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NASA NTRS2006

Measuring Constraint-Set Utility for Partitional Clustering Algorithms

Clustering with constraints is an active area of machine learning and data mining research. Previous empirical work has convincingly shown that adding constraints to clustering improves the performance of a variety of algorithms. However, in most of these experiments, results are averaged over different randomly chosen constraint sets from a given set of labels, thereby masking interesting properties of individual sets. We demonstrate that constraint sets vary significantly in how useful they are for constrained clustering; some constraint sets can actually decrease algorithm performance. We create two quantitative measures, informativeness and coherence, that can be used to identify useful constraint sets. We show that these measures can also help explain differences in performance for four particular constrained clustering algorithms.

constraints↗

NASA NTRS2012

Using Information From Prior Satellite Scans to Improve Cloud Detection Near the Day-Night Terminator

With geostationary satellite data it is possible to have a continuous record of diurnal cycles of cloud properties for a large portion of the globe. Daytime cloud property retrieval algorithms are typically superior to nighttime algorithms because daytime methods utilize measurements of reflected solar radiation. However, reflected solar radiation is difficult to accurately model for high solar zenith angles where the amount of incident radiation is small. Clear and cloudy scenes can exhibit very small differences in reflected radiation and threshold-based cloud detection methods have more difficulty setting the proper thresholds for accurate cloud detection. Because top-of-atmosphere radiances are typically more accurately modeled outside the terminator region, information from previous scans can help guide cloud detection near the terminator. This paper presents an algorithm that uses cloud fraction and clear and cloudy infrared brightness temperatures from previous satellite scan times to improve the performance of a threshold-based cloud mask near the terminator. Comparisons of daytime, nighttime, and terminator cloud fraction derived from Geostationary Operational Environmental Satellite (GOES) radiance measurements show that the algorithm greatly reduces the number of false cloud detections and smoothes the transition from the daytime to the nighttime clod detection algorithm. Comparisons with the Geoscience Laser Altimeter System (GLAS) data show that using this algorithm decreases the number of false detections by approximately 20 percentage points.

Yost, Christopher R.↗

NASA NTRS1992

A comparison of three SAR interference filters

Three interference filters are discussed and their ability to remove the interference while leaving target signal data is quantified. The filters are adaptive frequency-domain spike filtering; adaptive frequency-domain interference determination and masking; and interference-target correlation masking. Using Jet Propulsion Laboratory Airborne Synthetic Aperture Radar (JPL AIRSAR) data, the algorithms are applied to three data sets. The resultant compressed Stokes matrix data are compared with the normally processed interference-free image in a quantitative sense. The algorithms are evaluated by measuring the polarization signature, SNR, equivalent number of looks, and impulse response of the processed images.

Chapman, B.↗

NASA NTRS2011

Current Status of Multi-Angle Implementation of Atmospheric Correction (MAIAC) Algorithm

A new Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm has been developed for MODIS. MAIAC uses a time series and an image based rather than pixel-based processing to perform simultaneous retrievals of aerosol properties and surface bidirectional reflectance. It is a generic algorithm which works over all land surface types with the exception of snow. MAIAC has an internal Cloud Mask, a dynamic land-water-snow classification and a surface change mask which allows it to flexibly choose processing path over different surfaces. A distinct feature of MAIAC is a high 1 km resolution of aerosol retrievals including optical thickness and fine mode fraction, which is required in different applications including the air quality analysis. An overview of the algorithm, results of AERONET validation, and examples of comparison with MODIS Collection 5 aerosol product, including Deep Blue algorithm, will be presented for different parts of the world including continental USA, Persian Gulf region and India.

Lyapustin, A.↗

NASA NTRS2021

A Dark Target research aerosol algorithm for MODIS observations over eastern China: increasing coverage while maintaining accuracy at high aerosol loading

Satellite aerosol products such as the Dark Target (DT) produced from the MODerate resolution Imaging Spectroradiometer (MODIS) are useful for monitoring the progress of air pollution. Unfortunately, the DT often fails to retrieve during the heaviest aerosol events as well as the more moderate events in winter. Some of the literature at-tributes this lack of retrieval to the cloud mask. However, we found this lack of retrieval is mainly traced to thresholds used for masking of inland water and snow. Modifications to these two masks greatly increase 50 % of the retrievals of aerosol optical depth at 0.55 μm (AOD) greater than 1.0. The “extra”-high-AOD retrievals tend to be biased when com-pared with a ground-based sun photometer (AErosol RObotic NETwork, AERONET). Reducing bias in new retrievals re-quires two additional steps. One is an update to the assumed aerosol optical properties (aerosol model); the haze in this region is both less absorbing and lower in altitude than what is assumed in the global algorithm. The second is account-ing for the scale height of the aerosol, specifically that the heavy-aerosol events in the region are much closer to the surface than what is assumed by the global DT algorithm. The resulting combination of modified masking thresholds, new aerosol model, and lower aerosol layer scale height was applied to 3 months of MODIS observations (January–March2013) over eastern China. After these two additional steps are implemented, the significant increase in new retrievals introduces no overall bias at a high-AOD regime but does degrade other overall validation statistics. We also find that the research algorithm is able to identify additional pollution events that AERONET instruments may not due to different spatial sampling. Mean AOD retrieved from the re-search algorithm increases from 0.11 to 0.18 compared to values calculated from the operational DT algorithm during January to March of 2013 over the study area. But near Beijing, where the severe pollution occurs, the new algorithm increases AOD by as much as 3.0 for each 0.5°grid box over the previous operational-algorithm values.

Dark Target↗

NASA NTRS2019

An Automatic Light Rain Detection Algorithm on NASA MPLNET Lidar Observations in the Frame of WMO GALION Project

The water cycle strongly influences life on Earth. In particular, the precipitation modifies the atmospheric column thermodynamics through the process of evaporation and serves as a proxy for latent heat modulation. For this reason, a correct precipitation parameterization (especially low-intensity precipitation) at global scale, bedsides improving our understanding of the hydrological cycle, it is crucial to reduce the associated uncertainty of the global climate models to correctly forecast future scenarios, i.e. to apply fast mitigation strategies. In this study we developed an algorithm to automatically detect precipitation from lidar measurements obtained by the National and Aeronautics Space Administration (NASA) Micropulse lidar network (MPLNET) permanent observational site in Goddard. The algorithm, once full operational, will deliver in Near Real Time (latency 1.5h) a new rain mask product that will be publicly available on MPLNET website as part of the new Version 3 Level 1.5 data. The methodology, based on an image processing technique, can detect only light precipitation events (defined by intensity and duration) as the morphological filters used through the detection process are applied on the lidar volume depolarization ratio range corrected composite images, i.e. heavy rain events are unusable as the lidar signal is completely extinguished after few meters in the precipitation or no signal detected because of the water accumulated on the receiver optics. Results from the algorithm, besides filling a gap in precipitation and virga detection by radars, are of particular interest for the scientific community because will help to better understand long-term aerosol-cloud interactions and aerosol atmospheric removal (scavenging effect) by rain as multi-year database being available for several MPLNET permanent observational sites across the globe. Moreover, we developed the automatic algorithm at Universitat Politecnica de Catalunya (UPC) Barcelona, the unique permanent observation station member of MPLNET and the European Aerosol Lidar Network (EARLINET) In the future the algorithm can be then easily applied to any other lidar and/or ceilometer network infrastructure in the frame of World Meteorological Organization (WMO) Global Aerosol Watch (GAW) aerosol lidar observation network (GALION)

Simone Lolli↗

NASA NTRS2012

HCIT Broadband Contrast Performance Sensitivity Studies

The High Contrast Imaging Testbed (HCIT) at the Jet Propulsion Laboratory employs a broadband wavefront correction algorithm called Electric Field Conjugation (EFC) to obtain the required 10-10 contrast. This algorithm works with one deformable mirror (DM) to estimate the electric-field to be controlled, and with one or multiple DM's to create a "darkhole" in a predefined region of the image plane where terrestrial planets would be found. We have investigated the effects of absorbing dust particles on a flat optic, absorbing spots on the occulting mask, dead actuators on the DM, and the effects of control bandwidth on the efficiency of the EFC algorithm in a Lyot coronagraph configuration. The structural design of the optical system as well as the parameters of various optical elements used in the analysis is drawn from those of the HCIT system that have been implemented with one DM. The simulation takes into account the surface errors of various optical elements. Results of some of these studies have been verified by actual measurements.

Coronagraphy↗

NASA NTRS2004

The Geostationary Operational Environmental Satellite (GOES) Product Generation System

The Geostationary Operational Environmental Satellite (GOES) Product Generation System (GPGS) is introduced and described. GPGS is a set of computer programs developed and maintained at the Global Hydrology and Climate Center and is designed to generate meteorological data products using visible and infrared measurements from the GOES-East Imager and Sounder instruments. The products that are produced by GPGS are skin temperature, total precipitable water, cloud top pressure, cloud albedo, surface albedo, and surface insolation. A robust cloud mask is also generated. The retrieval methodology for each product is described to include algorithm descriptions and required inputs and outputs for the programs. Validation is supplied where applicable.

Haines, S. L.↗

NASA NTRS2015

Zernike Wavefront Sensor Modeling Development for LOWFS on WFIRST-AFTA

WFIRST-AFTA design makes use of an existing 2.4m telescope for direct imaging of exoplanets. To maintain the high contrast needed for the coronagraph, wavefront error (WFE) of the optical system needs to be continuously sensed and controlled. Low Order Wavefront Sensing (LOWFS) uses the rejected starlight from an immediate focal plane to sense wavefront changes (mostly thermally induced low order WFE) by combining the LOWFS mask (a phase plate located at the small center region with reflective layer) with the starlight rejection masks, i.e. Hybrid Lyot Coronagraph (HLC)'s occulter or Shaped Pupil Coronagraph (SPC)'s field stop. Zernike wavefront sensor (ZWFS) measures phase via the phase-contrast method and is known to be photon noise optimal for measuring low order aberrations. Recently, ZWFS was selected as the baseline LOWFS technology on WFIST/AFTA for its good sensitivity, accuracy, and its easy integration with the starlight rejection mask. In this paper, we review the theory of ZWFS operation, describe the ZWFS algorithm development, and summarize various numerical sensitivity studies on the sensor performance. In the end, the predicted sensor performance on SPC and HLC configurations are presented.

Zernike phase contrast↗

NASA NTRS2013

The Collection 6 'dark-target' MODIS Aerosol Products

Aerosol retrieval algorithms are applied to Moderate resolution Imaging Spectroradiometer (MODIS) sensors on both Terra and Aqua, creating two streams of decade-plus aerosol information. Products of aerosol optical depth (AOD) and aerosol size are used for many applications, but the primary concern is that these global products are comprehensive and consistent enough for use in climate studies. One of our major customers is the international modeling comparison study known as AEROCOM, which relies on the MODIS data as a benchmark. In order to keep up with the needs of AEROCOM and other MODIS data users, while utilizing new science and tools, we have improved the algorithms and products. The code, and the associated products, will be known as Collection 6 (C6). While not a major overhaul from the previous Collection 5 (C5) version, there are enough changes that there are significant impacts to the products and their interpretation. In its entirety, the C6 algorithm is comprised of three sub-algorithms for retrieving aerosol properties over different surfaces: These include the dark-target DT algorithms to retrieve over (1) ocean and (2) vegetated-dark-soiled land, plus the (3) Deep Blue (DB) algorithm, originally developed to retrieve over desert-arid land. Focusing on the two DT algorithms, we have updated assumptions for central wavelengths, Rayleigh optical depths and gas (H2O, O3, CO2, etc.) absorption corrections, while relaxing the solar zenith angle limit (up to 84) to increase pole-ward coverage. For DT-land, we have updated the cloud mask to allow heavy smoke retrievals, fine-tuned the assignments for aerosol type as function of season location, corrected bugs in the Quality Assurance (QA) logic, and added diagnostic parameters such as topographic altitude. For DT-ocean, improvements include a revised cloud mask for thin-cirrus detection, inclusion of wind speed dependence in the retrieval, updates to logic of QA Confidence flag (QAC) assignment, and additions of important diagnostic information. At the same time as we have introduced algorithm changes, we have also accounted for upstream changes including: new instrument calibration, revised land-sea masking, and changed cloud masking. Upstream changes also impact the coverage and global statistics of the retrieved AOD. Although our responsibility is to the DT code and products, we have also added a product that merges DT and DB product over semi-arid land surfaces to provide a more gap-free dataset, primarily for visualization purposes. Preliminary validation shows that compared to surface-based sunphotometer data, the C6, Level 2 (along swath) DT-products compare at least as well as those from C5. C6 will include new diagnostic information about clouds in the aerosol field, including an aerosol cloud mask at 500 m resolution, and calculations of the distance to the nearest cloud from clear pixels. Finally, we have revised the strategy for aggregating and averaging the Level 2 (swath) data to become Level 3 (gridded) data. All together, the changes to the DT algorithms will result in reduced global AOD (by 0.02) over ocean and increased AOD (by 0.02) over land, along with changes in spatial coverage. Changes in calibration will have more impact to Terras time series, especially over land. This will result in a significant reduction in artificial differences in the Terra and Aqua datasets, and will stabilize the MODIS data as a target for AEROCOM studie

Aerosol retrieval algorithms↗

NASA NTRS1998

Algorithms and Libraries

This exploratory study initiated our inquiry into algorithms and applications that would benefit by latency tolerant approach to algorithm building, including the construction of new algorithms where appropriate. In a multithreaded execution, when a processor reaches a point where remote memory access is necessary, the request is sent out on the network and a context--switch occurs to a new thread of computation. This effectively masks a long and unpredictable latency due to remote loads, thereby providing tolerance to remote access latency. We began to develop standards to profile various algorithm and application parameters, such as the degree of parallelism, granularity, precision, instruction set mix, interprocessor communication, latency etc. These tools will continue to develop and evolve as the Information Power Grid environment matures. To provide a richer context for this research, the project also focused on issues of fault-tolerance and computation migration of numerical algorithms and software. During the initial phase we tried to increase our understanding of the bottlenecks in single processor performance. Our work began by developing an approach for the automatic generation and optimization of numerical software for processors with deep memory hierarchies and pipelined functional units. Based on the results we achieved in this study we are planning to study other architectures of interest, including development of cost models, and developing code generators appropriate to these architectures.

Dongarra, Jack↗

NASA NTRS2010

Assessing the Relative Performance of Microwave-Based Satellite Rain Rate Retrievals Using TRMM Ground Validation Data

Space-borne microwave sensors provide critical rain information used in several global multi-satellite rain products, which in turn are used for a variety of important studies, including landslide forecasting, flash flood warning, data assimilation, climate studies, and validation of model forecasts of precipitation. This study employs four years (2003-2006) of satellite data to assess the relative performance and skill of SSM/I (F13, F14 and F15), AMSU-B (N15, N16 and N17), AMSR-E (Aqua) and the TRMM Microwave Imager (TMI) in estimating surface rainfall based on direct instantaneous comparisons with ground-based rain estimates from Tropical Rainfall Measuring Mission (TRMM) Ground Validation (GV) sites at Kwajalein, Republic of the Marshall Islands (KWAJ) and Melbourne, Florida (MELB). The relative performance of each of these satellite estimates is examined via comparisons with space- and time-coincident GV radar-based rain rate estimates. Because underlying surface terrain is known to affect the relative performance of the satellite algorithms, the data for MELB was further stratified into ocean, land and coast categories using a 0.25 terrain mask. Of all the satellite estimates compared in this study, TMI and AMSR-E exhibited considerably higher correlations and skills in estimating/observing surface precipitation. While SSM/I and AMSU-B exhibited lower correlations and skills for each of the different terrain categories, the SSM/I absolute biases trended slightly lower than AMSRE over ocean, where the observations from both emission and scattering channels were used in the retrievals. AMSU-B exhibited the least skill relative to GV in all of the relevant statistical categories, and an anomalous spike was observed in the probability distribution functions near 1.0 mm/hr. This statistical artifact appears to be related to attempts by algorithm developers to include some lighter rain rates, not easily detectable by its scatter-only frequencies. AMSU-B, however, agreed well with GV when the matching data was analyzed on monthly scales. These results signal developers of global rainfall products, such as the TRMM Multi-Satellite Precipitation Analysis (TMPA), and the Climate Data Center s Morphing (CMORPH) technique, that care must be taken when incorporating data from these input satellite estimates in order to provide the highest quality estimates in their products. 3

Wolff, David B.↗

NASA NTRS2008

Assessing the Relative Performance of Microwave-based Satellite Rain Rate Retrievals using TRMM Ground Validation Data

Space-borne microwave sensors provide critical rain information used in several global multi-satellite rain products, which in turn are used for a variety of important studies, including landslide forecasting, flash flood warning, data assimilation, climate studies, and validation of model forecast of precipitation. This study employs four years (2003-2006) of satellite data to assess the relative performance and skill of SSM/I (F13, F14 and F15), AMSU-B (N15, N16 and N17), AMSR-E (AQUA) and the TRMM Microwave Imager (TMI) in estimating surface rainfall based on direct instantaneous comparison with ground-based rain estimates from Tropical Rainfall Measuring Mission (TRMM) Ground Validation (GV) sites at Kwajalein, Republic of the Marshall Islands (KWAJ) and Melbourne, Florida (MELB). The relative performance of each of these satellites is examined via comparisons with GV radar-based rain rate estimates. Because underlying surface terrain is known to affect the relative performance of the satellite algorithms, the data for MELB was further stratified into ocean, land and coast categories using a 0.25 terrain mask. Of all the satellite estimates compared in this study, TMI and AMSR-E exhibited considerably higher correlations and skills in estimating/observing surface precipitation. While SSM/I and AMSU-B exhibited lower correlations and skills for each of the different terrain categories, the SSM/I absolute biases trended slightly lower than AMSRE over ocean, where the observations from both emission and scattering channels were used in the retrievals. AMSU-B exhibited the least skill relative to GV in all of the relevant statistical categories, and an anomalous spike was observed in the probability distribution functions near 1.0 mm hr-1. This statistical artifact appears to be related to attempts by algorithm developers to include some lighter rain rates, not easily detectable by its scatter-only frequencies. AMSU-B, however, agreed well with GV when the matching data was analyzed on monthly scales. These results signal developers of global rainfall products, such as the TRMM Multi-Satellite Precipitation Analysis (TMPA), and the Climate Data Center s Morphing (CMORPH) technique, that care must be taken when incorporating data from these input satellite estimates in order to provide the highest quality estimates in their products.

Wolff, David B.↗

NASA NTRS2017

Optimizing the Regularization in Broadband Wavefront Control Algorithm for WFIRST Coronagraph

The WFIRST/AFTA 2.4 m space telescope currently under study includes a stellar coronagraph for the imaging and the spectral characterization of extrasolar planets. The coronagraph employs sequential deformable mirrors to compensate for phase and amplitude errors. Using the optical model of an Occulting Mask Coronagraph (OMC) testbed at the Jet Propulsion Laboratory (JPL), we have investigated and compared through modeling and simulations the performance of several actuator regularization-schemes in broadband wavefront control algorithm used to generate dark holes in an OMC, such as a Hybrid Lyot Coronagraph (HLC). Using the concept of a Tikhonov filter constituting the G-matrix, we have explained what the different regularization schemes do to singular-modes during a wavefront control process called Electric Field Conjugation (EFC). In some cases we confirmed the numerical predictions with the testbed measured results. We present our findings in this paper.

Sidick, Erkin↗

NASA NTRS2021

Features and Characteristics of the New NASA MicroPuLse NETwork (MPLNET) Automatic Rain Detection Algorithm

S. Lolli↗

NASA NTRS2011

Assessing the Relative Performance of Microwave-Based Satellite Rain Rate Retrievals Using TRMM Ground Validation Data

Space-borne microwave sensors provide critical rain information used in several global multi-satellite rain products, which in turn are used for a variety of important studies, including landslide forecasting, flash flood warning, data assimilation, climate studies, and validation of model forecasts of precipitation. This study employs four years (2003-2006) of satellite data to assess the relative performance and skill of SSM/I (F13, F14 and F15), AMSU-B (N15, N16 and N17), AMSR-E (Aqua) and the TRMM Microwave Imager (TMI) in estimating surface rainfall based on direct instantaneous comparisons with ground-based rain estimates from Tropical Rainfall Measuring Mission (TRMM) Ground Validation (GV) sites at Kwajalein, Republic of the Marshall Islands (KWAJ) and Melbourne, Florida (MELB). The relative performance of each of these satellite estimates is examined via comparisons with space- and time-coincident GV radar-based rain rate estimates. Because underlying surface terrain is known to affect the relative performance of the satellite algorithms, the data for MELB was further stratified into ocean, land and coast categories using a 0.25deg terrain mask. Of all the satellite estimates compared in this study, TMI and AMSR-E exhibited considerably higher correlations and skills in estimating/observing surface precipitation. While SSM/I and AMSU-B exhibited lower correlations and skills for each of the different terrain categories, the SSM/I absolute biases trended slightly lower than AMSR-E over ocean, where the observations from both emission and scattering channels were used in the retrievals. AMSU-B exhibited the least skill relative to GV in all of the relevant statistical categories, and an anomalous spike was observed in the probability distribution functions near 1.0 mm/hr. This statistical artifact appears to be related to attempts by algorithm developers to include some lighter rain rates, not easily detectable by its scatter-only frequencies. AMSU-B, however, agreed well with GV when the matching data was analyzed on monthly scales. These results signal developers of global rainfall products, such as the TRMM Multi-Satellite Precipitation Analysis (TMPA), and the Climate Data Center s Morphing (CMORPH) technique, that care must be taken when incorporating data from these input satellite estimates in order to provide the highest quality estimates in their products.

Wolff, David B.↗

NASA NTRS2020

Dust Aerosol Retrieval Over the Oceans With the MODIS/VIIRS Dark‐Target Algorithm: 1. Dust Detection

To prepare for implementation of a new aerosol retrieval specifically designed for dust aerosol over ocean in the operational Dark-Target (DT) algorithms for the Moderate-resolution Imaging Spectrometer (MODIS) and Visible Infrared Imaging Radiometer Suite (VIIRS) satellite sensors, we focus on the challenge of detecting dust. We first survey the literature on existing dust detection algorithms and then develop an innovative algorithm that combines near-UV (deep blue), visible, and thermal infrared (TIR) wavelength spectral tests. The new detection algorithm is applied to Terra and Aqua MODIS granules and compared with other dust detection possibilities from existing MODIS products. Quantitative evaluation of the new dust detection algorithm is conducted using both a collocated AERONET-MODIS data set and collocated Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO)-MODIS data set. From comparison with both AERONET and CALIOP measurements, we estimate the new dust detection algorithm detects about 30% of weakly dusty pixels and more than 80% of heavily dusty pixels, with false detections in the range of 1–2%. The very low false detection rate is particularly noteworthy in comparison with existing literature. Compared with the dust flag currently available as part of the MODIS cloud mask product (MOD35/MYD35), and dust classification based on commonly used thresholds with aerosol optical depth (AOD) and Angstrom exponent (AE), the new dust detection algorithm finds more dusty pixels and fewer false detections.

spectral dust detection↗

NASA NTRS2008

Microwave Soil Moisture Retrieval Under Trees

Soil moisture is recognized as an important component of the water, energy, and carbon cycles at the interface between the Earth's surface and atmosphere. Current baseline soil moisture retrieval algorithms for microwave space missions have been developed and validated only over grasslands, agricultural crops, and generally light to moderate vegetation. Tree areas have commonly been excluded from operational soil moisture retrieval plans due to the large expected impact of trees on masking the microwave response to the underlying soil moisture. Our understanding of the microwave properties of trees of various sizes and their effect on soil moisture retrieval algorithms at L band is presently limited, although research efforts are ongoing in Europe, the United States, and elsewhere to remedy this situation. As part of this research, a coordinated sequence of field measurements involving the ComRAD (for Combined Radar/Radiometer) active/passive microwave truck instrument system has been undertaken. Jointly developed and operated by NASA Goddard Space Flight Center and George Washington University, ComRAD consists of dual-polarized 1.4 GHz total-power radiometers (LH, LV) and a quad-polarized 1.25 GHz L band radar sharing a single parabolic dish antenna with a novel broadband stacked patch dual-polarized feed, a quad-polarized 4.75 GHz C band radar, and a single channel 10 GHz XHH radar. The instruments are deployed on a mobile truck with an 19-m hydraulic boom and share common control software; real-time calibrated signals, and the capability for automated data collection for unattended operation. Most microwave soil moisture retrieval algorithms developed for use at L band frequencies are based on the tau-omega model, a simplified zero-order radiative transfer approach where scattering is largely ignored and vegetation canopies are generally treated as a bulk attenuating layer. In this approach, vegetation effects are parameterized by tau and omega, the microwave vegetation opacity and single scattering albedo. One goal of our current research is to determine whether the tau-omega model can work for tree canopies given the increased scatter from trees compared to grasses and crops, and. if so, what are effective values for tau and omega for trees.

O'Neill, P.↗