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NASA NTRS2020

The New Landsat Collection-2 Digital Elevation Model

The Landsat Collection-2 distribution introduces a new global Digital Elevation Model (DEM) for scene orthorectification. The new global DEM is a composite of the latest and most accurate freely available DEM sources and will include reprocessed Shuttle Radar Topographic Mission (SRTM) data (called NASADEM), high-resolution stereo optical data (ArcticDEM), a new National Elevation Dataset(NED) and various publicly available national datasets including the Canadian Digital Elevation Model (CDEM) and DEMs for Sweden, Norway and Finland (SNF). The new DEM will be available world-wide with few exceptions. It is anticipated that the transition from theCollection-1 DEM at 3 arcsecond to the new DEM will be seamless because processing methods to maintain a seamless transition were employed, void filling techniques were used, where persistent gaps were found, and the pixel spacing is the same between the two collections. Improvements to the vertical accuracy were realized by differencing accuracies of other elevation datasets to the new DEM. The greatest improvement occurred where ArcticDEM data were used, where an improvement of 35 meters was measured. By using theses improved vertical values in a line of sight algorithm, horizonta improvements were noted in some of the most mountainous regions over multiple 30-meter Landsat pixels. This new DEM will be used to process all of the scenes from Landsat 1-8 in Collection-2 processing and will be made available to the public by the end of 2020.

Shannon Franks↗
NASA NTRSDate not supplied

Application of Advanced Earth Observations and Model Simulations to Improve Air Quality Monitoring in the Hindu-Kush-Himalayan Region

Air pollution is a serious environmental health concern in the Hindu Kush Himalayan (HKH) region of south-central Asia, as rapid industrialization and population growth have led to increased anthropogenic emissions from transportation, residential, industrial, energy, and biomass burning sources. Natural emissions from dust and forest fires are additional sources of air pollutants that can exacerbate air quality in the region. The combination of the complex pollutant mixtures and atmospherically stable weather conditions during the winter monsoon can visibility reductions and hazardous air quality from persistent haze episodes. The Kathmandu Valley is especially vulnerable to extreme haze issues due to the surrounding mountains that restrict air movement and retains pollutants in the atmosphere. This study uses state-of-the-art satellite observations and modeling capabilities in conjunction with ground-based networks to provide a comprehensive data toolkit for advancing air quality monitoring and forecasting decisions in the HKH region. The toolkit includes new generation satellite observations from the TROPOspheric Monitoring Instrument (TROPOMI), Geostationary Environment Monitoring Spectrometer (GEMS), and Advanced Meteorological Imager, which provide high spatiotemporal information on NO2, HCHO, SO2, O3, and aerosol optical depth (AOD). Particulate matter with diameters less than 2.5 micrometers (PM2.5) are derived from the satellite-retrieved AOD using ground-based observations and forecast model data. The satellite observations are also used to initialize and constrain forecast model systems designed for the HKH region. This talk will highlight the performance of the air quality toolkit for enhancing decision-making processes during exceptional air quality events in the region. Note: Presentation includes additional attachment of full presentation with sound and animation (best when viewed as slide show) with runtime of 15 min 32 secs

Aaron Naeger↗
NASA NTRS1976

Breadboard linear array scan imager using LSI solid-state technology

The performance of large scale integration photodiode arrays in a linear array scan (pushbroom) breadboard was evaluated for application to multispectral remote sensing of the earth's resources. The technical approach, implementation, and test results of the program are described. Several self scanned linear array visible photodetector focal plane arrays were fabricated and evaluated in an optical bench configuration. A 1728-detector array operating in four bands (0.5 - 1.1 micrometer) was evaluated for noise, spectral response, dynamic range, crosstalk, MTF, noise equivalent irradiance, linearity, and image quality. Other results include image artifact data, temporal characteristics, radiometric accuracy, calibration experience, chip alignment, and array fabrication experience. Special studies and experimentation were included in long array fabrication and real-time image processing for low-cost ground stations, including the use of computer image processing. High quality images were produced and all objectives of the program were attained.

Tracy, R. A.↗
NASA NTRS1977

Multilayered (Hg,Cd)Te infrared detector

Multilayered mercury-cadmium telluride photoconductive detectors were developed which are capable of providing individual coverage of three separate spectral wavelength bands without the use of beam splitters. The multilayered "three-color" detector on a single dewar takes the place of three separate detector/filter/dewar units and enables simpler and more reliable mechanical and optical designs for multispectral scanners and radiometers. Wavelength channel design goals (in micrometers) were: 10.1 to 11.0, 11.0 to 12.0, and 13.0. Detectivity for all channels was 1 x 10 to the 10th power cm-Hz 1/2/Watt. A problem occurred in finding an epoxy layer which had good infrared transmission properties and which also was chemically and mechanically compatible with HgCdTe processing techniques. Data on 6 candidate bonding materials are surveyed and discussed.

Rae, W. G.↗
NASA NTRS1994

Interaction of ultraviolet and X-ray radiation with gamma rays produced by a jet in active galactic nuclei

Recent observations by the Compton Gamma-Ray Observatory give evidence for the existence of a type of blazar with strong gamma-ray emission. Data obtained by EGRET for the quasar 3C 279 show a spectrum between 100 MeV and 10 GeV. Photons of such energies should interact with the X-rays and produce positron/electron pairs. If the optical depth against pair production for the gamma rays is large (tau(gamma gamma) greater than 1), the gamma-ray spectrum should be affected. The importance of this process has been pointed out by, e.g., Maraschi, Ghisellini, & Celotti (1992). Several works (e.g., Dermer 1993; Zbyszewska 1993; Sikora, Begelman, & Rees 1993) concerning gamma-ray radiation from quasar 3C 279 have proposed a model in which the gamma rays are produced via interaction between a moving cloud of relativistic electrons and external soft photons. The presence of gamma rays in active galactic nuclei spectra gives constraints on the localization and the luminosity of the medium which produces ultraviolet/X-ray photons. We investigate what conditions should be fulfilled in the above model to avoid the absorption of the gamma rays due to pair production.

Zbyszewska, Magda↗
NASA NTRS2001

Remote Sensing of Cloud, Aerosol, and Water Vapor Properties from MODIS

MODIS is an earth-viewing cross-track scanning spectroradiometer launched on the Terra satellite in December 1999. MODIS scans a swath width sufficient to provide nearly complete global coverage every two days from a polar orbiting, sun-synchronous, platform at an altitude of 705 kilometers, and provides images in 36 spectral bands between 0.415 and 14.235 micrometers with spatial resolutions of 250 meters (2 bands), 500 meters (5 bands) and 1000 meters (29 bands). These bands have been carefully selected to enable advanced studies of land, ocean, and atmospheric processes. In this presentation we review the comprehensive set of remote sensing algorithms that have been developed for the remote sensing of atmospheric properties using MODIS data, placing primary emphasis on the principal atmospheric applications of (i) developing a cloud mask for distinguishing clear sky from clouds, (ii) retrieving global cloud radiative and microphysical properties, including cloud top pressure and temperature, effective emissivity, cloud optical thickness, thermodynamic phase, and effective radius, (iii) monitoring tropospheric aerosol optical thickness over the land and ocean and aerosol size distribution over the ocean, (iv) determining atmospheric profiles of moisture and temperature, and (v) estimating column water amount. The physical principles behind the determination of each of these atmospheric products will be described, together with an example of their application using MODIS observations. All products are archived into two categories: pixel-level retrievals (referred to as Level-2 products) and global gridded products at a latitude and longitude resolution of 1 degree (Level-3 products). An overview of the MODIS atmosphere algorithms and products, status, validation activities, and early level-2 and -3 results will be presented.

King, Michael D.↗
NASA NTRS2001

Remote Sensing of Cloud, Aerosol, and Land Properties from MODIS: Applications to the East Asia Region

MODIS is an earth-viewing cross-track scanning spectroradiometer launched on the Terra satellite in December 1999. MODIS scans a swath width sufficient to provide nearly complete global coverage every two days from a polar-orbiting, sun-synchronous platform at an altitude of 705 km, and provides images in 36 spectral bands between 0.415 and 14.235 microns with spatial resolutions of 250 m (two bands), 500 m (five bands) and 1000 m (29 bands). These bands have been carefully selected to enable advanced studies of land, ocean, and atmospheric processes. In this presentation we review the comprehensive set of remote sensing algorithms that have been developed for the remote sensing of atmospheric properties using MODIS data, placing primary emphasis on the principal atmospheric applications of (i) developing a cloud mask for distinguishing clear sky from clouds, (ii) retrieving global cloud radiative and microphysical properties, including cloud top pressure and temperature, effective emissivity, cloud optical thickness, thermodynamic phase, and effective radius, (iii) monitoring tropospheric aerosol optical thickness over the land and ocean and aerosol size distribution over the ocean, (iv) determining atmospheric profiles of moisture and temperature, and (v) estimating column water amount. The physical principles behind the determination of each of these atmospheric products will be described, together with an example of their application using MODIS observations to the east Asian region in Spring 2001. All products are archived into two categories: pixel-level retrievals (referred to as Level-2 products) and global gridded products at a latitude and longitude resolution of 1 degree (Level-3 products). An overview of the MODIS atmosphere algorithms and products, status, validation activities, and early level-2 and -3 results will be presented.

King, Michael D.↗
NASA NTRS2009

Technical Note: A Time-Dependent I(sub 0) Correction for Solar Occultation Instruments

Solar occultation has proven to be a reliable technique for the measurement of atmospheric constituents in the stratosphere. NASA's Stratospheric Aerosol and Gas Experiments (SAGE, SAGE II, and SAGE III) together have provided over 25 years of quality solar occultation data, a data record which has been an important resource for the scientific exploration of atmospheric composition and climate change. Herein, we describe an improvement to the processing of SAGE data that corrects for a previously uncorrected short-term timedependence in the calibration function. The variability relates to the apparent rotation of the scanning track with respect to the face of the sun due to the motion of the satellite. Correcting for this effect results in a decrease in the measurement noise in the Level 1 line-of-sight optical depth measurements of approximately 40% in the middle and upper stratospheric SAGE II and III where it has been applied. The technique is potentially useful for any scanning solar occultation instrument, and suggests further improvement for future occultation measurements if a full disk imaging system can be included.

Burton, Sharon P.↗
NASA NTRS2005

NASA Tech Briefs, May 2005

Topics covered include: Fastener Starter; Multifunctional Deployment Hinges Rigidified by Ultraviolet; Temperature-Controlled Clamping and Releasing Mechanism; Long-Range Emergency Preemption of Traffic Lights; High-Efficiency Microwave Power Amplifier; Improvements of ModalMax High-Fidelity Piezoelectric Audio Device; Alumina or Semiconductor Ribbon Waveguides at 30 to 1,000 GHz; HEMT Frequency Doubler with Output at 300 GHz; Single-Chip FPGA Azimuth Pre-Filter for SAR; Autonomous Navigation by a Mobile Robot; Software Would Largely Automate Design of Kalman Filter; Predicting Flows of Rarefied Gases; Centralized Planning for Multiple Exploratory Robots; Electronic Router; Piezo-Operated Shutter Mechanism Moves 1.5 cm; Two SMA-Actuated Miniature Mechanisms; Vortobots; Ultrasonic/Sonic Jackhammer; Removing Pathogens Using Nano-Ceramic-Fiber Filters; Satellite-Derived Management Zones; Digital Equivalent Data System for XRF Labeling of Objects; Identifying Objects via Encased X-Ray-Fluorescent Materials - the Bar Code Inside; Vacuum Attachment for XRF Scanner; Simultaneous Conoscopic Holography and Raman Spectroscopy; Adding GaAs Monolayers to InAs Quantum-Dot Lasers on (001) InP; Vibrating Optical Fibers to Make Laser Speckle Disappear; Adaptive Filtering Using Recurrent Neural Networks; and Applying Standard Interfaces to a Process-Control Language.

Source record↗
NASA NTRS2013

The Meteorology of Storms that Produce Narrow Bipolar Events

Narrow Bipolar Events (NBEs) are compact intracloud discharges that produce the most powerful lightning‐related radio frequency signals that have been observed. However, their luminosity is below the threshold for detectability from current and past spaceborne optical sensors. NBEs have been loosely associated with convective intensity, but their occurrence tends to be highly localized in time and space within a thunderstorm, and there remain many questions about whether and to what extent they are significantly related to meteorological processes within thunderstorms. Using the North Alabama Lightning Mapping Array (NALMA), the National Lightning Detection Network, and available Doppler and polarimetric radar data, case studies will be presented for storm events that produced large numbers of NBEs (~10s‐100s) during their lifetimes. NBEs are documented via a method that identifies high peak power (>40‐50 dBW) initial VHF sources within a specific altitude band in the upper levels of thunderstorms. The production of NBEs, including spatial and temporal variability, will be compared to the radar‐inferred kinematic and microphysical structure and evolution of thunderstorms, as well as their NALMA‐ and NLDN‐inferred electrical characteristics. The results should provide new insights into the relationships between NBEs and thunderstorm processes.

Lang, Timothy J.↗
NASA NTRS2019

Applicability of Spectral Decomposition by Varimax-Rotated, Principal Component Analysis to the Surface Biology and Geology (SBG) VNIR Mission Concept

Cyanobacterial and Harmful Algal Blooms (CyanoHABs) are a growing concern in coastal and inland waters. But, spectral interference from multiple constituents in optically complex waters can hamper application of remote sensing using traditional image processing methods. The Kent State University (KSU) spectral decomposition method can be applied to multispectral and hyperspectral remote sensing images (e.g. HICO and the NASA Glenn HSI2) to partition and identify signals related to cyanobacteria, algae, pigment degradation products and suspended sediment in each pixel. Fundamental to the use of remote sensing data is the ability to extract independent signals from correlated hyperspectral VNIR data cubes. The Kent State University varimax-rotated, principal component analysis method (VPCA) is important to integrate into the SBG VNIR mission concept because it provides greater specificity, a software-based SNR boost relative to hardware performance, and can assist with Cal/Val, Modeling and Applications. We present examples of the hyperspectral application of the KSU VPCA method with relevance to SBG. The information extracted by VPCA can be validated spectrally or spatially with laboratory and/or in situ sensors, which capture spatial or time series of information at discrete points within remote sensing images. Comparisons show hyperspectral sensors extract more components than multispectral ones, but more independent information can be extracted from multispectral sensors by VPCA than traditional band ratio approaches. The spectral decomposition method is capable of enhancing the signal to noise ratio (SNR) of the NASA Glenn, second-generation hyperspectral imager by a factor of 7x to 20x, with a spectral reproducibility of ±3%. The spectral decomposition method, when compared against existing remote sensing monitoring methods exhibits both greater specificity and a lower detection limit. The method has been validated with multispectral images in Lake Erie to quantify the Microcystis CyanoHAB and from the Indian River Lagoon, Florida to quantify the Brown Tide resulting from A. lagunesnsis. Field operations in the Western Basin of Lake Erie were conducted using a bbe Fluoroprobe to collect vertical profiles and horizontal tows along a transect from the Toledo to the Detroit Lighthouse during coincident satellite overpasses. Extraction of pixel values from the MODIS Aqua sensor yields agreement between in situ field and lab-based measures of cyanobacterial, cryptophyte, diatoms and green algae, suspended sediment and pigment degradation products with R2>0.8.

hyperspectral↗
NASA NTRS2020

Washington Health & Air Quality: Quantifying Air Quality Parameters and Validating Air Pollution Sources Impacting the Health of Puget Sound Residents Through the Use of NASA and ESA Remote Sensing Data

In the Puget Sound region of Washington, high levels of air pollutants put residents’ health at risk by increasing their likelihood of developing critical respiratory conditions. This project used remotely-sensed data to investigate aerosol optical depth (AOD) from NASA satellite sensors including the Terra and Aqua MODerate Resolution Imaging Spectroradiometer (MODIS) and European Space Agency Copernicus Sentinel-5 Precursor TROPOspheric Monitoring Instrument (TROPOMI). The team visualized the most recent data in Google Earth Engine (GEE) API to display air pollution trends in Washington State, which will support the Puget Sound Clean Air Agency’s (PSCAA) decision-making processes. The team performed linear regressions using the Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm to form a relationship between ground-level microscopic particles (PM2.5) and AOD in the Puget Sound region, validating the relationship using concentration readings taken from Environmental Protection Agency (EPA) air quality monitors. The team utilized estimated PM2.5 and other satellite data to produce a web-based tool and to evaluate the effectiveness of using such a tool for near real-time air quality monitoring within a particular region. The team found that the tool provides useful supplementary data that fills in the gaps of the PSCAA’s air monitoring network.

Health & Air Quality↗
NASA NTRSDate not supplied

Study of Fallout Metrics for Contamination Analysis

A challenge present in assessing contamination accumulation on many missions is predicting fallout during ground processing given the multiple and various orientations possible for surfaces such as optics and instruments. The best practice assumption has been to quantify particle build up on vertical surfaces as approximately 1/10 that of horizontal surfaces. This fractional relation is important when considering contamination allocations necessary to meet cleanliness requirements since spacecraft can be in many orientations during integration and testing. There is insufficient data to provide confidence in the 1/10 approximation, yet its use can have a significant effect on mission end of life contamination level predictions, leading to expenditures of precious resources to meet mission requirements. A study was conducted to compare and analyze the fallout in horizontal and vertical orientations. Silicon wafers were deployed in four different facilities. Data sets from a long term deployment of wafers were analyzed from a cleanroom facility housing integration of the James Webb Space Telescope (JWST) as well as from a shorter term deployment of wafers in three cleanroom facilities at Goddard Space Flight Center with lower activity. There are many variables influencing the relationship between fallout on vertical and horizontal wafers, including wafer position with respect to air flow, air changes in the facility, duration of exposure, and activity workload. The goal of this continuing study is to develop a tool to inform particulate accumulation predictions for future projects.

Contamination↗
NASA NTRS1979

Picture processing analysis of the optical structure of NGC 5128 /Centaurus A/

Results are presented for a detailed study of the peculiar elliptical galaxy NGC 5128 (Cen A), based on computer video analysis of several photographic plates of exceptional quality reduced to the standard UBV system. The picture-processing results and the measured properties of the elliptical and gaseous-disk components of NGC 5128 are examined, along with the distribution, spectral characteristics, and chemical composition of the H II regions in the disk. The data show that NGC 5128 consists of a giant E2 galaxy containing a significant amount of gas and dust situated predominantly in an equatorial disk where vigorous star formation is occurring. Reasons why NGC 5128 is so different from giant ellipticals in clusters are considered.

Dufour, R. J.↗
NASA NTRS1993

High-performance mass storage system for workstations

Reduced Instruction Set Computer (RISC) workstations and Personnel Computers (PC) are very popular tools for office automation, command and control, scientific analysis, database management, and many other applications. However, when using Input/Output (I/O) intensive applications, the RISC workstations and PC's are often overburdened with the tasks of collecting, staging, storing, and distributing data. Also, by using standard high-performance peripherals and storage devices, the I/O function can still be a common bottleneck process. Therefore, the high-performance mass storage system, developed by Loral AeroSys' Independent Research and Development (IR&D) engineers, can offload a RISC workstation of I/O related functions and provide high-performance I/O functions and external interfaces. The high-performance mass storage system has the capabilities to ingest high-speed real-time data, perform signal or image processing, and stage, archive, and distribute the data. This mass storage system uses a hierarchical storage structure, thus reducing the total data storage cost, while maintaining high-I/O performance. The high-performance mass storage system is a network of low-cost parallel processors and storage devices. The nodes in the network have special I/O functions such as: SCSI controller, Ethernet controller, gateway controller, RS232 controller, IEEE488 controller, and digital/analog converter. The nodes are interconnected through high-speed direct memory access links to form a network. The topology of the network is easily reconfigurable to maximize system throughput for various applications. This high-performance mass storage system takes advantage of a 'busless' architecture for maximum expandability. The mass storage system consists of magnetic disks, a WORM optical disk jukebox, and an 8mm helical scan tape to form a hierarchical storage structure. Commonly used files are kept in the magnetic disk for fast retrieval. The optical disks are used as archive media, and the tapes are used as backup media. The storage system is managed by the IEEE mass storage reference model-based UniTree software package. UniTree software will keep track of all files in the system, will automatically migrate the lesser used files to archive media, and will stage the files when needed by the system. The user can access the files without knowledge of their physical location. The high-performance mass storage system developed by Loral AeroSys will significantly boost the system I/O performance and reduce the overall data storage cost. This storage system provides a highly flexible and cost-effective architecture for a variety of applications (e.g., realtime data acquisition with a signal and image processing requirement, long-term data archiving and distribution, and image analysis and enhancement).

Chiang, T.↗
NASA NTRS2017

Hinode: A Decade of Success in Capturing Solar Activity

As the present solar cycle passes into its minimum phase, the Hinode mission marks its tenth year of investigating solar activity. Hinode's decade of successful observations have provided us with immeasurable insight into the solar processes that invoke space weather and thereby affect the interplanetary environment in which we reside. The mission's complementary suite of instruments allows us to probe transient, high energy events alongside long-term, cycle-dependent phenomena from magnetic fields at the Sun's surface out to highly thermalized coronal plasma enveloping active regions (ARs). These rich data sets have already changed the face of solar physics and will continue to provoke exciting research as new observational paradigms are pursued. Hinode was launched as part of the Science Mission Directorate's (SMD) Solar Terrestrial Probes Program in 2006. It is a sophisticated spacecraft equipped with a Solar Optical Telescope (SOT), an Extreme-ultraviolet Imaging Spectrometer (EIS), and an X-Ray Telescope (XRT) (see x 4). With high resolution and sensitivity, Hinode serves as a microscope for the Sun, providing us with unique capabilities for observing magnetic fields near the smallest scales achievable, while also rendering full-Sun coronal context in the highest thermal regimes. The 2014 NASA SMD strategic goals objective to "Understand the Sun and its interactions with the Earth and the solar system, including space weather" forms the basis of three underlying Heliophysics Science Goals. While Hinode relates to all three, the observatory primarily addresses: Explore the physical processes in the space environment from the Sun to the Earth and through the solar system. Within the NASA National Research Council (NRC) Decadal Survey Priorities, Hinode targets: (a) Determine the origins of the Sun's activity and predict the variations of the space environment and (d) Discover and characterize fundamental processes that occur both within the heliosphere and throughout the universe. In response to the 2012 NRC Decadal Survey Science Challenges and 2014 Heliophysics Roadmap Research Focus Areas, the Hinode mission has set forth four Prioritized Science Goals (PSGs): (a) Study the sources and evolution of highly energetic dynamic events; (b) Characterize cross-scale magnetic field topology and stability; (c) Trace mass and energy flow from the photosphere to the corona; and (d) Continue long term synoptic support to quantify cycle variability.

review↗
NASA NTRS1999

Optical Analysis of Transparent Polymeric Material Exposed to Simulated Space Environment

Transparent polymeric materials are being designed and utilized as solar concentrating lenses for spacecraft power and propulsion systems. These polymeric lenses concentrate solar energy onto energy conversion devices such as solar cells and thermal energy systems. The conversion efficiency is directly related to the transmissivity of the polymeric lens. The Environmental Effects Group of the Marshall Space Flight Center's Materials, Processes, and Manufacturing Department exposed a variety of materials to a simulated space environment and evaluated them for an, change in optical transmission. These materials include Lexan(TM), polyethylene terephthalate (PET). several formulations of Tefzel(TM). and Teflon(TM), and silicone DC 93-500. Samples were exposed to a minimum of 1000 Equivalent Sun Hours (ESH) of near-UV radiation (250 - 400 nm wavelength). Data will be presented on materials exposed to charged particle radiation equivalent to a five-year dose in geosynchronous orbit. These exposures were performed in MSFC's Combined Environmental Effects Test Chamber, a unique facility with the capability to expose materials simultaneously or sequentially to protons, low-energy electrons, high-energy electrons, near UV radiation and vacuum UV radiation.Prolonged exposure to the space environment will decrease the polymer film's transmission and thus reduce the conversion efficiency. A method was developed to normalize the transmission loss and thus rank the materials according to their tolerance to space environmental exposure. Spectral results and the material ranking according to transmission loss are presented.

Edwards, David L.↗
NASA NTRS1989

Cloud-generated radiative heating and its generation of available potential energy

The generation of zonal available potential energy (APE) by cloud radiative heating is discussed. The APE concept was mathematically formulated by Lorenz (1955) as a measure of the maximum amount of total potential energy that is available for conversion by adiabatic processes to kinetic energy. The rate of change of APE is the rate of the generation of APE minus the rate of conversion between potential and kinetic energy. By radiative transfer calculations, a mean cloud-generated radiative heating for a well defined set of cloud classes is derived as a function of cloud optical thickness. The formulation is suitable for using a general cloud parameter data set and has the advantage of taking into account nonlinearities between the microphysical and macrophysical cloud properties and the related radiation field.

Stuhlmann, R.↗