Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Shallow Water Equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5

Evaluation of HCMM data for assessing soil moisture and water table depth

Data were analyzed for variations in eastern South Dakota. Soil moisture in the 0-4 cm layer could be estimated with 1-mm soil temperatures throughout the growing season of a rainfed barley crop (% cover ranging from 30% to 90%) with an r squared = 0.81. Empirical equations were developed to reduce the effect of canopy cover when radiometrically estimating the 1-mm soil temperature, r squared = 0.88. The corrective equations were applied to an aircraft simulation of HCMM data for a diversity of crop types and land cover conditions to estimate the 0-4 cm soil moisture. The average difference between observed and measured soil moisture was 1.6% of field capacity. HCMM data were used to estimate the soil moisture for four dates with an r squared = 0.55 after correction for crop conditions. Location of shallow alluvial aquifers could be accomplished with HCMM predawn data. After correction of HCMM day data for vegetation differences, equations were developed for predicting water table depths within the aquifer (r=0.8).

Moore, D. G.↗

A Lagrangian method for a two layer shallow water model

One of the biggest drawbacks of Eulerian methods is the presence of the nonlinear convective terms which leads to inaccurate representations of advection and fronts. An alternative and conceptually simpler approach is the Lagrangian approach in which the fluid particles themselves are tracked and equations are derived based on local spatial interaction. In this formulation the nonlinear convective terms do not appear. The main drawback with the Lagrangian formulation, however, is that the local spatial interactions are time dependent. That is, at each time level, one must know the current neighbors of a given particle to accurately compute the forces acting on the particle. The Voroni Mesh which is continuously deforming and always linking nearest neighbors is needed. The effectiveness of a simple Lagrangian method for simulating the onset of a Kelvin-Helmholtz instability in a 2 layer fluid is demonstrated.

Augenbaum, J. M.↗

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.↗

Using Hough harmonics to validate and assess nonlinear shallow-water models

The implementation of a technique for locating programming errors in shallow-water codes, establishing the correctness of the code, and assessing the performance of the numerical model under various flow conditions is described. The right-hand side of the differential equations is modified in such a way that the exact solution of the nonlinear initial-value problem is known, so that the truncation errors of the numerical scheme can be studied in detail. The exact solution is prescribed to be any linear combination of Hough harmonics which propagate in time according to their natural frequencies.

Dee, Dick P.↗

Evaluation of spatial, radiometric and spectral thematic mapper performance for coastal studies

An area along the southeastern shore of the Chesapeake Bay was subsetted from TM imagery. The subsetted image was then enhanced and classified using an ERDAS 400 system. Results obtained were compared with a chart showing the distribution of both Zolsters marina and Rupplia martime in the Vaucluse Shores and which supports a large community of SAV. Radiative transfer models describing the irradiance reflectance of a water column containing SAV are being refined. Radiative transfer theory was used to model upwelling radiance for an orbiting sensor viewing an estuarine environment. Upwelling radiance was calculated for a clear maritime atmosphere, an optically shallow estuary of either clear or turbid water, and one of three bottom types: vegetation, sand, or mud using TM bands 1, 2, and 3 and MSS bands 4 and 5. A spectral quality index was defined similar to the equation for apparent contrast and used to evaluate the relative effectiveness of TM and MSS bands in detecting submerged vegetation.

Klemas, V.↗

Evidence for a Heterogeneous Distribution of Water in the Martian Interior

The abundance and distribution of H2O within the terrestrial planets, as well as its timing of delivery, is a topic of vital importance for understanding the chemical and physical evolution of planets and their potential for hosting habitable environments. Analysis of planetary materials from Mars, the Moon, and the eucrite parent body (i.e., asteroid 4Vesta) have confirmed the presence of H2O within their interiors. Moreover, H and N isotopic data from these planetary materials suggests H2O was delivered to the inner solar system very early from a common source, similar in composition to the carbonaceous chondrites. Despite the ubiquity of H2O in the inner Solar System, the only destination with any prospects for past or present habitable environments at this time, outside of the Earth, is Mars. Although the presence of H2O within the martian interior has been confirmed, very little is known regarding its abundance and distribution within the martian interior and how the martian water inventory has changed over time. By combining new analyses of martian apatites within a large number of martian meteorite types with previously published volatile data and recently determined mineral-melt partition coefficients for apatite, we report new insights into the abundance and distribution of volatiles in the martian crust and mantle. Using the subset of samples that did not exhibit crustal contamination, we determined that the enriched shergottite mantle source has 36-73 ppm H2O and the depleted shergottite mantle source has 14-23 ppm H2O. This result is consistent with other observed geochemical differences between enriched and depleted shergottites and supports the idea that there are at least two geochemically distinct reservoirs in the martian mantle. We also estimated the H2O content of the martian crust using the revised mantle H2O abundances and known crust-mantle distributions of incompatible lithophile elements. We determined that the bulk martian crust has approximately 1400 ppm H2O, which is likely distributed toward the martian surface. This crustal water abundance would equate to a global equivalent layer (GEL) of water at a depth of-229 m, which can account for at least some of the surface features on Mars attributed to flowing water and may be sufficient to support the past presence of a shallow sea on Mars' surface.

McCubbin, Francis↗

Physically-Derived Dynamical Cores in Atmospheric General Circulation Models

The algorithm chosen to represent the advection in atmospheric models is often used as the primary attribute to classify the model. Meteorological models are generally classified as spectral or grid point, with the term grid point implying discretization using finite differences. These traditional approaches have a number of shortcomings that render them non-physical. That is, they provide approximate solutions to the conservation equations that do not obey the fundamental laws of physics. The most commonly discussed shortcomings are overshoots and undershoots which manifest themselves most overtly in the constituent continuity equation. For this reason many climate models have special algorithms to model water vapor advection. This talk focuses on the development of an atmospheric general circulation model which uses a consistent physically-based advection algorithm in all aspects of the model formulation. The shallow-water model is generalized to three dimensions and combined with the physics parameterizations of NCAR's Community Climate Model. The scientific motivation for the development is to increase the integrity of the underlying fluid dynamics so that the physics terms can be more effectively isolated, examined, and improved. The expected benefits of the new model are discussed and results from the initial integrations will be presented.

Rood, Richard B.↗

Physically-Derived Dynamical Cores in Atmospheric General Circulation Models

The algorithm chosen to represent the advection in atmospheric models is often used as the primary attribute to classify the model. Meteorological models are generally classified as spectral or grid point, with the term grid point implying discretization using finite differences. These traditional approaches have a number of shortcomings that render them non-physical. That is, they provide approximate solutions to the conservation equations that do not obey the fundamental laws of physics. The most commonly discussed shortcomings are overshoots and undershoots which manifest themselves most overtly in the constituent continuity equation. For this reason many climate models have special algorithms to model water vapor advection. This talk focuses on the development of an atmospheric general circulation model which uses a consistent physically-based advection algorithm in all aspects of the model formulation. The shallow-water model of Lin and Rood (QJRMS, 1997) is generalized to three dimensions and combined with the physics parameterizations of NCAR's Community Climate Model. The scientific motivation for the development is to increase the integrity of the underlying fluid dynamics so that the physics terms can be more effectively isolated, examined, and improved. The expected benefits of the new model are discussed and results from the initial integrations will be presented.

Rood, Richard B.↗

Evaluation of a distributed catchment scale water balance model

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.

Troch, Peter A.↗

Experiments on strong interactions between solitary waves

Experiments on the interaction between solitary shallow-water waves propagating in the same direction have been performed in a rectangular channel. Two methods were devised to compensate for the dissipation of the waves in order to compare results with Hirota's (1971) solution for the collision of solitons described by the Korteweg-de Vries equation. Both qualitative and quantitative agreement with theory is obtained using the proposed corrections for wave damping.

Weidman, P. D.↗

Assimilation of TOPEX Sea Level Measurements with a Reduced-Gravity, Shallow Water Model of the Tropical Pacific Ocean

Sea surface height variability measured by TOPEX is analyzed in the tropical Pacific Ocean by way of assimilation into a wind-driven, reduced-gravity, shallow water model using an approximate Kalman filter and smoother. The analysis results in an optimal fit of the dynamic model to the observations, providing it dynamically consistent interpolation of sea level and estimation of the circulation. Nearly 80% of the expected signal variance is accounted for by the model within 20 deg of the equator, and estimation uncertainty is substantially reduced by the voluminous observation. Notable features resolved by the analysis include seasonal changes associated with the North Equatorial Countercurrent and equatorial Kelvin and Rossby waves. Significant discrepancies are also found between the estimate and TOPEX measurements, especially near the eastern boundary. Improvements in the estimate made by the assimilation are validated by comparisons with independent tide gauge and current meter observations. The employed filter and smoother are based on approximately computed estimation error covariance matrices, utilizing a spatial transformation and an symptotic approximation. The analysis demonstrates the practical utility of a quasi-optimal filter and smoother.

Fukumori, Ichiro↗

PBL Height from AIRS, GPS RO, and MERRA-2 Products in NASA GES DISC and Their 10 Year Seasonal Mean Intercomparison

Within the planetary boundary layer (PBL), surface forcing response, drag, turbulence, and vertical mixing are important processes and play a more critical role here than in the overlying “free atmosphere”. The PBL Height (PBLH) is an important parameter in climate models, weather forecasts, and air quality prediction. The NASA Goddard Earth Sciences Data and Information Services Center (GES DISC) provides data processing, archiving, and distribution services for numerous Earth science products. PBLH is a parameter in three products served by GES DISC, which are from the Atmospheric Infrared Sounder (AIRS), the Global Positioning System (GPS) radio occultation (RO) experiment, and the NASA reanalysis product Modern-Era Retrospective analysis for Research and Applications – 2 (MERRA-2). These products have different spatial and temporal resolutions and coverages, and their PBLH definitions are also different. To better serve the PBL research community, we have summarized the specifications of these products. A ten-year seasonal mean intercomparison is also conducted to provide further guidance to users. The intercomparison results show that MERRA-2 has a much shallower PBL than AIRS and GPS RO. An experimental study indicates the different PBLH definition in MERRA-2 caused smaller values of PBLH. The improvement of the water vapor retrieval in AIRS version 7 over version 6 results in the version 7 PBLH agreeing better with GPS RO and MERRA-2 than version 6, especially near the equator and low latitudes.

Feng Ding↗

A Proposal for an Integrated Geophysical Strategy to "Follow the Water" on Mars

The search for subsurface water has become a primary focus of Mars exploration. Its abundance and distribution (both as ground ice and groundwater) have important implications for understanding the geologic, hydrologic, and climatic evolution of the planet; the potential origin and continued survival of life; and the accessibility of a critical in situ resource for sustaining future human explorers. For these reasons, a principal goal of the Mars science, astrobiology, and the HEDS programs is to determine the 3-D distribution and state of subsurface H2O, at a resolution sufficient to permit reaching any desired volatile target by drilling. The three targets most often discussed are: groundwater, massive deposits of near-surface ground ice (associated with the ponded discharge of the outflow channels or the relic of a former ocean), and ice-saturated frozen ground. Based on the present best estimates of mean annual surface temperature, crustal thermal conductivity, geothermal heat flow, and groundwater freezing temperature, the mean thickness of frozen ground on Mars is expected to vary from approx. = 2.5 - 5 km at the equator to approx. = 6.5 - 13 km at the poles. However, natural variations in both crustal heat flow and thermal conductivity are likely to result in significant local departures from these predicted values. The recent discovery of "young" fluvial-like features, emanating from the slopes of local scarps, raises the possibility that liquid water may also exist episodically at shallow (approx. = 100 - 500 m) depth; however, the true nature and absolute age of these features remains highly uncertain. Although the belief that Mars is water-rich is supported by a wide variety geologic evidence, our ignorance about the heterogeneous nature and thermal evolution of the planet's crust effectively precludes geomorphic or theoretical attempts to quantitatively assess the current geographic and subsurface vertical distribution of ground ice and groundwater . For this reason, any exploration activity (such as drilling) whose success is contingent on the presence of subsurface water, must be preceded by a comprehensive high-resolution geophysical survey capable of assessing whether local reservoirs of water and ice actually exist. Terrestrial experience has demonstrated that the accurate identification of such targets is likely to require the application of multiple geophysical techniques. In this abstract we propose an integrated strategy for the geophysical exploration of Mars that we believe represents the fastest, most cost-effect, and technically capable approach to identifying the state and distribution of subsurface water. Additional information is contained in the original extended abstract.

Clifford, S. M.↗

Simplification of the Kalman filter for meteorological data assimilation

The paper proposes a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.

Dee, Dick P.↗

Technical Challenges of Drilling on Mars

In the last year, NASA's Mars science advisory committee (MEPAG: Mars Exploration Payload Advisory Group) has formally recommended that deep drilling be undertaken as a priority investigation to meet astrobiology and geology goals. This proposed new dimension in Mars exploration has come about for several reasons. Firstly, geophysical models of the martian subsurface environment indicate that we may well find liquid water (in the form of brines) under ground-ice at depths of several kilometers near the equator. On Earth we invariably find life forms associated with any environmental niche that supports liquid water. New data from the Mars Global Surveyor have shown that the most recent volcanism on Mars is very young so we cannot rule out contemporary volcanism -- in which case subsurface temperatures consistent with having water in its liquid phase may be found at relatively shallow depths. Secondly, in recent decades we have learned to our surprise that the Earth's subsurface (microbial) biosphere extends to depths of many kilometers and this discovery provides the basis for planning to explore the martian subsurface in search of ancient or even extant microbial life forms. We know (from Viking measurements) that all the biogenic elements (C, H, O, N, P, S) are available on Mars. What we therefore hope to learn is whether or not the evolution of life is inevitable given the necessary ingredients and, by implication, whether the Universe may be teeming with life. The feasibility of drilling deep into the surface of Mars has been the subject of increasing attention within NASA (and more recently among some of its international partners) for several years and this led to a broad-based feasibility study carried out by the Los Alamos National Laboratory and, subsequently, to the development of several hardware prototypes. This paper is intended to provide a general survey of that activity.

Briggs, Geoffrey↗

Wind-driven currents in a shallow lake or sea.

A technique is given for obtaining exact analytical solutions for wind-driven currents in a shallow lake or sea with a large class of bottom topographies which may or may not contain an island. Welander's second-order partial differential equation for the lake's surface displacement is used for determining the lake circulation. The technique, together with some results based on conformal mapping, is used to reduce the problem of finding solutions to Welander's equation for a closed body of water to the problem of solving an ordinary differential equation. The method is applied to an elliptically shaped lake and a circular lake containing an eccentrically located circular island.

Goldstein, M.↗

Spatial variation of corn canopy temperature as dependent upon soil texture and crop rooting characteristics

A soil plant atmosphere model for corn (Zea mays L.) together with the scaling theory for soil hydraulic heterogeneity are used to study the sensitivity of spatial variation of canopy temperature to field averaged soil texture and crop rooting characteristics. The soil plant atmosphere model explicitly solves a continuity equation for water flux resulting from root water uptake, changes in plant water storage and transpirational flux. Dynamical equations for root zone soil water potential and the plant water storage models the progressive drying of soil, and day time dehydration and night time hydration of the crop. The statistic of scaling parameter which describes the spatial variation of soil hydraulic conductivity and matric potential is assumed to be independent of soil texture class. The field averaged soil hydraulic characteristics are chosen to be representative of loamy sand and clay loam soils. Two rooting characteristics are chosen, one shallow and the other deep rooted. The simulation shows that the range of canopy temperatures in the clayey soil is less than 1K, but for the sandy soil the range is about 2.5 and 5.0 K, respectively, for the shallow and deep rooted crops.

Choudhury, B. J.↗

Abrupt Changes at the Permian/Triassic Boundary: Tempo of Events from High-Resolution Cyclostratigraphy

The Permian/Triassic (P/Tr) boundary (251.4 +/- 3 Myr) is marked by the most severe mass extinction in the geologic record. Recently, precise absolute dating has bracketed the marine extinctions and associated carbon-isotope anomaly within less than 1 Myr. We improve this resolution through high-resolution stratigraphy across the P/Tr boundary in the 331-m Gartnerkofel-1 core and nearby Reppwand outcrop section (Carnic Alps, Austria) utilizing FFT and wavelet timeseries analyses of cyclic components in down-hole core logs of density and natural gamma-ray intensity, and carbon-isotopic ratios of bulk samples. The wavelet analysis indicates continuity of deposition across the P/Tr boundary interval, and the timeseries analyses show evidence for persistent cycles in the ratio of approximately 40: 10: 4.7: 2.3 meters, correlated with Milankovitch-band orbital cycles of approximately 412: 100: 40: 20 kyr (eccentricity 1 and 2, obliquity, and precession), and giving a consistent average sedimentation rate of approximately 10 cm/1,000 yr. Milankovitch periods in delta C-13 and density in these shallow-water carbonates were most likely the result of climatically induced oscillations of sea level and climate, coupled with changes in ocean circulation and productivity, that affected sedimentation. Fluctuations in gamma radiation reflect varying input of clay minerals and the presence of shaly interbeds. Throughout the P/Tr boundary interval in the core, the 100,000-year eccentricity cycle seems to be dominant. Weaker obliquity and precession cycles are in line with the location of the Austrian section in the latest Permian, close to the Equator in the western bight of the Tethys, where obliquity and precessional effects on seasonal contrast might be subdued. Using the improved resolution provided by cycle analysis in the GK-1 core, we find that the dramatic change in the faunal record that marks the P/Tr boundary takes place over less than 6m, or less than 60,000 years. In the nearby Reppwand outcrop section, the same faunal changes occurs over only 0.8 m or about 8,000 years, close to the limit of time-resolution induced by bioturbation and reworking in these sediments. The sharp negative global carbon-isotope shift took place within less than or equal to 40,000 yr, and the isotope excursions persisted for approximately 480,000 yr into the Early Triassic. The results indicate that the severe marine faunal event that marks the P/Tr boundary was very sudden, perhaps less than the resolution window in the GK-1 core, and suggest a catastrophic cause. The wavelet-analysis approach to high-resolution cyclostratigraphy can be applied to other P/Tr boundary sections, and when combined with precise absolute dating and magnetostratigraphic methods promises a significant increase in resolution in determining the correlation and tempo of the end-Permian extinctions and related events worldwide.

Rampino, M. R.↗