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All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Who or What? Self-Replication and Function-Reproduction in the Origin of Life

In this presentation, we will present results on the fundamental properties of two classes of replicating systems: autocatalytic replicators that reproduce exact copies of a template molecule, and function reproducers that maintain a set of essential functions without replicating the identities of the functional moieties. We will describe the stability and behavior in-the-large of autocatalytic replicators. Most importantly, we have found no sharp distinction between an autocatalytic and a non-autocatalytic domain. We will also present a new derivation of von Kiedrowski's square-root rate law. Function - reproducers are proposed as an important component of protocells and we will present theoretical results on a simple model system that incorporates known peptide biophysics. For a wide range of parameters, we have shown that this type of system can improve its overall performance, even in the absence of any method for information storage. This type of system improvement is defined to be non-genomic evolution.

New, Michael H.↗
NASA NTRS1990

A new continuum model for suspensions of gyrotactic micro-organisms

A new continuum model is formulated for dilute suspensions of swimming micro-organisms with asymmetric mass distributions. Account is taken of randomness in a cell's swimming direction, p, by postulating that the probability density function for p satisfies a Fokker-Planck equation analogous to that obtained for colloid suspensions in the presence of rotational Brownian motion. The deterministic torques on a cell, viscous and gravitational, are balanced by diffusion, represented by an isotropic rotary diffusivity Dr, which is unknown a priori, but presumably reflects stochastic influences on the cell's internal workings. When the Fokker-Planck equation is solved, macroscopic quantities such as the average cell velocity Vc, the particle diffusivity tensor D and the effective stress tensor sigma can be computed; Vc and D are required in the cell conservation equation, and sigma in the momentum equation. The Fokker-Planck equation contains two dimensionless parameters, lambda and epsilon; lambda is the ratio of the rotary diffusion time Dr-1 to the torque relaxation time B (balancing gravitational and viscous torques), while epsilon is a scale for the local vorticity or strain rate made dimensionless with B. In this paper we solve the Fokker-Planck equation exactly for epsilon = 0 (lambda arbitrary) and also obtain the first-order solution for small epsilon. Using experimental data on Vc and D obtained with the swimming alga, Chlamydomonas nivalis, in the absence of bulk flow, the epsilon = 0 results can be used to estimate the value of lambda for that species (lambda approximately 2.2; Dr approximately 0.13 s-1). The continuum model for small epsilon is then used to reanalyse the instability of a uniform suspension, previously investigated by Pedley, Hill & Kessler (1988). The only qualitatively different result is that there no longer seem to be circumstances in which disturbances with a non-zero vertical wavenumber are more unstable than purely horizontal disturbances. On the way, it is demonstrated that the only significant contribution to sigma, other than the basic Newtonian stress, is that derived from the stresslets associated with the cells' intrinsic swimming motions.

NASA Discipline Number 28-20↗
NASA NTRS2020

Spatial Heterogeneity in CO2, CH4, and Energy Fluxes: Insights from Airborne Eddy Covariance Measurements Over the Mid-Atlantic Region

The exchange of carbon between the Earth’s atmosphere and biosphere influences the atmospheric abundances of carbon dioxide (CO2) and methane (CH4). Airborne eddy covariance can quantify surface-atmosphere exchange from landscape-to-regional scales, offering a unique perspective on carbon cycle dynamics. We use extensive airborne measurements to quantify fluxes of sensible heat, latent heat, CO2, and CH4across multiple ecosystems in the Mid-Atlantic region during September 2016 and May 2017. In conjunction with footprint analysis and land cover information, we use the airborne dataset to explore the effects of landscape heterogeneity on measured fluxes. Our results demonstrate large variability in CO2 uptake over mixed agricultural and forested sites, with fluxes ranging from -3.4 ± 0.7 to -11.5 ± 1.6μmol m-2s-1 for croplands and -9.1 ± 1.5 to -22.7 ± 3.2μmol m-2s-1for forests. We also report substantial CH4emissions of 32.3 ± 17.0to 76.1 ± 29.4nmol m-2s-1 from a brackish herbaceous wetland and 58.4± 12.0 to 181.2 ± 36.8nmol m-2s-1 from a freshwater forested wetland. Comparison of ecosystem-specific aircraft observations with measurements from eddy covariance flux towers along the flight path demonstrate that towers capture ~30–75% of the regional variability in ecosystem fluxes. Diel patterns measured at the tower sites suggest that peak, midday flux measurements from aircraft accurately predicts net daily CO2exchange. We discuss next steps in applying airborne observations to evaluate bottom-up flux models and improve understanding of the biophysical processes that drive carbon exchange from landscape-to-regional scales.

airborne measurements to quantify fluxes of sensib↗
NASA NTRS1994

Canopy reflectance modelling of semiarid vegetation

Three different types of remote sensing algorithms for estimating vegetation amount and other land surface biophysical parameters were tested for semiarid environments. These included statistical linear models, the Li-Strahler geometric-optical canopy model, and linear spectral mixture analysis. The two study areas were the National Science Foundation's Jornada Long Term Ecological Research site near Las Cruces, NM, in the northern Chihuahuan desert, and the HAPEX-Sahel site near Niamey, Niger, in West Africa, comprising semiarid rangeland and subtropical crop land. The statistical approach (simple and multiple regression) resulted in high correlations between SPOT satellite spectral reflectance and shrub and grass cover, although these correlations varied with the spatial scale of aggregation of the measurements. The Li-Strahler model produced estimated of shrub size and density for both study sites with large standard errors. In the Jornada, the estimates were accurate enough to be useful for characterizing structural differences among three shrub strata. In Niger, the range of shrub cover and size in short-fallow shrublands is so low that the necessity of spatially distributed estimation of shrub size and density is questionable. Spectral mixture analysis of multiscale, multitemporal, multispectral radiometer data and imagery for Niger showed a positive relationship between fractions of spectral endmembers and surface parameters of interest including soil cover, vegetation cover, and leaf area index.

Franklin, Janet↗
NASA NTRS2016

Recent Progresses in Incorporating Human Land-Water Management into Global Land Surface Models Toward Their Integration into Earth System Models

The global water cycle has been profoundly affected by human land-water management. As the changes in the water cycle on land can affect the functioning of a wide range of biophysical and biogeochemical processes of the Earth system, it is essential to represent human land-water management in Earth system models (ESMs). During the recent past, noteworthy progress has been made in large-scale modeling of human impacts on the water cycle but sufficient advancements have not yet been made in integrating the newly developed schemes into ESMs. This study reviews the progresses made in incorporating human factors in large-scale hydrological models and their integration into ESMs. The study focuses primarily on the recent advancements and existing challenges in incorporating human impacts in global land surface models (LSMs) as a way forward to the development of ESMs with humans as integral components, but a brief review of global hydrological models (GHMs) is also provided. The study begins with the general overview of human impacts on the water cycle. Then, the algorithms currently employed to represent irrigation, reservoir operation, and groundwater pumping are discussed. Next, methodological deficiencies in current modeling approaches and existing challenges are identified. Furthermore, light is shed on the sources of uncertainties associated with model parameterizations, grid resolution, and datasets used for forcing and validation. Finally, representing human land-water management in LSMs is highlighted as an important research direction toward developing integrated models using ESM frameworks for the holistic study of human-water interactions within the Earths system.

biogeochemistry↗
NASA NTRS2011

A Stochastic Model of Space Radiation Transport as a Tool in the Development of Time-Dependent Risk Assessment

A new computer model, the GCR Event-based Risk Model code (GERMcode), was developed to describe biophysical events from high-energy protons and heavy ions that have been studied at the NASA Space Radiation Laboratory (NSRL) [1] for the purpose of simulating space radiation biological effects. In the GERMcode, the biophysical description of the passage of heavy ions in tissue and shielding materials is made with a stochastic approach that includes both ion track structure and nuclear interactions. The GERMcode accounts for the major nuclear interaction processes of importance for describing heavy ion beams, including nuclear fragmentation, elastic scattering, and knockout-cascade processes by using the quantum multiple scattering fragmentation (QMSFRG) model [2]. The QMSFRG model has been shown to be in excellent agreement with available experimental data for nuclear fragmentation cross sections

Kim, Myung-Hee Y.↗
NASA NTRS1999

Real-Time Assimilation of Goes-Derived Products into A Mesoscale Model and It's Impact on Short-Term (06-36hr) Forecasts from 17 October 1998 through the Present

As the parameterizations of surface energy budgets in regional models have become more complete physically, models have the potential to be much more realistic in simulations of coupling between surface radiation, hydrology, and surface energy transfer. Realizing the importance of properly specifying the surface energy budget, many institutions are using land-surface models to represent the lower boundary forcing associated with biophysical processes and soil hydrology. However, the added degrees of freedom due to inclusion of such land-surface schemes require the specification of additional parameters within the model system such as vegetative resistances, green vegetation fraction, leaf area index, soil physical and hydraulic characteristics, stream flow, runoff, and the vertical distribution of soil moisture. Spatial heterogeneity of these parameters makes correct specification problematic since measurements are not routinely available. A technique has been developed for assimilating GOES-IR skin temperature tendencies, solar insolation, and surface albedo into the surface energy budget equation of a mesoscale model so that the simulated rate of temperature change closely agrees with the satellite observations. The technique has been successfully employed in a number of mesoscale models in case-study mode. We have taken the next step and developed a study to determine if assimilating these types of data into mesoscale models in real-time can improve short-term (648h) forecasts of temperature, relative humidity, and QPF on a daily basis over relatively large regions. Therefore, an operational modeling/assimilation system has been developed at the GHCC during the past summer that allows us to produce simulations out to 48 hours in a timely manor. The PSU/NCAR MM5 is used in a nested configuration with a 25 km grid covering the southeastern third of the US. The model has been on-line since 1 July 1998 and forecast products are posted on our web site. The satellite algorithms that generate data to be assimilated came on-line 17 October 1998. Quantitative assessment of the forecast quality is performed via traditional verification statistics. In addition, invaluable qualitative information is obtained through close collaboration with several NWSFO's who are using the MM5 products in real-time on a daily basis. The assimilation technique has been applied in an off-line mode since 17 October. Results based on bulk statistical verification of surface meteorology over the entire Southeastern US show that assimilating the GOES-derived land surface tendencies and solar radiation results in a significant reduction of the shelter air temperature and RH bias on a daily basis. In fact, the assimilation technique has produced improved temperature and RH forecasts for 97% of the 100 simulations performed to date. Work is currently underway to determine the sensitivity of the assimilation procedure to the availability of satellite data, length of assimilation period, model initialization, and synoptic-scale meteorological conditions. In addition, results from a detailed energy budget analysis using the Early Eta, our operational MM5, and the assimilation runs will help us to better understand the satellite assimilation the land-surface energy budge. Research during the spring-summer of 1999 will focus on the impact of the assimilation technique during the warm season where it is hypothesized that it can have a positive impact on QPF during conditions of weak synoptic-scale forcing.

Lapenta, William M.↗
NASA NTRS1998

A Technique for Assimilating GOES-Derived Land Surface Products into Regional Models to Improve the Representation of Land Surface Forcing

As the parameterizations of surface energy budgets in regional models have become more complete physically, models have the potential to be much more realistic in simulations of coupling between surface radiation, hydrology, and surface energy transfer. Realizing the importance of properly specifying the surface energy budget, many institutions are using land-surface models to represent the lower boundary forcing associated with biophysical processes and soil hydrology. However, the added degrees of freedom due to inclusion of such land-surface schemes require the specification of additional parameters within the model system such as vegetative resistances, green vegetation fraction, leaf area index, soil physical and hydraulic characteristics, stream flow, runoff, and the vertical distribution of soil moisture. A technique has been developed for assimilating GOES-IR skin temperature tendencies into the surface energy budget equation of a mesoscale model so that the simulated rate of temperature change closely agrees with the satellite observations. A critical assumption of the technique is that the availability of moisture (either from the soil or vegetation) is the least known term in the model's surface energy budget. Therefore, the simulated latent heat flux, which is a function of surface moisture availability, is adjusted based upon differences between the modeled and satellite-observed skin temperature tendencies. An advantage of this technique is that satellite temperature tendencies are assimilated in an energetically consistent manner that avoids energy imbalances and surface stability problems that arise from direct assimilation of surface shelter temperatures. The fact that the rate of change of the satellite skin temperature is used rather than the absolute temperature means that sensor calibration is not as critical. An advantage of this technique for short-range forecasts is that it does not require a complex land-surface formulation within the atmospheric model. As a result, the need to specify poorly known soil and vegetative characteristics is eliminated. The GOES assimilation technique has been incorporated into the PSU/NCAR MM5. Results will be presented to demonstrate the ability of the assimilation scheme to improve short-term simulations of near-surface air temperature and mixing ratio during the warm season for several selected cases during June of 1995 and June 1997 which exhibit a variety of atmospheric and land-surface conditions. In addition, the simulations produced by the assimilation technique will be compared with those produced by the MM5/BATS coupled model initialized with soil water content derived from a soil hydrology model.

Lapenta, William M.↗
NASA NTRS2004

Anthropogenic Land-use Change and the Dynamics of Amazon Forest Biomass

This project was focused on assessing the effects of prevailing land uses, such as habitat fragmentation, selective logging, and fire, on biomass and carbon storage in Amazonian forests, and on the dynamics of carbon sequestration in regenerating forests. Ancillary goals included developing GIs models to help predict the future condition of Amazonian forests, and assessing the effects of anthropogenic climate change and ENS0 droughts on intact and fragmented forests. Ground-based studies using networks of permanent plots were linked with remote-sensing data (including Landsat TM and AVHRR) at regional scales, and higher-resolution techniques (IKONOS imagery, videography, LIDAR, aerial photographs) at landscape and local scales. The project s specific goals were quite eclectic and included: Determining the effects of habitat fragmentation on forest dynamics, floristic composition, and the various components of above- and below-ground biomass. Assessing historical and physical factors that affect trajectories of forest regeneration and carbon sequestration on abandoned lands. Extrapolating results from local studies of biomass dynamics in fragmented and regenerating forests to landscape and regional scales in Amazonia, using remote sensing and GIS. Testing the hypothesis that intact Amazonian forests are functioning as a significant carbon sink. Examining destructive synergisms between forest fragmentation and fire. Assessing the short-term impacts of selective logging on aboveground biomass. Developing GIS models that integrate current spatial data on forest cover, deforestation, logging, mining, highway and roads, navigable rivers, vulnerability to wild fires, protected areas, and existing and planned infrastructure projects, in an effort to predict the future condition of Brazilian Amazonian forests over the next 20-25 years. Devising predictive spatial models to assess the influence of varied biophysical and anthropogenic predictors on Amazonian deforestation.

Laurance, William F.↗
NASA NTRS1988

Mechanism of rapid suppression of cell expansion in cucumber hypocotyls after blue-light irradiation

Rapid suppression of hypocotyl elongation by blue light in cucumber (Cucumis sativus L.) was studied to examine possible hydraulic and wall changes responsible for diminished growth. Cell-sap osmotic pressure, measured by vapor-pressure osmometry, was not decreased by blue light; turgor pressure, measured by the pressure-probe technique, remained constant during the growth inhibition; and stem hydraulic conductance, measured by dynamic and static methods, was likewise unaffected by blue light. Wall yielding properties were assessed by the pressure-block technique for in-vivo stress relaxation. Blue light reduced the initial rate of relaxation by 77%, but had little effect on the final amount of relaxation. The results demonstrate that blue irradiation acts to decrease the wall yielding coefficient, but not the yield threshold. Stress-strain (Instron) analysis showed that irradiation of the seedlings had little effect on the mechanical extensibilities of the isolated wall. The results indicate that blue light can reduce cell-wall loosening without affecting bulk viscoelastic properties, and indicate a chemorheological mechanism of cell-wall expansion.

NASA Discipline Number 40-30↗
NASA NTRS1984

Effects of Vegetation Canopy Structure on Microwave Scattering

The role of canopy structure on microwave backscattering is studied. Structure refers to the size, orientation, and vertical placement of scatterers in the canopy. Models to predict the backscattering coefficient, SIGMAO, of vegetation with explicit biophysical and explicit polarization-dependent parameters were developed. Preparation for field measurements with radar scatterometers was completed. Technical progress included: (1) the modification of the Attema and Ulaby (1977) model and its multilayer variation by Hoekman et al. (1983) to include polarization explicitly (i.e., to allow for separate backscattering cross sections, SIGMA, and extinction cross sections, Q, for each polarization), (2) the investigation of the modified model to isolate canopy element orientation parameters by the rationing of SIGMAO measurements for different polarization combinations, (3) the development of expressions for bistatic scattering and canopy-substrate scattering to supplement the models, (4) the performance of sensitivity analyses on these models, (5) the modification of the Attema and Ulaby model to alloy for changes, (6) the use of the modified model with a seasonal corn data set from Kansas (Eger et al., 1983), and (7) the initiation of preparations for empirical measurements with radar spectrometer and the Mobile Radar Scatterometer in irrigated cropland to test the models.

Paris, J. F.↗
NASA NTRS2014

Climate Change Effects on Agriculture: Economic Responses to Biophysical Shocks

Agricultural production is sensitive to weather and thus directly affected by climate change. Plausible estimates of these climate change impacts require combined use of climate, crop, and economic models. Results from previous studies vary substantially due to differences in models, scenarios, and data. This paper is part of a collective effort to systematically integrate these three types of models. We focus on the economic component of the assessment, investigating how nine global economic models of agriculture represent endogenous responses to seven standardized climate change scenarios produced by two climate and five crop models. These responses include adjustments in yields, area, consumption, and international trade. We apply biophysical shocks derived from the Intergovernmental Panel on Climate Change's representative concentration pathway with end-of-century radiative forcing of 8.5 W/m(sup 2). The mean biophysical yield effect with no incremental CO2 fertilization is a 17% reduction globally by 2050 relative to a scenario with unchanging climate. Endogenous economic responses reduce yield loss to 11%, increase area of major crops by 11%, and reduce consumption by 3%. Agricultural production, cropland area, trade, and prices show the greatest degree of variability in response to climate change, and consumption the lowest. The sources of these differences include model structure and specification; in particular, model assumptions about ease of land use conversion, intensification, and trade. This study identifies where models disagree on the relative responses to climate shocks and highlights research activities needed to improve the representation of agricultural adaptation responses to climate change.

farm crops↗
NASA NTRS2004

Spatially Complete Global Surface Albedos Derived from Terra/MODIS Data

Spectral land surface albedo is an important parameter for describing the radiative properties of the Earth. Accordingly it reflects the consequences of natural and human interactions, such as anthropogenic, meteorological, and phenological effects, on global and local climatological trends. Consequently, albedos are integral parts in a variety of research areas, such as general circulation models (GCMs), energy balance studies, modeling of land use and land use change, and biophysical, oceanographic, and meteorological studies. Recent production of land surface anisotropy, diffuse bihemispherical (white-sky) albedo and direct beam directional hemispherical (black-sky) albedo from observations acquired by the MODIS instruments aboard NASA s Terra and Aqua satellite platforms have provided researchers with unprecedented spatial, spectral, and temporal information on the land surface's radiative characteristics. Cloud cover, which cutails retrievals, and the presence of ephemeral and seasonal snow limit the snow-free data to approximately half the global land surfaces on an annual equal-angle basis. This precludes the MOD43B3 albedo products from being used in some remote sensing and ground-based applications, climate models, and global change research projects. An ecosystem-dependent temporal interpolation technique is described that has been developed to fill missing or seasonally snow-covered data in the official MOD43B3 albedo product. The method imposes pixel-level and local regional ecosystem-dependent phenological behavior onto retrieved pixel temporal data in such a way as to maintain pixel-level spatial and spectral detail and integrity. The phenological curves are derived from statistics based on the MODIS MOD12Q1 IGBP land cover classification product geolocated with the MOD43B3 data. The resulting snow-free value-added products provide the scientific community with spatially and temporally complete global white- and black-sky surface albedo maps and statistics. These products are stored on 1'(approximately 10 km) and coarser resolution equal-angle grids, and are computed for the first seven MODIS wavelengths, ranging from 0.47 through 2.1 microns, and for three broadband wavelengths, 0.3-0.7,0.3-5.0 and 0.7-5.0 microns.

King, Michael D.↗
NASA NTRS2005

Spatially Complete Global Surface Albedos Derived from Terra/MODIS Data

Spectral land surface albedo is an important parameter for describing the radiative properties of the Earth. Accordingly it reflects the consequences of natural and human interactions, such as anthropogenic, meteorological, and phenological effects, on global and local climatological trends. Consequently, albedos are integral parts in a variety of research areas, such as general circulation models (GCMs), energy balance studies, modeling of land use and land use change, and biophysical, oceanographic, and meteorological studies. Recent production of land surface anisotropy, diffuse bihemispherical (white-sky) albedo and direct beam directional hemispherical (black-sky) albedo from observations acquired by the MODIS instruments aboard NASA's Terra and &la satellite platforms have provided researchers with unprecedented spatial, spectral, and temporal information on the land surface's radiative characteristics. Cloud cover, which curtails retrievals, and the presence of ephemeral and seasonal snow limit the snow-free data to approximately half the global land surfaces on an annual equal-angle basis. This precludes the MOD43B3 albedo products from being used in some remote sensing and ground-based applications, &mate models, and global change research projects.

King, Michael D.↗
NASA NTRS2006

Spatially Complete Global Surface Albedos Derived from Terra/MODIS Data

Spectral land surface albedo is an important parameter for describing the radiative properties of the Earth. Accordingly it reflects the consequences of natural and human interactions, such as anthropogenic, meteorological, and phenological effects, on global and local climatological trends. Consequently, albedos are integral parts in a variety of research areas, such as general circulation models (GCMs), energy balance studies, modeling of land use and land use change, and biophysical, oceanographic, and meteorological studies. , Over five years of land surface anisotropy, diffuse bihemispherical (white-sky) albedo and direct beam directional hemispherical (black-sky) albedo from observations acquired by the MODIS instruments aboard NASA s Terra and Aqua satellite platforms have provided researchers with unprecedented spatial, spectral, and temporal information on the land surface s radiative characteristics. However, roughly 30% of the global land surface, on an annual equal-angle basis, is obscured due to persistent and transient cloud cover, while another 207% is obscured due to ephemeral and seasonal snow effects. This precludes the MOD43B3 albedo products from being directly used in some remote sensing and ground-based applications, climate models, and global change research projects. To provide researchers with the requisite spatially complete global snow-free land surface albedo dataset, an ecosystem-dependent temporal interpolation technique was developed to fill missing or lower quality data and snow covered values from the official MOD43B3 dataset with geophysically realistic values. The method imposes pixel-level and local regional ecosystem-dependent phenological behavior onto retrieved pixel temporal data in such a way as to maintain pixel-level spatial and spectral detail and integrity. The phenological curves are derived from statistics based on the MODIS MOD12Q1 IGBP land cover classification product geolocated with the MOD43B3 data.

King, Michael D.↗
NASA NTRS1991

Remote sensing of earth terrain

In remote sensing, the encountered geophysical media such as agricultural canopy, forest, snow, or ice are inhomogeneous and contain scatters in a random manner. Furthermore, weather conditions such as fog, mist, or snow cover can intervene the electromagnetic observation of the remotely sensed media. In the modelling of such media accounting for the weather effects, a multi-layer random medium model has been developed. The scattering effects of the random media are described by three-dimensional correlation functions with variances and correlation lengths corresponding to the fluctuation strengths and the physical geometry of the inhomogeneities, respectively. With proper consideration of the dyadic Green's function and its singularities, the strong fluctuation theory is used to calculate the effective permittivities which account for the modification of the wave speed and attenuation in the presence of the scatters. The distorted Born approximation is then applied to obtain the correlations of the scattered fields. From the correlation of the scattered field, calculated is the complete set of scattering coefficients for polarimetric radar observation or brightness temperature in passive radiometer applications. In the remote sensing of terrestrial ecosystems, the development of microwave remote sensing technology and the potential of SAR to measure vegetation structure and biomass have increased effort to conduct experimental and theoretical researches on the interactions between microwave and vegetation canopies. The overall objective is to develop inversion algorithms to retrieve biophysical parameters from radar data. In this perspective, theoretical models and experimental data are methodically interconnected in the following manner: Due to the complexity of the interactions involved, all theoretical models have limited domains of validity; the proposed solution is to use theoretical models, which is validated by experiments, to establish the region in which the radar response is most sensitive to the parameters of interest; theoretically simulated data will be used to generate simple invertible models over the region. For applications to the remote sensing of sea ice, the developed theoretical models need to be tested with experimental measurements. With measured ground truth such as ice thickness, temperature, salinity, and structure, input parameters to the theoretical models can be obtained to calculate the polarimetric scattering coefficients for radars or brightness temperature for radiometers and then compare theoretical results with experimental data. Validated models will play an important role in the interpretation and classification of ice in monitoring global ice cover from space borne remote sensors in the future. We present an inversion algorithm based on a recently developed inversion method referred to as the Renormalized Source-Type Integral Equation approach. The objective of this method is to overcome some of the limitations and difficulties of the iterative Born technique. It recasts the inversion, which is nonlinear in nature, in terms of the solution of a set of linear equations; however, the final inversion equation is still nonlinear. The derived inversion equation is an exact equation which sums up the iterative Neuman (or Born) series in a closed form and, thus, is a valid representation even in the case when the Born series diverges; hence, the name Renormalized Source-Type Integral Equation Approach.

Yueh, Herng-Aung↗