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NASA NTRS2005

Consistent Large-Eddy Simulation of a Temporal Mixing Layer Laden with Evaporating Drops: A Posteriori Modelling - Part 2

Large-eddy simulation (LES) is conducted of a three-dimensional temporal mixing layer whose lower stream is initially laden with liquid drops which may evaporate during the simulation. The gas-phase equations are written in an Eulerian frame for two perfect gas species (carrier gas and vapour emanating from the drops), while the liquid-phase equations are written in a Lagrangian frame. The effect of drop evaporation on the gas phase is considered through mass, species, momentum and energy source terms. The drop evolution is modelled using physical drops, or using computational drops to represent the physical drops. Simulations are performed using various LES models previously assessed on a database obtained from direct numerical simulations (DNS). These LES models are for: (i) the subgrid-scale (SGS) fluxes and (ii) the filtered source terms (FSTs) based on computational drops. The LES, which are compared to filtered-and-coarsened (FC) DNS results at the coarser LES grid, are conducted with 64 times fewer grid points than the DNS, and up to 64 times fewer computational than physical drops. It is found that both constant-coefficient and dynamic Smagorinsky SGS-flux models, though numerically stable, are overly dissipative and damp generated small-resolved-scale (SRS) turbulent structures. Although the global growth and mixing predictions of LES using Smagorinsky models are in good agreement with the FC-DNS, the spatial distributions of the drops differ significantly. In contrast, the constant-coefficient scale-similarity model and the dynamic gradient model perform well in predicting most flow features, with the latter model having the advantage of not requiring a priori calibration of the model coefficient. The ability of the dynamic models to determine the model coefficient during LES is found to be essential since the constant-coefficient gradient model, although more accurate than the Smagorinsky model, is not consistently numerically stable despite using DNS-calibrated coefficients. With accurate SGS-flux models, namely scale-similarity and dynamic gradient, the FST model allows up to a 32-fold reduction in computational drops compared to the number of physical drops, without degradation of accuracy; a 64-fold reduction leads to a slight decrease in accuracy.

two-phase flow↗

NASA NTRS2007

The Radiative Consistency of Atmospheric Infrared Sounder and Moderate Resolution Imaging Spectroradiometer Cloud Retrievals

The consistency of cloud top temperature (Tc) and effective cloud fraction (f) retrieved by the Atmospheric Infrared Sounder (AIRS)/Advanced Microwave Sounding Unit (AMSU) observation suite and the Moderate Resolution Imaging Spectroradiometer (MODIS) on the EOS-Aqua platform are investigated. Collocated AIRS and MODIS TC and f are compared via an 'effective scene brightness temperature' (Tb,e). Tb,e is calculated with partial field of view (FOV) contributions from TC and surface temperature (TS), weighted by f and 1-f, respectively. AIRS reports up to two cloud layers while MODIS reports up to one. However, MODIS reports TC, TS, and f at a higher spatial resolution than AIRS. As a result, pixel-scale comparisons of TC and f are difficult to interpret, demonstrating the need for alternatives such as Tb,e. AIRS-MODIS Tb,e differences ((Delta)Tb,e) for identical observing scenes are useful as a diagnostic for cloud quantity comparisons. The smallest values of DTb,e are for high and opaque clouds, with increasing scatter in (Delta)Tb,e for clouds of smaller opacity and lower altitude. A persistent positive bias in DTb,e is observed in warmer and low-latitude scenes, characterized by a mixture of MODIS CO2 slicing and 11-mm window retrievals. These scenes contain heterogeneous cloud cover, including mixtures of multilayered cloudiness and misplaced MODIS cloud top pressure. The spatial patterns of (Delta)Tb,e are systematic and do not correlate well with collocated AIRS-MODIS radiance differences, which are more random in nature and smaller in magnitude than (Delta)Tb,e. This suggests that the observed inconsistencies in AIRS and MODIS cloud fields are dominated by retrieval algorithm differences, instead of differences in the observed radiances. The results presented here have implications for the validation of cloudy satellite retrieval algorithms, and use of cloud products in quantitative analyses.

clouds↗

NASA NTRS2009

The Principle of Energetic Consistency: Application to the Shallow-Water Equations

If the complete state of the earth's atmosphere (e.g., pressure, temperature, winds and humidity, everywhere throughout the atmosphere) were known at any particular initial time, then solving the equations that govern the dynamical behavior of the atmosphere would give the complete state at all subsequent times. Part of the difficulty of weather prediction is that the governing equations can only be solved approximately, which is what weather prediction models do. But weather forecasts would still be far from perfect even if the equations could be solved exactly, because the atmospheric state is not and cannot be known completely at any initial forecast time. Rather, the initial state for a weather forecast can only be estimated from incomplete observations taken near the initial time, through a process known as data assimilation. Weather prediction models carry out their computations on a grid of points covering the earth's atmosphere. The formulation of these models is guided by a mathematical convergence theory which guarantees that, given the exact initial state, the model solution approaches the exact solution of the governing equations as the computational grid is made more fine. For the data assimilation process, however, there does not yet exist a convergence theory. This book chapter represents an effort to begin establishing a convergence theory for data assimilation methods. The main result, which is called the principle of energetic consistency, provides a necessary condition that a convergent method must satisfy. Current methods violate this principle, as shown in earlier work of the author, and therefore are not convergent. The principle is illustrated by showing how to apply it as a simple test of convergence for proposed methods.

Cohn, Stephen E.↗

NASA NTRS2004

Presyncopal/Non-Presyncopal Outcomes of Post Spaceflight Stand Tests are Consistent from Flight to Flight

The overall prevalence of orthostatic hypotension after short duration (6-18 d) spaceflight is 20% with existing countermeasures. However, it is not known if the outcomes of stand tests for orthostatic tolerance are consistent within individuals on subsequent flights, or if first time fliers are more (or less) likely to experience orthostatic hypotension and presyncope than are veteran astronauts. Fifty astronauts were studied retrospectively. Stand test data, which had been collected before and after spaceflight, were compared from at least two flights for each astronaut. For twenty-five of these astronauts, their first flight in this database was also their first time to fly into space. For the remaining 25, their first flight in this database was their second, third or fourth flight, as data were available. No subject became presyncopal during preflight testing. Of the 50 subjects, 45 (90%) had the same outcome on their first and second fligh ts of this study. Of 14 subjects on whom we had data from a third mission, 12 had the same stand test outcome on all three flights (86% same outcome across three flights). There was no correlation between flight duration and orthostatic tolerance (r = 0.39). These data support the idea that astronauts are predisposed to orthostatic tolerance/intolerance after spaceflight and that this predisposition is not altered by subsequent flights. Flight durations within this data set did not alter the likelihood of orthostatic intolerance and rookie fliers were no more likely to experience orthostatic intolerance than were veteran astronauts.

Martin, D. S.↗

NASA NTRS2012

Plasma Diffusion in Self-Consistent Fluctuations

The problem of particle diffusion in position space, as a consequence ofeleclromagnetic fluctuations is addressed. Numerical results obtained with a self-consistent hybrid code are presented, and a method to calculate diffusion coefficient in the direction perpendicular to the mean magnetic field is proposed. The diffusion is estimated for two different types of fluctuations. The first type (resuiting from an agyrotropic in itiai setting)is stationary, wide band white noise, and associated to Gaussian probability distribution function for the magnetic fluctuations. The second type (result ing from a Kelvin-Helmholtz instability) is non-stationary, with a power-law spectrum, and a non-Gaussian probabi lity distribution function. The results of the study allow revisiting the question of loading particles of solar wind origin in the Earth magnetosphere.

Smets, R.↗

NASA NTRS2013

Error Consistency Analysis Scheme for Infrared Ultraspectral Sounding Retrieval Error Budget Estimation

Great effort has been devoted towards validating geophysical parameters retrieved from ultraspectral infrared radiances obtained from satellite remote sensors. An error consistency analysis scheme (ECAS), utilizing fast radiative transfer model (RTM) forward and inverse calculations, has been developed to estimate the error budget in terms of mean difference and standard deviation of error in both spectral radiance and retrieval domains. The retrieval error is assessed through ECAS without relying on other independent measurements such as radiosonde data. ECAS establishes a link between the accuracies of radiances and retrieved geophysical parameters. ECAS can be applied to measurements from any ultraspectral instrument and any retrieval scheme with its associated RTM. In this manuscript, ECAS is described and demonstrated with measurements from the MetOp-A satellite Infrared Atmospheric Sounding Interferometer (IASI). This scheme can be used together with other validation methodologies to give a more definitive characterization of the error and/or uncertainty of geophysical parameters retrieved from ultraspectral radiances observed from current and future satellite remote sensors such as IASI, the Atmospheric Infrared Sounder (AIRS), and the Cross-track Infrared Sounder (CrIS).

Zhou, Daniel K.↗

NASA NTRS2012

Assess Calibration Consistency of MODIS and AVHRR Thermal Infrared Bands Using SNO Observations Corrected for Atmospheric Effects

Monitoring environmental changes from space requires extremely well-calibrated observations to achieve the necessary high accuracy and stability. The calibration differences between the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Advanced Very High Resolution Radiometer (AVHRR) thermal bands provide a valuable quality assessment of the instrument performance. This letter compares the calibration differences between the Aqua MODIS and NOAA-18 AVHRR bands at 11.0 and 12.0 /Lm using simultaneous nadir overpass observations obtained in nearly parallel orbits. Impacts due to the relative spectral-response differences between the two sensors are estimated by MODTRAN simulations with real-time atmospheric profiles of temperature, water vapor, atmospheric pressure and ozone, and surface skin temperatures. Results show that the temperature difference after the removal of atmospheric impacts is within 0.30 K (or 0.40% in radiance) across the effective calibration range (or the 1l.0 l'm band/channel. For the 12.0 pm band, the differences are OAO K (or 0.50%) at the typical radiance and up to 0.70 K (or 0.90%) close to the maximum radiance, indicating an excellent calibration consistency between MODIS and AVHRR for both bands.

Wu, Aisheng↗

NASA NTRS2013

A New Approach for Spectroradiometric Calibration Consistency on the Ground and in Space

A Space-based Calibration Transfer Spectroradiometer (SCATS) is combined with a ground calibration spectral albedo radiometric standard which consists of an opaque quartz glass Mie scattering diffuser (MSD) which has very good Lambertian scattering properties in both reflectance and transmittance modes. This system provides the capability for determining long term changes in the spectral albedo calibrations which operate in the solar reflective wavelength region. The spectral albedo calibration would be traceable to the SIRCUS and STARR NIST calibration facilities. The on-orbit radiometric standard is the Sun. The NIST traceable ground spectral albedo calibration is invariant between the ground and on-orbit over the instrument lifetime due to the use of a field of view defining mechanical baffle to differentiate between radiance and irradiance.

Heath, Donald F.↗

NASA NTRS2013

Surface Irradiances Consistent With CERES-Derived Top-of-Atmosphere Shortwave and Longwave Irradiances

The estimate of surface irradiance on a global scale is possible through radiative transfer calculations using satellite-retrieved surface, cloud, and aerosol properties as input. Computed top-of-atmosphere (TOA) irradiances, however, do not necessarily agree with observation-based values, for example, from the Clouds and the Earth's Radiant Energy System (CERES). This paper presents amethod to determine surface irradiances using observational constraints of TOA irradiance from CERES. A Lagrange multiplier procedure is used to objectively adjust inputs based on their uncertainties such that the computed TOA irradiance is consistent with CERES-derived irradiance to within the uncertainty. These input adjustments are then used to determine surface irradiance adjustments. Observations by the Atmospheric Infrared Sounder (AIRS), Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO), CloudSat, andModerate Resolution Imaging Spectroradiometer (MODIS) that are a part of the NASA A-Train constellation provide the uncertainty estimates. A comparison with surface observations from a number of sites shows that the bias [root-mean-square (RMS) difference] between computed and observed monthlymean irradiances calculated with 10 years of data is 4.7 (13.3) W/sq m for downward shortwave and 22.5 (7.1) W/sq m for downward longwave irradiances over ocean and 21.7 (7.8) W m22 for downward shortwave and 21.0 (7.6) W/sq m for downward longwave irradiances over land. The bias andRMS error for the downward longwave and shortwave irradiances over ocean are decreased from those without constraint. Similarly, the bias and RMS error for downward longwave over land improves, although the constraint does not improve downward shortwave over land. This study demonstrates how synergetic use of multiple instruments (CERES,MODIS, CALIPSO, CloudSat, AIRS, and geostationary satellites) improves the accuracy of surface irradiance computations.

Kato, Seiji↗

NASA NTRS2013

Consistency of Estimated Global Water Cycle Variations Over the Satellite Era

Motivated by the question of whether recent indications of decadal climate variability and a possible "climate shift" may have affected the global water balance, we examine evaporation minus precipitation (E-P) variability integrated over the global oceans and global land from three points of view-remotely sensed retrievals / objective analyses over the oceans, reanalysis vertically-integrated moisture convergence (MFC) over land, and land surface models forced with observations-based precipitation, radiation and near-surface meteorology. Because monthly variations in area-averaged atmospheric moisture storage are small and the global integral of moisture convergence must approach zero, area-integrated E-P over ocean should essentially equal precipitation minus evapotranspiration (P-ET) over land (after adjusting for ocean and land areas). Our analysis reveals considerable uncertainty in the decadal variations of ocean evaporation when integrated to global scales. This is due to differences among datasets in 10m wind speed and near-surface atmospheric specific humidity (2m qa) used in bulk aerodynamic retrievals. Precipitation variations, all relying substantially on passive microwave retrievals over ocean, still have uncertainties in decadal variability, but not to the degree present with ocean evaporation estimates. Reanalysis MFC and P-ET over land from several observationally forced diagnostic and land surface models agree best on interannual variations. However, upward MFC (i.e. P-ET) reanalysis trends are likely related in part to observing system changes affecting atmospheric assimilation models. While some evidence for a low-frequency E-P maximum near 2000 is found, consistent with a recent apparent pause in sea-surface temperature (SST) rise, uncertainties in the datasets used here remain significant. Prospects for further reducing uncertainties are discussed. The results are interpreted in the context of recent climate variability (Pacific Decadal Oscillation, Atlantic Meridional Overturning), and efforts to distinguish these modes from longer-term trends.

Robertson, F. R.↗

NASA NTRS2013

Consistency of Estimated Global Water Cycle Variations Over the Satellite Era

Robertson, F. R.↗

NASA NTRS2014

Remote Analysis of Regional Lunar Pyroclastic Deposits - Consistency and Precision of LRO Diviner Estimates

Allen et al. recently published a new method of estimating the FeO abundances of lunar pyroclastic deposits. This method is derived from orbital thermal infrared measurements by the Diviner Lunar Radiometer Experiment on the Lunar Reconnaissance Orbiter (LRO) spacecraft. The present study utilizes Diviner data from the Taurus Littrow regional pyroclastic deposit to assess the consistency and precision of such estimates.

Allen, Carlton C.↗

NASA NTRS2013

On Multiscale Modeling: Preserving Energy Dissipation Across the Scales with Consistent Handshaking Methods

A mesh objective crack band model was implemented within the generalized method of cells micromechanics theory. This model was linked to a macroscale finite element model to predict post-peak strain softening in composite materials. Although a mesh objective theory was implemented at the microscale, it does not preclude pathological mesh dependence at the macroscale. To ensure mesh objectivity at both scales, the energy density and the energy release rate must be preserved identically across the two scales. This requires a consistent characteristic length or localization limiter. The effects of scaling (or not scaling) the dimensions of the microscale repeating unit cell (RUC), according to the macroscale element size, in a multiscale analysis was investigated using two examples. Additionally, the ramifications of the macroscale element shape, compared to the RUC, was studied.

Pineda, Evan J.↗

NASA NTRS2016

Consistent Evaluation of ACOS-GOSAT, BESD-SCIAMACHY, CarbonTracker, and MACC Through Comparisons to TCCON

Consistent validation of satellite CO2 estimates is a prerequisite for using multiple satellite CO2 measurements for joint flux inversion, and for establishing an accurate long-term atmospheric CO2 data record. Harmonizing satellite CO2 measurements is particularly important since the differences in instruments, observing geometries, sampling strategies, etc. imbue different measurement characteristics in the various satellite CO2 data products. We focus on validating model and satellite observation attributes that impact flux estimates and CO2 assimilation, including accurate error estimates, correlated and random errors, overall biases, biases by season and latitude, the impact of coincidence criteria, validation of seasonal cycle phase and amplitude, yearly growth, and daily variability. We evaluate dry-air mole fraction (X(sub CO2)) for Greenhouse gases Observing SATellite (GOSAT) (Atmospheric CO2 Observations from Space, ACOS b3.5) and SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) (Bremen Optimal Estimation DOAS, BESD v2.00.08) as well as the CarbonTracker (CT2013b) simulated CO2 mole fraction fields and the Monitoring Atmospheric Composition and Climate (MACC) CO2 inversion system (v13.1) and compare these to Total Carbon Column Observing Network (TCCON) observations (GGG2012/2014). We find standard deviations of 0.9, 0.9, 1.7, and 2.1 parts per million vs. TCCON for CT2013b, MACC, GOSAT, and SCIAMACHY, respectively, with the single observation errors 1.9 and 0.9 times the predicted errors for GOSAT and SCIAMACHY, respectively. We quantify how satellite error drops with data averaging by interpreting according to (error(sup 2) equals a(sup 2) plus b(sup 2) divided by n (with n being the number of observations averaged, a the systematic (correlated) errors, and b the random (uncorrelated) errors). a and b are estimated by satellites, coincidence criteria, and hemisphere. Biases at individual stations have year-to-year variability of 0.3 parts per million, with biases larger than the TCCON predicted bias uncertainty of 0.4 parts per million at many stations. We find that GOSAT and CT2013b under-predict the seasonal cycle amplitude in the Northern Hemisphere (NH) between 46 and 53 degrees North latitude, MACC over-predicts between 26 and 37 degrees North latitude, and CT2013b under-predicts the seasonal cycle amplitude in the Southern Hemisphere (SH). The seasonal cycle phase indicates whether a data set or model lags another data set in time. We find that the GOSAT measurements improve the seasonal cycle phase substantially over the prior while SCIAMACHY measurements improve the phase significantly for just two of seven sites. The models reproduce the measured seasonal cycle phase well except for at Lauder_125HR (CT2013b) and Darwin (MACC). We compare the variability within 1 day between TCCON and models in June-July-August; there is correlation between 0.2 and 0.8 in the NH, with models showing 10-50 percent the variability of TCCON at different stations and CT2013b showing more variability than MACC. This paper highlights findings that provide inputs to estimate flux errors in model assimilations, and places where models and satellites need further investigation, e.g., the SH for models and 45-67 degrees North latitude for GOSAT and CT2013b.

ACOS-GOSAT↗

NASA NTRS2015

Consistency of CERES Radiances and Fluxes from Aqua and Suomi-NPP

The Clouds and Earth's Radiant Energy System (CERES) instruments on board Terra, Aqua, and Suomi-NPP have been providing data products critical to advancing our understanding of the effects of clouds and aerosols on radiative energy within the Earth-atmosphere system. The CERES instrument consists of a threechannel broadband scanning radiometer. The scanning radiometer measures radiances in shortwave (SW, 0.3-5 micron), window (WN, 8-12 micron), and total (0.3-200 micron) channels. The longwave (LW) component is derived as the difference between total and SW channels. These measured radiances at a given sun-Earthsatellite geometry are converted to outgoing reflected solar and emitted thermal TOA radiative fluxes by using CERES scene-type dependent angular distribution models (ADMs). The CERES instruments must remain radiometrically stable and correctly inter-calibrated to accurately capture changes in Earth"s radiation budget from interannual to decadal timescales. This presentation will focus on comparisons between collocated radiance measurements from CERES instruments on Aqua and on Suomi-NPP. As we do not have a set of ADMs that is constructed specifically for the CERES instrument on Suomi-NPP, CERES Aqua ADMs are used to invert fluxes from radiance measurements on Suomi-NPP. But the CERES Aqua footprint size is smaller than the CERES Suomi-NPP footprint size and the scene identifications provided by MODIS and VIIRS can also be different from each other. Will using Aqua ADMs for Suomi-NPP flux inversion increase the flux uncertainty? We will examine the deseasonalized flux anomaly time series using Aqua data alone and using combined Aqua and Suomi-NPP data. We will also present a simulation study to assess the Suomi-NPP flux uncertainty from using Aqua ADMs for the flux inversion.

Su, Wenying↗

NASA NTRS2016

Consistency Between Sun-Induced Chlorophyll Fluorescence and Gross Primary Production of Vegetation in North America

Accurate estimation of the gross primary production (GPP) of terrestrial ecosystems is vital for a better understanding of the spatial-temporal patterns of the global carbon cycle. In this study,we estimate GPP in North America (NA) using the satellite-based Vegetation Photosynthesis Model (VPM), MODIS (Moderate Resolution Imaging Spectrometer) images at 8-day temporal and 500 meter spatial resolutions, and NCEP-NARR (National Center for Environmental Prediction-North America Regional Reanalysis) climate data. The simulated GPP (GPP (sub VPM)) agrees well with the flux tower derived GPP (GPPEC) at 39 AmeriFlux sites (155 site-years). The GPP (sub VPM) in 2010 is spatially aggregated to 0.5 by 0.5-degree grid cells and then compared with sun-induced chlorophyll fluorescence (SIF) data from Global Ozone Monitoring Instrument 2 (GOME-2), which is directly related to vegetation photosynthesis. Spatial distribution and seasonal dynamics of GPP (sub VPM) and GOME-2 SIF show good consistency. At the biome scale, GPP (sub VPM) and SIF shows strong linear relationships (R (sup 2) is greater than 0.95) and small variations in regression slopes ((4.60-5.55 grams Carbon per square meter per day) divided by (milliwatts per square meter per nanometer per square radian)). The total annual GPP (sub VPM) in NA in 2010 is approximately 13.53 petagrams Carbon per year, which accounts for approximately 11.0 percent of the global terrestrial GPP and is within the range of annual GPP estimates from six other process-based and data-driven models (11.35-22.23 petagrams Carbon per year). Among the seven models, some models did not capture the spatial pattern of GOME-2 SIF data at annual scale, especially in Midwest cropland region. The results from this study demonstrate the reliable performance of VPM at the continental scale, and the potential of SIF data being used as a benchmark to compare with GPP models.

photosynthesis model↗

NASA NTRS2016

Providing Comprehensive and Consistent Access to Astronomical Observatory Archive Data: The NASA Archive Model

Since the turn of the millennium a constant concern of astronomical archives have begun providing data to the public through standardized protocols unifying data from disparate physical sources and wavebands across the electromagnetic spectrum into an astronomical virtual observatory (VO). In October 2014, NASA began support for the NASA Astronomical Virtual Observatories (NAVO) program to coordinate the efforts of NASA astronomy archives in providing data to users through implementation of protocols agreed within the International Virtual Observatory Alliance (IVOA). A major goal of the NAVO collaboration has been to step back from a piecemeal implementation of IVOA standards and define what the appropriate presence for the US and NASA astronomy archives in the VO should be. This includes evaluating what optional capabilities in the standards need to be supported, the specific versions of standards that should be used, and returning feedback to the IVOA, to support modifications as needed. We discuss a standard archive model developed by the NAVO for data archive presence in the virtual observatory built upon a consistent framework of standards defined by the IVOA. Our standard model provides for discovery of resources through the VO registries, access to observation and object data, downloads of image and spectral data and general access to archival datasets. It defines specific protocol versions, minimum capabilities, and all dependencies. The model will evolve as the capabilities of the virtual observatory and needs of the community change.

Virtual observatory; data archives; standards; IVO↗

NASA NTRS2016

Polarized Radiative Transfer of a Cirrus Cloud Consisting of Randomly Oriented Hexagonal Ice Crystals: The 3 x 3 Approximation for Non-Spherical Particles

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 x 10(exp 3) so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling- adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5 for I and within 1.5 for Q for all viewing angles. In 1971 Hansen showed that for scattering by spherical particles the 3 x 3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3 x 3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3 x 3 approximation leads to an absolute error 2 x 10(exp -6) for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

Polarization↗