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An approximation scheme which can be used to estimate unknown parameters in moving boundary problems is described. The model equations are fairly general nonlinear diffusion/reaction equations of one spatial variable. Conditions on the parameter sets and model equations are given. It is shown that the estimates obtained using the approximations will converge to best-fit parameters for the original model equations.
A physically based linear stochastic geometric canopy soil reflectance model is presented for characterizing spatial variability of semivegetated landscapes at subpixel and regional scales. Landscapes are conceptualized as stochastic geometric surfaces, incorporating not only the variability in geometric elements, but also the variability in vegetation and soil background reflectance which can be important in some scenes. The model is used to investigate several possible mechanisms which contribute to the often observed characteristic triangular shape of red-infrared scattergrams of semivegetated landscapes. Scattergrams of simulated semivegetated scenes are analyzed with respect to the scales of the satellite pixel and subpixel components. Analysis of actual aerial radiometric data of a pecan orchard is presented in comparison with ground observations as preliminary confirmation of the theoretical results.
Consideration is given to the study of the 100-Hz electric field noise observed from the Pioneer Venus Orbiter (PVO) by Scarf et al. (1987). It is suggested that the study incorrectly interprets the results as evidence for lightning and volcanism at Venus. Statistical evidence is presented, suggesting that the distribution of the noise is essentially random, within the zone of occurrence of ion troughs, and decreases at the lowest PVO altitudes, closest to the neutral atmosphere. It is found that the topographic clustering reported by Scarf et al. is an artifact of the variable spatial distribution of troughs and associated noise.
Surface biophysical estimates were derived from analysis of NOAA Advanced Very High Spectral Resolution (AVHRR) spectral data of the Senegalese area of west Africa. The parameters derived were of solar albedo, spectral visible and near-infrared band reflectance, spectral vegetative index, and ground temperature. Wet and dry linked AVHRR scenes from 1981 through 1985 in Senegal were analyzed for a semi-wet southerly site near Tambacounda and a predominantly dry northerly site near Podor. Related problems were studied to convert satellite derived radiance to biophysical estimates of the land surface. Problems studied were associated with sensor miscalibration, atmospheric and aerosol spatial variability, surface anisotropy of reflected radiation, narrow satellite band reflectance to broad solar band conversion, and ground emissivity correction. The middle-infrared reflectance was approximated with a visible AVHRR reflectance for improving solar albedo estimates. In addition, the spectral composition of solar irradiance (direct and diffuse radiation) between major spectral regions (i.e., ultraviolet, visible, near-infrared, and middle-infrared) was found to be insensitive to changes in the clear sky atmospheric optical depth in the narrow band to solar band conversion procedure. Solar albedo derived estimates for both sites were not found to change markedly with significant antecedent precipitation events or correspondingly from increases in green leaf vegetation density. The bright soil/substrate contributed to a high albedo for the dry related scenes, whereas the high internal leaf reflectance in green vegetation canopies in the near-infrared contributed to high solar albedo for the wet related scenes. The relationship between solar albedo and ground temperature was poor, indicating the solar albedo has little control of the ground temperature. The normalized difference vegetation index (NDVI) and the derived visible reflectance were more sensitive to antecedent rainfall amounts and green vegetation changes than were near-infrared changes. The information in the NDVI related to green leaf density changes primarily was from the visible reflectance. The contribution of the near-infrared reflectance to explaining green vegetation is largely reduced when there is a bright substrate.
A series of experimental investigations focused on studying the cause and effect of roughness on accreting glaze ice surfaces were conducted. Detailed microvideo observations were made of glaze ice accretions on 1 to 4 inch diameter cylinders in three icing wind tunnels (the Data Products of New England six inch test facility, the NASA Lewis Icing Research Tunnel, and the B. F. Goodrich Ice Protection Research Facility). Infrared thermal video recordings were made of accreting ice surfaces in the Goodrich facility. Distinct zones of surface water behavior were observed; a smooth wet zone in the stagnation region with a uniform water film; a rough zone where surface tension effects caused coalescence of surface water into stationary beads; a horn zone where roughness elements grow into horn shapes; a runback zone where surface water ran back as rivulets; and a dry zone where rime feathers formed. The location of the transition from the smooth to the rough zone was found to migrate with time towards the stagnation point. The behavior of the transition appeared to be controlled by boundary layer transition and bead formation mechanisms at the interface between the smooth and rough zones. Regions of wet ice growth and enhanced heat transfer were clearly visible in the infrared video recordings of glaze ice surfaces. A simple multi-zone modification to the current glaze ice accretion model was proposed to include spatial variability in surface roughness.
The finite volume approach in developing multi-dimensional, high-order accurate essentially non-oscillatory (ENO) schemes is considered. In particular, a two dimensional extension is proposed for the Euler equation of gas dynamics. This requires a spatial reconstruction operator that attains formal high order of accuracy in two dimensions by taking account of cross gradients. Given a set of cell averages in two spatial variables, polynomial interpolation of a two dimensional primitive function is employed in order to extract high-order pointwise values on cell interfaces. These points are appropriately chosen so that correspondingly high-order flux integrals are obtained through each interface by quadrature, at each point having calculated a flux contribution in an upwind fashion. The solution-in-the-small of Riemann's initial value problem (IVP) that is required for this pointwise flux computation is achieved using Roe's approximate Riemann solver. Issues to be considered in this two dimensional extension include the implementation of boundary conditions and application to general curvilinear coordinates. Results of numerical experiments are presented for qualitative and quantitative examination. These results contain the first successful application of ENO schemes to boundary value problems with solid walls.
The irregular space-time sampling of any finite region by an orbiting satellite raises difficult questions as to which frequencies and wavenumbers can be determined and which will alias into others. Conventional sampling theorems must be extended to account for both irregular data distributions and observational noise - the sampling irregularity making the system much more susceptible to noise than in regularly sampled cases. The problem is formulated here in terms of least-squares and applied to spacecraft in 10-day and 17-day repeating orbits. The 'diamond-pattern' laid down spatially in such repeating orbits means that either repeat period adequately samples the spatial variables, but the slow overall temporal coverage in the 17-day pattern leads to much greater uncertainty than in the shorter repeat cycle. The result is not definitive and it is not concluded that a 10-day orbit repeat is the most appropriate one. A major conclusion, however, is that different orbital choices have potentially quite different sampling characteristics which need to be analyzed in terms of the spectral characteristics of the moving sea surface.
Attempts to model the evolution of the slow-response parts of the climatic system such as the global ice mass are reviewed, and the fundamental laws governing the complete complex multidomain slow system, called the slow climatic attractor, are analyzed. The uses of paleoclimatic records are discussed, and a low-order model for the late Quaternary variations that constitutes a credible global representation of the slow climatic attractor is presented. It is shown that although according to the model the climatic system is centered on an unstable equilibrium, the points of the limit cycle attractor are quite stable and robust. It is also noted that one major deficiency of the model is its inability to portray the geographic spatial variability of climatic mean states. However, at least with regard to atmospheric CO2, estimates of the geographic fields of all significant atmospheric and surface boundary layer climate variables are deducible.
In deriving the surface latent heat flux with the bulk formula for the thermal forcing of some ocean circulation models, two approximations are commonly made to bypass the use of atmospheric humidity in the formula. The first assumes a constant relative humidity, and the second supposes that the sea-air humidity difference varies linearly with the saturation humidity at sea surface temperature. Using climatological fields derived from the Marine Deck and long time series from ocean weather stations, the errors introduced by these two assumptions are examined. It is shown that the errors reach above 100 W/sq m over western boundary currents and 50 W/sq m over the tropical ocean. The two approximations also introduce erroneous seasonal and spatial variabilities with magnitudes over 50 percent of the observed variabilities.
Thermal infrared Multispectral Scanner (TIMS) data were collected at a resolution of 5 to 10 m from a tropical rain forest over an elevation gradient from 35 to 2700 m in the Braulio Carrillo National Park in Costa Rica. Flight lines were repeated with a 15 to 30 minute time difference for measurement of forest canopy thermal response over time. Concurrent radiosonde measurements of atmospheric profiles of air temperature and moisture provided inputs to LOWTRAN6 for atmospheric radiance corrections of the TIMS data. Techniques for using calibrated aircraft-based thermal scanner data to examine tropical forest canopy thermal properties are described. Forest canopy temperature changes over time assessed between repeated, duplicated flight lines were combined with estimates of surface radiative energy measurements from towers above the forest canopy to determine temperature spatial variability, calculate Thermal Response Numbers (TRN), and estimate evapotranspiration along the elevation gradient from selected one hectare forest inventory plots.
NASA conducted the GLObal Backscatter Experiment (GLOBE) Survey Mission over the near coastal and remote Pacific Ocean during 6 to 30 Nov. 1989 (GLOBE 1) and 13 May to 5 Jun. 1990 (GLOBE 2). These missions studied the optical, physical, and chemical properties of atmospheric aerosols. Particular emphasis was given to the magnitude and spatial variability of aerosol backscatter coefficients at mid-infrared wavelengths, and to the remote middle and upper troposphere, where these aerosol properties are poorly understood. Survey instruments were selected to provide either direct beta measurements at the key wavelengths, empirical links with long term or global scale aerosol climatologies, or aerosol microphysics data required to model any of these quantities. The survey deployment included both long distance 6 to 8 hour transit flights and detailed 4 to 6 hour local flights. Several general features were observed from preliminary Survey data analyses. Validation and intercomparison results have shown good agreement, usually better than a factor of two. Atmospheric aerosols frequently exhibited a three layer vertical structure, with (1) high and fairly uniform backscatter in the shallow cloud capped marine boundary layer; (2) moderate and highly variable backscatter in a deeper overlaying cloud pumped layer; and (3) low, regionally uniform, but seasonally and latitudinally variable backscatter in the middle and upper troposphere. The survey missions represent two isolated snapshots of a small portion of the global aerosol system. Consequently, Survey results can best be understood by synthesizing them with the more comprehensive GLOBE data base, which is being compiled at NASA-Marshall.
Experiments using atmospheric general circulation models have shown that the atmospheric circulation is very sensitive to small changes in sea surface temperature in the tropical western Pacific Ocean warm pool region. The mutual sensitivity of the ocean and the atmosphere in the warm pool region places stringent requirements on models of the coupled ocean atmosphere system. At present, the situation is such that diagnostic studies using available data sets have been unable to balance the surface energy budget in the warm pool region to better than 50 to 80 W/sq m. The Tropical Ocean Global Atmosphere (TOGA) Coupled Ocean Atmosphere Response Experiment (COARE) is an observation and modelling program that aims specifically at the elucidation of the physical process which determine the mean and transient state of the warm pool region and the manner in which the warm pool interacts with the global ocean and atmosphere. This project focuses on one very important aspect of the ocean atmosphere interface component of TOGA COARE, namely the temporal and spatial variability of surface radiative fluxes in the warm pool region.
A hyperbolic grid generation scheme formulated from grid orthogonality and cell volume specification is generalized such that high quality three-dimensional grids can be obtained for a wide variety of geometries. The speed of the scheme is one to two orders of magnitude faster than typical elliptic grid generation methods. The robustness of the scheme is significantly enhanced by several new techniques. By using a spatially variable smoothing coefficient, orthogonality and smoothness of the grid are maintained around complex concave and convex surface topologies. A metric correction procedure is employed to guarantee that the grid marches out of a corner by bisecting the angles subtended by the neighboring points. Extra robustness at severe convex corners is achieved by special local treatments. Different extrapolation methods are used to provide smoothness at floating edges and axis regions. The versatility of the new hyperbolic grid generation scheme is demonstrated by three-dimensional grids generated for external components of the intergrated Space Shuttle vehicle and the SOFIA telescope.
Methane flux was linearly correlated with plant biomass (r = 0.97, n = 6 and r = 0.95, n = 8) at two locations in a Florida Everglades Cladium marsh. One location, which had burned 4 months previously, exhibited a greater increase in methane flux as a function of biomass relative to sites at an unburned location. However, methane flux data from both sites fit a single regression (r = 0.94, n = 14) when plotted against net CO2 exchange suggesting that either methanogenesis in Everglades marl sediments is fueled by root exudation below ground, or that factors which enhance photosynthetic production and plant growth are also correlated with methane production and flux in this oligotrophic environment. The data presented are the first to show a direct relationship between spatial variability in plant biomass, net ecosystem production, and methane emission in a natural wetland.
Landsurface hydrological parameterizations are implemented in the NASA Goddard Institute for Space Studies (GISS) General Circulation Model (GCM). These parameterizations are: (1) runoff and evapotranspiration functions that include the effects of subgrid scale spatial variability and use physically based equations of hydrologic flux at the soil surface, and (2) a realistic soil moisture diffusion scheme for the movement of water in the soil column. A one dimensional climate model with a complete hydrologic cycle is used to screen the basic sensitivities of the hydrological parameterizations before implementation into the full three dimensional GCM. Results of the final simulation with the GISS GCM and the new landsurface hydrology indicate that the runoff rate, especially in the tropics is significantly improved. As a result, the remaining components of the heat and moisture balance show comparable improvements when compared to observations. The validation of model results is carried from the large global (ocean and landsurface) scale, to the zonal, continental, and finally the finer river basin scales.
Recent airborne thermal infrared observations of Mars from the Kuiper Airborne Observatory (KAO) have provided evidence for the presence of carbonates, sulfates, and hydrates. Using the optical properties of calcite and anhydrite, it was estimated that CO3's and SO4's constituted about 1 to 3 and 10 to 15 wt. percent, repectively of the materials composing the atmospheric dust. Using the derived value as an estimate of total CO3 abundance, and making an assumption that the CO3's were uniformly distributed within the Martian regolith, it was estimated that such a CO3 reservoir could contain roughly 2 to 5 bars of CO2. While the results indicate that several volatile-bearing materials are present on Mars, the observations from the KAO are inherently limited in their ability to determine the spatial distributions of these materials. However, previous spacecraft observations of Mars provide both the spectral coverage necessary to identify these materials, as well as the potential for investigating their spatial variability. This has prompted us to pursue a reinvestigation of the Mariner 6 and 7 infrared spectrometer and Mariner 9 infrared interferometer spectrometer observations. The former data have been recently made available in digital format and calibration of wavelengths and intensities are almost complete. Additionally, we are pursuing the derivation of optical constants of more appropriate carbonates and sulfates.
The objectives are to study the distribution of ozone (O3) and aerosols across the polar regions during the winter and spring periods and to relate these observations to chemical and dynamical processes that can contribute to the chemical perturbation of the polar stratosphere and the possible destruction of O3. The distribution and characteristics of stratospheric aerosols and polar stratospheric clouds (PSCs) are required to understand heterogeneous chemical processes that can lead to O3 depletion, and observation of O3 variations are important in the direct detection of O3 depletion and in tracing atmospheric dynamics. An airborne Differential Absorption Lidar (DIAL) system is operated in a zenith mode from the NASA DC-8 aircraft to obtain data on the large scale spatial variability of O3, and aerosol/PSC's in the lower stratosphere from about 11 to 23 km for O3, and 11 to 28 km for aerosols. The variability of O3 and aerosols/PSCs is studied in relation to chemical processes that can produce O3 depletion and to dynamics in the lower stratosphere that transport gases and aerosols inside the vortex and in some cases, across the edge of the vortex.
Recent climate modeling experiments have identified the critical need for a better understanding of land surface - atmosphere interactions. An important issue in global climate modeling is to be able to relate land surface and atmospheric processes. In the past this link has been inadequately represented due to the lack of understanding of the interaction between the processes and also due to the large spatial variability of the hydrological and soil properties. A project was initiated at the Marshall Space Flight Center (MSFC) in FY-90 under the Center's Directorate Discretionary Fund (CDDF) to study small-scale effects of vegetation on the distribution and fluxes of soil moisture. Installation of a large array of instruments was accomplished during that first year (FY-90). During this second year of the project, the instrumentation and data collection systems were improved and data has begun to be taken. Preliminary analysis of the data show that the equipment has been functioning properly. Some of the preliminary results that have recently been analyzed are given.