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At least 361 records · Page 20

Electrical Charging of the Clouds of Titan

We have used recent data on graphitic cloud particles in the atmosphere or Titan to compute the electrical charging of the particles (radii ranging from 0.01 microns to 0.26 microns). The charging on the nightside was rather similar to that obtained earlier (Borucki et al, Icarus, 72, 604-622, 1987) except that charge distributions on the particles are now computed and recently obtained cloud particle sizes and density distributions were employed. The negative charge on particles of 0.26 microns peaked at 9 at 150 km altitude. The computations were repeated for the dayside with the addition of photoelectron emission by the particles as a result of the absorption of solar UV radiation. Particles (except the very smallest) now became positively charged with particles of radius 0.26 microns being charged up to +47. Next, very small particles (radii approximately 3 x 10^-4 microns) of polycyclic aromatic hydrocarbons (PAHs) were introduced and treated as sources of negative ions since they could be either neutral or carry one negative charge. Moreover, they are mobile so that they had to be treated like molecular size negative ions although much more massive. They had the effect of substantially reducing the electron densities in the altitude range 190 to 310 km to values less than the negative PAH densities and increasing the peak electron charge on the larger particles. Particles of radius 0.26 microns bore peak charges of plus or minus 47 at altitudes of approximately 250 km. The simulated effect of PAHs on the nightside proved to be much less pronounced; at the peak negative PAH density, it was less than the electron density. The physics governing these results will be discussed.

Borucki, William J.↗

Electrical Charging of Aerosols and Conductivity of Titan's Atmosphere

We have used recent data on graphitic cloud particles in the atmosphere of Titan to compute the electrical charging of the particles (radii ranging from 0.01 microns to 0.26 microns). The charging on the nightside was rather similar to that obtained earlier except that charge distributions on the particles are now computed and recently obtained cloud particle sizes and density distributions were employed. The negative charge on particles of 0.26 microns peaked at 9 at 150 km altitude. The computations were repeated for the dayside with the addition of photoelectron emission by the particles as a result of the absorption of solar UV radiation. Particles (except the very smallest) now became positively charged with particles of radius 0.26 microns being charged up to +47. Next, very small particles (radii approx. 3 x 10 (sup -4) microns) of polycyclic aromatic hydrocarbons (PAHs) were introduced and treated as sources of negative ions since they could be either neutral or carry one negative charge. Moreover, they are mobile so that they had to be treated like molecular size negative ions although much more massive. They had the effect of substantially reducing the electron densities in the altitude range 190 to 310 km to values less than the negative PAH densities and increasing the peak electron charge on the larger particles. Particles of radius 0.26 microns bore peak charges of approx. +47 at altitudes of approx. 250 km. The simulated effect of PAHs on the nightside proved to be much less pronounced; at the peak negative PAH density, it was less than the electron density. The physics governing these results will be discussed.

Borucki, W. J.↗

Independent Pixel and Two Dimensional Estimates of LANDSAT-Derived Cloud Field Albedo

A theoretical study has been conducted on the effects of cloud horizontal inhomogeneity on cloud albedo bias. A two-dimensional (2D) version of the Spherical Harmonic Discrete Ordinate Method (SHDOM) is used to estimate the albedo bias of the plane parallel (PP-IPA) and independent pixel (IPA-2D) approximations for a wide range of 2D cloud fields obtained from LANDSAT. They include single layer trade cumulus, open and closed cell broken stratocumulus, and solid stratocumulus boundary layer cloud fields over ocean. Findings are presented on a variety of averaging scales and are summarized as a function of cloud fraction, mean cloud optical depth, cloud aspect ratio, standard deviation of optical depth, and the gamma function parameter Y (a measure of the width of the optical depth distribution). Biases are found to be small for small cloud fraction or mean optical depth, where the cloud fields under study behave linearly. They are large (up to 0.20 for PP-IPA bias, -0.12 for IPA-2D bias) for large v. On a scene average basis PP-IPA bias can reach 0.30, while IPA-2D bias reaches its largest magnitude at -0.07. Biases due to horizontal transport (IPA-2D) are much smaller than PP-IPA biases but account for 20% RMS of the bias overall. Limitations of this work include the particular cloud field set used, assumptions of conservative scattering, constant cloud droplet size, no gas absorption or surface reflectance, and restriction to 2D radiative transport. The LANDSAT data used may also be affected by radiative smoothing.

Chambers, L. H.↗

Issues Regarding the Assimilation of Cloud and Precipitation Data

This is the authors' response to a set of criticisms regarding a previously published work. It briefly addresses the main criticisms. In particular, it explains why some papers identified as having some fundamental flaws were referenced in the original work without detailed exposition of those flaws. It also explains why parts of the conclusion criticized as being contradictory are, in fact, not. It further highlights the need for more publishing of scientific criticisms. In the December 2007, special issue of the Journal of Atmospheric Sciences devoted to the Workshop on Assimilation of Satellite Cloud and Precipitation Observations, the authors published an article summarizing the many critical issues that render observations of cloud and precipitation difficult to analyze. Essentially, these include the inaccuracies of both current instruments and the relationships between what is actually observed (infrared or microwave energy detected at the altitude of the satellite) to what is desired (e.g., estimates of cloud drop sizes or rain rates) and the chaotic nature of atmospheric behavior and the complex mathematics describing it. The paper also included recommendations for future research and brief descriptions of many previous works concerning the subject. One reader is now attempting to publish a criticism of that paper. Her three complaints are that there was insufficient explanation of the identification of some cited works as being fundamentally flawed, that as a review the paper should have referenced some works additional to those it did, and that two recommendations were contradictory. Each of these complaints is addressed briefly in this response. First we explain why a brief list of works cited in our paper were identified as "flawed" with only a brief explanation. The design and conduct of the experiments reported in those papers violate well-established fundamentals such that, once the errors are recognized, their interpretations are no longer supported. Unfortunately, over the years, no researchers have bothered to publish criticisms of those papers, such that there are now too many to address in any single paper not devoted to that purpose. Yet, those papers are so often cited that we could not simply ignore them. Furthermore, if we had cited them without warning our readers regarding their flaws, we would have perpetrated a great disservice. In our response, however, we do offer further explanation of why some details, neglected in these papers, are critical to proper scientific evaluation. Neither did we offer insufficient references. Although we intentionally did not claim to be a "review' paper, we did cite 100 papers. That number is approximately 5 times the usual amount cited in journal articles. Although we only referenced few papers published after 2005, that was because our manuscript was submitted in January 2006, with its final, editorially-reviewed form in June 2006. We therefore could not reference papers published after this date. The problem here is that our paper was "in press" for 18 months. Finally, we explain that a careful reading of our paper reveals that our recommendations are not contradictory. Essentially, although we recommend 2 very distinct research approaches, these are complimentary and either alone is insufficient to accelerate progress. In conclusion, we recommend that the scientific community expends greater effort in publishing careful scientific criticisms so that others do not face the same dilemma we did. Likely this requires some reward system for doing so.

Errico, Ronald M.↗

Spectral Kernel Approach to Study Radiative Response of Climate Variables and Interannual Variability of Reflected Solar Spectrum

The radiative kernel approach provides a simple way to separate the radiative response to different climate parameters and to decompose the feedback into radiative and climate response components. Using CERES/MODIS/Geostationary data, we calculated and analyzed the solar spectral reflectance kernels for various climate parameters on zonal, regional, and global spatial scales. The kernel linearity is tested. Errors in the kernel due to nonlinearity can vary strongly depending on climate parameter, wavelength, surface, and solar elevation; they are large in some absorption bands for some parameters but are negligible in most conditions. The spectral kernels are used to calculate the radiative responses to different climate parameter changes in different latitudes. The results show that the radiative response in high latitudes is sensitive to the coverage of snow and sea ice. The radiative response in low latitudes is contributed mainly by cloud property changes, especially cloud fraction and optical depth. The large cloud height effect is confined to absorption bands, while the cloud particle size effect is found mainly in the near infrared. The kernel approach, which is based on calculations using CERES retrievals, is then tested by direct comparison with spectral measurements from Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY) (a different instrument on a different spacecraft). The monthly mean interannual variability of spectral reflectance based on the kernel technique is consistent with satellite observations over the ocean, but not over land, where both model and data have large uncertainty. RMS errors in kernel ]derived monthly global mean reflectance over the ocean compared to observations are about 0.001, and the sampling error is likely a major component.

Jin, Zhonghai↗

Total Lightning Characteristics with Respect to Radar-Derived Mesocyclone Strength

Recent work investigating the microphysical and kinematic relationship between a storm's updraft, its total lightning production, and manifestations of severe weather has resulted in development of tools for improved nowcasting of storm intensity. The total lightning jump algorithm, which identifies rapid increases in total lightning flash rate that often precede severe events, has shown particular potential to benefit warning operations. Maximizing this capability of total lightning and its operational implementation via the lightning jump may best be done through its fusion with radar and radar‐derived intensity metrics. Identification of a mesocyclone, or quasi‐steady rotating updraft, in Doppler velocity is the predominant radar‐inferred early indicator of severe potential in a convective storm. Fused lightning‐radar tools that capitalize on the most robust intensity indicators would allow enhanced situational awareness for increased warning confidence. A foundational step toward such tools comes from a better understanding of the updraft‐centric relationship between intensification of total lightning production and mesocyclone development and strength. The work presented here utilizes a sample of supercell case studies representing a spectrum of severity. These storms are analyzed with respect to total lightning flash rate and the lightning jump alongside mesocyclone strength derived objectively from the National Severe Storms Laboratory (NSSL) Mesocyclone Detection Algorithm (MDA) and maximum azimuthal shear through a layer. Early results indicate that temporal similarities exist in the trends between total lightning flash rate and low‐ to mid‐level rotation in supercells. Other characteristics such as polarimetric signatures of rotation, flash size, and cloud‐to‐ground flash ratio are explored for added insight into the significance of these trends with respect to the updraft and related processes of severe weather production.

Stough, Sarah M.↗

Preliminary Findings of Inflight Icing Field Test to Support Icing Remote Sensing Technology Assessment

NASA and the National Center for Atmospheric Research have developed an icing remote sensing technology that has demonstrated skill at detecting and classifying icing hazards in a vertical column above an instrumented ground station. This technology has recently been extended to provide volumetric coverage surrounding an airport. Building on the existing vertical pointing system, the new method for providing volumetric coverage will utilize a vertical pointing cloud radar, a multifrequency microwave radiometer with azimuth and elevation pointing, and a NEXRAD radar. The new terminal area icing remote sensing system processes the data streams from these instruments to derive temperature, liquid water content, and cloud droplet size for each examined point in space. These data are then combined to ultimately provide icing hazard classification along defined approach paths into an airport.

remote sensors↗

Ice-Accretion Test Results for Three Large-Scale Swept-Wing Models in the NASA Icing Research Tunnel

Icing simulation tools and computational fluid dynamics codes are reaching levels of maturity such that they are being proposed by manufacturers for use in certification of aircraft for flight in icing conditions with increasingly less reliance on natural-icing flight testing and icing-wind-tunnel testing. Sufficient high-quality data to evaluate the performance of these tools is not currently available. The objective of this work was to generate a database of ice-accretion geometry that can be used for development and validation of icing simulation tools as well as for aerodynamic testing. Three large-scale swept wing models were built and tested at the NASA Glenn Icing Research Tunnel (IRT). The models represented the Inboard (20 percent semispan), Midspan (64 percent semispan) and Outboard stations (83 percent semispan) of a wing based upon a 65 percent scale version of the Common Research Model (CRM). The IRT models utilized a hybrid design that maintained the full-scale leading-edge geometry with a truncated afterbody and flap. The models were instrumented with surface pressure taps in order to acquire sufficient aerodynamic data to verify the hybrid model design capability to simulate the full-scale wing section. A series of ice-accretion tests were conducted over a range of total temperatures from -23.8 to -1.4 C with all other conditions held constant. The results showed the changing ice-accretion morphology from rime ice at the colder temperatures to highly 3-D scallop ice in the range of -11.2 to -6.3 C. Warmer temperatures generated highly 3-D ice accretion with glaze ice characteristics. The results indicated that the general scallop ice morphology was similar for all three models. Icing results were documented for limited parametric variations in angle of attack, drop size and cloud liquid-water content (LWC). The effect of velocity on ice accretion was documented for the Midspan and Outboard models for a limited number of test cases. The data suggest that there are morphological characteristics of glaze and scallop ice accretion on these swept-wing models that are dependent upon the velocity. This work has resulted in a large database of ice-accretion geometry on large-scale, swept-wing models.

Wing Aerodynamics↗

Ice-Accretion Test Results for Three Large-Scale Swept-Wing Models in the NASA Icing Research Tunnel

Icing simulation tools and computational fluid dynamics codes are reaching levels of maturity such that they are being proposed by manufacturers for use in certification of aircraft for flight in icing conditions with increasingly less reliance on natural-icing flight testing and icing-wind-tunnel testing. Sufficient high-quality data to evaluate the performance of these tools is not currently available. The objective of this work was to generate a database of ice-accretion geometry that can be used for development and validation of icing simulation tools as well as for aerodynamic testing. Three large-scale swept wing models were built and tested at the NASA Glenn Icing Research Tunnel (IRT). The models represented the Inboard (20% semispan), Midspan (64% semispan) and Outboard stations (83% semispan) of a wing based upon a 65% scale version of the Common Research Model (CRM). The IRT models utilized a hybrid design that maintained the full-scale leading-edge geometry with a truncated afterbody and flap. The models were instrumented with surface pressure taps in order to acquire sufficient aerodynamic data to verify the hybrid model design capability to simulate the full-scale wing section. A series of ice-accretion tests were conducted over a range of total temperatures from -23.8 deg C to -1.4 deg C with all other conditions held constant. The results showed the changing ice-accretion morphology from rime ice at the colder temperatures to highly 3-D scallop ice in the range of -11.2 deg C to -6.3 deg C. Warmer temperatures generated highly 3-D ice accretion with glaze ice characteristics. The results indicated that the general scallop ice morphology was similar for all three models. Icing results were documented for limited parametric variations in angle of attack, drop size and cloud liquid-water content (LWC). The effect of velocity on ice accretion was documented for the Midspan and Outboard models for a limited number of test cases. The data suggest that there are morphological characteristics of glaze and scallop ice accretion on these swept-wing models that are dependent upon the velocity. This work has resulted in a large database of ice-accretion geometry on large-scale, swept-wing models.

Wind-Tunnel Tests↗

Seasonal, Spectral, and Regional Characterization of Deep Convective Clouds Top-of-Atmosphere Bidirectional Reflectance for Improved Satellite Intercalibration

The NASA CERES project provides the scientific community with regional broadband fluxes designed for long-term climate monitoring. The CERES climate quality dataset requires that the CERES instrument, as well as the MODIS and VIIRS imager records to be radiometrically stable over time. Deep Convective Clouds (DCCs) are spectrally uniform, near-Lambertian natural diffusers offering high signal-to-noise ratio and stable radiometric response in the VIS-NIR spectrum. For shortwave infrared (SWIR) wavelengths greater than 1.2µm, the DCC response is significantly influenced by cloud particle size and atmospheric absorption. Previous studies improved the characterization of the SWIR band DCC radiance, by using channel specific monthly empirical BRDFs as well as using the probability density function mean statistic to track the SWIR band stability. Also, that the DCC radiance is greater over land than over ocean and that the TWP DCC radiance has the lowest tropical DCC radiance. This study confirms and improves upon the previous studies. The study stratified the tropics regionally into land and ocean domains and applied their respective ocean-only and land-only empirical monthly BRDFs and normalized the land DCC BRDF corrected radiances with their ocean counterpart. This approach provided the most stable DCC response. The DCC BRDF corrected radiance monthly standard error was 0.24%, 0.62%, 0.59%, and 0.43% for the 1.24µm, 1.37µm, 1.61µm, and 2.25µm SWIR bands, which reduced the standard error 20%, 13%, 24%, and 26%, respectively when compared with the all-surface approach. The same approach was attempted over the Tropical Western Pacific and found not to be an improvement over the tropical domain. Further stratification of the tropical domain will need to balance sufficient sampling while accounting for regional DCC radiance differences.

Prathana Khakurel↗

Quantifying Burned Area and Smoke from Prescribed and Smaller Fires: West Palm Beach, Florida

In the Central and Southeastern U.S. (C&SE), small, short-lived fires are often underestimated by satellites due to their size, timing, cloud cover, and rapid regrowth or plowing after burns. Satellite data are essential for the National Emissions Inventory, as ground-based inventories are historically incomplete and geographically inconsistent. Agricultural burning, a widespread annual practice in many U.S. regions, significantly impacts air quality on local to regional scales. As part of NASA’s Health and Air Quality Applied Sciences (HAQAST) team, we develop a burned area inventory to account for these ‘missing’ small fires. Our study focuses on West Palm Beach, FL, near Lake Okeechobee, where agriculture fields are burned annually fall-spring for crop management and harvest. This region poses challenges for satellite detection due to frequent rain, flooding, and cloud cover.

Emily Gargulinski↗

Arcmimute scale HI and IRAS observations toward high latitude cloud G86.5+59.6

G86.5+59.6 is a degree-sized high latitude cloud originally selected for investigation by Heiles, Reach, and Koo (1988) on the basis of its appearance on the IRAS Skyflux images at 60 and 100 micrometers. Because of the interesting possibility that this is an intermediate velocity cloud colliding with HI in the Galactic plane, we have examined this region further, both at low resolution over an extended field to provide some context and at higher (arcminute) resolution within the cloud.

Martin, Peter G.↗

Relationships between the Raindrop Size Distribution and Properties of the Environment and Clouds Inferred from TRMM

Variability in the raindrop sized distribution (DSD) has long been recognized as a source of uncertainty in relationships between radar reflectivity Z and rain rate R. In this study, we analyze DSD retrievals from two years of data gathered by the Tropical Rainfall Measuring Mission (TRMM) satellite and processed with a combined radar-radiometer retrieval algorithm over the global oceans equatorward of 35◦. Numerous variables describing properties of each reflectivity profile, large-scale organization, and the background environment are examined for relationships to the reflectivity-normalized median drop diameter, epsilonDSD. In general, we find that higher freezing levels and relative humidities are associated with smaller epsilonDSD. Within a given environment, the mesoscale organization of precipitation and the vertical profile of reflectivity are associated with DSD characteristics. In the tropics, the smallest epsilonDSD values are found in large but shallow convective systems, where warm rain formation processes are thought to be predominant, whereas larger sizes are found in the stratiform regions of organized deep convection. In the extratropics, the largest epsilonDSD values are found in the scattered convection that occurs when cold, dry continental air moves over the much warmer ocean after the passage of a cold front. The geographical distribution of the retrieved DSDs is consistent with many of the observed regional Z−R relationships found in the literature as well as discrepancies between the TRMM radar-only and radiometer-only precipitation products. In particular, mid-latitude and tropical regions near land tend to have larger drops for a given reflectivity, whereas the smallest drops are found in the eastern Pacific Intertropical Convergence Zone.

raindrop size distribution↗

Launch vehicle effluent measurements during the August 20, 1977, Titan 3 launch at Air Force Eastern Test Range

Airborne effluent measurements within the launch cloud and visible and infrared measurements of cloud physical behavior are discussed. Airborne effluent measurements include concentrations of HCl, Cl2, NO, NOX, and particulates as a function of time during each sampling pass through the exhaust cloud. The particle size distribution was measured for each pass through the cloud. Mass concentration as a function of particle diameter was measured over the size range of 0.05- to 25 micron diameter, and particle number density was measured as a function of diameter over a size range of 0.5 to 7.5 micron. Effluent concentrations in the cloud ranged from about 30 ppm several minutes after launch to about 1 to 2 ppm at 100 minutes. Maximum Cl2 concentrations were about 40 to 55 ppb and by 20 minutes were less than 1.0 ppb. A tabulated listing of the airborne data is given in the appendix. Usable cloud imaging data were limited to the first 16 minutes after launch.

Woods, D. C.↗

Small-Scale Drop Size Variability: Impact on Estimation of Cloud Optical Properties

Most cloud radiation models and conventional data processing techniques assume that the mean number of drops of a given radius is proportional to volume. The analysis of microphysical data on liquid water drop sizes shows that, for sufficiently small volumes, this proportionality breaks down; the number of cloud drops of a given radius is instead proportional to the volume raised to a drop size-dependent nonunit power. The coefficient of proportionality, a generalized drop concentration, is a function of the drop size. For abundant small drops the power is unity as assumed in the conventional approach. However, for rarer large drops, it falls increasingly below unity. This empirical fact leads to drop clustering, with the larger drops exhibiting a greater degree of clustering. The generalized drop concentration shows the mean number of drops per cluster, while the power characterizes the occurrence frequency of clusters. With a fixed total number of drops in a cloud, a decrease in frequency of clusters is accompanied by a corresponding increase in the generalized concentration. This initiates a competing process missed in the conventional models: an increase in the number of drops per cluster enhances the impact of rarer large drops on cloud radiation while a decrease in the frequency suppresses it. Because of the nonlinear relationship between the number of clustered drops and the volume, these two opposite tendencies do not necessarily compensate each other. The data analysis suggests that clustered drops likely have a stronger radiative impact compared to their unclustered counterpart; ignoring it results in underestimation of the contribution from large drops to cloud horizontal optical path.

Knyazikhin, Y.↗

Remote Sensing Data from CLARET: A Prototype Cart Data Set

A data set containing radiation, meteorological, and cloud sensor observations is documented. It was prepared for use by the Department of Energy's Atmospheric Radiation Measurement (ARM) program and other interested scientists. These data are a precursor of the types of data that ARM Cloud And Radiation Testbed (CART) sites will provide. The data are from the Cloud Lidar And Radar Exploratory Test (CLARET) conducted by the Wave Propagation Laboratory during autumn 1989 in the Denver-Boulder area of Colorado primarily for the purpose of developing new cloud-sensing techniques on cirrus. After becoming aware of this experiment, ARM scientists requested archival of subsets or the data to assist in the developing ARM program. Five CLARET cases were selected: two with cirrus, one with stratus, one with mixed-phase clouds, and one with clear skies. The cases range from 2 to 9.5 h in length. A pyranometer, pyrgeometer, pyrheliometer, and an infrared radiometer constituted the ensemble of instruments that provided surface radiation data. A lidar, radar, and ceilometer observed the cloud geometrical structure, and visual reports and all-sky camera observations were assimilated to provide cloud cover data. Radiosondes, wind profiler, RASS (profiling virtual temperature), microwave radiometers (observing column integrated liquid water and water vapor), and standard surface measurements provided meteorological data. Satellite data from the stratus case and one cirrus case were analyzed for statistics on cloud cover and top height. The main body of the selected data are available on diskette from the Wave Propagation Laboratory or Los Alamos National Laboratory. In addition to documenting the data set, this report describes CLARET and gives a bibliography of publications associated with the project. Some preliminary results of CLARET' research are also summarized. Simultaneous CO 2 lidar and radar backscatter measurements were shown to provide estimates of the effective radius of ice particles. Simultaneous radar and infrared radiometer data appear useful for estimating column-integrated numbers and average sizes of ice cloud particles. Ice water content obtained with this method compared favorably with values from another empirical technique using radar data alone. Depolarization of the CO 2 lidar signal from ice clouds was surprisingly small, suggesting that calculation of backscatter from nonspherical particles for this lidar is a tractable problem. Examples are also cited of CO 2 lidar measurements of the effective radius of water cloud drop size distributions and of inference of the size of pristine ice crystals that assume a particular orientation in the air. These parameters are all important to radiative transfer through clouds.

Clouds (Meteorology)↗

Cellular Statistical Models of Broken Cloud Fields. Part IV: Effects of Pixel Size on Idealized Satellite Observations

In the fourth part of our “Cellular Statistical Models of Broken Cloud Fields” series we use the binary Markov processes framework for quantitative investigation of the effects of low resolution of idealized satellite observations on the statistics of the retrieved cloud masks. We assume that the cloud fields are Markovian and are characterized by the “actual” cloud fraction (CF) and scale length. We use two different models of observations: a simple discrete-point sampling and a more realistic “pixel” protocol. The latter is characterized by a state attribution function (SAF) which has the meaning of the probability that the pixel with a certain CF is declared cloudy in the observed cloud mask. The stochasticity of the SAF means that the cloud/clear attribution is not ideal and can be affected by external or unknown factors. We show that the observed cloud masks can be accurately described as Markov chains of pixels and use the master-matrix formalism (introduced in Part III of the series) for analytical computation of their parameters: the “observed” CF and scale length. This procedure allows us to establish a quantitative relationship (which is pixel-size dependent) between the actual and the observed cloud-field statistics. The feasibility of restoring the former from the latter is considered. The adequacy of our analytical approach to idealized observations is evaluated using numerical simulations. Comparison of the observed parameters of the simulated datasets with their theoretical expectations showed an agreement within 0.005 for the CF, while for the scale length it is within 1% in the sampling case and within 4% in the pixel case.

Mikhail D. Alexandrov↗