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A well-organized, very low energy ocean swell system off the East Coast of the United States was tracked with the Seasat synthetic aperture radar from deep water, across the continental shelf, and into shallow water. The results indicate that spaceborne imaging radar may be used to accurately measure ocean wavelength and direction, even in coastal areas and in the presence of a mixed ocean.
Standard vector calculus formulas of Cartesian three space are projected onto the surface of a sphere. This produces symmetric equations with three nonindependent horizontal velocity components. Each orthogonal axis has a velocity component that rotates around its axis (eastward velocity rotates around the north–south axis) and a specific angular momentum component that is the product of the velocity component multiplied by the cosine of axis’ latitude. Angular momentum components align with the fixed axes and simplify several formulas, whereas the rotating velocity components are not orthogonal and vary with location. Three symmetric coordinates allow vector resolution and calculus operations continuously over the whole spherical surface, which is not possible with only two coordinates. The symmetric equations are applied to one-layer shallow water models on cubed-sphere and icosahedral grids, the latter being computationally simple and applicable to an ocean domain. Model results are presented for three different initial conditions and five different resolutions.
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a quantum mechanical representation, we use the space of quantum density operators to model the unresolved degrees of freedom of the original dynamics in a statistical sense, and the framework of quantum measurement to predict their contributions to the resolved dynamics. The embedded dynamics is discretized by a positivity preserving process, leading to a compressed representation that is invariant under the dynamical symmetries of the resolved dynamics. We present a data based formulation of the closure scheme and apply it to a closure problem for the shallow water equations. The numerical results demonstrate that our closure model can accurately predict the main features of the true dynamics, including for out of sample initial conditions.
The Hyperspectral Imager for the Coastal Ocean (HICO) aboard the International Space Station has offered for the first time a dedicated space-borne hyperspectral sensor specifically designed for remote sensing of the coastal environment. However, several processing steps are required to convert calibrated top-of-atmosphere radiances to the desired geophysical parameter(s). These steps add various amounts of uncertainty that can cumulatively render the geophysical parameter imprecise and potentially unusable if the objective is to analyze trends and/or seasonal variability. This research presented here has focused on: (1) atmospheric correction of HICO imagery; (2) retrieval of bathymetry using an improved implementation of a shallowwater inversion algorithm; (3) propagation of uncertainty due to environmental noise through the bathymetry retrieval process; (4) issues relating to consistent geo-location of HICO imagery necessary for time series analysis, and; (5) tide height corrections of the retrieved bathymetric dataset. The underlying question of whether a temporal change in depth is detectable above uncertainty is also addressed. To this end, nine HICO images spanning November 2011 to August 2012, over the Shark Bay World Heritage Area, Western Australia, were examined. The results presented indicate that precision of the bathymetric retrievals is dependent on the shallow water inversion algorithm used.Within this study, an average of 70% of pixels for the entire HICO-derived bathymetry dataset achieved a relative uncertainty of less than +/-20%. A per-pixel t-test analysis between derived bathymetry images at successive timestamps revealed observable changes in depth to as lowas 0.4 m. However, the present geolocation accuracy of HICO is relatively poor and needs further improvements before extensive time series analysis can be performed.
We consider the parallel-in-time solution of both linear and nonlinear hyperbolic partial differential equation (PDE) systems in one spatial dimension. In the nonlinear setting, the discretized equations are solved with a preconditioned residual iteration based on a global linearization. The linear(ized) equation systems are approximately solved parallel-in-time using a block preconditioner applied in the characteristic variables of the underlying linear(ized) hyperbolic PDE. This change of variables is motivated by the observation that intervariable coupling between characteristic variables is weak, at least locally where spatio-temporal variations in the eigenvectors of the associated flux Jacobian are sufficiently small, while that between the original variables is not. For an ℓ-dimensional system of PDEs, applying the preconditioner consists of solving a sequence of ℓ scalar linear(ized)-advection-like problems, each associated with a different characteristic wave-speed in the underlying linear(ized) PDE. Furthermore, we approximately solve these linear advection problems using multigrid reduction-in-time (MGRIT); however, any other suitable parallel-in-time method could be used. Numerical examples are shown for the (linear) acoustics equations in heterogeneous media and for the (nonlinear) shallow water equations and Euler equations of gas dynamics with shocks and rarefactions. For many test problems, the solver converges in just a handful of iterations and with mesh-independent convergence rates.
The rotation of Earth breaks time-reversal and reflection symmetries in an opposite sense north and south of the equator, leading to a topological origin for certain atmospheric and oceanic equatorial waves. Away from the equator, the rotating shallow-water and stably stratified primitive equations exhibit Poincaré inertia–gravity waves that have nontrivial topology as evidenced by their strict superinertial time scale and a phase singularity in frequency–wavevector space. This nontrivial topology then predicts, via the principle of bulk-interface correspondence, the existence of two equatorial waves along the equatorial interface, the Kelvin and Yanai waves. To directly test the nontrivial topology of Poincaré-gravity waves in observations, we examine ERA5 data and study cross correlations between the wind velocity and geopotential height of the midlatitude stratosphere at the 50 hPa height. We find the predicted vortex and antivortex in the relative phase of the geopotential height and velocity at the high frequencies of the waves. By contrast, lower-frequency planetary waves are found to have trivial topology also as expected from theory. These results demonstrate a new way to understand stratospheric waves and provide a new qualitative tool to investigate waves in other components of the climate system.
Flooding events pose significant risk to human life, property, and infrastructure. Physically-consistent quantification of altered flood risks in global models requires hyper-resolution (~1 km) or fine flood simulations using two-dimensional (2D) physics schemes, both of which are unavailable in the current generation Earth System Models. Here, in this work, we have developed the River Dynamical Core (RDycore), which is an open-source, 2D shallow water equation (SWE) library for the U.S. Department of Energy's Energy Exascale Earth System Model (E3SM). RDycore uses PETSc and libCEED libraries that allows it to run efficiently on CPUs and GPUs, as well as select a time-integration algorithm at runtime without requiring any code modifications. RDycore achieves spatial error convergence rates for problems with analytical and manufactured solutions similar to those reported previously in the literature, or consistent with the implemented first-order spatial discretization scheme. RDycore's accuracy in predicting flooding for a well-studied dam break problem is comparable to existing SWE models. For a problem with 471 million grid cells, RDycore achieves a speedup of 6.6x and 7.6x on GPUs compared to CPUs when using 320 compute nodes on DOE's Perlmutter and Frontier supercomputers, respectively. The one-way coupling of the RDycore library within E3SM is demonstrated by performing multiple 5-day flooding simulations during Hurricane Harvey driven by five precipitation datasets. The E3SM--RDycore simulations at 30 m spatial resolution accurately simulate maximum water height during the hurricane when benchmarked against a previously published study and achieve a speedup of 15x (Perlmutter) and 21x (Frontier) on GPUs relative to CPUs. The work presented here is the foundational step in providing hardware and algorithmic portability framework for simulating kilometer-scale river dynamics within E3SM.
Three near-neutral boundary layer data sets were investigated with the aim of finding a dependence of wind stress on both wind speed and significant wave height. The data set most representative of open-ocean wave height, wind speed, and momentum flux conditions, was selected and analyzed by means of the least-squares method to produce a new parameterization for the wind stress as a function of both wind speed and significant wave height. This study shows that the wind stress, and consequently the drag coefficient, decreases with increasing wave height for a fixed wind speed. The study also shows that the curvature of the wind profile decreases with increasing wave height and that the C(DN) = A + BU-bar(10) form for the drag coefficient parameterization is inadequate. A drag coefficient that applies to both smooth and rough flows is proposed. These results are more applicable for open-ocean deep-water conditions and less applicable for sheltered, closed, shallow water sites.
The author has identified the following significant results. Bands 6 and 7 have fine structure as obtained by proper selection of digital levels in processing the CCT's. This is contrary to the imagery density received. This means that the small lakes can be classified in IR for different types of water masses. At least four distinct water masses have been determined for test lakes. They are shoreline, shallow water, and two deep waters. One deep water is patchy and presents difficulty in training set selection. The excellent weather and a completely successful field test form a significant happening. It required 12 orbits over the test area before perfect weather occurred.
The author has identified the following significant results. Evidence of a heat sink produced by perched water tables was detected with HCMM night thermal data. The region of shallow water was not visible on HCMM visible or day IR imagery. The results are consistant with previous aircraft investigations.
The Opportunity instruments have provided compelling evidence that the sulfate-rich chemical and siliciclastic sediments at the Meridiani Planum landing site were deposited in shallow water. The local paleo-environment is most often characterized as a broad, shallow sea or large playa, with surface conditions cycling between wet and dry episodes, interbedding evaporates with eolian fine sediments [e.g., 1,2]. This particular working hypothesis is reasonable, considering the area characterized by the rover s mobility. An alternative, marine origin will be considered here, a working hypothesis that we feel provides a better fit to the local-scale results identified by Opportunity, and the regional-scale characteristics of Meridiani Planum provided by data from orbiting spacecraft, when considered together.
The validity of some of the simplifying assumptions in a conceptual water balance model is investigated by comparing simulation results from the conceptual model with simulation results from a three-dimensional physically based numerical model and with field observations. We examine, in particular, assumptions and simplifications related to water table dynamics, vertical soil moisture and pressure head distributions, and subsurface flow contributions to stream discharge. The conceptual model relies on a topographic index to predict saturation excess runoff and on Philip's infiltration equation to predict infiltration excess runoff. The numerical model solves the three-dimensional Richards equation describing flow in variably saturated porous media, and handles seepage face boundaries, infiltration excess and saturation excess runoff production, and soil driven and atmosphere driven surface fluxes. The study catchments (a 7.2 sq km catchment and a 0.64 sq km subcatchment) are located in the North Appalachian ridge and valley region of eastern Pennsylvania. Hydrologic data collected during the MACHYDRO 90 field experiment are used to calibrate the models and to evaluate simulation results. It is found that water table dynamics as predicted by the conceptual model are close to the observations in a shallow water well and therefore, that a linear relationship between a topographic index and the local water table depth is found to be a reasonable assumption for catchment scale modeling. However, the hydraulic equilibrium assumption is not valid for the upper 100 cm layer of the unsaturated zone and a conceptual model that incorporates a root zone is suggested. Furthermore, theoretical subsurface flow characteristics from the conceptual model are found to be different from field observations, numerical simulation results, and theoretical baseflow recession characteristics based on Boussinesq's groundwater equation.
As a result of the 1991 Persian Gulf war, between mid-January and June 1991, the Persian Gulf was contaminated with an estimated 4 to 6 million barrels of crude oil, released directly into the Gulf from refinement facilities, transhipment terminals, and moored tankers along the coast of Kuwait, and precipitated from oil fire smoke plumes. To assess the environmental impact of the oil, an international team of marine scientists representing 14 nations was assembled under the auspices of the United Nations International Oceanic Commission and the Regional Organization for Protection of the Marine Environment to conduct detailed surveys of the Persian Gulf, the Strait of Hormuz, and the Gulf of Oman, including hydrographic, chemical, and biological measurements. To supplement the field surveys and to serve as an aid in data interpretation, astronauts aboard the Space Shuttle Atlantis photographed water features and coastal habitats in the Persian Gulf during mission STS-45 (24 March to 02 April 1992). The astronauts collected 111 hand-held, color photographs of the Gulf (72 70-mm photographs and 39 5-inch photographs) from an altitude of 296 km (160 n.mi.). The photographs reveal distributions in water turbidity associated with outflow from the Shatt-al-Arab and water circulation along the entire coast of Iran and the Strait of Hormuz, coastal wetlands and shallow-water habitats, and sticks appearing in the sunglint pattern, which appear to be oil.
Over the last 15 years a striking pattern of diversification has been documented in the fossil record of benthic marine invertebrates. Higher taxa (orders) tend to originate onshore, diversify offshore, and retreat into deep-water environments. Previous studies attribute this macroevolutionary pattern to a variety of causes, foremost among them the role of nearshore disturbance in providing opportunities for the evolution of novel forms accorded ordinal rank. Our analysis of the post-Paleozoic record of ordinal first appearances indicates that the onshore preference of ordinal origination occurred only in the Mesozoic prior to the Turonian stage of the Cretaceous, a period characterized by relatively frequent anoxic/dysoxic bottom conditions in deeper marine environments. Later, in the Cretaceous and Cenozoic, ordinal origination of benthic organisms did not occur exclusively, or even preferentially, in onshore environments. This change in environmental pattern of ordinal origination roughly correlates with Late Cretaceous: (i) decline in anoxia/dysoxia in offshore benthic environments; (ii) extinction of faunas associated with dysoxic conditions; (iii) increase in bioturbation with the expansion of deep burrowing forms into offshore environments; and (iv) offshore expansion of bryozoan diversity. We also advance a separate argument that the Cenomanian/Turonian and latest Paleocene global events eliminated much of the deep-water benthos. This requires a more recent origin of modern vent and deep-sea faunas, from shallower water refugia, than the Paleozoic or early Mesozoic origin of these faunas suggested by other workers.
This report studies tsunamis caused by asteroids, both those that arise from atmospheric blast waves moving across the water surface from airburst asteroids, and those that arise when the asteroid reaches the water and forms a crater. We perform numerical experiments that compare simulations using depth-averaged models (shallow water and several forms of Boussinesq) with linearized Euler (acoustics plus gravity) and ALE hydrocode simulations. We find that neither of the depth-averaged models do a good job of initiating the tsunami, but in some cases can be used to propagate a solution generated by a higher-fidelity method. A list of our conclusions and recommendations for further study is given in Section 5.
A successful processing algorithm for extracting water depth information from ERTS data has been developed. Depth charts for two geographical areas have been constructed representing different solar illumination and water transparency conditions. Absolute depth calculations for water depth to 4.5 fathoms have been demonstrated for the Little Bahama Bank. Depth Charts also were constructed using data in Band 4 and 5 of the ERTS-1 MSS for areas in Lake Michigan. This data represented a low sun angle, poor light transmission in water conditions and gave useful results to 200 meters. In both cases, the ERTS map represented an update in shallow water detail in comparison with available navigation charts for the areas tested. Present processing costs to provide MSS depth charts are estimated to be on the order of $1.50 per sq. mile. The updating of navigation charts for areas hazardous to shipping is an achievable direct application.
In terrestrial and marine ecosystems, remote sensing has been used to estimate gross primary productivity (GPP) for decades, but few applications exist for shallow freshwater ecosystems.Here we show field-based GPP correlates with satellite and airborne lake color across a range of optically and limnologically diverse lakes in interior Alaska. A strong relationship between in situ GPP derived from stable oxygen isotopes (δ18O) and space-based lake color from satellites (e.g. Landsat-8, Sentinel-2 and CubeSats) and airborne imagery (AVIRIS-NG) demonstrates the potential power of this technique for improving spatial and temporal monitoring of lake GPP when coupled with additional field validation measurements across different systems. In shallow waters clear enough for sunlight to reach lake bottoms, both submerged vegetation (macrophytes and algae) and phytoplankton likely contribute to GPP. The stable isotopes and remotely sensed shallow lake color used here integrate both components. These results demonstrate the utility of lake color as a feasible means for mapping lake GPP from remote sensing. This novel methodology estimates GPP from remote sensing in shallow lakes by combining field measurements of oxygen isotopes with airborne, satellite and CubeSat imagery. This use of lake color for providing insight into ecological processes of shallow lakes is recommended, especially for remote arctic and boreal landscapes.
An advanced signal processing methodology is being developed to monitor the height of condensed water thru the wall of a steel pipe while operating at temperatures as high as 250deg. Using existing techniques, previous study indicated that, when the water height is low or there is disturbance in the environment, the predicted water height may not be accurate. In recent years, the use of the autocorrelation and envelope techniques in the signal processing has been demonstrated to be a very useful tool for practical applications. In this paper, various signal processing techniques including the auto correlation, Hilbert transform, and the Shannon Energy Envelope methods were studied and implemented to determine the water height in the steam pipe. The results have shown that the developed method provides a good capability for monitoring the height in the regular conditions. An alternative solution for shallow water or no water conditions based on a developed hybrid method based on Hilbert transform (HT) with a high pass filter and using the optimized windowing technique is suggested. Further development of the reported methods would provide a powerful tool for the identification of the disturbances of water height inside the pipe.