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Iterative error correction of asymptotically large associative memories is equivalent to a one-step learning rule. This rule is the inverse of the activation function of the memory. Spectral representations of nonlinear activation functions are used to obtain the inverse in closed form for Sparse Distributed Memory, Selected-Coordinate Design, and Radial Basis Functions.
The HALOE experiment measures vertical profiles of aerosol extinction at five infrared wavelengths. Four of these observations are obtained using a combination of gas filter and broadband radiometer measurements in bands of HF, HCl, CH4, and NO centered at wavelengths of 2.45, 3.40, 3.45, and 5.26 microns, respectively. The fifth is obtained using broadband radiometer measurements of CO2 transmission at 2.79 microns. Error analysis shows that the random extinction uncertainties are generally less than 10 percent in the aerosol layer, increasing to over 20 percent at the profile tops. HALOE spectral extinction measurements are shown to be consistent with predicted spectral extinction for stratospheric sulfate aerosol. Profile comparisons between HALOE and independent sources result in generally good agreement in the shape and magnitude of peak extinction and the altitude where the peak extinction occurs. In addition, global aerosol distributions obtained from the data are consistent with expected aerosol morphology. Although the validation is preliminary, the HALOE aerosol data appear to be of excellent quality and to accurately represent optical characteristics and distribution of the aerosols.
In this paper we study the influence of line-merging regions at the intermediate long-wavelength side of a continuum threshold on the computed model atmosphere structure and predicted spectrum. In order to model these regions sufficiently accurately, we have developed two concepts. First, we have extended the occupation probability formalism of Hummer and Mihalas to non-local thermodynamic equilibrium (non-LTE) plasmas. Second, in order to treat the very complicated opacity in the line merging region, we have generalized the concept of opacity distribution functions to treat non-LTE situations. All Rydberg states are consistently included within this framework, so that no arbitrary cutoff of high (LTE) levels is made. We have calculated several pure hydrogen models atmospheres for two effective temperatures, T(sub eff) = 20000 and 35000 K, and discussed the differences between models calculated with various treatments of the line merging. In particular, we have shown that the error in the predicted profiles of Balmer lines resulting from the neglect of line merging is typically of the order of 3-4%, while the errors in the far-UV portion of the Balmer continuum reaches 15-35%. The errors generally decrease with increasing effective temperature. At the same time, the internal accuracy of the models is shown to be about or below 0.5% for all predicted spectral features. We conclude that for interpreting current high-accuracy spectrophotometric observations models including the line merging are necessary, and that the formalism developed in this paper is capable of providing a sufficiently accurate and robust modeling technique.
We present a spectral analysis of a approx 30 day, near-continuous observation of the Seyfert 1 galaxy NGC 7469 with RXTE. Daily integrations show strong spectral changes during the observation. Our main result is that we find the X-ray spectral index to be correlated with the UV flux. Furthermore, the broadband X-ray photon flux is also correlated with the UV continuum. These correlations point toward a model in which the X-rays originate via thermal Comptonization of UV seed photons. Furthermore, the UV is also correlated with the extrapolation of the X-ray power law into the soft X-ray/EUV region. Our data analysis therefore reopens the possibility that the UV photons and their variability arise from reprocessing, as long as the primary source of heating is photoelectric absorption in the re-processor, rather than Compton down-scattering. A coherent picture of the X-ray/UV variability can therefore be constructed whereby absorption and reprocessing of EUV/soft X-rays in a standard accretion disk produce a variable seed photon distribution, which is in turn up-scattered into the X-ray band. We also find a significant correlation between the 2-10 keV flux and the 6.4 keV iron K-alpha line, suggesting that at least some portion of the line originates within approx. 1 light day of the X-ray continuum source. Neither the power-law photon index nor the Compton reflection component are correlated with the 2-10 keV flux. The latter is not correlated with the iron K-alpha line flux either. We do find an apparent correlation between the X-ray spectral index and the strength of the Compton reflection component. In an Appendix we show, however, that this can be produced by a combination of statistical and systematic errors. We conclude that the apparent variations in the Compton reflection component may be an artifact of these effects.
Studying the Doppler shifts and the temperature dependence of Doppler shifts in moss regions can help us understand the heating processes in the core of the active regions. In this paper we have used an active region observation recorded by the Extreme-ultraviolet Imaging Spectrometer (EIS) onboard Hinode on 12-Dec- 2007 to measure the Doppler shifts in the moss regions. We have distinguished the moss regions from the rest of the active region by defining a low density cut-off as derived by Tripathi et al. (2010). We have carried out a very careful analysis of the EIS wavelength calibration based on the method described in Young, O Dwyer and Mason (2012). For spectral lines having maximum sensitivity between log T = 5.85 and log T = 6.25 K, we find that the velocity distribution peaks at around 0 km/s with an estimated error of 4 km/s. The width of the distribution decreases with temperature. The mean of the distribution shows a blue shift which increases with increasing temperature and the distribution also shows asymmetries towards blue-shift. Comparing these results with observables predicted from different coronal heating models, we find that these results are consistent with both steady and impulsive heating scenarios. Further observational constraints are needed to distinguish between these two heating scenarios.
Electronic shot noise is an unavoidable reality in all optical techniques that depend on measuring light intensity. For steady-state, time-averaged measurements the impact of shot noise can be easily reduced by increasing the exposure time, or by averaging over multiple-exposures. That is not the case for unsteady measurements, where time histories of light intensity variations need to be created either by high-speed photography (unsteady PSP) or via photoelectron counting (spectrally resolved Rayleigh scattering) over short time durations using a photo-multiplier tube (PMT) and photon counting electronics. Electronic shot noise introduces a fixed amount of random error, which can overwhelm the light intensity variation caused by turbulent fluctuations. Spectrum computed from such time series shows a fixed noise floor that is independent of the number of data points in the time series. For a fixed optical system, where the collected power of the luminescent light (uPSP), or the scattered light (Rayleigh) is fixed, one needs to resort to special techniques to obtain enough signal-to noise ratio (SNR). For the uPSP application it is shown that averaging of the adjacent pixels improves SNR; although this may lead to a sacrifice of spatial resolution. A second means is to increase the exposure time, which leads to a lowering of the frequency range. For the Rayleigh application, improvements of SNR can be achieved via two different cross-correlation based approaches. The first involves measuring the light intensity using two PMTs using short, contiguous gates; thereby, creating two time-series of data. The second one involves collecting one long time-series of data using one set of measurement device, followed by an odd-even splitting into two time series. When the two time-series are cross-correlated, and a power spectrum is calculated, a significant reduction in the shot noise floor can be achieved. Examples from measurements of density and velocity fluctuations spectra from two different Rayleigh setup are presented to demonstrate the process.
Five years of spatially complete snow-free land surface albedo data have been prepared using high quality white-sky and black-sky land surface albedo observations (MOD43B3) from the MODIS instrument aboard NASA's Terra satellite platform. The data were generated using an updated ecosystem-dependent temporal interpolation technique. In this paper, we describe the refinements in the technique and the creation of a spatially complete snow-free five-year aggregate climatology product. This paper also describes an error analysis of the interpolation technique. The filled albedo products are examined through comparisons of temporal and spatial trends for pixels that have been filled versus pixels that have been retained in the original MOD43B3 values. The variability in the trends showcase how the filling technique maintains the pixel-level spatial, spectral, and temporal integrity of the MOD43B3 data. These comparisons are made for both a single-year of filled data, year 2002, and for the five-year aggregate climatology product.
The technique for inverting a vegetation canopy reflectance model described earlier (Goel and Strebel, 1983) is investigated further. The novel concept of an 'angle transform' is introduced. This concept allows the formation of functions of reflectances at different view zenith and azimuth angles, which are either sensitive or insensitive to a certain agronomic parameter. A proper combination of these functions can allow determination of all the important agronomic and spectral parameters from measured canopy reflectance data. The technique is demonstrated using Suits' (1972) model for homogeneous canopies. It is shown that leaf area index, leaf reflectance and transmittance, and average leaf angle all can be determined from the canopy reflectance at a set of selected view zenith and azimuth angles. A sensitivity analysis of the calculated values to the errors in the data is also carried out. Guidelines are formulated for the number and types of observations required to obtain the values of a particular canopy variable to within a given degree of accuracy for a given level of error in the measurement of canopy reflectance.
Motivated by the needs of Mars data assimilation. particularly quantification of measurement errors and generation of averaging kernels. we have evaluated atmospheric temperature retrievals from Mars Global Surveyor (MGS) Thermal Emission Spectrometer (TES) radiances. Multiple sets of retrievals have been considered in this study; (1) retrievals available from the Planetary Data System (PDS), (2) retrievals based on variants of the retrieval algorithm used to generate the PDS retrievals, and (3) retrievals produced using the Mars 1-Dimensional Retrieval (M1R) algorithm based on the Optimal Spectral Sampling (OSS ) forward model. The retrieved temperature profiles are compared to the MGS Radio Science (RS) temperature profiles. For the samples tested, the M1R temperature profiles can be made to agree within 2 K with the RS temperature profiles, but only after tuning the prior and error statistics. Use of a global prior that does not take into account the seasonal dependence leads errors of up 6 K. In polar samples. errors relative to the RS temperature profiles are even larger. In these samples, the PDS temperature profiles also exhibit a poor fit with RS temperatures. This fit is worse than reported in previous studies, indicating that the lack of fit is due to a bias correction to TES radiances implemented after 2004. To explain the differences between the PDS and Ml R temperatures, the algorithms are compared directly, with the OSS forward model inserted into the PDS algorithm. Factors such as the filtering parameter, the use of linear versus nonlinear constrained inversion, and the choice of the forward model, are found to contribute heavily to the differences in the temperature profiles retrieved in the polar regions, resulting in uncertainties of up to 6 K. Even outside the poles, changes in the a priori statistics result in different profile shapes which all fit the radiances within the specified error. The importance of the a priori statistics prevents reliable global retrievals based a single a priori and strongly implies that a robust science analysis must instead rely on retrievals employing localized a priori information, for example from an ensemble based data assimilation system such as the Local Ensemble Transform Kalman Filter (LETKF).
Fast response, spectrally linear standard detector in the form of a blackbody cavity radiometer calibrates rapidly responding photodetectors against a calibrated standard detector. A power amplifier with maximum available gain reduces error signal without stability loss. It may be used as a blackbody radiator by manipulation of the bridge variable arm.
Computer programs were developed for evaluating homogeneous path transmittance with line-by-line and quasi-random band model formulations. Spectral transmittances for some selected bands of different gases (CO, N2O, CO2, H2O) were obtained using these programs. Results of theoretical computations are compared with available experimental measurements. Significant errors are observed in the results obtained from a quasi-random band model formulation, indicating that it is inadequate to meet the accuracy requirements for atmospheric work.
A comparison is made of the simulated climates of nonlinear models based on the primitive equations (PE), balance equations (BE), and quasi-geostrophic (QG) equations. The models and numerical procedures are identical in all possible respects. The models are highly truncated spectral forms of Lorenz's (1960) energy preserving two-layer model. Two means of making use of the information contained in the (presumed known) short-term prediction error statistics are investigated. An unrealistically high level of thermal forcing is used so that the model climates are sufficiently different to allow any improvements due to the empirical methods to be observed. The general tuning problem is outlined and the QG model is tuned, using data obtained from a PE model run, to minimize the mean squared short term prediction error.
Proton and helium nuclei differential spectra were gathered with a balloon borne magnet spectrometer. The data were fitted to the assumption that the differential flux can be represented by a power law in rigidity. In the rigidity range 10 to 25 GV/c the spectral indices were found to be -(2.74 plus or minus 0.04) for protons and -(2.71 plus or minus 0.05) for helium nuclei. A brief discussion is given by systematic errors.
A novel multireceiver configuration for carrier arraying and/or signal arraying is presented. The proposed configuration is obtained by formulating the carrier and/or signal arraying problem as an optimal estimation problem, and it consists of two stages. The first stage optimally estimates various phase processes received at different receivers with coupled phase-locked loops wherein the individual loops acquire and track their respective receivers' phase processes but are aided by each other in an optimal manner via LF error signals. The proposed configuration results in the minimization of the the effective radio loss at the combiner output, and thus maximization of energy per bit to noise power spectral density ratio is achieved. A novel adaptive algorithm for the estimator of the signal model parameters when these are not known a priori is also presented.
Daily monitoring of PKS 2155-304 with the IUE satellite throughout November 1991 revealed dramatic large-amplitude rapid variations in the UV flux of this BL Lac object. Many smaller, rapid flares are superposed on a general doubling of the intensity. During the five-day period when sampling was roughly continuous, the rapid flaring had an apparent quasi-periodic nature, with peaks repeating every 0.7 day. The short- and long-wavelength UV light curves are well correlated with each other, and with the optical light curve deduced from the Fine Error Sensor on IUE. The formal lag is zero, but the cross-correlation is asymmetric in the sense that the shorter wavelength emission leads the longer. The UV spectral shape varies a small but significant amount. The correlation between spectral shape and intensity is complex. The sign of the correlation is consistent with the nonthermal acceleration processes expected in relativistic plasmas, so that the present results are consistent with relativistic jet models, which can also account for quasi-periodic flaring.
Several groups have recently been working to improve the near-infrared spectrum of water vapor on HITRAN. The unit-conversion errors found by Giver, et al have now been corrected on the recently released HITRAN-2000. The most important aspect of this article for atmospheric absorption was increasing all the HITRAN-1996 intensities of the 940 nm band by nearly 15%. New intensity measurements of this band by Brown, et al (submitted to J. Mol. Spec.) have now been included in the latest HITRAN. However, Belmiloud, et al discuss new data in the 633-1175 nm region which they expect will substantially increase the calculated absorption of solar radiation by water vapor. They suggest the 4 bands at 725, 820, 940, and 1130 nm are all stronger than the sum of the line intensities currently on HITRAN. For the 725 and 820 nm bands, their recommended intensity increases are 10% and 15%, about the same as previously noted by Grossmann and Browell and Ponsardin and Browell. Belmiloud, et al only suggest a 6% increase for the 940 nm. band over the corrected HITRAN-1996 intensities, but a large 38% increase for the 1130 nm band. The new data discussed by Belmiloud, et al have now been published in greater detail by Schermaul, et al. The intensity increase for the 1130 nm band discussed by Belmiloud, et al is very substantial; it is important to quickly determine if the HITRAN intensity values are in error by as much as they claim. Only intensity errors for the strong lines could result in the total band intensity being in error by such a large amount. To quickly get a number of spectra of the entire near-infrared region from 650 to 1650 nm, we used the Solar Spectral Flux Radiometer with our 25-meter base path White absorption cell. This moderate resolution spectrometer is a flight instrument that has flown on the Sandia Twin Otter for the ARESE 11 experiment. The measured band profiles were then compared to calculated spectra using the latest HITRAN line intensities, convolved with the instrumental resolution. Our spectra for the 725 and 820 nm bands show somewhat more absorption than the HITRAN simulations, about as expected by Belmiloud, el al. The total absorption for our spectra of the 940 nm band agrees well with the HITRAN simulations; this HITRAN spectral region now has the new measurements of Brown, et al. Our spectra of the 1130 nm band have somewhat more absorption than the HITRAN simulations, but not as much as the 38% intensity increase for this band suggested by Belmiloud, et al. An intensity increase of about 20% on average would be more compatible with our data. Finally, our spectra of the 1370 nm band are fairly well modeled by the HITRAN simulations, despite the known problems of the older HITRAN data in this region.
The problem of how the scale, or spatial resolution, of reflectance data impacts retrievals of vegetation leaf area index (LAI) and fraction absorbed photosynthetically active radiation (PAR) has been investigated. We define the goal of scaling as the process by which it is established that LAI and FPAR values derived from coarse resolution sensor data equal the arithmetic average of values derived independently from fine resolution sensor data. The increasing probability of land cover mixtures with decreasing resolution is defined as heterogeneity, which is a key concept in scaling studies. The effect of pixel heterogeneity on spectral reflectances and LAI/FPAR retrievals is investigated with 1 km Advanced Very High Resolution Radiometer (AVHRR) data aggregated to different coarse spatial resolutions. It is shown that LAI retrieval errors at coarse resolution are inversely related to the proportion of the dominant land cover in such pixel. Further, large errors in LAI retrievals are incurred when forests are minority biomes in non-forest pixels compared to when forest biomes are mixed with one another, and vice-versa. A physically based technique for scaling with explicit spatial resolution dependent radiative transfer formulation is developed. The successful application of this theory to scaling LAI retrievals from AVHRR data of different resolutions is demonstrated
The purpose of this work is twofold. First, given the computational resources available today, it is possible to reach, using DNS, higher Reynolds numbers than in Briggs et al.. In the present study, the microscale Reynolds numbers reached in the low- and high-energy homogeneous regions are, respectively, 32 and 69. The results reported earlier can thus be complemented and their robustness in the presence of increased turbulence studied. The second aim of this work is to perform a detailed and documented LES of the shear-free mixing layer. In that respect, the creation of a DNS database at higher Reynolds number is necessary in order to make meaningful LES assessments. From the point of view of LES, the shear-free mixing-layer is interesting since it allows one to test how traditional LES models perform in the presence of an inhomogeneity without having to deal with difficult numerical issues. Indeed, as argued in Briggs et al., it is possible to use a spectral code to study the shear-free mixing layer and one can thus focus on the accuracy of the modelling while avoiding contamination of the results by commutation errors etc. This paper is organized as follows. First we detail the initialization procedure used in the simulation. Since the flow is not statistically stationary, this initialization procedure has a fairly strong influence on the evolution. Although we will focus here on the shear-free mixing layer, the method proposed in the present work can easily be used for other flows with one inhomogeneous direction. The next section of the article is devoted to the description of the DNS. All the relevant parameters are listed and comparison with the Veeravalli & Warhaft experiment is performed. The section on the LES of the shear-free mixing layer follows. A detailed comparison between the filtered DNS data and the LES predictions is presented. It is shown that simple eddy viscosity models perform very well for the present test case, most probably because the flow seems to be almost isotropic in the small-scale range that is not resolved by the LES.