Dynamic Height Field Research Articles

Watertight Incremental Heightfield Tessellation.

In this article, we propose a method for the interactive visualization of medium-scale dynamic heightfields without visual artifacts. Our data fall into a category too large to be rendered directly at full resolution, but small enough to fit into GPU memory without pre-filtering and data streaming. We present the real-world use case of unfiltered flood simulation data of such medium scale that need to be visualized in real time for scientific purposes. Our solution facilitates compute shaders to maintain a guaranteed watertight triangulation in GPU memory that approximates the interpolated heightfields with view-dependent, continuous levels of detail. In each frame, the triangulation is updated incrementally by iteratively refining the cached result of the previous frame to minimize the computational effort. In particular, we minimize the number of heightfield sampling operations to make adaptive and higher-order interpolations viable options. We impose no restriction on the number of subdivisions and the achievable level of detail to allow for extreme zoom ranges required in geospatial visualization. Our method provides a stable runtime performance and can be executed with a limited time budget. We present a comparison of our method to three state-of-the-art methods, in which our method is competitive to previous non-watertight methods in terms of runtime, while outperforming them in terms of accuracy.

Reconstruction of Three‐Dimensional Temperature and Salinity Fields From Satellite Observations

AbstractObservation of the ocean is crucial to the studies of ocean dynamics, climate change, and biogeochemical cycle. However, current oceanic observations are patently insufficient, because the in situ observations are of difficulty and high cost while the satellite remote‐sensed measurements are mainly the sea surface data. To make up for the shortage of ocean interior data and make full use of the abundant satellite data, here we develop a data‐driven deep learning model to estimate ocean subsurface and interior variables from satellite‐observed sea surface data. Exclusively and simply using satellite data, three‐dimensional ocean temperature and salinity fields are successfully reconstructed, which are at 26 level depths from 0 to 2,000 m. We further design a scheme to increase the horizontal resolution from 1° to 1/4°, which is higher than the Argo gridded data. Estimations from our model are accurate, reliable, and stable for a wide range of research areas and periods. Dynamic height fields that are derived from the estimated temperature and salinity, as well as the associated ocean geostrophic flows, are also calculated and analyzed, which indicates the potentials of our model for reconstructing the ocean circulation fields as well. This study enriches oceanic observations with respect to vertical dimension and horizontal resolution, which can largely make up for the paucity of the subsurface and deep ocean observation, both before and during Argo era. This work also provides some new foundations for and insights into geoscience and climate change fields.

Three-Dimensional Dynamic Visualization of Coastal Zones for Sea-land Integration

Ai, B.; Xia, Y.; Li, Z.; Yang, F., and Ji, M., 2020. Three-dimensional dynamic visualization of coastal zones for sea-land integration. In: Zheng, C.W.; Wang, Q.; Zhan, C., and Yang, S.B. (eds.), Air-Sea Interaction and Coastal Environments of the Maritime and Polar Silk Roads. Journal of Coastal Research, Special Issue No. 99, pp. 85-91. Coconut Creek (Florida), ISSN 0749-0208.The three-dimensional visualization of coastal zones for sea-land integration faces difficulties such as multisource terrain data fusion, tidal dynamic changes, and sea surface simulation. This paper proposes a method to convert the depth reference of water depth data into the 1985 national elevation benchmarks, which integrates multisource sea-land terrain data by vertical datums, converts rectangular coordinates and establishes a digital elevation model for sea-land terrain integration. Based on the dynamic characteristics of the sea surface with tides, this paper calculates the tidal level of the nearshore tide station using numerical tidal harmonic analysis and a prediction model. The dynamic sea surface height field away from the mainland is established by inverse distance weighted spatial interpolation. The paper simulates the sea surface by Phillips spectrum analysis and fast Fourier transform and achieves dynamic effects for the sea surface by concave-convex mapping and wave mapping, enhancing the reality of dynamic sea surface expression. In addition, this paper designs and develops the Coastal Zone Terrain Three-Dimensional Dynamic Visualization System, which realizes functions such as sea-land integrated three-dimensional terrain roaming, sea surface simulation visualization and the automatic generation of instantaneous coastlines at any time.

Horizontal circulation and volume transports in the Weddell Gyre derived from Argo float data

Argo floats provide both hydrographic and trajectory data, affording the opportunity to investigate surface to mid-depth ocean dynamics. Here, Argo float data are used to determine the absolute geostrophic velocity field of the upper 50–2000 m of the Weddell Gyre, from which the overall circulation pattern is investigated. The Weddell Gyre plays a pivotal role in the modification of climate by advecting heat towards the Antarctic ice shelves and by modifying the water masses that feed into the lowest limb of the global ocean overturning circulation. Warm Deep Water, the source water mass that delivers heat to the Weddell Gyre, is conveniently located within the upper 2000 m domain covered by the floats; we investigate its volume transport as it circulates the gyre. Full depth volume transports are estimated by applying a quadratic function to extrapolate the relative dynamic height field component to the full ocean depth, using CTD profiles from ship-based surveys to determine an extrapolation error. Major new insights are provided by this study. There is an established double-gyre structure to the circulation, with a strong eastern cell and a weaker western cell. Regional variation of the baroclinic component of the flow field is revealed, indicating a northeast-to-southwest reduction in the baroclinic flow, along with a strong meridional gradient of baroclinic flow along the northern limb of the gyre, especially east of ∼25°W. The zonal mean gyre strength away from the shelf edge is 32 ± 5 Sv (1 Sv = 1 × 106 m3 s−1), of which 13 ± 3 Sv are associated with the advection of Warm Deep Water. There is a considerable amount of recirculation within the gyre interior, where water does not traverse the full zonal extent of the gyre. The recirculation is stronger in the eastern cell of the observed double-gyre structure. The interior circulation cells partly explain the large variations in previous gyre strength estimates. We provide an extensive review of previous estimates in context of the new results obtained.

The Gulf Stream North Wall: Ageostrophic Circulation and Frontogenesis

AbstractEastward zonal jets are common in the ocean and atmosphere, for example, the Gulf Stream and jet stream. They are characterized by atypically strong horizontal velocity, baroclinic vertical structure with an upward flow intensification, large change in the density stratification meridionally across the jet, large-scale meanders around a central latitude, narrow troughs and broad crests, and a sharp and vertically sloping northern (poleward) “wall” defined by horizontal maxima in the lateral gradients of both velocity and density. Measurements and realistic oceanic simulations show these features in the Gulf Stream downstream from its western boundary separation point. A diagnostic theory based on the conservative balance equations is developed to calculate the 3D velocity field associated with the dynamic height field. When applied to an idealized representation of a meandering jet, it explains the spatial structure of the associated ageostrophic secondary circulation around the jet and the positive frontogenetic tendency along the northern wall in the meander sector located upstream from the trough. This provides a basis for understanding why submesoscale instabilities and cross-wall intrusion and streamer events are more prevalent along the sector downstream from the trough and at the crest where there is not such a frontogenetic tendency. An important attribute for this frontogenesis pattern is the 3D shape of the jet, whose idealization is summarized above.

Evaluation of CMIP5 dynamic sea surface height multi-model simulations against satellite observations

We evaluate the representation of dynamic sea surface height (SSH) fields of 33 global coupled models (GCMs) contributed to the fifth phase of the Coupled Model Intercomparison Project (CMIP5). We use observations from satellite altimetry and basic performance metrics to quantify the ability of the GCMs to replicate observed SSH of the time-mean, seasonal cycle, and inter-annual variability patterns. The time-mean SSH representation has markedly improved from CMIP3 to CMIP5, both in terms of overall reduction in root-mean square differences, and in terms of reduced GCM ensemble spread. Biases of the time-mean SSH field in the Indian and Pacific Ocean equatorial regions are consistent with biases in the zonal surface wind stress fields identified with independent measurements. In the Southern Ocean, the latitude of the maximum meridional gradient of the zonal mean SSH CMIP5 models is shifted equatorward, consistent with the GCMs’ spatial biases in the maximum of the zonal mean westerly surface wind stress fields. However, while the Southern Ocean SSH gradients correlate well with the maximum Antarctic circumpolar current transports, there is no significant correlation with the maximum zonal mean wind stress amplitudes, consistent with recent findings that the eddy parameterisations in GCMs dominate over wind stress amplitudes in this region. There is considerable spread across the CMIP5 ensemble for the seasonal and interannual SSH variability patterns. Because of the short observational period, the interannual variability patterns depend on the time-period over which they are derived, while no such dependency is found for the time-mean patterns. The model performance metrics for SSH presented here provide insight into GCM shortcoming due to inadequate model physics or processes. While the diagnostics of CMIP5 GCM performance relative to observations reveal that some models are clearly better than others, model performance is sensitive to the spatio-temporal scales chosen.

Variability of the Atlantic off‐equatorial eastward currents during 1993–2010 using a synthetic method

We have developed, validated, and applied a synthetic method to monitor the off‐equatorial eastward currents in the central tropical Atlantic. This method combines high‐density expendable bathythermograph (XBT) temperature data along the AX08 transect with altimetric sea level anomalies (SLAs) to estimate dynamic height fields from which the mean properties of the North Equatorial Countercurrent (NECC), the North Equatorial Undercurrent (NEUC) and the South Equatorial Undercurrent (SEUC), and their variability can be estimated on seasonal to interannual timescales. On seasonal to interannual timescales, the synthetic method is well suited for reconstructions of the NECC variability, reproduces the variability of the NEUC with considerable skill, and less efficiently describes variations of the SEUC, which is located in a region of low SLA variability. A positive correlation is found between interannual variations of the NECC transport and two indices based on an interhemispheric sea surface temperature (SST) gradient and southeasterly wind stress in the central tropical Atlantic. The NEUC is correlated on interannual timescales with SSTs and meridional wind stress in the Gulf of Guinea and zonal equatorial wind stress. This study shows that both altimetry and XBT data can be effectively combined for near‐real‐time inference of the dynamic and thermodynamic properties of the tropical Atlantic current system.

Low-Complexity Intervisibility in Height Fields

Global illumination systems require intervisibility information between pairs of points in a scene. This visibility problem is computationally complex, and current interactive implementations for dynamic scenes are limited to crude approximations or small amounts of geometry. We present a novel algorithm to determine intervisibility from all points of dynamic height fields as visibility horizons in discrete azimuthal directions. The algorithm determines accurate visibility along each azimuthal direction in time linear in the number of output visibility horizons. This is achieved by using a novel visibility structure we call the convex hull tree. The key feature of our algorithm is its ability to incrementally update the convex hull tree such that at each receiver point only the visible parts of the height field are traversed. This results in low time complexity; compared to previous work, we achieve two orders of magnitude reduction in the number of algorithm iterations and a speedup of 2.4 to 41 on **image** height fields, depending on geometric content. © 2012 Wiley Periodicals, Inc.

Flow fields around the Emperor Seamounts detected from current data

Bathymetric influences of the Emperor Seamounts (ESs) on the local and large‐scale flow fields in the subarctic North Pacific were investigated by analyzing data of directly measured velocity obtained using Argo floats, near‐surface buoys, and moored current meters. The local influences were evident in notable deflections of two relatively strong (∼0.05 m s−1) eastward flows over ESs. A Taylor cap induced by the eastward flow impinging against the Nintoku Seamount (around 42.0°N, 170.5°E) was clearly identified in the climatological flow field at 1000 m depth. This flow pattern was also identified in the near‐surface flow field (15 m depth) and dynamic height field at 200 dbar relative to 2000 dbar, indicating the Taylor cap is stable or frequently generated and extends to the surface. An anticyclonic flow was found over the Suiko Seamount (around 45.0°N, 170.5°E). The influences on the large‐scale flow field were found in data obtained from current meters moored over the southeastern flank of the Suiko Seamount and Argo float trajectories. These data indicate for the first time from velocity observations that there is a seasonally varying boundary current along the eastern side of ESs partially compensating for the Sverdrup transport to the east of ESs, and hence, the seasonally varying component of the subarctic gyre in the North Pacific is divided into two subgyres by ESs.

Scalable Height Field Self-Shadowing

We present a new method suitable for general purpose graphics processing units to render self-shadows on dynamic height fields under dynamic light environments in real-time. Visibility for each point in the height field is determined as the exact horizon for a set of azimuthal directions in time linear in height field size and the number of directions. The surface is shaded using the horizon information and a high-resolution light environment extracted on-line from a high dynamic range cube map, allowing for detailed extended shadows. The desired accuracy for any geometric content and lighting complexity can be matched by choosing a suitable number of azimuthal directions. Our method is able to represent arbitrary features of both high- and low-frequency, unifying hard and soft shadowing. We achieve 23 fps on 1024×1024 height fields with 64 azimuthal directions under a 256×64 environment lighting on an Nvidia GTX 280 GPU.

Vertical motion in the upper ocean from glider and altimetry data

This study represents a first attempt to combine new glider technology data with altimetry measurements to understand the upper ocean dynamics and vertical exchanges in areas with intense horizontal density gradients. In July 2008, just two weeks after Jason‐2 altimeter was launched, a glider mission took place along a satellite track in the Alboran Sea (Western Mediterranean). The mission was designed to be almost simultaneous with the satellite passage. Dynamic height from glider reveals a sharp gradient (∼15 cm) and corresponds very well with the absolute dynamic topography from Jason‐1 & Jason‐2 tandem mission (r > 0.97, rms differences < 1.6 cm). We blend both data sets (glider and altimetry) to obtain a consistent and reliable 3D dynamic height field. Using quasi‐geostrophic dynamics, we diagnose large‐scale vertical motions (∼1 m day−1) which may provide a local mechanism for the subduction of the chlorophyll tongue observed by the glider.

Fast Global Illumination on Dynamic Height Fields

AbstractWe present a real‐time method for rendering global illumination effects from large area and environmental lights on dynamic height fields. In contrast to previous work, our method handles inter‐reflections (indirect lighting) and non‐diffuse surfaces. To reduce sampling, we construct one multi‐resolution pyramid for height variation to compute direct shadows, and another pyramid for each indirect bounce of incident radiance to compute inter‐reflections. The basic principle is to sample the points blocking direct light, or shedding indirect light, from coarser levels of the pyramid the farther away they are from a given receiver point. We unify the representation of visibility and indirect radiance at discrete azimuthal directions (i.e., as a function of a single elevation angle) using the concept of a “casting set” of visible points along this direction whose contributions are collected in the basis of normalized Legendre polynomials. This analytic representation is compact, requires no precomputation, and allows efficient integration to produce the spherical visibility and indirect radiance signals. Sub‐sampling visibility and indirect radiance, while shading with full‐resolution surface normals, further increases performance without introducing noticeable artifacts. Our method renders 512×512 height fields (> 500K triangles) at 36Hz.

Fast Soft Self‐Shadowing on Dynamic Height Fields

AbstractWe present a new, real‐time method for rendering soft shadows from large light sources or lighting environments on dynamic height fields. The method first computes a horizon map for a set of azimuthal directions. To reduce sampling, we compute a multi‐resolution pyramid on the height field. Coarser pyramid levels are indexed as the distance from caster to receiver increases. For every receiver point and every azimuthal direction, a smooth function of blocking angle in terms of log distance is reconstructed from a height difference sample at each pyramid level. This function's maximum approximates the horizon angle. We then sum visibility at each receiver point over wedges determined by successive pairs of horizon angles. Each wedge represents a linear transition in blocking angle over its azimuthal extent. It is precomputed in the order‐4 spherical harmonic (SH) basis, for a canonical azimuthal origin and fixed extent, resulting in a 2D table. The SH triple product of 16D vectors representing lighting, total visibility, and diffuse reflectance then yields the soft‐shadowed result. Two types of light sources are considered; both are distant and low‐frequency. Environmental lights require visibility sampling around the complete 360 ° azimuth, while key lights sample visibility within a partial swath. Restricting the swath concentrates samples where the light comes from (e.g. 3 azimuthal directions vs. 16‐32 for a full swath) and obtains sharper shadows. Our GPU implementation handles height fields up to 1024 × 1024 in real‐time. The computation is simple, local, and parallel, with performance independent of geometric content.

Circulation and heat fluxes during the austral fall in George VI Sound, Antarctic Peninsula

Abstract A mesoscale survey was conducted in northern George VI Sound as part of the United States Southern Ocean Global Ocean Ecosystems Dynamics program in austral fall 2001 to examine the circulation and heat fluxes. The absolute dynamic height field is determined from a combination of measured currents detided using model-predicted tidal currents, streamfunction fitting, and the thermal wind equation based on hydrographic measurements. The results have revealed surface coastal currents of 0.2 m s−1 intruding into northern George VI Sound from Marguerite Bay (MB) and mesoscale eddies formed within the deep trough. Both Antarctic surface waters and modified circumpolar deep water were transported into the sound along the eastern side of the sound while ice shelf influenced waters exited to MB along the western side. Analysis indicates that predominant southward winds during the season were responsible for driving the basin-wide circulation in the sound. Both convergence of horizontal heat transports and vertical upwelling heat fluxes were significant to the contribution or delay of local ice formation in George VI Sound, which is critical for the austral winter ecosystem.

Surface currents in the tropical Atlantic across high density XBT line AX08

Three temperature sections that cross the tropical Atlantic obtained from high density XBT transects are used to identify the major surface currents and to compute their water mass transports. The dynamic heights are computed using XBT temperature profiles with salinity derived from historical T‐S relationships. The values of dynamic height estimated from altimeter data used in conjunction with climatological dynamic height fields are within 3 cm of the XBT‐derived values. The error in XBT‐derived dynamic height introduced by using historical T‐S relationships instead of actual salinity values are estimated to be of the order of 1.5 cm. Dynamic height estimates using the actual salinity values underestimate those obtained using historical T‐S relationships. The structure exhibited in the dynamic height and altimeter‐derived sea height fields do not reveal all the upper ocean currents, making these temperature sections presented here critical for computing transports and identifying currents in this region.

Diagnosis of the Three-Dimensional Circulation in Mesoscale Features with Large Rossby Number

Several diagnoses of three-dimensional circulation, using density and velocity data from a high-resolution, upper-ocean SeaSoar and acoustic Doppler current profiler (ADCP) survey of a cyclonic jet meander and adjacent cyclonic eddy containing high Rossby number flow, are compared. The Q-vector form of the quasigeostrophic omega equation, two omega equations derived from iterated geostrophic intermediate models, an omega equation derived from the balance equations, and a vertical velocity diagnostic using a primitive equation model in conjunction with digital filtering are used to diagnose vertical and horizontal velocity fields. The results demonstrate the importance of the gradient wind balance in flow with strong curvature (high Rossby number). Horizontal velocities diagnosed from the intermediate models (the iterated geostrophic models and the balance equations), which include dynamics between those of quasigeostrophy and the primitive equations, are significantly reduced (enhanced) in comparison with the geostrophic velocities in regions of strong cyclonic (anticyclonic) curvature, consistent with gradient wind balance. The intermediate model relative vorticity fields are functionally related to the geostrophic relative vorticity field; anticyclonic vorticity is enhanced and cyclonic vorticity is reduced. The iterated geostrophic, balance equation and quasigeostrophic vertical velocity fields are similar in spatial pattern and scale, but the iterated geostrophic (and, to a lesser degree, the balance equation) vertical velocity is reduced in amplitude compared with the quasigeostrophic vertical velocity. This reduction is consistent with gradient wind balance, and is due to a reduction in the forcing of the omega equation through the geostrophic advection of ageostrophic relative vorticity. The vertical velocity diagnosed using a primitive equation model and a digital filtering technique also exhibits reduced magnitude in comparison with the quasigeostrophic field. A method to diagnose the gradient wind from a given dynamic height field has been developed. This technique is useful for the analysis of horizontal velocity in the presence of strong flow curvature. Observations of the nondivergent ageostrophic velocity field measured by the ADCP compare closely with the diagnosed gradient wind ageostrophic velocity.

Effect of salinity on density in the Leeuwin Current System

Climatological temperature and salinity fields are used to calculate the salinity contribution to density and dynamic height fields in the Leeuwin Current System (LCS). While the temperature gradient is primarily linear, with warmest water to the north, the salinity fields are spatially inhomogeneous. A comparison of density fields, calculated with constant and variable salinity, shows that, off Western Australia, the density field is primarily determined by temperature. Off southwestern Australia, the density field is dependent on warm and salty (subtropical) and fresh and cold (sub‐Antarctic) water masses. While the dynamic height fields, calculated with constant and variable salinity, show similar flow patterns off Western Australia, different flow patterns are found off southwestern Australia. In addition to the analysis of climatological fields, a primitive equation ocean model is used in a process‐oriented study to investigate the role of salinity in the formation of currents and eddies in the LCS. Two identical ocean models, one with a climatological salinity field and the other with no horizontal salinity gradients, are run and compared with each other. Despite the model runs being initialized with similar temperature distributions, there are relatively large temperature and density differences in the southwestern Australian region due to the advection of water masses by the Leeuwin Current. On the basis of the climatological analyses and the results of the model experiments, it is concluded that, descriptively and dynamically, both temperature and salinity are essential to accurately characterize the large‐scale circulation of the LCS.

Applications of EOF Analysis to the Spatial Estimation of Circulation Features in the Ocean Sampled by High-Resolution CTD Soundings

Abstract The application of empirical orthogonal function analysis to the estimation of geostrophic circulation features in the ocean is studied with particular reference to spatial series of near-synoptic profiles of CTD data retrieved during intensive surveys of the Alboran Sea (western Mediterranean) and the Bransfield Strait (Antarctica). In both regions, horizontal interpolation of principal components of the observed specific volume profiles provides an efficient method of generating a fully three-dimensional representation of the dynamic height field and geostrophic flow structure, which retains the full resolution of the input profile data. Principal components of profiles sampled by “shallow” soundings are estimated using a simple least squares regression method, leading to a more accurate estimate of dynamic height than one based on profile substitution. Spatial correlation and cross-validation analysis yield consistent results in identifying those vertical modes that account for most of the res...

The mean and variability of ocean circulation past northern New Zealand: Determining the representativeness of hydrographic climatologies

Eastward flow in the Tasman Sea, from the separated East Australia Current, reattaches to the shelf break near North Cape, New Zealand, and then continues alongshore to the southeast as the East Auckland Current. A series of three permanent warm core eddies occurs along the offshore side. The mean transport of the East Auckland Current is about 9 Sv, with an additional 10 Sv or more of circulation in the eddies. An extensive hydrographic data set, archived broad scale expendable bathythermograph (XBT) data, two repeating high‐resolution XBT transects, neutrally buoyant float trajectories, and TOPEX altimetric data are used to estimate the temperature and absolute flow fields and to characterize variability. The aim is to examine the usefulness of time series information and absolute velocity measurements in the interpretation of hydrographic snapshots and climatologies, as well as to describe a region having intrinsic oceanographic interest and complexity. Issues of representativeness of the hydrographic data, of the magnitude and scales of the underlying variability, of the existence of permanent fine‐scale features, and of the appropriateness of deep reference levels are addressed directly. The relatively well sampled hydrographic climatology is shown to contain the equivalent of as many as 10 independent realizations. Temperature errors, relative to the true mean, are typically a few tenths of a degree. Significant seasonal bias is identified in the surface layer, and interannual bias is seen in the position of an eddy near North Cape. The dynamic height field at 1000 dbar relative to 2000 dbar is similar to estimates based on float trajectories and the assumption of geostrophic dynamics. This study underlines the value of time series data in the interpretation of a hydrographic climatology, in quantifying the errors in the estimated mean field as well as determining the magnitude and nature of variability. It also highlights the fact that the mean circulation of the oceans contains significant mesoscale structure, unnoticed in coarsely smoothed climatologies.

The Adriatic Sea General Circulation. Part II: Baroclinic Circulation Structure

Abstract In the second part of the paper dedicated to the Adriatic Sea general circulation, the horizontal structure of the hydrographic parameters and dissolved oxygen fields is described on a seasonal timescale. Maps of temperature and salinity climatological fields reveal the enhanced seasonal variability of the Adriatic Sea, which at the surface is associated with the major dilution effects of river runoff. The density and derived dynamic height fields show for the first time the baroclinic geostrophic structure of the general circulation. Winter is dominated by compensation effects between temperature and salinity fronts along the western coastline. The resulting baroclinic circulation is weak and suggests the presence of barotropic current components not accessible by the dataset. Spring and summer seasons have the smallest spatial scales in the temperature and salinity fields and stronger subbasin-scale gyres and current systems, which have been classified in a schematic representation of the circu...