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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Evaluating cloud liquid detection against Cloudnet using cloud radar Doppler spectra in a pre-trained artificial neural network

Detection of liquid-containing cloud layers in thick mixed-phase clouds or multi-layer cloud situations from ground-based remote-sensing instruments still poses observational challenges, yet improvements are crucial since the existence of multi-layer liquid layers in mixed-phase cloud situations influences cloud radiative effects, cloud lifetime, and precipitation formation processes. Hydrometeor target classifications such as from Cloudnet that require a lidar signal for the classification of liquid are limited to the maximum height of lidar signal penetration and thus often lead to underestimations of liquid-containing cloud layers. Here we evaluate the Cloudnet liquid detection against the approach of Luke et al. (2010) which extracts morphological features in cloud-penetrating cloud radar Doppler spectra measurements in an artificial neural network (ANN) approach to classify liquid beyond full lidar signal attenuation based on the simulation of the two lidar parameters particle backscatter coefficient and particle depolarization ratio. We show that the ANN of Luke et al. (2010) which was trained under Arctic conditions can successfully be applied to observations at the mid-latitudes obtained during the 7-week-long ACCEPT field experiment in Cabauw, the Netherlands, in 2014. In a sensitivity study covering the whole duration of the ACCEPT campaign, different liquid-detection thresholds for ANN-predicted lidar variables are applied and evaluated against the Cloudnet target classification. Independent validation of the liquid mask from the standard Cloudnet target classification against the ANN-based technique is realized by comparisons to observations of microwave radiometer liquid-water path, ceilometer liquid-layer base altitude, and radiosonde relative humidity. In addition, a case-study comparison against the cloud feature mask detected by the space-borne lidar aboard the CALIPSO satellite is presented. Three conclusions were drawn from the investigation. First, it was found that the threshold selection criteria of liquid-related lidar backscatter and depolarization alone control the liquid detection considerably. Second, all threshold values used in the ANN framework were found to outperform the Cloudnet target classification for deep or multi-layer cloud situations where the lidar signal is fully attenuated within low liquid layers and the cloud radar is able to detect the microphysical fingerprint of liquid in higher cloud layers. Third, if lidar data are available, Cloudnet is at least as good as the ANN. The times when Cloudnet outperforms the ANN in liquid detections are often associated with situations where cloud dynamics smear the imprint of cloud microphysics on the radar Doppler spectra.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2012

Validation of Satellite-Based Objective Overshooting Cloud-Top Detection Methods Using CloudSat Cloud Profiling Radar Observations

Two satellite infrared-based overshooting convective cloud-top (OT) detection methods have recently been described in the literature: 1) the 11-mm infrared window channel texture (IRW texture) method, which uses IRW channel brightness temperature (BT) spatial gradients and thresholds, and 2) the water vapor minus IRW BT difference (WV-IRW BTD). While both methods show good performance in published case study examples, it is important to quantitatively validate these methods relative to overshooting top events across the globe. Unfortunately, no overshooting top database currently exists that could be used in such study. This study examines National Aeronautics and Space Administration CloudSat Cloud Profiling Radar data to develop an OT detection validation database that is used to evaluate the IRW-texture and WV-IRW BTD OT detection methods. CloudSat data were manually examined over a 1.5-yr period to identify cases in which the cloud top penetrates above the tropopause height defined by a numerical weather prediction model and the surrounding cirrus anvil cloud top, producing 111 confirmed overshooting top events. When applied to Moderate Resolution Imaging Spectroradiometer (MODIS)-based Geostationary Operational Environmental Satellite-R Series (GOES-R) Advanced Baseline Imager proxy data, the IRW-texture (WV-IRW BTD) method offered a 76% (96%) probability of OT detection (POD) and 16% (81%) false-alarm ratio. Case study examples show that WV-IRW BTD.0 K identifies much of the deep convective cloud top, while the IRW-texture method focuses only on regions with a spatial scale near that of commonly observed OTs. The POD decreases by 20% when IRW-texture is applied to current geostationary imager data, highlighting the importance of imager spatial resolution for observing and detecting OT regions.

Bedka, Kristopher M.↗
NASA NTRS1990

Molecular clouds without detectable CO

The clouds identified by Desert, Bazell, and Boulanger (DBB clouds) in their search for high-latitude molecular clouds were observed in the CO (J = 1-0) line, but only 13 percent of the sample was detected. The remaining 87 percent are diffuse molecular clouds with CO abundances of about 10 to the -6th, a typical value for diffuse clouds. This hypothesis is shown to be consistent with Copernicus data. The DBB clouds are shown to ben an essentially complete catalog of diffuse molecular clouds in the solar vicinity. The total molecular surface density in the vicinity of the sun is then only about 20 percent greater than the 1.3 solar masses/sq pc determined by Dame et al. (1987). Analysis of the CO detections indicates that there is a sharp threshold in extinction of 0.25 mag before CO is detectable and is derived from the IRAS I(100) micron threshold of 4 MJy/sr. This threshold is presumably where the CO abundance exhibits a sharp increase

Blitz, Leo↗
NASA NTRS1994

Analysis of cloud top height and cloud coverage from satellites using the O2 A and B bands

Cloud height and cloud coverage detection are important for total ozone retrieval using ultraviolet and visible scattered light. Use of the O2 A and B bands, around 761 and 687 nm, by a satellite-borne instrument of moderately high spectral resolution viewing in the nadir makes it possible to detect cloud top height and related parameters, including fractional coverage. The measured values of a satellite-borne spectrometer are convolutions of the instrument slit function and the atmospheric transmittance between cloud top and satellite. Studies here determine the optical depth between a satellite orbit and the Earth or cloud top height to high accuracy using FASCODE 3. Cloud top height and a cloud coverage parameter are determined by least squares fitting to calculated radiance ratios in the oxygen bands. A grid search method is used to search the parameter space of cloud top height and the coverage parameter to minimize an appropriate sum of squares of deviations. For this search, nonlinearity of the atmospheric transmittance (i.e., leverage based on varying amounts of saturation in the absorption spectrum) is important for distinguishing between cloud top height and fractional coverage. Using the above-mentioned method, an operational cloud detection algorithm which uses minimal computation time can be implemented.

Kuze, Akihiko↗
NASA NTRS1999

Raman LIDAR Detection of Cloud Base

Advantages introduced by Raman lidar systems for cloud base determination during precipitating periods are explored using two case studies of light rain and virga conditions. A combination of the Raman lidar derived profiles of water vapor mixing ratio and aerosol scattering ratio, together with the Raman scattered signals from liquid drops, can minimize or even eliminate some of the problems associated with cloud boundary detection using elastic backscatter lidars.

Demoz, Belay↗
NASA NTRS2015

Automated Point Cloud Correspondence Detection for Underwater Mapping Using AUVs

An algorithm for automating correspondence detection between point clouds composed of multibeam sonar data is presented. This allows accurate initialization for point cloud alignment techniques even in cases where accurate inertial navigation is not available, such as iceberg profiling or vehicles with low-grade inertial navigation systems. Techniques from computer vision literature are used to extract, label, and match keypoints between "pseudo-images" generated from these point clouds. Image matches are refined using RANSAC and information about the vehicle trajectory. The resulting correspondences can be used to initialize an iterative closest point (ICP) registration algorithm to estimate accumulated navigation error and aid in the creation of accurate, self-consistent maps. The results presented use multibeam sonar data obtained from multiple overlapping passes of an underwater canyon in Monterey Bay, California. Using strict matching criteria, the method detects 23 between-swath correspondence events in a set of 155 pseudo-images with zero false positives. Using less conservative matching criteria doubles the number of matches but introduces several false positive matches as well. Heuristics based on known vehicle trajectory information are used to eliminate these.

Sonar↗
NASA NTRS1998

The detection of clouds, aerosols and marine atmospheric boundary layer characteristics from simulated GLAS data

Scheduled for launch in 2001 as part of NASA's Earth Observing System (EOS), the Geoscience Laser Altimeter System (GLAS) will provide continuous laser sounding of the earth's atmosphere from space for the first time. From its polar orbit about 600 km above the surface, GLAS will employ a 40 Hz solid state laser operating at 1064 nm to measure topography to an accuracy of 10 cm. Simultaneously, the atmospheric channels (1064 and 532 nm) of GLAS will provide profiles of atmospheric backscatter from 40 km to the ground with 75 meter vertical resolution (Spinhirne and Palm, 1996). These measurements will give scientists an unprecedented global data set on the vertical structure of clouds and aerosols which will greatly aid research efforts aimed at understanding their effects on climate and their role in climate change (Hartman, 1994). To better understand and predict the performance of the GLAS atmospheric channels, a computer model was developed to simulate the type of signal that the instrument would likely produce. The model uses aircraft lidar data and provides realistic simulated GLAS data sets over large areas spanning a wide range of atmospheric conditions. These simulated GLAS datasets are invaluable for designing and testing algorithms for the retrieval of parameters such as cloud and aerosol layer height, optical depth and extinction cross section. This work is currently proceeding and in this paper we will present results of the cloud and aerosol detection algorithm with emphasis on the detection of Marine Atmospheric Boundary Layer (MABL) aerosol. In addition, we use a recently developed technique to ascertain the feasability of estimating MABL moisture and temperature structure from spaceborne systems such as GLAS.

Palm, Stephen P.↗
NASA NTRS2022

Cloud Mask Intercomparison eXercise (CMIX): An evaluation of cloud masking algorithms for Landsat 8 and Sentinel-2

Cloud cover is a major limiting factor in exploiting time-series data acquired by optical spaceborne remote sensing sensors. Multiple methods have been developed to address the problem of cloud detection in satellite imagery and a number of cloud masking algorithms have been developed for optical sensors but very few studies have carried out quantitative intercomparison of state-of-the-art methods in this domain. This paper summarizes results of the first Cloud Masking Intercomparison eXercise (CMIX) conducted within the Committee Earth Observation Satellites (CEOS) Working Group on Calibration & Validation (WGCV). CEOS is the forum for space agency coordination and cooperation on Earth observations, with activities organized under working groups. CMIX, as one such activity, is an international collaborative effort aimed at intercomparing cloud detection algorithms for moderate-spatial resolution (10–30 m) spaceborne optical sensors. The focus of CMIX is on open and free imagery acquired by the Landsat 8 (NASA/USGS) and Sentinel-2 (ESA) missions. Ten algorithms developed by nine teams from fourteen different organizations representing universities, research centers and industry, as well as space agencies (CNES, ESA, DLR, and NASA), are evaluated within the CMIX. Those algorithms vary in their approach and concepts utilized which were based on various spectral properties, spatial and temporal features, as well as machine learning methods. Algorithm outputs are evaluated against existing reference cloud mask datasets. Those datasets vary in sampling methods, geographical distribution, sample unit (points, polygons, full image labels), and generation approaches (experts, machine learning, sky images). Overall, the performance of algorithms varied depending on the reference dataset, which can be attributed to differences in how the reference datasets were produced. The algorithms were in good agreement for thick cloud detection, which were opaque and had lower uncertainties in their identification, in contrast to thin/semi-transparent clouds detection. Not only did CMIX allow identification of strengths and weaknesses of existing algorithms and potential areas of improvements, but also the problems associated with the existing reference datasets. The paper concludes with recommendations on generating new reference datasets, metrics, and an analysis framework to be further exploited and additional input datasets to be considered by future CMIX activities.

Sergii Skakun↗
DOE OSTI2024

Broadband and filter radiometers at Ross Island, Antarctica: detection of cloud ice phase versus liquid water influences on shortwave and longwave radiation

Abstract. Surface radiometer data from Ross Island, Antarctica, collected during the austral summer 2015–2016 by the US Department of Energy Atmospheric Radiation Measurement (ARM) program West Antarctic Radiation Experiment (AWARE), are used to evaluate how shortwave and longwave irradiance respond to changing cloud properties as governed by contrasting meteorological regimes. Shortwave atmospheric transmittance is derived from pyranometer measurements, and cloud conservative-scattering optical depth is derived from filter radiometer measurements at 870 nm. With onshore flow associated with marine air masses, clouds contain mostly liquid water. With southerly flow over the Transantarctic Mountains, orographic forcing induces substantial cloud ice water content. These ice and mixed-phase clouds attenuate more surface shortwave irradiance than the maritime-influenced clouds and also emit less longwave irradiance due to colder cloud base temperature. These detected irradiance changes are in a range that can mean onset or inhibition of surface melt over ice shelves. This study demonstrates how basic and relatively low-cost broadband and filter radiometers can be used to detect subtle climatological influences of contrasting cloud microphysical properties at very remote locations.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2001

Cloud Overlapping Detection Algorithm Using Solar and IR Wavelengths With GOSE Data Over ARM/SGP Site

One of the most perplexing problems in satellite cloud remote sensing is the overlapping of cloud layers. Although most techniques assume a 1-layer cloud system in a given retrieval of cloud properties, many observations are affected by radiation from more than one cloud layer. As such, cloud overlap can cause errors in the retrieval of many properties including cloud height, optical depth, phase, and particle size. A variety of methods have been developed to identify overlapped clouds in a given satellite imager pixel. Baum el al. (1995) used CO2 slicing and a spatial coherence method to demonstrate a possible analysis method for nighttime detection of multilayered clouds. Jin and Rossow (1997) also used a multispectral CO2 slicing technique for a global analysis of overlapped cloud amount. Lin et al. (1999) used a combination infrared, visible, and microwave data to detect overlapped clouds over water. Recently, Baum and Spinhirne (2000) proposed 1.6 and 11 microns. bispectral threshold method. While all of these methods have made progress in solving this stubborn problem, none have yet proven satisfactory for continuous and consistent monitoring of multilayer cloud systems. It is clear that detection of overlapping clouds from passive instruments such as satellite radiometers is in an immature stage of development and requires additional research. Overlapped cloud systems also affect the retrievals of cloud properties over the ARM domains (e.g., Minnis et al 1998) and hence should identified as accurately as possible. To reach this goal, it is necessary to determine which information can be exploited for detecting multilayered clouds from operational meteorological satellite data used by ARM. This paper examines the potential information available in spectral data available on the Geostationary Operational Environmental Satellite (GOES) imager and the NOAA Advanced Very High Resolution Radiometer (AVHRR) used over the ARM SGP and NSA sites to study the capability of detecting overlapping clouds

Kawamoto, Kazuaki↗
NASA NTRS2001

Cloud Overlapping Detection Algorithm Using Solar and IR Wavelengths with GOES Data Over ARM/SGP Site

One of the most perplexing problems in satellite cloud remote sensing is the overlapping of cloud layers. Although most techniques assume a one layer cloud system in a given retrieval of cloud properties, many observations are affected by radiation from more than one cloud layer. As such, cloud overlap can cause errors in the retrieval of many properties including cloud height, optical depth, phase, and particle size. A variety of methods have been developed to identify overlapped clouds in a given satellite imager pixel. Baum et al used CO2 slicing and a spatial coherence method to demonstrate a possible analysis method for nighttime detection of multilayered clouds. Jin and Rossow also used a multispectral CO2 slicing technique for a global analysis of overlapped cloud amount. Lin et al. used a combination infrared (IR), visible (VIS), and microwave data to detect overlapped clouds over water. Recently, Baum and Spinhirne proposed a 1.6 and 11 micron bispectral threshold method. While all of these methods have made progress in solving this stubborn problem none have yet proven satisfactory for continuous and consistent monitoring of multilayer cloud systems. It is clear that detection of overlapping clouds from passive instruments such as satellite radiometers is in an immature stage of development and requires additional research. Overlapped cloud systems also affect the retrievals of cloud properties over the Atmospheric Radiation Measurement (ARM) domains and hence should be identified as accurately as possible. To reach this goal, it is necessary to determine which information can be exploited for detecting multilayered clouds from operational meteorological satellite data used by ARM. This paper examines the potential information available in spectral data available on the Geostationary Operational Environmental Satellite (GOES) imager and the National Oceanic Atmospheric Administration (NOAA) Advanced Very High Resolution Radiometer (AVHRR) used over the ARM Program's Southern Great Plains (SGP), and North Slope of Alaska (NSA) sites to study the capability of detecting overlapping clouds.

Kawamoto, K.↗
NASA NTRS2012

HyspIRI Cloud Mask Detection Algorithm Theoretical Basis Document

The Hyperspectral Infrared Imager (HyspIRI) satellite includes a thermal infrared (TIR) multispectral scanner with seven spectral bands in the thermal infrared (TIR) between 7 and 12 μm and one band in the mid-infrared between 3 and 5 μm designed to measure hot targets. The TIR bands have a NEΔT of <0.2 K at 300K and all bands have a spatial scale of 60 m. The two primary Level-2 products that will be generated by HyspIRI TIR data are land surface temperature and emissivity. A critical aspect of minimizing uncertainties in these products and in generating global Level-3 products is an accurate and reliable cloud mask algorithm. This document describes the methodology behind developing the HyspIRI Cloud Mask Algorithm (HyCMA), and challenges associated with cloud detection. The HyCMA will derive its heritage from previously well established cloud mask algorithms such as the Landsat ACCAA, MODIS MOD35 and AVHRR.

Hook, Simon J.↗
NASA NTRS2001

The Role of Clear Sky Identification in the Study of Cloud Radiative Effects: Combine Analysis from ISCCP and the Scanner of Radiation Budget (ScaRaB)

Since the effect of clouds on the earth's radiation balance is often estimated as the difference of net radiative fluxes at the top of the atmosphere between all situations and monthly averaged clear sky situations of the same regions, a reliable identification of clear sky is important for the study of cloud radiative effects. The Scanner for Radiation Balance (ScaRaB) radiometer on board the Russian Meteor-3/7 satellite provided earth radiation budget observations from March 1994 to February 1995 with two ERBE-Re broad-band longwave and shortwave channels. Two narrow-band channels, in the infrared atmospheric window and in the visible band, have been added to the ScaRaB instrument to improve the cloud scene identification. The International Satellite Cloud Climatology Project (ISCCP) method for cloud detection and determination of cloud and surface properties uses the same narrow-band channels as ScaRaB, but is employed to a collection of measurements at a better spatial resolution of about 5 km. By applying the original ISCCP algorithms to the ScaRaB data, the clear sky frequency is about 5% lower than the one over quasi-simultaneous original ISCCP data, an indication that the ISCCP cloud detection is quite stable. However, one would expect an about 10 to 20% smaller clear sky occurrence over the larger ScaRaB pixels. Adapting the ISCCP algorithms to the reduced spatial resolution of 60 km and to the different time sampling of the ScaRaB data leads therefore to a reduction of a residual cloud contamination. A sensitivity study with time-space collocated ScaRaB and original ISCCP data at a spatial resolution of 1deg longitude x 1deg latitude shows that the effect of clear sky identification method plays a higher role on the clear sky frequency and therefore on the statistics than on the zonal mean values of the clear sky fluxes. Nevertheless, the zonal outgoing longwave fluxes corresponding to ERBE clear sky are in general about 2 to 10 W/sq m higher than those obtained from the ScaRaB adapted ISCCP clear sky identifications. The latter are close to (about 1 W/sq m higher) fluxes corresponding to clear sky regions from original ISCCP data, whereas ScaRaB clear sky LW fluxes obtained with the original ISCCP identification lie about 1 to 2 W/sq m below. Especially in the tropics where water vapor abundance is high, the ERBE clear sky LW fluxes seem to be systematically overestimated by about 4 W/sq m, and SW fluxes are lower by about 5 to 10 W/sq m. However, the uncertainty in the analysis of monthly mean zonal cloud radiative effects is also produced by the low frequency of clear sky occurrence, illustrated when averaging over pixels or even over regions of 4deg longitude x 5deg latitude, corresponding to the spatial resolution of General Circulation Models. The systematic bias in the clear sky fluxes is not reflected in the zonal cloud radiative effects, because the clear sky regions selected by the different algorithms can occur in different geographic regions with different cloud properties.

Rossow, W. B.↗
DOE OSTI2021

HAIMOS Ensemble Forecasts for Intra-day and Day- Ahead GHI, DNI and Ramps

The objective of this research is to develop a hybrid physics-based/data-driven forecast model to improve direct normal and global horizontal irradiance (DNI and GHI) prediction for horizons ranging from 1 to 72 hours. Project objectives also address key gaps in state-of-the-art solar forecasting: accurate probabilistic solar forecasts and the forecasting of large irradiance ramps (ramp onset and magnitude). The proposed model ensembles Numerical Weather Prediction (NWP) forecasts, determinist physics-based algorithms, and new-generation cloud cover products (high-resolution rapid refresh satellite images and Large Eddy Simulations). The result is the Hybrid Adaptive Input Model Objective Selection (HAIMOS) ensemble model. HAIMOS blends state of the art machine learning methodologies with physics-based models for cloud cover and cloud optical depth forecasts. The technical activities followed a two-pronged strategy. First, the preprocessing of data, the selection of inputs to the nonlinear approximators, the type of approximator and objective functions, and post-processing ensembling techniques included in HAIMOS were all optimized adaptively to find the best model for a specific goal (reduce DNI/GHI forecast error, improve the prediction of ramp onset, etc.). Second, a large effort was put in improving cloud identification and the forecast of cloud cover and cloud optical depth. To this end, new-generation cloud parametrization products were developed in this work. These include improved algorithms to assist in cloud identification, cloud classification and cloud parametrization from satellite images – three key factors in the accuracy of 1 to 6-hours irradiance forecasts and prediction of ramp onset. Furthermore, we also included cloud information extracted from high resolution rapid refresh satellite images (GOES-16) and Large Eddy Simulations (LES). LES was used to model the atmosphere in detail over locations of interest and produce cloud optical depth forecasts. Once these data streams were validated, they were used as input data to the HAIMOS forecast. The model was developed using data from several climatologically distinct locations with potential for high solar penetration. In the last year of the project, we conducted a validation campaign according to the guidelines stipulated by the Topic Area 1 project as described in the FOA. This effort brings, for the first time, proven machine-learning methodologies for generating state-of-the-art solar forecasts interweaved with detailed physics-based models for cloud detection, and cloud optical depth forecasts. HAIMOS will generate accurate irradiance probabilistic forecast to assist in reducing solar generation prediction error. Globally optimized solar forecast models are more likely to impact solar energy stakeholders. The goal of this project was to increase the state-of-the-art forecast skill from their present values of 10 to 35%. At the end of the project, we achieved between 30% and 50% forecast skill across a wide range of horizons for both GHI and DNI.

14 SOLAR ENERGY↗
NASA NTRS1986

Wavelength dependence of coherent and incoherent satellite-based lidar measurements of wind velocity and aerosol backscatter

The results are presented of a capability study of Earth orbiting lidar systems, at various wavelengths from 1.06 to 10.6 microns, for the measurement of wind velocity and aerosol backscatter, and for the detection of clouds. Both coherent and incoherent lidar systems were modeled and compared for the aerosol backscatter and cloud detection applications.

Kavaya, M. J.↗
NASA NTRS1997

Investigation of Cloud Properties and Atmospheric Profiles with MODIS

The WINter Cloud Experiment (WINCE) was directed and supported by personnel from the University of Wisconsin in January and February. Data sets of good quality were collected by the MODIS Airborne Simulator (MAS) and other instruments on the NASA ER2; they will be used to develop and validate cloud detection and cloud property retrievals over winter scenes (especially over snow). Software development focused on utilities needed for all of the UW product executables; preparations for Version 2 software deliveries were almost completed. A significant effort was made, in cooperation with SBRS and MCST, in characterizing and understanding MODIS PFM thermal infrared performance; crosstalk in the longwave infrared channels continues to get considerable attention.

Menzel, Paul↗
NASA NTRS2007

Processing AIRS Scientific Data Through Level 2

The Atmospheric Infrared Spectrometer (AIRS) Science Processing System (SPS) is a collection of computer programs, denoted product generation executives (PGEs), for processing the readings of the AIRS suite of infrared and microwave instruments orbiting the Earth aboard NASA s Aqua spacecraft. AIRS SPS at an earlier stage of development was described in "Initial Processing of Infrared Spectral Data' (NPO-35243), NASA Tech Briefs, Vol. 28, No. 11 (November 2004), page 39. To recapitulate: Starting from level 0 (representing raw AIRS data), the PGEs and their data products are denoted by alphanumeric labels (1A, 1B, and 2) that signify the successive stages of processing. The cited prior article described processing through level 1B (the level-2 PGEs were not yet operational). The level-2 PGEs, which are now operational, receive packages of level-1B geolocated radiance data products and produce such geolocated geophysical atmospheric data products such as temperature and humidity profiles. The process of computing these geophysical data products is denoted "retrieval" and is quite complex. The main steps of the process are denoted microwave-only retrieval, cloud detection and cloud clearing, regression, full retrieval, and rapid transmittance algorithm.

Oliphant, Robert↗