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Method for Pre-Conditioning a Measured Surface Height Map for Model Validation

This software allows one to up-sample or down-sample a measured surface map for model validation, not only without introducing any re-sampling errors, but also eliminating the existing measurement noise and measurement errors. Because the re-sampling of a surface map is accomplished based on the analytical expressions of Zernike-polynomials and a power spectral density model, such re-sampling does not introduce any aliasing and interpolation errors as is done by the conventional interpolation and FFT-based (fast-Fourier-transform-based) spatial-filtering method. Also, this new method automatically eliminates the measurement noise and other measurement errors such as artificial discontinuity. The developmental cycle of an optical system, such as a space telescope, includes, but is not limited to, the following two steps: (1) deriving requirements or specs on the optical quality of individual optics before they are fabricated through optical modeling and simulations, and (2) validating the optical model using the measured surface height maps after all optics are fabricated. There are a number of computational issues related to model validation, one of which is the "pre-conditioning" or pre-processing of the measured surface maps before using them in a model validation software tool. This software addresses the following issues: (1) up- or down-sampling a measured surface map to match it with the gridded data format of a model validation tool, and (2) eliminating the surface measurement noise or measurement errors such that the resulted surface height map is continuous or smoothly-varying. So far, the preferred method used for re-sampling a surface map is two-dimensional interpolation. The main problem of this method is that the same pixel can take different values when the method of interpolation is changed among the different methods such as the "nearest," "linear," "cubic," and "spline" fitting in Matlab. The conventional, FFT-based spatial filtering method used to eliminate the surface measurement noise or measurement errors can also suffer from aliasing effects. During re-sampling of a surface map, this software preserves the low spatial-frequency characteristic of a given surface map through the use of Zernike-polynomial fit coefficients, and maintains mid- and high-spatial-frequency characteristics of the given surface map by the use of a PSD model derived from the two-dimensional PSD data of the mid- and high-spatial-frequency components of the original surface map. Because this new method creates the new surface map in the desired sampling format from analytical expressions only, it does not encounter any aliasing effects and does not cause any discontinuity in the resultant surface map.

Sidick, Erkin↗

Elemental abundances in stone meteorites.

Measurement of abundances of Na, Al, Sc, Cr, Mn, Fe, Co, and Cu by instrumental neutron activation analyses of 103 chondrites and 17 achondrites. Various sources of error in the method, including sampling errors, are discussed in detail. Examination of the patterns of coherence of the elements determined suggests the presence of effects of fractionation during condensation from the solar nebula of matter parental to chondrites. Such effects seem to be exhibited both in the abundances of lithophilic elements, perhaps being related to varied temperatures of accretion and in the abundances of those elements which would be affected by metal-silicate fractionation in the solar nebula. Atomic abundances relative to Si vary little in carbonaceous chondrites, suggesting that efficient mixing processes operated on these meteorites prior to or during their formation. It is suggested that, at present, no single class of carbonaceous chondrites is clearly more primitive than another. Carbonaceous and unequilibrated ordinary chondrites may represent aggregates of material accreted from the solar nebula at relatively low temperatures. The present data support a model of equilibration and minor mobilization of nonvolatile elements within small domains of chondrites after accretion. Such a model would be consistent with the petrologic types of Van Schmus and Wood (1967).

Schmitt, R. A.↗

Simulation of the earth's monthly average regional radiation balance derived from satellite measurements

Computer simulations of satellite-derived earth radiation parameters are used to determine the source and size of errors arising from measuring parameters over 1 month on a 2.5 deg x 2.5 deg longitude-latitude grid. November 1979 GOES data are used as a source of radiation parameter fields within each region. A mathematical model is given for the data-processing algorithms that are used to produce daily, monthly, and monthly hourly estimates of shortwave, longwave and net radiant exitance. Resulting retrieval errors are found to be due to insufficient knowledge of the temporal distribution of measurements. These errors, in combination with similar sampling errors produce biases in monthly net radiant exitance which are complex, regionally-dependent functions of the local time of the measurements. The 40 region standard errors of estimate for three satellites ranged from 2 to 3 W per sq. m., while single satellite errors ranged from 5 to 19 W per sq. m. A three-satellite system is therefore recommended to reduce biases.

Brooks, D. R.↗

Arctic sea ice leads from advanced very high resolution radiometer images

A large number of advanced very high resolution radiometer (AVHRR) images from throughout 1989 are analyzed to determine lead characteristics. The units of analysis are square 200-km cells, and there are 270 such cells in the data set. Clouds are masked manually. Leads determine from images of the potential open water delta, a scaled version of the surface temperature or albedo that weights thin ice by its thermal or brightness impact. The lead fraction is determined as the mean delta, the monthly mean lead fraction ranges from 0.02 in winter to 0.06 in summer in the central Arctic and is near 0.08 in the winter in the peripheral seas. A method of accounting for lead width sampling errors due to the finite sample areas is introduced. In the central Arctic the observed mean lead width for a threshold of delta = 0.1 ranges from 2 or 3 km (near the resolution of the instrument) in the winter to 6 km in the summer. In the peripheral seas it is about 5 km in the winter. Width distributions are often more heavily weighted in the tail than exponential distributions and are well approximated by a power law. The along-track, number density power law N = aw(exp -6) has a mean exponent of b = 1.60 (standard deviation 0.18) and shows some seasonal variability. Mean floe widths in the central Arctic are 40 to 50 km in the winter, dropping to about 10 km in the summer. For floes the power law has a mean exponent of 0.93 and exhibits a clearer annual cycle. Lead orientation is determined with a method based on the direction of maximum extent.

Lindsay, R. W.↗

Assessing the Impact of Pre-gpm Microwave Precipitation Observations in the Goddard WRF Ensemble Data Assimilation System

The forthcoming Global Precipitation Measurement (GPM) Mission will provide next generation precipitation observations from a constellation of satellites. Since precipitation by nature has large variability and low predictability at cloud-resolving scales, the impact of precipitation data on the skills of mesoscale numerical weather prediction (NWP) is largely affected by the characterization of background and observation errors and the representation of nonlinear cloud/precipitation physics in an NWP data assimilation system. We present a data impact study on the assimilation of precipitation-affected microwave (MW) radiances from a pre-GPM satellite constellation using the Goddard WRF Ensemble Data Assimilation System (Goddard WRF-EDAS). A series of assimilation experiments are carried out in a Weather Research Forecast (WRF) model domain of 9 km resolution in western Europe. Sensitivities to observation error specifications, background error covariance estimated from ensemble forecasts with different ensemble sizes, and MW channel selections are examined through single-observation assimilation experiments. An empirical bias correction for precipitation-affected MW radiances is developed based on the statistics of radiance innovations in rainy areas. The data impact is assessed by full data assimilation cycling experiments for a storm event that occurred in France in September 2010. Results show that the assimilation of MW precipitation observations from a satellite constellation mimicking GPM has a positive impact on the accumulated rain forecasts verified with surface radar rain estimates. The case-study on a convective storm also reveals that the accuracy of ensemble-based background error covariance is limited by sampling errors and model errors such as precipitation displacement and unresolved convective scale instability.

microwave observations↗

Sampling, aggregation, and variance estimation for area, yield, and production in LACIE

An approximately 2% sampling error was achieved in LACIE by sampling only approximately 2% of the sampling frame. The sample design in the yardstick region for which historical data were available down to a substratum level to support missing data resulting from cloud cover provided the most accurate estimate possible. The implemented strategy provided data of sufficient quality and quantity to support required performance levels and also to satisfy the existing constraints. The allocation scheme appeared to provide the most efficient usage of the available data and gave segment coverage of major producing areas and thus improved the probability of an accurate estimate.

Hallum, C. R.↗

Radiometric analysis of the longwave infrared channel of the Thematic Mapper on LANDSAT 4 and 5

The first objective was to evaluate the postlaunch radiometric calibration of the LANDSAT Thematic Mapper (TM) band 6 data. The second objective was to determine to what extent surface temperatures could be computed from the TM and 6 data using atmospheric propagation models. To accomplish this, ground truth data were compared to a single TM-4 band 6 data set. This comparison indicated satisfactory agreement over a narrow temperature range. The atmospheric propagation model (modified LOWTRAN 5A) was used to predict surface temperature values based on the radiance at the spacecraft. The aircraft data were calibrated using a multi-altitude profile calibration technique which had been extensively tested in previous studies. This aircraft calibration permitted measurement of surface temperatures based on the radiance reaching the aircraft. When these temperature values are evaluated, an error in the satellite's ability to predict surface temperatures can be estimated. This study indicated that by carefully accounting for various sensor calibration and atmospheric propagation effects, and expected error (1 standard deviation) in surface temperature would be 0.9 K. This assumes no error in surface emissivity and no sampling error due to target location. These results indicate that the satellite calibration is within nominal limits to within this study's ability to measure error.

Schott, John R.↗

Estimation of the diurnal cycle of oceanic precipitation from SSM/I data

A study of differences between the morning and evening monthly rainfall for 5 x 5 deg cells over the oceans from the SSM/I data has been conducted. The monthly rainfalls are estimated from the technique given by Wilheit et al. The difference between the morning and evening monthly rainfall arises due to the various random errors involved in the retrieval process, the sampling error in the observations, and the diurnal component of oceanic rainfall. The diurnal component is weak but clearly visible when averaged over large areas and for long time periods. The analysis shows that morning rainfall is consistently greater than evening rainfall. The Northern Hemisphere seem to have a larger diurnal variation than does the Southern Hemisphere. The maximum ratio between the morning and evening monthly rainfall is 1.7 while 1.2 is the more typical value.

Sharma, Awdhesh K.↗

Sampling data for OSSEs

An OSSE should for the sake of realism incorporate at least some of the high-frequency, small-scale phenomena that are suppressed by atmospheric models; these phenomena should be present in the realistic atmosphere sampled by all observing sensor systems whose data are being used. Errors are presently generated for an OSSE in a way that encompasses representational errors, sampling, geophysical local bias, random error, and sensor filtering.

Hoffman, Ross↗

Sampling submicrometer particles suspended in near sonic and supersonic free jets

Aerosols containing solid, spherical stearic acid particles with a mean diameter of 0.8 micron and a geometric standard deviation of 1.28 were sampled with small bore front-facing aspirating probes in near-sonic and supersonic unheated free jets. The results are compared to compute the sampling error associated with a high-speed jet sample.

Martone, J. A.↗

Nonsimultaneous coupled laser velocimeter measurement technique: Error prediction for spatially noncoincident measurements

A technique for obtaining orthogonal velocity components from nonorthogonal measurements using the NASA Ames Research Center Long-Range Laser Velocimeter (LRLV) is briefly discussed. A description is then presented of the error that occurs when these nonorthogonal measurements are spatially noncoincident because of positioning inaccuracies, and equations are developed for predicting this error. Sample data are presented and a prediction of the expected error for two typical applications is made. To cover other cases in general, a parametric study is conducted and the results are presented in a tabular format.

Reinath, M. S.↗

Precipitation and Latent Heating Distributions from Satellite Passive Microwave Radiometry. Part II: Evaluation of Estimates Using Independent Data

Rainfall rate estimates from spaceborne microwave radiometers are generally accepted as reliable by a majority of the atmospheric science community. One of the Tropical Rainfall Measuring Mission (TRMM) facility rain-rate algorithms is based upon passive microwave observations from the TRMM Microwave Imager (TMI). In Part I of this series, improvements of the TMI algorithm that are required to introduce latent heating as an additional algorithm product are described. Here, estimates of surface rain rate, convective proportion, and latent heating are evaluated using independent ground-based estimates and satellite products. Instantaneous, 0.5 deg. -resolution estimates of surface rain rate over ocean from the improved TMI algorithm are well correlated with independent radar estimates (r approx. 0.88 over the Tropics), but bias reduction is the most significant improvement over earlier algorithms. The bias reduction is attributed to the greater breadth of cloud-resolving model simulations that support the improved algorithm and the more consistent and specific convective/stratiform rain separation method utilized. The bias of monthly 2.5 -resolution estimates is similarly reduced, with comparable correlations to radar estimates. Although the amount of independent latent heating data is limited, TMI-estimated latent heating profiles compare favorably with instantaneous estimates based upon dual-Doppler radar observations, and time series of surface rain-rate and heating profiles are generally consistent with those derived from rawinsonde analyses. Still, some biases in profile shape are evident, and these may be resolved with (a) additional contextual information brought to the estimation problem and/or (b) physically consistent and representative databases supporting the algorithm. A model of the random error in instantaneous 0.5 deg. -resolution rain-rate estimates appears to be consistent with the levels of error determined from TMI comparisons with collocated radar. Error model modifications for nonraining situations will be required, however. Sampling error represents only a portion of the total error in monthly 2.5 -resolution TMI estimates; the remaining error is attributed to random and systematic algorithm errors arising from the physical inconsistency and/or nonrepresentativeness of cloud-resolving-model-simulated profiles that support the algorithm.

Yang, Song↗

Precipitation and Latent Heating Distributions from Satellite Passive Microwave Radiometry: Evaluation of Estimates Using Independent Data - Part 2

Rainfall rate estimates from space-borne k&ents are generally accepted as reliable by a majority of the atmospheric science commu&y. One-of the Tropical Rainfall Measuring Mission (TRh4M) facility rain rate algorithms is based upon passive microwave observations fiom the TRMM Microwave Imager (TMI). Part I of this study describes improvements in the TMI algorithm that are required to introduce cloud latent heating and drying as additional algorithm products. Here, estimates of surface rain rate, convective proportion, and latent heating are evaluated using independent ground-based estimates and satellite products. Instantaneous, OP5resolution estimates of surface rain rate over ocean fiom the improved TMI algorithm are well correlated with independent radar estimates (r approx. 0.88 over the Tropics), but bias reduction is the most significant improvement over forerunning algorithms. The bias reduction is attributed to the greater breadth of cloud-resolving model simulations that support the improved algorithm, and the more consistent and specific convective/stratiform rain separation method utilized. The bias of monthly, 2.5 deg. -resolution estimates is similarly reduced, with comparable correlations to radar estimates. Although the amount of independent latent heating data are limited, TMI estimated latent heating profiles compare favorably with instantaneous estimates based upon dual-Doppler radar observations, and time series of surface rain rate and heating profiles are generally consistent with those derived from rawinsonde analyses. Still, some biases in profile shape are evident, and these may be resolved with: (a) additional contextual information brought to the estimation problem, and/or; (b) physically-consistent and representative databases supporting the algorithm. A model of the random error in instantaneous, 0.5 deg-resolution rain rate estimates appears to be consistent with the levels of error determined from TMI comparisons to collocated radar. Error model modifications for non-raining situations will be required, however. Sampling error appears to represent only a fraction of the total error in monthly, 2S0-resolution TMI estimates; the remaining error is attributed to physical inconsistency or non-representativeness of cloud-resolving model simulated profiles supporting the algorithm.

Yang, Song↗

Sampling of the Diurnal Cycle of Precipitation using TRMM

We examine the temporal sampling of tropical regions using observations from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and Precipitation Radar (PR). We conclude that PR estimates at any one hour, even using three years of data, are inadequate to describe the diurnal cycle of precipitation over regions smaller than 12 degrees, due to high spatial variability in sampling. We show that the optimum period of accumulation is four hours. Diurnal signatures display half as much sampling error when averaged over four hours of local time. A similar pattern of sampling variability is found in the TMI data, despite the TMI's wider swath and increased sampling. These results are verified using an orbital model. The sensitivity of the sampling to satellite altitude is presented, as well as sampling patterns at the new TRMM altitude of 402.5 km.

Negri, Andrew J.↗

Emperical Tests of Acceptance Sampling Plans

Acceptance sampling is a quality control procedure applied as an alternative to 100% inspection. A random sample of items is drawn from a lot to determine the fraction of items which have a required quality characteristic. Both the number of items to be inspected and the criterion for determining conformance of the lot to the requirement are given by an appropriate sampling plan with specified risks of Type I and Type II sampling errors. In this paper, we present the results of empirical tests of the accuracy of selected sampling plans reported in the literature. These plans are for measureable quality characteristics which are known have either binomial, exponential, normal, gamma, Weibull, inverse Gaussian, or Poisson distributions. In the main, results support the accepted wisdom that variables acceptance plans are superior to attributes (binomial) acceptance plans, in the sense that these provide comparable protection against risks at reduced sampling cost. For the Gaussian and Weibull plans, however, there are ranges of the shape parameters for which the required sample sizes are in fact larger than the corresponding attributes plans, dramatically so for instances of large skew. Tests further confirm that the published inverse-Gaussian (IG) plan is flawed, as reported by White and Johnson (2011).

White, K. Preston, Jr.↗

Oscillating-flow regenerator test rig: Woven screen and metal felt results

We present correlating expressions, in terms of Reynolds or Peclet numbers, for friction factors, Nusselt numbers, enhanced axial conduction ratios, and overall heat flux ratios in four porous regenerator samples representative of stirling cycle regenerators: two woven screen samples and two random wire samples. Error estimates and comparison of data with others suggest our correlations are reliable, but we need to test more samples over a range of porosities before our results will become generally useful.

Gedeon, D.↗

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↗