Search NASA⌕ Search

SEARCH · Search NASA

Results for “FOUR-DIMENSIONAL CALCULATIONS”

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.

Global Pattern of Potential Evaporation Calculated from the Penman-Monteith Equation Using Satellite and Assimilated Data

Potential evaporation (E(0)) has been found to be useful in many practical applications and in research for setting a reference level for actual evaporation. All previous estimates of regional or global E(0) are based upon empirical formulae using climatologic meteorologic measurements at isolated stations (i.e., point data). However, the Penman-Monteith equation provides a physically based approach for computing E(0), and by comparing 20 different methods of estimating E(0), Jensen et al. (1990) showed that the Penman-Monteith equation provides the most accurate estimate of monthly E(0) from well-watered grass or alfalfa. In the present study, monthly total E(0) for 24 months (January 1987 to December 1988) was calculated from the Penman-Monteith equation, with prescribed albedo of 0.23 and surface resistance of 70 s/m, which are considered to be representative of actively growing well-watered grass covering the ground. These calculations have been done using spatially representative data derived from satellite observations and data assimilation results. Satellite observations were used to obtain solar radiation, fractional cloud cover, air temperature, and vapor pressure, while four-dimensional data assimilation results were used to calculate the aerodynamic resistance. Meteorologic data derived from satellite observations were compared with the surface measurements to provide a measure of accuracy. The accuracy of the calculated E(0) values was assessed by comparing with lysimeter observations for evaporation from well-watered grass at 35 widely distributed locations, while recognizing that the period of present calculations was not concurrent with the lysimeter measurements and the spatial scales of these measurements and calculations are vastly different. These comparisons suggest that the error in the calculated E(0) values may not be exceeded, on average, 20% for any month or location, but are more likely to be about 15%. These uncertainties are difficult to quantify for mountainous areas or locations close to extensive water bodies. The difference between the calculated and observed E(0) is about 5% when all month and locations were considered. Errors are expected to be less than 15% for averages of E(0) over large areas or several months. Further comparisons with lysimeter observations could provide a better appraisal of the calculated values. Global pattern of E(0) was presented, together with zonal average values.

Choudhury, Bhaskar J.↗

Protostellar formation in rotating interstellar clouds. V - Nonisothermal collapse and fragmentation

Numerical calculations are presented for rigorous models spanning a four-dimensional parameter space of initial conditions of the three-dimensional collapse of rotating protostellar clouds, encompassing radiative transfer in the Eddington approximation and detailed thermodynamical relations. It is found that protostellar formation may involve a few stages of hierarchical fragmentation terminated by increased thermal pressure in the nonisothermal regime, that high thermal energy clouds remain nearly axisymmetric during the first dynamic collapse phase, and that very slowly rotating clouds can fragment. The presolar nebula was probably formed from a cloud with very little initial rotation.

Boss, Alan R.↗

On-line estimation of error covariance parameters for atmospheric data assimilation

A simple scheme is presented for on-line estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximum-likelihood approach in which estimates are produced on the basis of a single batch of simultaneous observations. Simple-sample covariance estimation is reasonable as long as the number of available observations exceeds the number of tunable parameters by two or three orders of magnitude. Not much is known at present about model error associated with actual forecast systems. Our scheme can be used to estimate some important statistical model error parameters such as regionally averaged variances or characteristic correlation length scales. The advantage of the single-sample approach is that it does not rely on any assumptions about the temporal behavior of the covariance parameters: time-dependent parameter estimates can be continuously adjusted on the basis of current observations. This is of practical importance since it is likely to be the case that both model error and observation error strongly depend on the actual state of the atmosphere. The single-sample estimation scheme can be incorporated into any four-dimensional statistical data assimilation system that involves explicit calculation of forecast error covariances, including optimal interpolation (OI) and the simplified Kalman filter (SKF). The computational cost of the scheme is high but not prohibitive; on-line estimation of one or two covariance parameters in each analysis box of an operational bozed-OI system is currently feasible. A number of numerical experiments performed with an adaptive SKF and an adaptive version of OI, using a linear two-dimensional shallow-water model and artificially generated model error are described. The performance of the nonadaptive versions of these methods turns out to depend rather strongly on correct specification of model error parameters. These parameters are estimated under a variety of conditions, including uniformly distributed model error and time-dependent model error statistics.

Dee, Dick P.↗

SAGE III/ISS Ozone and NO2 Validation Using Diurnal Scaling Factors

We developed a set of solar zenith angle, latitude- and altitude-dependent scaling factors to account for the diurnal variability in ozone (O3) and nitrogen dioxide (NO2) when comparing Stratospheric Aerosol and Gas Experiment (SAGE) III/ISS observations to observations from other times of day. The scaling factors are calculated as a function of solar zenith angle from the four-dimensional output of a global atmospheric chemistry model simulation of 2017–2020 that shows good agreement with observed vertical profiles. Using a global atmospheric chemistry model allows us to account for both chemically and dynamically driven variability. Both year-specific scale factors and a multi-year monthly climatology are available to decrease the uncertainty in inter-instrument comparisons and allow consistent comparisons between observations from different times of day. We describe the variability in the diurnal scale factors as a function of space and time. The quasi-biennial oscillation (QBO) appears to be a contributing factor to interannual variability in the NO2 scaling factors, leading to differences between years that switch sign with altitude. We show that application of these scaling factors improves the comparison between SAGE III/ISS and OSIRIS NO2 and between SAGE III/ISS and OMPS LP, OSIRIS, and ACE-FTS O3 observations. The comparisons between SAGE III/ISS O3 for sunrise or sunset vs. Microwave Limb Sounder (MLS) daytime or nighttime observations are also more consistent when we apply the diurnal scaling factors. There is good agreement between SAGE III/ISS V5.2 ozone and correlative measurements, with differences within 5 % between 20 and 50 km when corrected for diurnal variability. Similarly, the SAGE III/ISS V5.2 NO2 agreement with correlative measurement is mostly within 10 %. While the scale factors were designed for use with SAGE III/ISS observations, they can easily be applied to other observation intercomparisons as well.

Sarah A. Strode↗

The Implementation and Evaluation of the Emergency Response Dose Assessment System (ERDAS) at Cape Canaveral Air Station/Kennedy Space Center

The Emergency Response Dose Assessment System (ERDAS) is a system which combines the mesoscale meteorological prediction model RAMS with the diffusion models REEDM and HYPACT. Operators use a graphical user interface to run the models for emergency response and toxic hazard planning at CCAS/KCS. The Applied Meteorology Unit has been evaluating the ERDAS meteorological and diffusion models and obtained the following results: (1) RAMS adequately predicts the occurrence of the daily sea breeze during non-cloudy conditions for several cases. (2) RAMS shows a tendency to predict the sea breeze to occur slightly earlier and to move it further inland than observed. The sea breeze predictions could most likely be improved by better parameterizing the soil moisture and/or sea surface temperatures. (3) The HYPACT/REEDM/RAMS models accurately predict launch plume locations when RAMS winds are accurate and when the correct plume layer is modeled. (4) HYPACT does not adequately handle plume buoyancy for heated plumes since all plumes are presently treated as passive tracers. Enhancements should be incorporated into the ERDAS as it moves toward being a fully operational system and as computer workstations continue to increase in power and decrease in cost. These enhancements include the following: activate RAMS moisture physics; use finer RAMS grid resolution; add RAMS input parameters (e.g. soil moisture, radar, and/or satellite data); automate data quality control; implement four-dimensional data assimilation; modify HYPACT plume rise and deposition physics; and add cumulative dosage calculations in HYPACT.

Evans, Randolph J.↗

A Method for Assessing the Quality of Model-Based Estimates of Ground Temperature and Atmospheric Moisture Using Satellite Data

A method is developed for validating model-based estimates of atmospheric moisture and ground temperature using satellite data. The approach relates errors in estimates of clear-sky longwave fluxes at the top of the Earth-atmosphere system to errors in geophysical parameters. The fluxes include clear-sky outgoing longwave radiation (CLR) and radiative flux in the window region between 8 and 12 microns (RadWn). The approach capitalizes on the availability of satellite estimates of CLR and RadWn and other auxiliary satellite data, and multiple global four-dimensional data assimilation (4-DDA) products. The basic methodology employs off-line forward radiative transfer calculations to generate synthetic clear-sky longwave fluxes from two different 4-DDA data sets. Simple linear regression is used to relate the clear-sky longwave flux discrepancies to discrepancies in ground temperature ((delta)T(sub g)) and broad-layer integrated atmospheric precipitable water ((delta)pw). The slopes of the regression lines define sensitivity parameters which can be exploited to help interpret mismatches between satellite observations and model-based estimates of clear-sky longwave fluxes. For illustration we analyze the discrepancies in the clear-sky longwave fluxes between an early implementation of the Goddard Earth Observing System Data Assimilation System (GEOS2) and a recent operational version of the European Centre for Medium-Range Weather Forecasts data assimilation system. The analysis of the synthetic clear-sky flux data shows that simple linear regression employing (delta)T(sub g)) and broad layer (delta)pw provides a good approximation to the full radiative transfer calculations, typically explaining more thin 90% of the 6 hourly variance in the flux differences. These simple regression relations can be inverted to "retrieve" the errors in the geophysical parameters, Uncertainties (normalized by standard deviation) in the monthly mean retrieved parameters range from 7% for (delta)T(sub g) to approx. 20% for the lower tropospheric moisture between 500 hPa and surface. The regression relationships developed from the synthetic flux data, together with CLR and RadWn observed with the Clouds and Earth Radiant Energy System instrument, ire used to assess the quality of the GEOS2 T(sub g) and pw. Results showed that the GEOS2 T(sub g) is too cold over land, and pw in upper layers is too high over the tropical oceans and too low in the lower atmosphere.

Wu, Man Li C.↗

Development of simplified airborne computations for fuel conservative descents in a time-based metered air traffic environment

The NASA has developed and flight-tested a simple flight management descent algorithm designed to improve the accuracy of delivering an airplane in a fuel-conservative manner to a metering fix at a time designated by air traffic control. This algorithm provides a three-dimensional path with terminal area time constraints (four-dimensional) for an airplane to make an idle-thrust, clean-configured (landing gear up, flaps zero, and speed brakes retracted) descent to arrive at the metering fix at a predetermined time, altitude, and airspeed. The descent path is calculated for a constant Mach/airspeed schedule from linear approximations of airplane performance with considerations given for gross weight, wind, and nonstandard pressure and temperature effects. Applications of the four-dimensional and descent planning capabilities of the algorithm to conventional airplanes is being investigated. This report describes the flight management descent algorithm and presents the results of the flight tests flown with the Terminal Configured Vehicle airplane.

Knox, C. E.↗

A fast routine for computing

A routine for calculating multidimensional histograms of multivariate data using a combination table look up and search procedure is described. The software was originally developed to computer four-dimensional histograms from LANDSAT multispectral imagery, but the concept can be used on other types of data and the program can be modified for the desired type of output information.

Jayroe, R. R., Jr.↗

A Brief Survey of the Equilibrium and Transport Properties of Critical Fluids and the Degree to Which Microgravity is Required for Their Experimental Investigation

The modern theory of second order phase transitions is very successful in calculating the critical exponents as an asymptotic expansion in powers of epsilon = 4 - D, the deviation of D = 3, the spatial dimension of the actual physical system from that of the abstract four-dimensional reference model. This remarkable mathematical 'tour de force' leaves unanswered, however, many fundamental questions concerning the exact nature of how the fluctuations interact. I discuss here some experiments which would help to further our understanding of the equilibrium critical properties. Especially promising would be a measurement of the temperature dependence of the turbidity very close to the critical point. This has the promise of determining the small and elusive but fundamentally important anomalous dimension exponent eta. I also review various ways of measuring the critical transport coefficients and point out some cases where ground based experiments may usefully supplement flight experiments.

Ferrell, Richard A.↗

The dependence of the shape and stability of captive rotating drops on multiple parameters

Asymptotic and numerical techniques in bifurcation theory are applied to the Young-Laplace equation governing meniscus shape in order to analyze the dependence of the shape and stability of rigidly rotating drops held captive between corotating solid faces on multiple parameters. Asymptotic analysis of the evolution of drop shape from the cylindrical as a function of distance between the solid faces, drop volume, rotational Bond number and gravitational Bond number shows that some shape bifurcations from cylinders to wavy, axisymmetric menisci are ruptured by small changes in drop volume or gravity. Computer calculations of axisymmetric drop shapes based on a finite element representation of the interface and numerical algorithms for tracking shape families and singular points are then used to map drop stability for the four-dimensional parameter space. The results of the asymptotic and numerical analyses are shown to agree well within the limited range of parameters where the asymptotic analysis is valid.

Ungar, L. H.↗

Performance Evaluation of Conflict-Free Trajectory Taxiing in Airport Ramp Area Using Fast-Time Simulations

The German Aerospace Center (DLR) and the National Aeronautics and Space Administration (NASA) have been collaborating to conduct joint research addressing future surface traffic management challenges. The surface management tool from DLR, called Taxi Routing for Aircraft: Creation and Controlling (TRACC), was adapted to be integrated in NASA's fast-time simulation environment called Surface Operations Simulator and Scheduler (SOSS). The research described in this paper 1) applied TRACC to trajectory-based ramp traffic management, where TRACC generates conflict-free aircraft trajectories in a congested ramp area, 2) investigated the feasibility of the concept through the integrated TRACC-SOSS fast-time simulation, and 3) evaluated the performance of the integrated system. For this activity, TRACC was adapted for ramp operations at Charlotte Douglas International Airport, called TRACC_PB (TRACC for pushback optimization). TRACC_PB provides four-dimensional taxi trajectories with a command speed profile for each aircraft following standard taxi routes within the ramp area. In this study, departures are given the Target Movement Area entry Times (TMATs) provided by the baseline surface metering scheduler based on NASA's Spot and Runway Departure Advisor (SARDA). TRACC_PB also calculates optimal pushback times for departures, as well as the times when arrivals shall enter the ramp, the Target Movement area Exit Times (TMETs). The initial results showed that the TRACC_PB successfully generated conflict-free trajectories for the ramp area taxi operations and improved taxiing efficiency compared to the baseline results. TRACC_PB aimed to provide conflict-free taxi routes avoiding any stops while taxiing. This resulted in longer gate hold times for departures and postponed throughput values compared to the baseline simulation without trajectory optimization. Having conflict-free routes without stoppage also created shorter taxi times but required renegotiation of the given TMATs. TRACC_PB also achieved reductions in both fuel consumption and engine emissions (17% for departures and 10% for arrivals), which correlate with the ramp taxi time reduction.

trajectory-based taxi operations↗

Comparisons among a new soil index and other two- and four-dimensional vegetation indices

The 2-D difference vegetation index (DVI) and perpendicular vegetation index (PVI), and the 4-D green vegetation index (GVI) are compared in Landsat MSS data from grain sorghum (Sorghum bicolor, L. Moench) fields for the years 1973 to 1977. PVI and DVI were more closely related to LAI than was GVI. A new 2-D soil line index (SLI), the vector distance from the soil line origin to the point of intersection of PVI with the soil line, is defined and compared with the 4-D soil brightness index, SBI. SLI (based on MSS and MSS7) and SL16 (based on MSS5 and MSS6) were smaller in magnitude than SBI but contained similar information about the soil background. These findings indicate that vegetation and soil indices calculated from the single visible and reflective infrared band sensor systems, such as the AVHRR of the TIROS-N polar orbiting series of satellites, will be meaningful for synoptic monitoring of renewable vegetation. Previously announced in STAR as N83-14567

Wiegand, C. L.↗

Comparisons among a new soil index and other two- and four-dimensional vegetation indices

The 2-D difference vegetation index (DVI) and perpendicular vegetation index (PVI), and the 4-D green vegetation index (GVI) are compared in LANDSAT MSS data from grain sorghum (Sorghum bicolor, L. Moench) fields for the years 1973 to 1977. PVI and DVI were more closely related to LAI than was GVI. A new 2-D soil line index (SLI), the vector distance from the soil line origin to the point of intersection of PVI with the soil line, is defined and compared with the 4-D soil brightness index, SBI. SLI (based on MSS and MSS7) and SL16 (based on MSS 5 and MSS 6) were smaller in magnitude than SBI but contained similar information about the soil background. These findings indicate that vegetation and soil indices calculated from the single visible and reflective infrared band sensor systems, such as the AVHRR of the TIROS-N polar orbiting series of satellites, will be meaningful for synoptic monitoring of renewable vegetation.

Wiegand, C. L.↗

Model Error Estimation for the CPTEC Eta Model

Statistical data assimilation systems require the specification of forecast and observation error statistics. Forecast error is due to model imperfections and differences between the initial condition and the actual state of the atmosphere. Practical four-dimensional variational (4D-Var) methods try to fit the forecast state to the observations and assume that the model error is negligible. Here with a number of simplifying assumption, a framework is developed for isolating the model error given the forecast error at two lead-times. Two definitions are proposed for the Talagrand ratio tau, the fraction of the forecast error due to model error rather than initial condition error. Data from the CPTEC Eta Model running operationally over South America are used to calculate forecast error statistics and lower bounds for tau.

Tippett, Michael K.↗

A Coupled fcGCM-GCE Modeling System: A 3D Cloud Resolving Model and a Regional Scale Model

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and ore sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1998 and 1999). Also, at Goddard, we have implemented several Goddard microphysical schemes (21CE, several 31CE), Goddard radiation (including explicity calculated cloud optical properties), and Goddard Land Information (LIS, that includes the CLM and NOAH land surface models) into a next generation regional scale model, WRF. In this talk, I will present: (1) A Brief review on GCE model and its applications on precipitation processes (microphysical and land processes), (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), (3) A discussion on the Goddard WRF version (its developments and applications), and (4) The characteristics of the four-dimensional cloud data sets (or cloud library) stored at Goddard.

Tao, Wei-Kuo↗

Conical-Domain Model for Estimating GPS Ionospheric Delays

The conical-domain model is a computational model, now undergoing development, for estimating ionospheric delays of Global Positioning System (GPS) signals. Relative to the standard ionospheric delay model described below, the conical-domain model offers improved accuracy. In the absence of selective availability, the ionosphere is the largest source of error for single-frequency users of GPS. Because ionospheric signal delays contribute to errors in GPS position and time measurements, satellite-based augmentation systems (SBASs) have been designed to estimate these delays and broadcast corrections. Several national and international SBASs are currently in various stages of development to enhance the integrity and accuracy of GPS measurements for airline navigation. In the Wide Area Augmentation System (WAAS) of the United States, slant ionospheric delay errors and confidence bounds are derived from estimates of vertical ionospheric delay modeled on a grid at regularly spaced intervals of latitude and longitude. The estimate of vertical delay at each ionospheric grid point (IGP) is calculated from a planar fit of neighboring slant delay measurements, projected to vertical using a standard, thin-shell model of the ionosphere. Interpolation on the WAAS grid enables estimation of the vertical delay at the ionospheric pierce point (IPP) corresponding to any arbitrary measurement of a user. (The IPP of a given user s measurement is the point where the GPS signal ray path intersects a reference ionospheric height.) The product of the interpolated value and the user s thin-shell obliquity factor provides an estimate of the user s ionospheric slant delay. Two types of error that restrict the accuracy of the thin-shell model are absent in the conical domain model: (1) error due to the implicit assumption that the electron density is independent of the azimuthal angle at the IPP and (2) error arising from the slant-to-vertical conversion. At low latitudes or at mid-latitudes under disturbed conditions, the accuracy of SBAS systems based upon the thin-shell model suffers due to the presence of complex ionospheric structure, high delay values, and large electron density gradients. Interpolation on the vertical delay grid serves as an additional source of delay error. The conical-domain model permits direct computation of the user s slant delay estimate without the intervening use of a vertical delay grid. The key is to restrict each fit of GPS measurements to a spatial domain encompassing signals from only one satellite. The conical domain model is so named because each fit involves a group of GPS receivers that all receive signals from the same GPS satellite (see figure); the receiver and satellite positions define a cone, the satellite position being the vertex. A user within a given cone evaluates the delay to the satellite directly, using (1) the IPP coordinates of the line of sight to the satellite and (2) broadcast fit parameters associated with the cone. The conical-domain model partly resembles the thin-shell model in that both models reduce an inherently four-dimensional problem to two dimensions. However, unlike the thin-shell model, the conical domain model does not involve any potentially erroneous simplifying assumptions about the structure of the ionosphere. In the conical domain model, the initially four-dimensional problem becomes truly two-dimensional in the sense that once a satellite location has been specified, any signal path emanating from a satellite can be identified by only two coordinates; for example, the IPP coordinates. As a consequence, a user s slant-delay estimate converges to the correct value in the limit that the receivers converge to the user s location (or, equivalently, in the limit that the measurement IPPs converge to the user s IPP).

Sparks, Lawrence↗