The spectral efficiency of a representative uplink of a given length, in interference-limited, spatially-distributed wireless networks with hexagonal cells, simple power control, and multiantenna linear Minimum-Mean-Square-Error receivers is found to approach an asymptote as the numbers of base-station antennas N and wireless nodes go to infinity. An approximation for the area-averaged spectral efficiency of a representative link (averaged over the spatial base-station and mobile distributions), for Poisson distributed base stations, is also provided. For large N, in the interference-limited regime, the area-averaged spectral efficiency is primarily a function of the ratio of the product of N and the ratio of base-station to wireless-node densities, indicating that it is possible to scale such networks by linearly increasing the product of the number of base-station antennas and the relative density of base stations to wireless nodes, with wireless-node density. The results are useful for designers of wireless systems with high inter-cell interference because it provides simple expressions for spectral efficiency as a function of tangible system parameters like base-station and wireless-node densities, and number of antennas. These results were derived combining infinite random matrix theory and stochastic geometry.

Neural networks (NNs) are developed for estimating the error variances of individual infrared and microwave atmospheric temperature and humidity profile retrievals, thus potentially significantly improving their assimilation into numerical weather prediction models. Currently, most assimilation processes require error covariance matrices that are typically estimated over diverse profile ensembles. In addition to these “ensemble error variances,” this work explores the estimation of “sample error variances” that are relevant to a single sample of the ensemble (that is, an individual profile retrieval and its error at each pressure level). This analysis is facilitated by considering an individual profile retrieval as the most likely sample from a distribution of retrievals, given an individual sensor observation vector. The sample error variance is defined as the variance of this distribution. The approach described in this paper does not attempt to compute these retrieval distributions explicitly, as this is computationally prohibitive for hyperspectral sounders. Instead, NNs are trained to estimate the variances of these distributions directly. Examples over ocean utilizing AIRS/AMSU soundings on the NASA Aqua satellite and those from a proposed hyperspectral microwave sounder show that the predicted sample error variances agree well with the true sample error variances as determined by European Centre for Medium-Range Weather Forecasts analyzes colocated to the sensor observations. Furthermore, simple quality indicators derived using thresholding of the sample variance estimates compare favorably to AIRS Level-2 Version-5 quality flags.

An asymptotic technique is presented for finding the spectral efficiency of multiantenna links in spatially distributed wireless networks where transmitters have channel-state-information (CSI) corresponding to their target receiver. Transmitters are assumed to transmit independent data streams on a limited number of channel modes which limits the rank of transmit covariance matrices. An approximation for the spectral efficiency in the interference-limited regime as a function of link-length, interferer density, number of antennas per receiver and transmitter, number of transmit streams, and path-loss exponent is derived. It is found that targeted-receiver CSI, which can be acquired with low overhead in duplex systems with reciprocity, can increase spectral efficiency several fold, particularly when link lengths are large, node density is high, or both. Additionally, the per-link spectral efficiency is found to be a function of the ratio of node density to the number of receiver antennas, and it can often be improved if nodes transmit using fewer streams. These results are validated for finite-sized systems by Monte-Carlo simulation and are asymptotic in the regime where the number of users and antennas per receiver approach infinity.

Active and passive microwave remote sensing estimates of surface precipitation based on signals from hydrometeors aloft require correction for evaporated precipitation that would otherwise reach the ground. This paper develops and compares two near-surface evaporation correction methods using two years of data from 509 globally distributed rain gauges and three passive millimeter-wave Advanced Microwave Sounding Units (AMSUs) aboard National Oceanic and Atmospheric Administration (NOAA) satellites (NOAA-15, NOAA-16, and NOAA-18). The first type of correction is a scale factor that minimizes the bias between the means of annual AMSU and rain gauge precipitation accumulations (in millimeters per year) for each of 12 infrared-based surface classifications. The scale factor for the second correction method is computed using a neural network trained using both surface classification and annual average relative humidity pro files. AMSU surface precipitation retrievals using both methods were compared to the annual accumulations for 509 rain gauges uncorrected for wind effects, where different data were used for training and accuracy evaluation. The rms annual accumulation retrieval errors for AMSU using surface classification and relative humidity corrections were 236 and 222 mm/y, respectively, compared to 190 mm/y for corresponding Global Precipitation Climatology Project data, which utilizes more satellite sensors and over 6500 rain gauges.

This paper compares two methods for correcting passive or active microwave surface precipitation estimates based on hydrometeors sensed aloft that may evaporate before landing. These corrections were derived using two years of data from 516 globally distributed rain gauges and passive millimeter-wave Advanced Microwave Sounding Units (AMSU) aboard three NOAA satellites (N15, N16, and N18). The first correction reduces rms differences between rain gauges and AMSU annual precipitation accumulations (mm) by a separate factor for each infrared-based surface classification, while the second correction factor uses a 3-2-1 neural network (NN) trained using both surface classification and annual average relative humidity profiles. Different data were used for training and accuracy evaluation. The NN results agreed with rain gauges better than did surface classification corrections alone. The rms annual accumulation errors relative to the 516 uncorrected rain gauges using AMSU with surface classification and NN corrections were 223 and 209 mm/yr, respectively, compared to 152 mm/yr for GPCP, which incorporates rain gauge data and data from more satellite sensors.

This paper presents and evaluates a global precipitation retrieval algorithm for the Special Sensor Microwave Imager/Sounder (SSMIS). It is based on those developed earlier for the Advanced Microwave Sounding Unit (AMSU) and employs neural networks trained with 122 global storms that spanned a year and were simulated using the fifth-generation National Center for Atmospheric Research/Penn State Mesoscale Model (MM5) and a radiative transfer program validated using AMSU observations. Only non-icy surfaces at latitudes less than 50° have been analyzed because their surface effects are more predictable. Sensitivity to surface emissivity variations was reduced by using only more surface-insensitive principal components of brightness temperature. Based on MM5 simulations, retrievals for land are slightly less accurate than those for sea and all are useful for rates above 1 mm/h. F-16 SSMIS, NOAA-15 AMSU, and Global Precipitation Climatology Project (GPCP) annual estimates generally agree. SSMIS retrieves less precipitation for some areas partly due to its higher resolution that resolves precipitation better. SSMIS overestimates precipitation over under-vegetated land requiring the near-surface evaporation correction illustrated earlier for AMSU.

This letter evaluates the ability of the U.S. National Polar-orbiting Operational Environmental Satellite System 22-channel Advanced Technology Microwave Sounder (ATMS) to retrieve surface precipitation rates (millimeters per hour); water path estimates for rain, snow, and graupel (millimeters); and peak vertical wind (convective strength, meters per second). Simulated retrieval accuracies for ATMS were compared to those for its predecessor the Advanced Microwave Sounding Unit (AMSU), both of which sample the 23- to 190-GHz spectrum. ATMS retrieves all precipitation parameters up to ~ 25% more accurately than AMSU except for cloud ice and snow water paths, which are comparable. Image sharpening of the ATMS Nyquist-sampled observations below 90 GHz further improves the recovery of small features but amplifies noise so that the benefits are restricted primarily to finely structured convective systems.

In this paper a second-order method for blind source separation of noisy instantaneous linear mixtures is presented for the case where the signal orderkis unknown. Its performance advantages are illustrated by simulations and by application to Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) multichannel visible/infrared data. The model assumes thatmmixturesxof dimensionnare observed, wherex=Ap+Gw, and the underlying signal vectorphas kAis the mixing matrix,Gis diagonal, andwis a normalized white-noise vector. The algorithm estimates the Second-Order separation matrixA, signal Orderk, and Noise and is therefore designated as SOON. SOON first iteratively estimateskandGusing a scree metric, singular-value decomposition, and the expectation-maximization algorithm, and then determines the values ofAPandW. The final step estimatesAand the set ofmsignal vectorspusing a variant of the joint-diagonalization method used in the Second-Order Blind Identification (SOBI) and Second-Order NonStationary (SONS) source-separation algorithms. The SOON extension of SOBI and SONS significantly improves their separation of simulated sources hidden in noise. SOON also reveals interesting thermal dynamics within AVIRIS multichannel visible/infrared imaging data not found by noise-adjusted principal-component analysis.

A new global precipitation retrieval algorithm for the millimeter-wave Advanced Microwave Sounding Unit is presented that also retrieves Arctic precipitation rates over surface snow and ice. This algorithm improves upon its predecessor by excluding some surface-sensitive channels and by reducing the number of principal components (PCs) used to represent those that remain. The training sets were also modified to better represent cold regions. The algorithm still incorporates conversion of brightness temperatures to nadir, spatial filtering to better detect pixels scattering near 54 GHz, PC filtering of surface effects, and use of separate neural networks trained with the fifth-generation National Center for Atmospheric Research/Penn State Mesoscale Model (MM5) for land and sea, where warm and cold ocean are now treated differently. The validity of the snowfall detections is supported by nearly coincident CloudSat radar observations, and the physics of the model is largely validated by the reasonable agreement in annual precipitation obtained for 231 globally distributed rain gauges, including many at latitudes where snowfall dominates. Observed annual global precipitation statistics are also presented to permit comparisons with other algorithms and sensors.

This paper evaluates the ability of the United States National Polar Orbiting Environmental Sensor System (NPOESS) Advanced Technology Microwave Sounder (ATMS) to retrieve surface precipitation rates (mm/h); water path estimates for rain, snow, and graupel (mm); and peak vertical wind (convective strength, m/s). Simulated retrieval accuracies for ATMS were compared to those for its predecessor, AMSU. These retrieval algorithms employ neural networks trained using atmospheric parameters and their corresponding brightness temperatures predicted by a global ground-truth model, NCEP/MM5/TBSCAT/F(lambda), for 106 global storms. ATMS performs better than AMSU for all retrieved parameters except for snow and cloud ice, where they perform comparably. Image sharpening amplifies noise and so its benefits are restricted primarily to relatively rare isolated storms.

An improved surface precipitation rate retrieval algorithm for Advanced Microwave Sounding Unit (AMSU) data is presented. Its reduced sensitivity to surface effects improves its sensitivity to stratiform precipitation and permits it to work over most snow and sea ice. It is trained using 106 globally and seasonally distributed cloud-resolving MM5 storm simulations that predicted well AMSU brightness temperatures observed simultaneously. The improvements result mostly from the choice of frequencies and principal components feeding the final neural network estimators. The retrievals perform well in terms of simulated rms retrieval errors, plausible global precipitation maps, global precipitation frequency statistics in terms of latitude and precipitation rate, and in comparisons with other sensors and algorithms, including nearly coincident CLOUDSAT data.

This paper develops a global precipitation rate retrieval algorithm for the advanced microwave sounding unit (AMSU), which observes 23-191 GHz. The algorithm was trained using a numerical weather prediction (NWP) model (MM5) for 106 globally distributed storms that predicted brightness temperatures consistent with those observed simultaneously by AMSU. Neural networks were trained to retrieve hydrometeor water-paths, peak vertical wind, and 15-min average surface precipitation rates for rain and snow at 15-km resolution at all viewing angles. Different estimators were trained for land and sea, where surfaces classed as snow or ice were generally excluded from this paper. Surface-sensitive channels were incorporated by using linear combinations [principal components (PCs)] of their brightness temperatures that were observed to be relatively insensitive to the surface, as determined by visual examination of global images of each brightness temperature spectrum PC. This paper also demonstrates that multiple scattering in high microwave albedo clouds may help explain the observed consistency for a global set of 122 storms between AMSU-observed 50-191-GHz brightness temperature distributions and corresponding distributions predicted using a cloud-resolving mesoscale NWP model (MM5) and a two-stream radiative transfer model that models icy hydrometeors as spheres with frequency-dependent densities. The AMSU/MM5 retrieval algorithm developed in Part I of this paper is evaluated in Part II on a separate paper.

This paper evaluates the performance of the global precipitation rate retrieval algorithm for the Advanced Microwave Sounding Unit (AMSU) that was described in Part I of this paper. AMSU is in polar orbit on several National Ocean and Atmospheric Administration (NOAA) operational weather satellites. Predicted rms retrieval errors based on a 15-km resolution 0.5–1.0-mm/h MM5 truth were 0.88, 0.83, 1.13, and 3.04 for stratiform, warm rain, ice-free rain, and convective rain, respectively, which were averaged over all view angles for land and sea up to 73$^{\circ}$latitude. For MM5 rates of 4–8 mm/h, these rms errors increased to 2.8, 3.4, 3.9, and 4.9 mm/h, respectively. The corresponding rms retrieval accuracies for MM5 hydrometeor water paths between 0.125 and 0.25 mm for rainwater, snow, and graupel were 0.19, 0.10, and 0.22 mm, respectively. The rms retrieval accuracy for the 0.125–0.25-m/s peak vertical wind was 0.08 m/s. Biases are small for cumulative precipitation estimates, although an upward correction factor of 1.37 is derived for convective precipitation rate probability distributions. Differences between these retrievals and those from the conically scanned Advanced Microwave Scanning Radiometer for the Earth Observing System instrument and an alternate NOAA AMSU algorithm are also characterized.

This paper develops global retrieval algorithms for surface precipitation rate (mm/h), peak vertical wind (m/s), and water-paths (mm) for rainwater, snow, graupel, cloud water, cloud ice, and the sum of rainwater, snow, and graupel, for the Advanced Microwave Sounding Unit (AMSU) aboard the NOAA-15, -16, and -17 satellites. These retrieved products are expected to be available to researchers and operational users shortly after each orbit is completed, thus providing up to 4-6 precipitation-rate images each day for nearly every spot on earth with nominal 15-km resolution. The same algorithm could be adapted to similar instruments such as AMSU/MHS on the NOAA-18 satellite and AMSU/HSB aboard the Aqua satellite. The algorithm was trained using a numerical weather prediction model (MM5) for 106 globally distributed storms that predicted brightness temperatures consistent with those observed simultaneously by AMSU. Neural networks were trained to retrieve hydrometeor water-paths and 15-minute average surface precipitation rates for rain and snow at ~15-km resolution for land and sea at all viewing angles. Different estimators were trained for land and sea, where surfaces classed as snow or ice were generally excluded from this study. Surface- sensitive channels were incorporated by using linear combinations (principal components) of their brightness temperatures that were observed to be relatively insensitive to the surface, as determined by visual examination of global images of each brightness-temperature-spectrum principal component. Predicted rms errors for retrieved precipitation rates, hydrometeor water paths, and peak vertical wind were evaluated using independent samples of MM5 truth. AMSU and AMSR-E retrieved precipitation rates were also compared.

This paper compares surface precipitation rates retrieved for the United States Great Plains (USGP) during the summer of 2004 using the Advanced Microwave Sounding Unit (AMSU) aboard the United States NOAA-15 and -16 satellites with similar precipitation products produced by AMSR-E aboard the NASA Aqua satellite, SSM/I aboard the United States DMSP F-13, -14, and -15 satellites, TMI aboard the NASA TRMM satellite, and a doppler radar product (NOWRAD) of the Weather Services International Corporation (WSI). AMSU surface precipitation rates were retrieved using neural network algorithms trained with either a cloud-resolving MM5 physical model for 106 global storms (the AMSU/MM5 algorithm), or summer NEXRAD radar data for the USGP (the AMSU/NR algorithm). Observed correlation coefficients between log10(X + 0.01) for NOWRAD surface precipitation rates X (mm/h) at 0.25- degree resolution and those for other sensors were, in declining order, 0.82, 0.79, 0.78, 0.71, and 0.68 for TMI, SSM/I, AMSU/NR, AMSR-E, and AMSU/MM5, respectively. Higher correlation coefficients were obtained when TMI was regarded as truth: 0.86, 0.83, 0.82, 0.80, and 0.78 for SSM/I, AMSU/NR, NOWRAD, AMSU/MM5, and AMSR-E, respectively. Other sensor comparisons include false alarm statistics for all pairs of sensors, rms and mean differences with respect to NOWRAD, precipitation-rate distribution functions, and observed correlations between NOWRAD and AMSU/MM5 precipitation and hydrometeor water path retrievals.

Receivers with N antennas in single-hop, ad-hoc wireless networks with nodes randomly distributed on an infinite plane with uniform area density are studied. Transmitting nodes have single antennas and transmit simultaneously in the same frequency band with power P that decays with distance via the commonly-used inverse-polynomial model with path-loss- exponent (PLE) greater than 2. This model applies to shared spectrum systems where multiple links share the same frequency band. In the interference-limited regime, the average spectral efficiency of a representative link E[C] (b/s/Hz/link) is found to grow as log(N) and linearly with PLE, and its variance decays as 1/N. The average signal-to-interference-plus-noise-ratio (SINR) on a representative link is found to grow faster than linearly with N. With multiple-input-multiple-output (MIMO) links where transmit nodes have multiple antennas without Channel- State-Information, it is found that E[C] in the network can be improved if nodes transmit using the optimum number of antennas compared to the optimum selfish strategy of transmitting equal-power streams from every antenna. The results are extended to random code-division-multiple-access systems where the optimum spreading factor for a given link length is found. These results are developed as asymptotic expressions using infinite random matrix theory and are validated by Monte-Carlo simulations.

Only instruments on geostationary or comparable platforms can view global precipitation at the ~15-min interval that is necessary to monitor rapidly evolving convective events. This paper compares the abilities of 11 alternative passive microwave sensors to retrieve surface precipitation rates and hydrometeor water paths. Five instruments observe selected frequencies from 116 to 429 GHz with a filled-aperture antenna, and six instruments observe from 52 to 191 GHz with a U-shaped aperture synthesis array. The analysis is based on neural network retrieval methods and 122 global MM5-simulated storms that are generally consistent with the simultaneous Advanced Microwave Sounding Unit observations. Several instruments show considerable promise in retrieving hydrometeor water paths and 15-min average precipitation rates ~1-100 mm/h with spatial resolutions that vary from ~15 to ~50 km. This space/time resolution is potentially adequate to support assimilation of precipitation information into cloud-resolving numerical weather prediction models.

Surface Prior-Information Reflectance Estimation (SPIRE) algorithms estimate changes in spectral reflectance using imperfect prior spatial and spectral information. This paper combines spectral and spatial processing to estimate local changes in spectral reflectance between pairs of spectral images under spatially and spectrally varying multiplicative and additive noise, which arise from variations in illumination and atmospheric effects. This approach extends the spatial SPIRE algorithms that were described earlier and utilizes only a prior reflectance image cube and ensembles of typical multiplicative and additive illumination noise spectral vectors that are deduced from images cubes of similar scenes. The method minimizes the impact of environmental noise by replacing with their prior equivalents low-spatial-frequency content and low-order principal components that are known to be noisy based on prior noise spectra. This filtering and substitution process occurs in log space when minimizing the effects of multiplicative noise. Tests on Hyperspectral Digital Imagery Collection Experiment visible near-infrared–shortwave infrared data demonstrated the algorithm's superior ability to estimate absolute reflectance changes under varying illumination conditions. SPIRE performance was nearly identical to the empirical line method (ELM) ground-truth-based atmospheric compensation results and was better than the physics-based ATmospheric REMoval (ATREM) code overall, particularly, under high clouds and haze. A “Selective SPIRE” technique that chooses between combined-spatial/spectral and spectral-only SPIRE reflectance estimates was developed; it maximizes estimation performance on both changed and unchanged pixels. Minimum-distance classification experiments demonstrated Selective SPIRE's superior performance relative to both ATREM and ELM in cross-image supervised classification applications.

Only instruments on geostationary or comparable platforms can view global precipitation at the ~15-minute intervals necessary to monitor rapidly evolving convective events. This paper compares the abilities of ten such alternative passive microwave sensors to retrieve surface precipitation rates and hydrometeor water paths-five instruments observe various frequencies from 116 GHz to 429 GHz with a filled-aperture antenna, and five observe various frequencies from 52 to 191 GHz with a U-shaped aperture synthesis array. The analysis is based on neural network retrieval methods and 122 global MM5- simulated storms that are generally consistent with simultaneous AMSU observations. Several instruments show considerable promise for retrieving hydrometeor water paths and 15-minute average precipitation rates ~1-100 mm/h with spatial resolutions that vary from ~15 km to ~50 km. This space/time resolution is potentially adequate to support assimilation into cloud-resolving numerical weather prediction models.

simulation system as a test-bed for precipitation retrieval development for satellite-borne millimeter-wave instruments. The sensitivity study was performed by comparing radiance histograms observed by satellite instruments (AMSU-A/B) over 122 diverse global storms with those simulated by variations of the MM5/RTM system for the same storm set. The radiances simulated by a baseline MM5/RTM model had earlier been shown to agree well with AMSU observations [1]. The simulated radiances were found to be very sensitive to the Mie backscattering fraction and the abundances, altitudes, and models [F(λ)] of both snow and graupel. AMSU retrieval performance was then evaluated assuming large random changes to MM5 and the RTM. The surface precipitation-rate rms retrieval accuracy was found to be robust to those changes, i.e., unchanged within ~± 5 percent and ~± 17 percent for precipitation rates ~< 8 mm/h and ~< 174 mm/h, respectively.

This paper addresses the following: 1) millimeter-wave scattering by icy hydrometeors and 2) the consistency between histograms of millimeter-wave atmospheric radiances observed by satellite instruments [Advanced Microwave Sounding Unit-A/B (AMSU-A/B)] and those predicted by a mesoscale numerical weather prediction (NWP) model (MM5) in combination with a two-stream radiative transfer model (TBSCAT). This observed consistency at 15-km resolution supports use of MM5/TBSCAT as a useful simulation tool for designing and assessing global millimeter-wave systems for remote sensing of precipitation and related parameters at 50-200 GHz. MM5 was initialized by National Center for Environmental Prediction NWP analyses on a 1deg grid approximately 5 h prior to each AMSU transit and employed the Goddard explicit cloud physics model. The scattering behavior of icy hydrometeors, including snow and graupel, was assumed to be that of spheres having an ice density F(lambda) and the same average Mie scattering cross sections as computed using a discrete-dipole approximation implemented by DDSCAT for hexagonal plates and six-pointed rosettes, respectively, which have typical dimensional ratios observed aloft. No tuning beyond the stated assumptions was employed. The validity of these approximations was tested by varying F(lambda) for snow and graupel so as to minimize discrepancies between AMSU and MM5/TBSCAT radiance histograms over 122 global storms. Differences between these two independent determinations of F(lambda) were less than ~0.1 for both snow and graupel. Histograms of radiances for AMSU and MM5/TBSCAT generally agree for 122 global storms and for subsets of convective, stratiform, snowy, and nonglaciated precipitation

Accurate global observation of precipitation for all latitudes and seasons, and for all land, sea, and ice surfaces remains an elusive goal. One major obstacle to progress is lack of reliable global ground truth on horizontal and vertical scales consistent with those observed by satellite. For example, radar and scatter-dependent radiometric techniques respond to precipitation aloft, not on the ground, and can be unduly sensitive to large hydrometeors. On the other hand, rain gauges are excessively sensitive to local rainfall inhomogeneities and wind, and well-instrumented sites are rare. This paper quantitatively compares satellite observations with mesoscale numerical weather predictions of microwave brightness temperatures at those millimeter wavelengths most sensitive to hydrometeor structures and to the physics of precipitation. Only such models with high horizontal and vertical resolution allow comparisons of different sensors in detail. A Mesoscale Model, MM5, and a forward radiance program, TBSCAT, have been used to simulate radiances that would be observed from the Advanced Microwave Sounding Unit (AMSU-A and AMSU-B) aboard the NOAA-16 satellite for twenty-four globally representative storm systems, including /spl sim/28,200 AMSU-A and 255,640 AMSU-B footprints, spanning a year. Good agreement has been obtained between histograms of coincident MM5-simulated and observed AMSU-A and AMSU-B radiances by adjusting ice parameter values in TBSCAT. Ice parameter values are consistent with the scattering for ice habits observed aloft, as computed using a Discrete Dipole Approximation program, DDSCAT6.1. These results suggest the potential use of MM5 as a rich new statistical form of ground-truth that will permit development of better precipitation estimators and improved understanding of precipitation itself, particularly in the more problematic areas of the globe.

The National Polar-orbiting Operational Environmental Satellite System (NPOESS) Aircraft Sounder Testbed-Microwave (NAST-M) includes spectrometers operating near the oxygen lines at 50-57, 118.75, and 424.76 GHz, and a spectrometer centered on the water vapor absorption line at 183.31 GHz. All four of the spectrometers' antenna horns are collocated, have 3-dB (full-width at half-maximum) beamwidths of 7.5/spl deg/, and are directed at a single mirror that scans cross-track beneath the aircraft with a swath up to 100-km wide. The first part of the paper describes the instrumentation and calibration for the newly installed spectrometers at 183.31 and 424.76 GHz. The second part demonstrates the potential performance of NAST-M, by presenting radiance images and precipitation rate and cell-top retrievals obtained during overflights of isolated convective storm cells, and by comparing these results with coincident visible images. NAST-M radiances are also compared with visible, infrared, and radar images. The nonlinear retrieval method was trained with a simple precipitation model. The data were obtained during the Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL-FACE 2002) and the Pacific THORpex (THe Observing-system Research and predictability experiment) Observing System Test (PTOST 2003).

Arctic precipitation has been imaged by the passive Advanced Microwave Sounding Unit (AMSU) and Humidity Sounder for Brazil (HSB) aboard the Aqua satellite, and by nearly identical instruments (AMSU-A and AMSU-B) aboard the National Oceanographic and Atmospheric Administration NOAA-15, -16, and -17 satellites. Events were considered to be precipitation if they exhibited appropriate radiometric signatures and morphological evolution over consecutive satellite overpasses at 100-minute intervals. For such Arctic events, the observed cold perturbations near 183/spl plusmn/7 GHz were as much as 20 K, and the cold perturbations near 52.8 GHz were on the order of 1 K. These observed clumped cold perturbations imply the presence of scattering hydrometeors of diameter > 1 mm, which will precipitate. A comparison of these images with those of brightness temperatures from window channels that are sensitive to surface emissivity shows that such events are not likely to be the result of surface variations. Arctic precipitation rate estimates have been calculated using a precipitation-rate algorithm developed previously for mid-latitude climates. For example, on July 20, 2002 a precipitation event /spl sim/200/spl times/1000 km in size was observed by Aqua AMSU/HSB moving /spl sim/100 km/h from /spl sim/80/spl deg/ N toward northern Canada, and is consistent morphologically with numerical weather predictions. These estimates require substantial scaling to be accurate for polar atmospheres. Without careful modeling, areas of dry air can sometimes be mistakenly flagged as precipitation.

The National Polar-orbiting Operational Environmental Satellite System (NPOESS) Aircraft Sounder Testbed-Microwave, or NAST-M , has added two spectrometers to its original suite of spectrometers operating near the oxygen lines at 50-57 GHz and the oxygen line at 118.75 GHz. The NAST-M suite now includes a spectrometer that is centered on the water vapor absorption line at 183.31 GHz, and another that is centered on the oxygen absorption line at 424.76 GHz. This addition has increases the ability of NAST-M to retrieve humidity profiles and to sense smaller-diameter hydrometeors. All four of the spectrometers' horns are collocated, have 3-dB (full-width at half-max) points of 7.5/spl deg/, and are directed at a single scanning mirror, which produces a cross-track scan beneath the aircraft with a swath width of approximately 100 km. Aircraft carrying NAST-M cruise at altitudes of 17 to 20 km, yielding a nadir surface spatial resolution of /spl sim/ 2.6 km.

The National Polar-orbiting Operational Environmental Satellite System (NPOESS) Aircraft Sounder Testbed-Microwave, or NAST-M, has added two spectrometers to its original suite operating near the oxygen lines at 50-57 GHz and the oxygen line at 118.75 GHz. These new spectrometers are centered on the water vapor absorption line at 183.31 GHz and the oxygen absorption line at 424.76 GHz. This addition has increased the ability of NAST-M to retrieve humidity profiles and to sense smaller-diameter hydrometeors. The co-aligned NAST-M suite concurrently imaged clouds and convective cells during the Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL-FACE 2002) and the 2003 Pacific THORpex (The Observing-system Research and predictability experiment) Observing System Test (THORpex 2003).

The Atmospheric Infrared Sounder (AIRS), the Advanced Microwave Sounding Unit (AMSU), and the Humidity Sounder for Brazil (HSB) form an integrated cross-track scanning temperature and humidity sounding system on the Aqua satellite of the Earth Observing System (EOS). AIRS is an infrared spectrometer/radiometer that covers the 3.7-15.4-/spl mu/m spectral range with 2378 spectral channels. AMSU is a 15-channel microwave radiometer operating between 23 and 89 GHz. HSB is a four-channel microwave radiometer that makes measurements between 150 and 190 GHz. In addition to supporting the National Aeronautics and Space Administration's interest in process study and climate research, AIRS is the first hyperspectral infrared radiometer designed to support the operational requirements for medium-range weather forecasting of the National Ocean and Atmospheric Administration's National Centers for Environmental Prediction (NCEP) and other numerical weather forecasting centers. AIRS, together with the AMSU and HSB microwave radiometers, will achieve global retrieval accuracy of better than 1 K in the lower troposphere under clear and partly cloudy conditions. This paper presents an overview of the science objectives, AIRS/AMSU/HSB data products, retrieval algorithms, and the ground-data processing concepts. The EOS Aqua was launched on May 4, 2002 from Vandenberg AFB, CA, into a 705-km-high, sun-synchronous orbit. Based on the excellent radiometric and spectral performance demonstrated by AIRS during prelaunch testing, which has by now been verified during on-orbit testing, we expect the assimilation of AIRS data into the numerical weather forecast to result in significant forecast range and reliability improvements.

Precipitation rates (mm per hour) with 15- and 50-km horizontal resolution are among the initial products of Atmospheric Infrared Sounder/Advanced Microwave Sounding Unit/Humidity Sounder for Brazil (AIRS/AMSU/HSB). They will help identify the meteorological state of the atmosphere and any AIRS soundings potentially contaminated by precipitation. These retrieval methods can also be applied to the AMSU 23-191-GHz data from operational weather satellites such as NOAA-15, -16, and -17. The global extension and calibration of these methods are subjects for future research. The precipitation-rate estimation method presented is based on the opaque-channel approach described by Staelin and Chen (2000), but it utilizes more channels (17) and training data and infers 54-GHz band radiance perturbations at 15-km resolution. The dynamic range now reaches 100 mm/h. The method utilizes neural networks trained using the National Weather Service's Next Generation Weather Radar (NEXRAD) precipitation estimates for 38 coincident rainy orbits of NOAA-15 AMSU data obtained over the eastern United States and coastal waters during a full year. The rms discrepancies between AMSU and NEXRAD were evaluated for the following NEXRAD rain-rate categories:32 mm/h. The rms discrepancies for the 3790 15-km pixels not used to train the estimator were 1.0, 2.0, 2.3, 2.7, 3.5, 6.9, 19.0, and 42.9 mm/h, respectively. The 50-km retrievals were computed by spatially filtering the 15-km retrievals. The rms discrepancies over the same categories for all 4709 50-km pixels flagged as potentially precipitating were 0.5, 0.9, 1.1, 1.8, 3.2, 6.6, 12.9, and 22.1 mm/h, respectively. Representative images of precipitation for tropical, mid-latitude, and snow conditions suggest the method's potential global applicability.

A new set of algorithms has been developed to estimate spectral reflectance in remote sensing imagery. These algorithms are called surface prior information reflectance estimation (SPIRE) algorithms and estimate surface spectral reflectance using prior spatial and spectral information about the surface reflectance. This paper describes SPIRE algorithms that employ spatial processing of single-channel data to estimate local changes in spectral reflectance under spatially and spectrally varying multiplicative and additive noise caused by variations in illumination and atmospheric effects. Rather than modeling the physics of the atmosphere and illumination (using a physics-based code such as the Atmospheric Removal (ATREM) program), or using ground truth spectra at known locations to compensate for these effects [using the empirical line method (ELM)], prior information about the low spatial frequency content of the scene in each spectral channel is used instead. HYDICE visible near-infrared shortwave infrared (VNIR-SWIR) hyperspectral data were used to compare the performance of SPIRE, ATREM, and ELM atmospheric compensation algorithms. The spatial SPIRE algorithm performance was found to be nearly identical to the ELM ground-truth-based results, while spatial SPIRE performed better than ATREM overall and significantly better under high clouds and haze.

The concept of microwave sounding from geostationary orbit is over three decades old, but can now be facilitated using submillimetre-wave sounding technology. A "GEM" concept has been pursued in the U.S. in the past few years, and now a "GOMAS" proposal has been submitted to ESA for implementation. The principle is to extend the number of bands usually exploited for sounding (54 GHz for temperature and 183 GHz for humidity) to higher frequencies (118 and 425 GHz for temperature, 380 GHz for humidity), so as to obtain higher geometric resolution for a given antenna size. Measurements in absorption bands at frequencies differently affected by liquid and ice water, enable simultaneous retrieval of temperature and humidity profiles, cloud ice and liquid columnar amounts and gross profile and, most important, precipitation, appropriately sampled at time intervals of some 15 minutes. The paper will highlight the basic concepts and technical features of the GEM/GOMAS project and comment about feasibility and sizing elements.

Data collected by airborne infrared (NAST-I, MAMS) and microwave (NAST-M) sensors during CAMEX-3 (Florida, summer 1998) are used to quantify the cloud impact on atmospheric sounding performance in several ways. First, the degrees of freedom introduced by clouds are estimated by applying principal component transforms to cloud-perturbed (clear minus cloudy) NAST spectra. These results are then compared to those obtained using radiances simulated using two-level clouds. Finally, the radiance cloud-clearing performance for NAST-type clouds is evaluated and compared with results for simulated two-level clouds.

The temperature profile retrieval performance of airborne and spaceborne atmospheric infrared sounders is significantly degraded by clouds. The impact due to two-level clouds is quantitatively assessed in two ways using simulated radiances from the Atmospheric InfraRed Sounder (AIRS), the Advanced Microwave Sounding Unit (AMSU), and the Microwave Humidity Sounder (MHS). First, cloud characterization (cloud flagging) techniques were developed to identify cloud-contaminated pixels. Second, a neural network was trained to estimate clear-column infrared radiances from cloud-contaminated 3/spl times/3 pixel clusters of infrared and microwave radiances (cloud clearing). This algorithm reduced the a priori radiance error due to clouds by at least a factor of three for those 4- and 15-micron sounding channels with weighting function peaks located from 0-10 km. Radiance cloud-clearing errors (RMS) for infrared channels with weighting functions peaking from 10 to 0 km ranged from 0.1 to 0.7 K for the 4-micron channels and from 0.1 to 1.2 K for the 15-micron channels. Combining microwave and infrared data at the pixel level always yielded results superior to infrared alone. It was found that microwave surface emissivity uncertainties are a key contributor to residual errors.

This paper extends prior work on estimating instantaneous rain rates using data from the NASA Advanced Microwave Sounding Unit (AMSU) aboard the NOAA-15 satellite (Staelin and Chen, IEEE TGARS, vol. 38, pp. 2322-32, 2000) by utilizing more AMSU channels, training orbits, and seasons of the year, and by 1) inferring 15-km perturbations for the 50-km resolution channels, 2) adapting the algorithm to include cold dry atmospheres, 3) training using only the most reliable NOAA NEXRAD 3-GHz radar data, 4) applying the method to snowfall rate retrievals, and 5) preliminary global testing of the resulting algorithm over land and sea. The 15- and 50-km resolution algorithms were tested at AMSU rain rates up to 160 and 100 mm/h, respectively.

The National Polar-Orbiting Operational Environmental Satellite System (NPOESS) Aircraft Sounder Testbed (NAST) has been developed and deployed on the NASA ER-2 high-altitude aircraft. The testbed consists of two co-located cross-track scanning instruments: a Fourier transform interferometer spectrometer (NAST-I) with spectral coverage of 3.7-15.5 /spl mu/m and a passive microwave spectrometer (NAST-M) with 17 channels near the oxygen absorption lines at 50-57 GHz and 118.75 GHz. The testbed provides the first coregistered imagery from high-resolution microwave and infrared sounders and will provide new data that will help (1) validate meteorological satellite environmental data record feasibility, (2) define future satellite instrument specifications, and (3) demonstrate operational issues in ground validation, data calibration, and retrievals of meteorological parameters. To help validate the performance and potential of NAST-M, imagery was collected from more than 20 overpasses of hurricanes Bonnie and Earl during the Convection and Moisture Experiment (CAMEX-3), Florida, boreal summer 1998. The warm core and convection morphology of Hurricane Bonnie (August, 1998) is clearly revealed both by aircraft-based microwave brightness temperature imagery and temperature retrievals within the eye. Radiance comparisons with the Advanced Microwave Sounding Unit on the NOAA-15 satellite and radiosonde observations yield root mean-squared agreements of approximately 1 K or less.

Promising agreement over land and sea has been obtained between NEXRAD 3-GHz radar observations of precipitation rate and retrievals based on simultaneous passive observations at 50-191 GHz from the Advanced Microwave Sounding Unit (AMSU) on the NOAA-15 meteorological satellite. A neural network with three hidden nodes and one linear output node operated on 15 km resolution data at 183/spl plusmn/1 and 183/spl plusmn/7 GHz, plus the cosine of scan angle, to produce estimates that match well the morphology of NEXRAD hurricane and frontal precipitation data smoothed to 15-km resolution. A second neural network operated on the same three parameters used in the first network, but smoothed to 50-km resolution, plus spatially-filtered cold perturbations detected in three AMSU tropospheric temperature-sounding channels (channels 4-6), which also have 50-km resolution. Comparison with the same NEXRAD data smoothed to 50-km resolution yielded root mean square (rms) discrepancies for two frontal systems and two passes over Hurricane Georges of /spl sim/1.1 mm/h, and /spl plusmn/1.4 dB for those precipitation events over 4 mm/h. Only 8.9% of the total AMSU-derived rainfall was in areas where AMSU saw more than 1-mm/h and NEXRAD saw less than 1-mm/h, and only 6.2% of the total NEXRAD-derived rainfall was in areas where NEXRAD saw more than 1-mm/h and AMSU saw less than 1-mm/h.

The use of passive 118-GHz O/sub 2/ observations of rain cells for precipitation cell-top altitude estimation is demonstrated by using a multilayer feedforward neural network retrieval system. Rain cell observations at 118 GHz were compared with estimates of the cell-top altitude obtained by optical stereoscopy. The observations were made with 2-4-km horizontal spatial resolution by using the millimeter-wave temperature sounder (MTS) scanning spectrometer aboard the NASA ER-2 research aircraft during the Genesis of Atlantic Lows Experiment (GALE) and the Cooperative Huntsville Meteorological Experiment (COHMEX) in 1986. The neural network estimator applied to MTS spectral differences between clouds, and nearby clear air yielded an rms discrepancy of 1.76 km for a combined cumulus, mature, and dissipating cell set and 1.44 km for the cumulus-only set. An improvement in rms discrepancy to 1.36 km was achieved by including additional MTS information on the absolute atmospheric temperature profile. An incremental method for training neural networks was developed that yielded robust results, despite the use of as few as 56 training spectra. Comparison of these results with a nonlinear statistical estimator shows that superior results can be obtained with a neural network retrieval system. Imagery of estimated cell-top altitudes was created from 118-GHz spectral imagery gathered from CAMEX, September through October 1993, and from cyclone Oliver, February 7, 1993.

A technique for retrieving atmospheric humidity profiles using passive microwave spectral observations from satellite and multilayer feedforward neural networks (MFNN) is introduced. Relative humidity retrievals on a global scale from simulated radiances at fifteen frequencies between 23.8 and 183.3 GHz yielded rms errors in relative humidity of 6-14% over ocean and 6-15% over land at pressure levels ranging from 131 mbar to 1013 mbar. Comparison with a combined statistical and physical iterative retrieval scheme shows that superior retrievals can be obtained at a lower computational cost using MFNN.

Estimation of atmospheric relative humidity profiles using passive remote sensing techniques is difficult when the temperature profile is not well known, and such retrievals approach singularity when the atmosphere is nearly isothermal. A retrieval method that is more robust near isothermal regions and temperature inversions is described. Its robust character results from an iterative combination of statistical methods based on a priori data, which stabilize the effects of any singularities, and physical methods that reflect the nonlinear character of the equation of radiative transfer and the dependence of measurements on uncertain surface reflectivities and temperature profiles. This method can be used to interpret data from meteorological satellites. It was tested extensively using simulated clear-sky microwave observations from space at 89 GHz, 166 GHz, and three frequencies near the 183-GHz water vapor resonance and the 60-GHz oxygen band, which is sensitive to the atmospheric temperature profile. Humidity profiles from the tropical, midlatitude, and arctic regions were retrieved. Relative humidity profiles retrieved using the statistical iterative method typically had errors between 5 and 10% in the 300-1000 mbar pressure region. These errors were somewhat less in the tropics and greater in the polar regions, and represented significantly better performances than a linear statistical retrieval method.>

An experiment in which the third Stokes parameter thermal emission from a periodic water surface was measured is documented. This parameter is shown to be related to the direction of periodicity of the periodic surface and to approach brightnesses of up to 30 K at X-band for the surface used in the experiment. The surface actually analyzed was a "two-layer" periodic surface; the theory of thermal emission from such a surface is derived and the theoretical results are found to be in good agreement with the experimental measurements. These results further the idea of using the third Stokes parameter emission as an indicator of wind direction over the ocean.>

Algorithms are developed simultaneously with systolic architectures for multidimensional adaptive filtering Because of the extremely high data rate required for real-time video processing, there is a strong motivation to limit the size of any adaptation problem. Combining the McClellan transformations with systolic arrays to adapt and implement the least-squares filter yields a novel solution to the problem of adapting a large zero-phase finite impulse response (FIR) multidimensional filter, having arbitrary directional biases, with only a few parameters. These filters can be adapted abruptly on a block-by-block basis without causing blocking effects. After developing a basic processing element for a systolic array realization of the Chebyshev structure for the McClellan transformation, it is shown that for a given 2-D transformation function, the adaptation of the 1-D prototype filter becomes a small multichannel adaptation problem similar to adaptive array problems. A similar approach is also taken in developing algorithms to adapt the 2-D transformation function.>

The McClellan transformation is developed as an efficient parametrization for a least-squares (LS) adaptive filter. It is shown that the McClellan transformation is a decomposition that roughly corresponds to separating the specification of a multidimensional filter into a normal component, parameterized by the 1D prototype filter, and a tangential component, parameterized by the transformation function. Such a decomposition gives an adaptive system the potential to exploit directional biases in any direction, as opposed to separable filters, which have their symmetry constrained by the two fixed axes. Using the Chebychev recursive implementation of the McClellan transformation, it is also shown that for a given transformation function, the adaptation of the 1D prototype filter becomes a small vector-adaptation problem, similar to adaptive-array problems. For real-time LS block adaptation, such an adaptation algorithm can be performed efficiently using systolic arrays.>

Traditional block transform image coding systems generate artifacts near block boundaries which degrade low bit rate coded images. To reduce these artifacts, a class of unitary transformations, called lapped orthogonal transforms (LOT), is investigated. The basis function on which the signal is projected are overlapped for adjacent blocks. An example of an LOT optimized in terms of energy compaction is numerically derived, using an augmented Lagrangian optimization algorithm. Using this LOT, intraframe coding experiments for 256*240 pixel images were performed at bit rates between 0.1 and 0.35 bits/pixel. The LOT improved the coded image subjective quality over other transforms. The LOT was also used in interframe full-motion video coding experiments for head and shoulder sequences at 28 and 56 kb/s. Significant improvement resulted at low data rates and if no motion compensation were used. However, the improvement was no longer significant at 56 kb/s with full motion compensation.>

A new derivation for the lapped orthogonal transform (LOT) is presented. It has basis functions that overlap adjacent blocks and decay smoothly to zero, and so it can reduce the blocking effect to very low levels, without any data overhead. It is shown that a quasioptimal LOT can be computed with an algorithm based on the discrete cosine transform (DCT), with only 30% more computation than the DCT. Unlike earlier approaches to the reduction of blocking effects, there is no penalty in coding gain for the LOT, which actually increases the coding gain by 0.25 dB for a first-order Markov process with rho =0.95.>

A set of adaptive transform coding schemes is developed that is based on a family of composite block source models for imagery. An iterative maximum-likelihood algorithm is developed for resolving model parameters from training set data. Both unconstrained (adaptive transform, adaptive quantization) and constrained (fixed transform, adaptive quantization) coders are obtained from the image model parameters. The resulting coders give excellent performance in coding test imagery at a variety of bit rates, and they consistently outperform the adaptive transform coders of W.H. Chen and C.H. Smith (1977). For example, a 2-dB improvement over the Chen and Smith scheme is obtained with a constrained coder with 128 classes operating at 0.5 bits/pixel. Computational limitations inhibit the design of unconstrained order with more than approximately 15 classes.>

A technique for the design of finite-impulse-response (FIR) filters for decimation and interpolation in multirate systems is introduced. FIR prefilters and postfilters that jointly minimize a frequency-weighted mean-square error between the original and reconstructed signals can be designed. There is no need for ideal filter prototypes: the optimal pre-postfilter pair is determined from the signal and noise spectra and the up-sampling and down-sampling factors. Some examples of image and speech processing show that the mean square optimal filter pair leads to typical SNR improvements of 2-6 dB, in comparison to other commonly used filters.>

The short-space Fourier transform (SSFT) is introduced as a means of describing discrete multi-dimensional signals of finite extent. It is an adaptation of the short-time Fourier transform developed for one-dimensional infinite-duration signals such as speech. By reflectively extending the finite signal segment, one can imagine an infinite duration signal which is "continuous." The proposed SSFT is the multidimensional generalization of the short-time Fourier transform operating upon the resulting infinite duration signal. Because boundary "discontinuities" are avoided, the proposed SSFT provides a transform representation free of extraneous spectral energy. An efficient algorithm for computing the SSET is described. SSFT image coding, an important application of the new transform method, provides localized spectral information without the undesirable phenomenon of "blocking effects."