973

Task 1: Water Depth Management, 1388

The author has identified the following significant results. ERTS-1 MSS data taken on October 10, 1972, of the Little Bahama Bank are being used to demonstrate the use of ERTS-1 data for mapping of shallow water features for the purpose of upgrading world navigation charts. Marked reflectance differences occur for the shallow water areas in bands 4, 5, and 6. Digital processing of two adjacent data tapes within the ERTS-1 frame covering an area of about 40 by 40 miles has been completed. Correlation of depth measurements to 5 meters has been successful. A mathematical model for depth measurements using ratio of voltages in band 4 and 5 has been successfully developed and is being tested for accuracy. Additional studies for areas near Puerto Rico and in northern Lake Michigan will be undertaken. Satellite data will also provide geographical evidence for verifying existence or nonexistence of doubtful shoal waters now appearing on world charts and considered to be hazardous to shipping.

Polcyn, F. C.↗
NASA NTRS1997

Evolution of Nonlinear Internal Waves in China Seas

Synthetic Aperture Radar (SAR) images from ERS-I have been used to study the characteristics of internal waves of Taiwan in the East China Sea, and east of Hainan Island in the South China Sea. Rank-ordered packets of internal solitons propagating shoreward from the edge of the continental shelf were observed in the SAR images. Based on the assumption of a semidiurnal tidal origin, the wave speed can be estimated and is consistent with the internal wave theory. By using the SAR images and hydrographic data, internal waves of elevation have been identified in shallow water due to a thicker mixed layer as compared with the bottom layer on the continental shelf. The generation mechanism includes the influences of the tide and the Kuroshio intrusion across the continental shelf for the formations of elevation internal waves. The effects of water depth on the evolution of solitons and wave packets are modeled by nonlinear Kortweg-deVries (KdV) type equation and linked to satellite image observations. The numerical calculations of internal wave evolution on the continental shelf have been performed and compared with the SAR observations. For a case of depression waves in deep water, the solitons first disintegrate into dispersive wave trains and then evolve to a packet of elevation waves in the shallow water area after they pass through a turning point of approximately equal layer depths has been observed in the SAR image and simulated by numerical model.

Liu, Antony K.↗
DOE OSTI2021

Light Regulation of Phytoplankton Growth in San Francisco Bay Studied Using a 3D Sediment Transport Model

In San Francisco Bay (SFB), light availability is largely determined by the concentration of suspended particulate matter (SPM) in the water column. SPM exhibits substantial variation with time, depth, and location. To study how SPM influences light and phytoplankton growth, we coupled a sediment transport model with a hydrodynamic model and a biogeochemical model. The coupled models were used to simulate conditions for the year of 2011 with a focus on northern SFB. For comparison, two simulations were conducted with ecosystem processes driven by SPM concentrations supplied by the sediment transport model and by applying a constant SPM concentration of 20 mg l –1 . The sediment transport model successfully reproduced the general pattern of SPM variation in northern SFB, which improved the chlorophyll-a simulation resulting from the biogeochemical model, with vertically integrated primary productivity varying greatly, from 40 g[C] m –2 year –1 over shoals to 160 g[C] m –2 year –1 in the deep channel. Primary productivity in northern SFB is influenced by euphotic zone depth ( Ze ). Our results show that Ze in shallow water regions (<2 m) is mainly determined by water depth, while Ze in deep water regions is controlled by SPM concentration. As a result, Ze has low (high) values in shallow (deep) water regions. Large (small) differences in primary productivity exist between the two simulations in deep (shallow) water regions. Furthermore, we defined a new parameter F light for “averaged light limitation” in the euphotic zone. The averaged chlorophyll-a concentration in the euphotic zone and F light share a similar distribution such that both have high (low) values in shallow (deep) water regions. Our study demonstrates that light is a critical factor in regulating the phytoplankton growth in northern SFB, and a sediment transport model improves simulation of light availability in the water column.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2003

Compositional Grading in an Impact-produced Spherule Bed, Barberton Greenstone Belt, South Africa: A Key to Condensation History of Rock Vapor Clouds

The chemical and physical processes by which spherules form during the condensation of impact-produced rock vapor clouds are poorly understood. Although efforts have been made to model the processes of spherule formation, there is presently a paucity of field data to constrain the resulting theoretical models. The present study examines the vertical compositional variability in a single early Archean spherule bed in the Barberton Greenstone Belt (BGB), South Africa, in order to better identify the process by which impact vapor clouds condense and spherules form and accumulate. The BGB spherule beds are suitable for this type of study because of their great thickness, often exceeding 25cm of pure spherules, due to the massive sizes of the impactors. Two main problems complicate analysis of vertical compositional variability of graded spherule beds: (1) differential settling of particles in both the vapor and water column due to density and size differences and (2) turbulence within the vapor cloud. The present study compares sections of spherule bed S3 from four different depositional environments in the Barberton Greenstone Belt: (1) The Sheba Mine section (SAF-381) was deposited under fairly low energy conditions in deep water, providing a nice fallout sequence, and also has abundant Ni-rich spinels; (2) Jay's Chert section (SAF-380) was deposited in subaerial to shallow-water conditions with extensive post-depositional reworking by currents. The spherules also have preserved spinels; (3) the Loop Road section (loc. SAF-295; samp. KSA-7) was moderately reworked and has only rare preservation of spinels; and (4) the shallow-water Barite Syncline section (loc. SAF-206; samp KSA-1) has few to no spinels preserved and is not reworked. Although all of the spherule beds have been altered by silica diagenesis and K-metasomatism, most of the compositional differences between these sections appear to reflect their diagenetic histories, possibly related to their differing depositional environments. Sulfate diagenesis in the Barite Syncline and Loop road sections may account for the loss of spinels.

Krull, A. E.↗
NASA NTRS2008

Tide Corrections for Coastal Altimetry: Status and Prospects

Knowledge of global oceanic tides has markedly advanced over the last two decades, in no small part because of the near-global measurements provided by satellite altimeters, and especially the long and precise Topex/Poseidon time series e.g. [2]. Satellite altimetry in turn places very severe demands on the accuracy of tidal models. The reason is clear: tides are by far the largest contributor to the variance of sea-surface elevation, so any study of non-tidal ocean signals requires removal of this dominant tidal component. Efforts toward improving models for altimetric tide corrections have understandably focused on deep-water, open-ocean regions. These efforts have produced models thought to be generally accurate to about 2 cm rms. Corresponding tide predictions in shelf and near-coastal regions, however, are far less accurate. This paper discusses the status of our current abilities to provide near-global tidal predictions in shelf and near-coastal waters, highlights some of the difficulties that must be overcome, and attempts to divine a path toward some degree of progress. There are, of course, many groups worldwide who model tides over fairly localized shallow-water regions, and such work is extremely valuable for any altimeter study limited to those regions, but this paper considers the more global models necessary for the general user. There have indeed been efforts to patch local and global models together, but such work is difficult to maintain over many updates and can often encounter problems of proprietary or political nature. Such a path, however, might yet prove the most fruitful, and there are now new plans afoot to try again. As is well known, tides in shallow waters tend to be large, possibly nonlinear, and high wavenumber. The short spatial scales mean that current mapping capabilities with (multiple) nadir-oriented altimeters often yield inadequate coverage. This necessitates added reliance on numerical hydrodynamic models and data assimilation, which in turn necessitates very accurate bathymetry with high spatial resolution. Nonlinearity means that many additional compound tides and overtides must be accounted for in our predictions, which increases the degree of modeling effort and increases the amounts of data required to disentangle closely aliased tides.

Ray, Richard D.↗