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NASA NTRS1999

Longwave Radiative Flux Calculations in the TOVS Pathfinder Path A Data Set

A radiative transfer model developed to calculate outgoing longwave radiation (OLR) and downwelling longwave, surface flux (DSF) from the Television and Infrared Operational Satellite (TIROS) Operational Vertical Sounder (TOVS) Pathfinder Path A retrieval products is described. The model covers the spectral range of 2 to 2800 cm in 14 medium medium spectral bands. For each band, transmittances are parameterized as a function of temperature, water vapor, and ozone profiles. The form of the band transmittance parameterization is a modified version of the approach we use to model channel transmittances for the High Resolution Infrared Sounder 2 (HIRS2) instrument. We separately derive effective zenith angle for each spectral band such that band-averaged radiance calculated at that angle best approximates directionally integrated radiance for that band. We develop the transmittance parameterization at these band-dependent effective zenith angles to incorporate directional integration of radiances required in the calculations of OLR and DSF. The model calculations of OLR and DSF are accurate and differ by less than 1% from our line-by-line calculations. Also, the model results are within 1% range of other line-by-line calculations provided by the Intercomparison of Radiation Codes in Climate Models (ICRCCM) project for clear-sky and cloudy conditions. The model is currently used to calculate global, multiyear (1985-1998) OLR and DSF from the TOVS Pathfinder Path A Retrievals.

Mehta, Amita↗
NASA NTRS1999

Land-Atmosphere Interactions: Successes, Problems and Prospects

After two decades of active research, a much better understanding of the broader role of biospheric processes on the local climate has emerged. A surface-albedo increase, particularly in desert border regions of the subtropics (as well as the deforested tropical regions), leads to a net surface energy deficit, which in turn leads to a relative sinking and reduced rainfall. On the other hand, studies of the influence of altered ratios of evapotranspiration and sensible fluxes, in situations where the net solar income is unchanged, show that evapotranspiration is a more desirable flux for increased precipitation and vitality of the biosphere. Besides providing water vapor and convective available potential energy (CAPE) to the lower troposphere, evapotranspiration helps in building larger CAPE before "turning on" the moist-convection. Larger CAPE in the lower troposphere enables convection to reach into the deeper atmosphere thereby heating the upper troposphere; indeed, moist-convection is also accompanied by the evaporation of falling precipitation that cools and moistens the lower atmosphere. While convective, as opposed to stratiform, precipitation reduces the fractional cloud cover; it also allows more solar radiation to reach the surface thereby invigorating surface fluxes. These, together with moist convection and associated downdrafts help to maintain the characteristic upper temperature limit(s) of the moist-land as well as oceanic regions. Regardless of the above understanding, several important problems continue to hinder the accurate simulation of a realistic land atmosphere interaction in a numerical model (both GCM and/or Meso-scale models). Among the unsolved problems are parameterization of sub-grid scale land processes that include small-scale variability of soil moisture, snow-cover and snow-physics, the biodiversity of the biosphere, orography, local drainage characteristics under natural conditions, and surface flow over the natural terrain. A well-known non-linear response of surface fluxes to these variations makes the problem of parameterizing land-atmosphere interaction processes hard-to-address and simulate, particularly in a GCM. In our presentation, we will discuss how orographic, snow-cover, and water table interactions can be included into a Simple Biosphere Model such as SiB/SSiB. Figure I shows how, in the Russian region, spring snowmelt affects the soil moisture profile. Corresponding figure 2 shows how interaction with the water table decreases the natural evapotranspiration in the Sahel region simulation. While these simulations need better validation with data, the simulations reveal that surface processes are sensitive to these parameterizations. With these developments, we continue to advance our understanding of the interaction of land with the atmosphere aloft, but the intrinsic variability of the newer parameters, e. g., hydraulic properties of the soil, diminish the positive influences of these advances on the improved climate simulation with GCMs.

Sud, Y. C.↗
NASA NTRS2000

Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD)

This paper presents a multidisciplinary shape parameterization approach. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft object animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in a similar manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminated plate structures) and high-fidelity (e.g., nonlinear computational fluid dynamics and detailed finite element modeling analysis tools. This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, camber, and free-form surface. Results are presented for a multidisciplinary design optimization application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, and a simple performance module.

Samareh, Jamshid A.↗
NASA NTRS2000

Lightning Scaling Laws Revisited

Scaling laws relating storm electrical generator power (and hence lightning flash rate) to charge transport velocity and storm geometry were originally posed by Vonnegut (1963). These laws were later simplified to yield simple parameterizations for lightning based upon cloud top height, with separate parameterizations derived over land and ocean. It is demonstrated that the most recent ocean parameterization: (1) yields predictions of storm updraft velocity which appear inconsistent with observation, and (2) is formally inconsistent with the theory from which it purports to derive. Revised formulations consistent with Vonnegut's original framework are presented. These demonstrate that Vonnegut's theory is, to first order, consistent with observation. The implications of assuming that flash rate is set by the electrical generator power, rather than the electrical generator current, are examined. The two approaches yield significantly different predictions about the dependence of charge transfer per flash on storm dimensions, which should be empirically testable. The two approaches also differ significantly in their explanation of regional variability in lightning observations.

Boccippio, D. J.↗
NASA NTRS2000

Radiative Properties of Cirrus Clouds in the Infrared (8-13 microns) Spectral Region

Atmospheric radiation in the infrared (IR) 8-13 microns spectral region contains a wealth of information that is very useful for the retrieval of ice cloud properties from aircraft or space-borne measurements. To provide the scattering and absorption properties of nonspherical ice crystals that are fundamental to the IR retrieval implementation, we use the finite-difference time domain (FDTD) method to solve for the extinction efficiency, single-scattering albedo, and the asymmetry parameter of the phase function for ice crystals smaller than 40 microns. For particles larger than this size, the improved geometric optics method (IGOM) can be employed to calculate the asymmetry parameter with an acceptable accuracy, provided that we properly account for the inhomogeneity of the refracted wave due to strong absorption inside the ice particle. A combination of the results computed from the two methods provides the asymmetry parameter for the entire practical range of particle sizes between 1 micron and 10000 microns over wavelengths ranging from 8 microns to 13 microns. For the extinction and absorption efficiency calculations, several methods including the IGOM, Mie solution for equivalent spheres (MSFES), and the anomalous diffraction theory (ADT) can lead to a substantial discontinuity in comparison with the FDTD solutions for particle sizes on the order of 40 microns. To overcome this difficulty, we have developed a novel approach called the stretched scattering potential method (SSPM). For the IR 8-13 microns spectral region, we show that SSPM is a more accurate approximation than ADT, MSFES, and IGOM. The SSPM solution can be further refined numerically. Through a combination of the FDTD and SSPM, we have computed the extinction and absorption efficiency for hexagonal ice crystals with sizes ranging from 1 to 10000 microns at 12 wavelengths between 8 and 13 microns Calculations of the cirrus bulk scattering and absorption properties are performed for 30 size distributions obtained from various field campaigns for midlatitude and tropical cirrus cloud systems. Parameterization of these bulk scattering properties is carried out by using second-order polynomial functions for the extinction efficiency and the single-scattering albedo and the power law expression for the asymmetry parameter. We note that the volume-normalized extinction coefficient can be separated into two parts: one is inversely proportional to effective size and is independent of wavelength, and the other is the wavelength-dependent effective extinction efficiency. Unlike conventional parameterization efforts, the present parameterization scheme is more accurate because only the latter part of the volume-normalized extinction coefficient is approximated in terms of an analytical expression. After averaging over size distribution, the single-scattering albedo is shown to decrease with an increase in effective size for wavelengths shorter than 10.0 microns whereas the opposite behavior is observed for longer wavelengths. The variation of the asymmetry parameter as a function of effective size is substantial when the effective size is smaller than 50 microns. For effective sizes larger than 100 microns, the asymmetry parameter approaches its asymptotic value. The results derived in this study can be useful to remote sensing applications involving IR window bands under cirrus cloud conditions.

Yang, Ping↗
NASA NTRS2002

Surface Temperature Assimilation in the Global Land Data Assimilation System (GLDAS)

The Global Land Data Assimilation System (GLDAS) is a global land parameterization that uses prescribed meteorology as forcing in order to determine regular gridded land surface states (temperature and moisture) and other properties (e.g. water and heat fluxes). In the present experiment, the assimilation of surface skin temperature is incorporated into the land parameterizations. The meteorological forcing was derived from the Goddard Earth Observing System (GEOS-3) Data Assimilation System (DAS) for the full year of 1998 GLDAS can use several land parameterizations, but here we use the Mosaic land surface model and the Common Land Model (CLM). TOVS surface temperature observations are assimilated into GLDAS. The TOVS observations are less frequent that observations used in previous experiments (ISCCP). The purpose of this presentation is to evaluate the impact of the TOVS assimilation on both Mosaic and CLM. We will especially consider the impact of coarse temporal observations on the assimilation and bias correction.

Bosilovich, Michael G.↗
NASA NTRS2002

Confronting Models with Data: The GEWEX Cloud Systems Study

The GEWEX Cloud System Study (GCSS; GEWEX is the Global Energy and Water Cycle Experiment) was organized to promote development of improved parameterizations of cloud systems for use in climate and numerical weather prediction models, with an emphasis on the climate applications. The strategy of GCSS is to use two distinct kinds of models to analyze and understand observations of the behavior of several different types of clouds systems. Cloud-system-resolving models (CSRMs) have high enough spatial and temporal resolutions to represent individual cloud elements, but cover a wide enough range of space and time scales to permit statistical analysis of simulated cloud systems. Results from CSRMs are compared with detailed observations, representing specific cases based on field experiments, and also with statistical composites obtained from satellite and meteorological analyses. Single-column models (SCMs) are the surgically extracted column physics of atmospheric general circulation models. SCMs are used to test cloud parameterizations in an un-coupled mode, by comparison with field data and statistical composites. In the original GCSS strategy, data is collected in various field programs and provided to the CSRM Community, which uses the data to "certify" the CSRMs as reliable tools for the simulation of particular cloud regimes, and then uses the CSRMs to develop parameterizations, which are provided to the GCM Community. We report here the results of a re-thinking of the scientific strategy of GCSS, which takes into account the practical issues that arise in confronting models with data. The main elements of the proposed new strategy are a more active role for the large-scale modeling community, and an explicit recognition of the importance of data integration.

Randall, David↗
NASA NTRS2003

Task III: Development of an Effective Computational Methodology for Body Force Representation of High-speed Rotor 37

A framework for an effective computational methodology for characterizing the stability and the impact of distortion in high-speed multi-stage compressor is being developed. The methodology consists of using a few isolated-blade row Navier-Stokes solutions for each blade row to construct a body force database. The purpose of the body force database is to replace each blade row in a multi-stage compressor by a body force distribution to produce same pressure rise and flow turning. To do this, each body force database is generated in such a way that it can respond to the changes in local flow conditions. Once the database is generated, no hrther Navier-Stokes computations are necessary. The process is repeated for every blade row in the multi-stage compressor. The body forces are then embedded as source terms in an Euler solver. The method is developed to have the capability to compute the performance in a flow that has radial as well as circumferential non-uniformity with a length scale larger than a blade pitch; thus it can potentially be used to characterize the stability of a compressor under design. It is these two latter features as well as the accompanying procedure to obtain the body force representation that distinguish the present methodology from the streamline curvature method. The overall computational procedures have been developed. A dimensional analysis was carried out to determine the local flow conditions for parameterizing the magnitudes of the local body force representation of blade rows. An Euler solver was modified to embed the body forces as source terms. The results from the dimensional analysis show that the body forces can be parameterized in terms of the two relative flow angles, the relative Mach number, and the Reynolds number. For flow in a high-speed transonic blade row, they can be parameterized in terms of the local relative Mach number alone.

Tan, Choon-Sooi↗
NASA NTRS2003

Sensitivity of Middle Atmospheric Temperature and Circulation in the UIUC Mesosphere-Stratosphere-Troposphere GCM to the Treatment of Subgrid-Scale Gravity-Wave Breaking

The sensitivity of the middle atmospheric temperature and circulation to the treatment of mean- flow forcing due to breaking gravity waves was investigated using the University of Illinois at Urbana-Champaign 40-layer Mesosphere-Stratosphere-Troposphere General Circulation Model (MST-GCM). Three GCM experiments were performed. The gravity-wave forcing was represented first by Rayleigh friction, and then by the Alexander and Dunkerton (AD) parameterization with weak and strong breaking effects of gravity waves. In all experiments, the Palmer et al. parameterization was included to treat the breaking of topographic gravity waves in the troposphere and lower stratosphere. Overall, the experiment with the strong breaking effect simulates best the middle atmospheric temperature and circulation. With Rayleigh friction and the weak breaking effect, a large warm bias of up to 60 C was found in the summer upper mesosphere and lower thermosphere. This warm bias was linked to the inability of the GCM to simulate the reversal of the zonal winds from easterly to westerly crossing the mesopause in the summer hemisphere. With the strong breaking effect, the GCM was able to simulate this reversal, and essentially eliminated the warm bias. This improvement was the result of a much stronger meridional transport circulation that possesses a strong vertical ascending branch in the summer upper mesosphere, and hence large adiabatic cooling. Budget analysis indicates that 'in the middle atmosphere the forces that act to maintain a steady zonal-mean zonal wind are primarily those associated with the meridional transport circulation and breaking gravity waves. Contributions from the interaction of the model-resolved eddies with the mean flow are small. To obtain a transport circulation in the mesosphere of the UIUC MST-GCM that is strong enough to produce the observed cold summer mesopause, gravity-wave forcing larger than 100 m/s/day in magnitude is required near the summer mesopause. In the tropics, only with the AD parameterization can the model produce realistic semiannual oscillations.

Yang, Fanglin↗
NASA NTRS2004

Tropical Diabatic Heating and the Role of Convective Processes as Represented in Several Contemporary Climate Models

One of the most fundamental properties of the global heat balance is the net heat input into the tropical atmosphere that helps drive the planetary atmospheric circulation. Although broadly understood in terms of its gross structure and balance of source / sink terms, incorporation of the relevant processes in predictive models is still rather poor. The work reported here examines the tropical radiative and water cycle behavior as produced by four contemporary climate models. Among these are the NSIPP-2 (NASA Seasonal to Interannual Prediction Project) which uses the RAS convective parameterization; the FVCCM, a code using finite volume numerics and the CCM3.6 physics; FVCCM-MCRAS again having the finite volume numerics, but MCRAS convective parameterization and a different radiation treatment; and, finally, the NCEP GSM which uses the RAS. Using multi-decadal integrations with specified SSTs we examine the statistics of radiative / convective processes and associated energy transports, and then estimate model energy flux sensitivities to SST changes. In particular the behavior of the convective parameterizations is investigated. Additional model integrations are performed specifically to assess the importance representing convective inhibition in regulating convective cloud-top structure and moisture detrainment as well as controlling surface energy fluxes. To evaluate the results of these experiments, a number of satellite retrievals are used: TRMM retrievals of vertical reflectivity structure, rainfall rate, and inferred diabatic heating are analyzed to show both seasonal and interannual variations in vertical structure of latent heat release. Top-of-atmosphere radiative fluxes from ERBS and CERES are used to examine shortwave and longwave cloud forcing and to deduce required seasonal energy transports. Retrievals of cloud properties from ISCCP and water vapor variations from SSM/T-2 are also used to understand behavior of the humidity fields. These observations are supplemented with output form the DOE Reanalysis-2.

Robertson, Franklin R.↗
NASA NTRS1994

A Study of the Relationship Between Anthropogenic Sulfate and Cloud Drop Nucleation

The characteristics of the cloud drop size distribution near cloud base are initially determined by the aerosol particles that serve as CCN and by the local updraft velocity. Chemical reactions of the emitted gaseous sulfur compounds due to human activities will alter, through gas-to-particle conversion, the aerosol size distribution, total number, and its chemical composition. Recently, Boucher and Rodhe and Jones et.al have each developed parameterizations relating cloud drop concentration to sulfate mass or aerosol number concentration, respectively, and used them to develop estimates of the indirect forcing by anthropogenic sulfate aerosols. THese parameterizations made use of measure relationships in continental and maritime clouds. However, these relationships are inherently noisy, yielding more than a factor of 2 variation in cloud drop concentration for a given aerosol number (or for a given sulfate mass) concentration. The large spatial and temporal variabilities in the concentration, chemical characteristics, and size distribution of aerosols have made it difficult to develop such a parameterization from data. In this paper, our focus is to develop a means for relating the predicted anthropogenic sulfate mass to cloud drop number concentration over the range of expected conditions associated with continental and marine aerosol. We start with an assumed pre-existing particle size distribution and develop an approximation of the altered distribution after addition of anthropogenic sulfate. We thereby develop a conservative estimate of the possible change in cloud drop number concentration due to anthropogenic sulfate.

Chuang, Catherine C.↗
NASA NTRS2004

Florida Thunderstorms: A Faucet of Reactive Nitrogen to the Upper Troposphere

During the NASA Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL-FACE) enhanced mixing ratios of nitric oxide were measured in the anvils of thunderstorms and in clear air downwind of storm systems on flights of a Wl3-57F high-altitude aircraft. Mixing ratios greater than l0 - 20 times background were readily observed over distances of 25-120 km due to lightning activity. In many of the Florida storms deposition of NO occurred up to near the tropopause but major deposition usually occurred 1 - 2 km below the tropopause, or mostly within the visible anvil volume formed prior to storm decay. Observations from two storms of very different anvil size and electrical activity allowed estimates of the total mass of NO, vented to the middle and upper troposphere. Using the cloud-to ground (CG) flash accumulations from the National Lightning Detection Network, climatological intra-cloud (IC) to CG ratios, and assuming that CG and IC flashes were of equivalent efficiency for NO production, the ranges of production per flash for a moderate-sized and a large storm were (0.51 - 1.0) x l0(exp 26) and (2.3 - 3.1) x 10(exp 26) molecules NO/flash, respectively. Using the recently determined average global flash rate of 44 8, a gross extrapolation of these two storms to represent possible global annual production rates yield 1.6 - 3.2 and 7.3 - 9.9 Tg(N)/yr, respectively. If the more usual assumption is made that IC efficiency is l/l0th that of CG activity, the ranges of production for the moderate-sized and large storm were (1.3 - 2.7) x l0(exp 26) and (6.0 - 8.1) x l0(exp 26) molecules NO/CG flash, respectively. The estimates from the large storm may be high because there is indirect evidence that the IC/CG ratio was larger than would be derived from climatology. These two storms and others studied did not have flash rates that scaled as approx. H(sup 5) where H is the cloud top altitude. The observed CG flash accumulations and NO(x) mass production estimate for the month of July over the Florida area were compared with a representative 3D global Chemistry-Transport Model (CTMJ that uses the Price et al. lightning parameterization. For two land grid points representing the Florida peninsula the model compared well with the observations: CG flash rates were low by only a factor of approx. 2. When the model grid points included the coastal regions of Florida the flash accumulations were lower than observed by a factor of 3.4 - 4.6. It is recommended that models using the Price et al. parameterization allow any global coastal grid point to maintain the land rather than the marine flash rate parameterization. The convection in this CTM underestimated the actual cloud top heights over Florida by 1 - 2 km and thus the total lightning flash rates and the altitude range of reactive nitrogen deposition. Broad scale (20 - 120 km) median mixing ratios of NO within anvils over Florida were significantly larger than in storms previously investigated over Colorado and New Mexico.

Ridley, B.↗
NASA NTRS2004

Offline GCSS Intercomparison of Cloud-Radiation Interaction and Surface Fluxes

Simulations of deep tropical clouds by both cloud-resolving models (CRMs) and single-column models (SCMs) in the GEWEX Cloud System Study (GCSS) Working Group 4 (WG4; Precipitating Convective Cloud Systems), Case 2 (19-27 December 1992, TOGA-COARE IFA) have produced large differences in the mean heating and moistening rates (-1 to -5 K and -2 to 2 grams per kilogram respectively). Since the large-scale advective temperature and moisture "forcing" are prescribed for this case, a closer examination of two of the remaining external types of "forcing", namely radiative heating and air/sea hear and moisture transfer, are warranted. This paper examines the current radiation and surface flux of parameterizations used in the cloud models participating in the GCSS WG4, be executing the models "offline" for one time step (12 s) for a prescribed atmospheric state, then examining the surface and radiation fluxes from each model. The dynamic, thermodynamic, and microphysical fluids are provided by the GCE-derived model output for Case 2 during a period of very active deep convection (westerly wind burst). The surface and radiation fluxes produced from the models are then divided into prescribed convective, stratiform, and clear regions in order to examine the role that clouds play in the flux parameterizations. The results suggest that the differences between the models are attributed more to the surface flux parameterizations than the radiation schemes.

Tao, W.-K.↗
NASA NTRS2000

Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD)

This paper presents a multidisciplinary shape parameterization approach. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft object animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in the same manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminate plate structures) and high-fidelity (e.g., nonlinear computational fluid dynamics and detailed finite element modeling) analysis tools. This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, camber, and free-form surface. Results are presented for a multidisciplinary application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, and a simple performance module.

Samareh, Jamshid A.↗
NASA NTRS1998

The Use of Correlated k-Distributions to Account for the Radiative Effect of Molecular Absorption Upon Satellite Measured Radiances

Establishing the radiative effect of molecular absorption (emission) in the atmosphere is critical to the proper interpretation of satellite retrieved radiances. Without an accurate accounting for molecular absorption, the assignment of radiative transfer processes to observed radiative effects could be fraught errors. Moreover, since the spectral characteristics of molecular absorption can change quickly with wavenumber, the adaptation of climate model parameterizations has the potential to lead to dubious results unless the chosen spectral range corresponds closely to the response function of the satellite instrument. Thus, an initiative has been undertaken to construct parameterizations that will account for the molecular absorption found in the spectral ranges of several satellite radiometers. Because of its efficiency and accuracy in calculating the molecular absorption for nonhomogeneous paths, the correlated k-distribution procedure has proven to be the most effective parameterization (Fu and Liou, 1992, and Kratz, 1995). A further advantage of the correlated k- distribution procedure is its ability to be incorporated directly into multiple scattering routines that consider scattering, as well as absorption, by clouds and aerosol particles.

Kratz, David P.↗
NASA NTRS2007

New, Improved Bulk-microphysical Schemes for Studying Precipitation Processes in WRF: Comparisons with Other Schemes - Part 1

Advances in computing power allow atmospheric prediction models to be mn at progressively finer scales of resolution, using increasingly more sophisticated physical parameterizations and numerical methods. The representation of cloud microphysical processes is a key component of these models, over the past decade both research and operational numerical weather prediction models have started using more complex microphysical schemes that were originally developed for high-resolution cloud-resolving models (CRMs). A recent report to the United States Weather Research Program (USWRP) Science Steering Committee specifically calls for the replacement of implicit cumulus parameterization schemes with explicit bulk schemes in numerical weather prediction (NWP) as part of a community effort to improve quantitative precipitation forecasts (QPF). An improved Goddard bulk microphysical parameterization is implemented into a state-of the-art of next generation of Weather Research and Forecasting (WRF) model. High-resolution model simulations are conducted to examine the impact of microphysical schemes on two different weather events (a midlatitude linear convective system and an Atllan"ic hurricane). The results suggest that microphysics has a major impact on the organization and precipitation processes associated with a summer midlatitude convective line system. The 31CE scheme with a cloud ice-snow-hail configuration led to a better agreement with observation in terms of simulated narrow convective line and rainfall intensity. This is because the 3ICE-hail scheme includes dense ice precipitating (hail) particle with very fast fall speed (over 10 m/s). For an Atlantic hurricane case, varying the microphysical schemes had no significant impact on the track forecast but did affect the intensity (important for air-sea interaction)

Tao, W.-K.↗
NASA NTRS2007

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Lisano, Michael E.↗
NASA NTRS2006

Sulfur in Earth's Mantle and Its Behavior During Core Formation

The density of Earth's outer core requires that about 5-10% of the outer core be composed of elements lighter than Fe-Ni; proposed choices for the "light element" component of Earth's core include H, C, O, Si, S, and combinations of these elements [e.g. 1]. Though samples of Earth's core are not available, mantle samples contain elemental signatures left behind from the formation of Earth's core. The abundances of siderophile (metal-loving) elements in Earth's mantle have been used to gain insight into the early accretion and differentiation history of Earth, the process by which the core and mantle formed, and the composition of the core [e.g. 2-4]. Similarly, the abundance of potential light elements in Earth's mantle could also provide constraints on Earth's evolution and core composition. The S abundance in Earth's mantle is 250 ( 50) ppm [5]. It has been suggested that 250 ppm S is too high to be due to equilibrium core formation in a high pressure, high temperature magma ocean on early Earth and that the addition of S to the mantle from the subsequent accretion of a late veneer is consequently required [6]. However, this earlier work of Li and Agee [6] did not parameterize the metalsilicate partitioning behavior of S as a function of thermodynamic variables, limiting the different pressure and temperature conditions during core formation that could be explored. Here, the question of explaining the mantle abundance of S is revisited, through parameterizing existing metal-silicate partitioning data for S and applying the parameterization to core formation in Earth.

Chabot, Nancy L.↗