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At least 1,171 records · Page 65

Derivation of Capabilities and Resources for Treating Medical Conditions in Deep Space

BACKGROUND: Medical care in spaceflight requires the adaptation of terrestrial standards to the constraints of the space environment. However, there is often conflict between the ideal resources required for treatment and diagnosis of a medical condition, and the constraints on their mass, volume, data needs, etc. This optimization of trades between medical risk and resources will be a significant challenge for deep space medical system design. METHODS: A team of physicians with a broad range of expertise reviewed the 120 medical conditions on the condition list for NASA’s Informing Mission Planning via analysis of Complex Tradespaces Medical Database (IMPACT-MD). Each team member was assigned a subset of conditions based on their experience and training. The assigned physician generated a proposed list of capabilities, definitions, and resources required to treat each condition based on terrestrial practice guidelines, medical literature, and subject matter expertise. Additional specialists were consulted for conditions where expertise was not present within the main group. The proposed list was then reviewed by the broader team and modified as needed to achieve consensus. Each capability and resource was then assigned parameters to define quantity required per medical event, necessity, training level required, and primacy order of any alternative resources. These capabilities and resources were placed into condition specific tables and delivered to a team of engineers who added mass and volume data for each specific resource and converted the table into a database for use as input to a computational model to simulate spaceflight (IMPACT) DISCUSSION: This process ensures that a minimum of three subject matter experts review and agree upon the scope of practice, medical diagnostic tools, and treatment modalities that would be necessary to address emergent and non-emergent conditions that may arise during spaceflight to inform requirements during the vehicle design phase. The method is scalable to any design reference mission and permits modification of the existing database as information, conditions or experience are added. By including specialists, generalists, and those with subject matter expertise in the spaceflight environment on the team, we ensure that the included capabilities represent a realistic and actionable foundation for planning deep space missions.

D R Levin↗

Impact Simulation of Composite Panels for Aerospace Applications

The aerospace research community has been working towards the development of a comprehensive framework for the design of composite structures at the component, subassembly, assembly, and system levels. Such a framework requires accurate, efficient and easy-to-use mathematical and computational models that are in sync with physical reality. The research work in this paper is designed to help an aerospace structural engineer move towards this goal by simulating dynamic impact to composite panels. First, the existing orthotropic visco-elastic visco-plastic material model in LS-DYNA commercial finite element program, MAT_COMPOSITE_TABULATED_PLASTICITY_DAMAGE (MAT_213) is enhanced with the development and use of rate-dependent damage data. Using state-of-the-art experimental procedures, impact validation test data are created. Second, the versatility of the constitutive model is examined by its ability to simulate a low velocity (27 ft/s, 8 m/s) impact test, and two high velocity impact tests (385–417 ft/s, 117–127 m/s) that straddle the ballistic limit of the projectile and the composite panels. Third, these impact events are modeled using three different finite element types – under-integrated and fully-integrated solid elements, and fully-integrated thin shell elements. Insight into accuracy versus numerical efficiency is gained by comparing the performance of solid versus thin shell elements. The numerical results show that accurate predictions of these impact events can be obtained with reasonable effort and care.

Simulations↗

Searching for GRB Counterparts to GW Events from the Third Gravitational Wave Observing Run with Fermi-GBM and Swift-BAT

We present Fermi Gamma-ray Burst Monitor (Fermi-GBM) and Swift Burst Alert Telescope (Swift-BAT) observations of gravitational-wave (GW) events detected during the third LIGO/Virgo/KAGRA Collaboration observing run (O3). Using Fermi-GBM on-board triggers as well as sub-threshold searches in both Fermi-GBM and Swift-BAT ground data, we search for coincident gamma-ray transients associated with the GW events. No new joint events were found. We therefore calculate flux upper limits for the associated gamma-ray luminosity of each GW event. Using the lack of electromagnetic (EM) emission from binary black hole (BBH) mergers, we begin to constrain theoretical models of any such emission.

GRB↗

Searching for GRB Counterparts to GW Events from the Third Gravitational Wave Observing Run with Fermi-GBM and Swift-BAT

We present Fermi Gamma-ray Burst Monitor (Fermi-GBM) and Swift Burst Alert Telescope (Swift-BAT) observations of gravitational-wave (GW) events detected during the third LIGO/Virgo/KAGRA Collaboration observing run (O3). Using Fermi-GBM on-board triggers as well as sub-threshold searches in both Fermi-GBM and Swift-BAT ground data, we search for coincident gamma-ray transients associated with the GW events. No new joint events were found. We therefore calculate flux upper limits for the associated gamma-ray luminosity of each GW event. Using the lack of electromagnetic (EM) emission from binary black hole (BBH) mergers, we begin to constrain theoretical models of any such emission.

GRB↗

Hydrocarbon Burn Facility, SWMU 007 Per- and Polyfluoroalkyl Substances (PFAS) Assessment Report Addendum

This document discusses the Per-and Polyfluoroalkyl Substances (PFAS) assessment activities performed from May through August 2023 at the Hydrocarbon Burn Facility (HBF) located at Kennedy Space Center (KSC), Florida. HBF was used for firefighting training between 1966 and 1994. Aqueous film-forming foams (AFFFs) that contained PFAS were used as suppressants for fighting petroleum fuel fires during training. PFAS sampling was first completed at HBF in 2015. This PFAS Assessment Report Addendum (ARA) is a continuation of sampling efforts, with an overall objective to further delineate PFAS concentrations in groundwater to the pGCTLs and the United States Environmental Protection Agency (EPA) Tapwater Regional Screening Levels (RSLs) dated November 2023 and better understand groundwater to surface water interaction at the Site. The field activities presented in this PFAS ARA were conducted between May and August 2023 and included the collection of 132 direct push groundwater samples and the collection of five colocated surface water, sediment, and pore water samples from locations south/southeast of HBF in August 2023. Exceedances of the pGCTLs and Tapwater RSLs were observed in the direct push groundwater results; however, groundwater has been delineated to the pGCTLs. Exceedances of the Florida provisional Surface Water Screening Levels (pSWSLs) were observed in surface water and porewater, and concentrations of PFAS in these media confirm PFAS migration within surface channels to the south of the HBF site area. Maximum sediment concentrations, which correlate with the maximum surface water and porewater concentrations, demonstrate that PFAS impacted surface water is the source of sediment impacts. Overall, elevated concentrations of PFAS are centered on the HBF site area that trend north and south along the surface water filled swales and along the edge of Banana River. Based on analytical results, not all surface water features in this area exhibit evidence of transport. PFAS migration/transport appears to be more dominant in surface water features during the wet season. Discharges to the Banana River primarily occur where surface water facilitates transport. In contrast, groundwater transport is more effective during the dry season. During precipitation events in either the dry season or the wet season, there appears to be migration from the intermediate groundwater zone to the shallow zone into the surface water features. Additional sampling and data collection is recommended to support further refinement of PFAS groundwater delineation, a remedial alternative evaluation, and the fate and transport model.

Jennifer Buel↗

Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by the Interplanetary Network

We present the results of a search for gravitational waves associated with 223 gamma ray bursts (GRBs) detected by the InterPlanetary Network (IPN) in 2005-2010 during LIGO's fifth and sixth science runs and Virgo's first, second, and third science runs. The IPN satellites provide accurate times of the bursts and sky localizations that vary significantly from degree scale to hundreds of square degrees. We search for both a well-modeled binary coalescence signal, the favored progenitor model for short GRBs, and for generic, unmodeled gravitational wave bursts. Both searches use the event time and sky localization to improve the gravitational wave search sensitivity as compared to corresponding all-time, all-sky searches. We find no evidence of a gravitational wave signal associated with any of the IPN GRBs in the sample, nor do we find evidence for a population of weak gravitational wave signals associated with the GRBs. For all IPN-detected GRBs, for which a sufficient duration of quality gravitational wave data are available, we place lower bounds on the distance to the source in accordance with an optimistic assumption of gravitational wave emission energy of 10(exp−2) solar mass c(exp 2) at 150 Hz, and find a median of 13 Mpc. For the 27 short-hard GRBs we place 90% confidence exclusion distances to two source models: a binary neutron star coalescence, with a median distance of 12 Mpc, or the coalescence of a neutron star and black hole, with a median distance of 22 Mpc. Finally, we combine this search with previously published results to provide a population statement for GRB searches in first-generation LIGO and Virgo gravitational wave detectors and a resulting examination of prospects for the advanced gravitational wave detectors.

gravitational wave detectors↗

Magnetospheric origin of energetic (at least 50 keV) ions upstream of the bow shock - The October 31, 1977, event

Energetic particle data gathered by the ISEE-1 and IMP-7 and -8 spacecraft on Oct. 31, 1977 while travelling inside the plasma sheet upstream of the earth's bow shock are analyzed for an indication of the source of the 30 keV-1 MeV particles observed. The IMP spacecraft also travelled through the magnetosphere and the dawn bow shock during the measurement data. The data included records of magnetospheric bursts of energetic protons, which had intensities about 2-8 times higher inside the plasma sheet than did the proton intensities. The magnetospheric bursts began about 40 min before the ISEE recorded an upstream ion event and 2 hr before its cutoff. Other data indicated that the appearance of upstream ions was controlled by the interplanetary magnetic field. The ions arose in the plasma sheet of the magnetosphere and in 'leaking' upstream experienced a separation of ions from electrons, a condition caused by the interplanetary magnetic field. A phenomenological model is developed for the process of injection of energetic particles upstream of the bow shock in a manner that is not commensurate with Fermi acceleration.

Anagnostopoulos, G. C.↗

Testing of the anemometer circuit: Data report

The following text discusses results from the electronic step testing and the beginning of velocity step testing in the shock tube. It should be kept in mind that frequency response is always measured as the time from the beginning of the event to the minimum (positive inflection) of the 'bucket' that immediately follows the response. This report is not a complete account of the results from square wave testing. Some data is still in the process of being analyzed and efforts are being made to fit the data to both Freymuth's third order theory and modelled responses from SPICE circuit simulation software.

Moen, Michael J.↗

The Use of a Satellite Climatological Data Set to Infer Large Scale Three Dimensional Flow Characteristics

Ever since the first satellite image loops from the 6.3 micron water vapor channel on the METEOSAT-1 in 1978, there have been numerous efforts (many to a great degree of success) to relate the water vapor radiance patterns to familiar atmospheric dynamic quantities. The realization of these efforts is becoming evident with the merging of satellite derived winds into predictive models (Velden et al., 1997; Swadley and Goerss, 1989). Another parameter that has been quantified from satellite water vapor channel measurements is upper tropospheric relative humidity (UTH) (e.g., Soden and Bretherton, 1996; Schmetz and Turpeinen, 1988). These humidity measurements, in turn, can be used to quantify upper tropospheric water vapor and its transport to more accurately diagnose climate changes (Lerner et al., 1998; Schmetz et al. 1995a) and quantify radiative processes in the upper troposphere. Also apparent in water vapor imagery animations are regions of subsiding and ascending air flow. Indeed, a component of the translated motions we observe are due to vertical velocities. The few attempts at exploiting this information have been met with a fair degree of success. Picon and Desbois (1990) statistically related Meteosat monthly mean water vapor radiances to six standard pressure levels of the European Centre for Medium Range Weather Forecast (ECMWF) model vertical velocities and found correlation coefficients of about 0.50 or less. This paper presents some preliminary results of viewing climatological satellite water vapor data in a different fashion. Specifically, we attempt to infer the three dimensional flow characteristics of the mid- to upper troposphere as portrayed by GOES VAS during the warm ENSO event (1987) and a subsequent cold period in 1998.

Lerner, Jeffrey A.↗

Integrating Interball into the ISTP

The grant supported correlative studies of Interball-1 and ISTP observations. Our activities focussed on three tasks: (1) using the two-point measurements of Interball-I and its subspacecraft Magion-4 to verify the impulsive penetration model for solar wind-magnetosphere interaction, (2) examining simultaneous Wind solar wind and Interball-1 magnetosheath observations to identify the origin of transient pressure variations in the Earth's magnetosheath, and (3) preparing a book published by Kluwer containing the conference proceedings from a meeting we held in Kosice, Slovakia. The impulsive penetration model predicted the occurrence of magnetosheath plasma blobs detached from the magnetopause deep within the magnetosphere. We searched the entire Interball1/Magion-4 data set to demonstrate that this never happens. Consequently, we proved the model invalid. We examined a series of strong (factor of 2 to 3), transient (10s to I min) flux pulses within the magnetosheath. We showed that the pulses occurred in pairs bounding regions of either greatly depressed fluxes (in the case of events seen far from the magnetopause) or magnetospheric intervals (in the case of events seen near the magnetopause). We interpreted the flux pulses as the signatures of hot flow anomalies downstream from the foreshock and suggested that such anomalies may be an important cause of magnetopause motion. Following a successful conference in Kosice, Slovakia that was attended by many ISTP and Interball scientists, we prepared a book for publication by Kluwer.

Sibeck, David G.↗

SERVIR-Africa: Developing an Integrated Platform for Floods Disaster Management in Africa

SERVIR-Africa is an ambitious regional visualization and monitoring system that integrates remotely sensed data with predictive models and field-based data to monitor ecological processes and respond to natural disasters. It aims addressing societal benefits including floods and turning data into actionable information for decision-makers. Floods are exogenous disasters that affect many parts of Africa, probably second only to drought in terms of social-economic losses. This paper looks at SERVIR-Africa's approach to floods disaster management through establishment of an integrated platform, floods prediction models, post-event flood mapping and monitoring as well as flood maps dissemination in support of flood disaster management.

Macharia, Daniel↗

Climate Scenarios for the NASA / USAID SERVIR Project: Challenges for Multiple Planning Horizons

SERVIR, an acronym meaning "to serve" in Spanish, is a joint venture between NASA and the U.S. Agency for International Development (USAID) which provides satellite-based Earth observation data, modeling, and science applications to help developing nations in Central America, East Africa and the Himalayas improve environmental decision making. Anticipating climate variability / climate change impacts has now become an important component of the SERVIR efforts to build capacity in these regions. Uncertainty in hydrometeorological components of climate variations and exposure to extreme events across scales from weather to climate are of particular concern. We report here on work to construct scenarios or outlooks that are being developed as input drivers for decision support systems (DSSs) in a variety of settings. These DSSs are being developed jointly by a broad array NASA Applied Science Team (AST) Investigations and user communities in the three SERVIR Hub Regions, Central America, East Africa and the Himalayas. Issues span hydrologic / water resources modeling, agricultural productivity, and forest carbon reserves. The scenarios needed for these efforts encompass seasonal forecasts, interannual outlooks, and likely decadal / multi-decadal trends. Providing these scenarios across the different AST efforts enables some level of integration in considering regional responses to climate events. We will discuss a number of challenges in developing this continuum of scenarios including the identification and "mining" of predictability, addressing multiple continental regions, issues of downscaling global model integrations to regional / local applications (i.e. hydrologic and crop modeling). We compare / contrast the role of the U.S. National Multi- Model Experiment initiative in seasonal forecasts and the CMIP-5 climate model experiments in supporting these efforts. Examples of these scenarios, their use, and an assessment of their utility as well as limitations will be presented.

Robertson, Franklin R.↗

Automated Impact Assessment: A New Approach to ISS Payload Operations Anomaly Response

The International Space Station (ISS) Payload Operations and Integration Center (POIC) is undergoing rapid growth as the space station program focuses on science and commercial activities. The ISS is expanding its onboard capabilities to support additional science activities. In parallel, the POIC is expanding the capabilities of our operations tools to support the higher pace of payload activities being executed each week. An effect of these changes is that anomaly resolution has become more challenging. In the event of a real-time system fault, operators are responsible for analyzing telemetry displays, anomaly monitoring tools, documentation, and system models in order to produce failure impacts and recovery strategies. This approach to operations relies on the operator to ingest, process, and analyze information from an array of deterministic sources to provide actionable data on impacted systems and activities. Changing the existing approach of anomaly response is necessary if the ISS community is to succeed in the age of science and commercialization of space. The creation of a tool that captures deterministic technical systems knowledge and integrates existing telemetry, documentation, and planning information will allow the burden of impact assessment to be automated, thereby allowing the operator to focus on non-deterministic tasks, such as recovering failed systems and restoring critical payload operations.

Hall, R. Mason↗

Radio Follow-up of a Candidate γ-Ray Transient in the Sky Localization Area of GW170608

After the identification of a candidate γ-ray transient in the error region of the binary black hole (BBH) merger GW150914 by the Fermi satellite, the question of whether BBH mergers can be associated with electromagnetic counterparts remains highly debated. Here, we present radio follow-up observations of GW170608, a BBH merger that occurred during the second observing run (O2) of the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO). Our radio follow-up focused on a specific field contained in the GW170608 sky localization area, where a candidate high-energy transient was detected by the Fermi Large Area Telescope (LAT). We make use of data collected at 1.4 GHz with the Karl G. Jansky Very Large Array (VLA), as well as with the VLA Lowband Ionosphere and Transient Experiment (VLITE). Our analysis is sensitive to potential radio afterglows with luminosity densities L(1.4GHz) ≳ 6 x 10^(28) erg/sHz. In the most optimistic theoretical models, ≈20% of BBH events occurring in massive hosts could be associated with outflows as radio luminous as this. Although we find no evidence for the presence of a radio counterpart associated with the LAT candidate in the GW170608 error region, our analysis demonstrates the feasibility of future radio follow-up observations of well-localized BBHs. Comparing our radio upper limits with theoretical expectations for the radio afterglows potentially associated with jets launched in BBH mergers, we find that for jets of energy ≈10^(49) erg seen on-axis, only jet angles θ(jet)≳40° are compatible with the observations.

Kyle Artkop↗

Arctic Biogeochemical and Optical Properties of Dissolved Organic Matter Across River to Sea Gradients

Arctic landscapes are warming and becoming wetter due to changes in precipitation and the timing of snowmelt which consequently alters seasonal runoff and river discharge patterns. These changes in hydrology lead to increased mobilization and transport of terrestrial dissolved organic matter (DOM) to Arctic coastal seas where significant impacts on biogeochemical cycling can occur. Here, we present measurements of dissolved organic carbon (DOC) and chromophoric DOM (CDOM) in the Yukon River-to-Bering Sea system and two river plumes on the Alaska North Slope which flow into the Beaufort Sea. Our sampling characterized optical and biogeochemical properties of DOM during high and low river discharge periods for the Yukon River-Bering Sea system. The average DOC concentration at the multiple Yukon River mouths ranged from a high of 10.36 mg C L-1 during the ascending limb of the 2019 freshet (late May), 6.4 mg C L-1 during the descending limb of the 2019 freshet (late June), and a low of 3.86 mg C L-1 during low river discharge in August 2018. CDOM absorption coefficient at 412 nm (aCDOM(412)) averaged 8.23 m-1, 5.07 m-1, and 1.9 m-1, respectively. Several approaches to model DOC concentration based on its relationship with CDOM properties demonstrated cross-system seasonal and spatial robustness for these Arctic coastal systems despite spanning an order of magnitude decrease in DOC concentration from the lower Yukon River to the Northern Bering Sea as well as the North Slope systems. “Snapshot” fluxes of DOC and CDOM across the Yukon River Delta to Norton Sound were calculated from our measurements and modeled water fluxes forced with upstream USGS river gauge data. Our findings suggest that during high river flow, DOM reaches the delta largely unaltered by inputs or physical and biogeochemical processing and that the transformations of Yukon River DOM largely occur in the plume. However, during low summer discharge, multiple processes including local precipitation events, microbial decomposition, photochemistry, and likely others can alter the DOM properties within the lower Yukon River and Delta prior to flowing into Norton Sound.

Arctic↗

Forecasting Lightning Threat using Cloud-Resolving Model Simulations

Two new approaches are proposed and developed for making time and space dependent, quantitative short-term forecasts of lightning threat, and a blend of these approaches is devised that capitalizes on the strengths of each. The new methods are distinctive in that they are based entirely on the ice-phase hydrometeor fields generated by regional cloud-resolving numerical simulations, such as those produced by the WRF model. These methods are justified by established observational evidence linking aspects of the precipitating ice hydrometeor fields to total flash rates. The methods are straightforward and easy to implement, and offer an effective near-term alternative to the incorporation of complex and costly cloud electrification schemes into numerical models. One method is based on upward fluxes of precipitating ice hydrometeors in the mixed phase region at the-15 C level, while the second method is based on the vertically integrated amounts of ice hydrometeors in each model grid column. Each method can be calibrated by comparing domain-wide statistics of the peak values of simulated flash rate proxy fields against domain-wide peak total lightning flash rate density data from observations. Tests show that the first method is able to capture much of the temporal variability of the lightning threat, while the second method does a better job of depicting the areal coverage of the threat. Our blended solution is designed to retain most of the temporal sensitivity of the first method, while adding the improved spatial coverage of the second. Exploratory tests for selected North Alabama cases show that, because WRF can distinguish the general character of most convective events, our methods show promise as a means of generating quantitatively realistic fields of lightning threat. However, because the models tend to have more difficulty in predicting the instantaneous placement of storms, forecasts of the detailed location of the lightning threat based on single simulations can be in error. Although these model shortcomings presently limit the precision of lightning threat forecasts from individual runs of current generation models,the techniques proposed herein should continue to be applicable as newer and more accurate physically-based model versions, physical parameterizations, initialization techniques and ensembles of forecasts become available.

McCaul, Eugene W., Jr.↗

GERMcode: A Stochastic Model for Space Radiation Risk Assessment

A new computer model, the GCR Event-based Risk Model code (GERMcode), was developed to describe biophysical events from high-energy protons and high charge and energy (HZE) particles that have been studied at the NASA Space Radiation Laboratory (NSRL) for the purpose of simulating space radiation biological effects. In the GERMcode, the biophysical description of the passage of HZE particles in tissue and shielding materials is made with a stochastic approach that includes both particle track structure and nuclear interactions. The GERMcode accounts for the major nuclear interaction processes of importance for describing heavy ion beams, including nuclear fragmentation, elastic scattering, and knockout-cascade processes by using the quantum multiple scattering fragmentation (QMSFRG) model. The QMSFRG model has been shown to be in excellent agreement with available experimental data for nuclear fragmentation cross sections. For NSRL applications, the GERMcode evaluates a set of biophysical properties, such as the Poisson distribution of particles or delta-ray hits for a given cellular area and particle dose, the radial dose on tissue, and the frequency distribution of energy deposition in a DNA volume. By utilizing the ProE/Fishbowl ray-tracing analysis, the GERMcode will be used as a bi-directional radiation transport model for future spacecraft shielding analysis in support of Mars mission risk assessments. Recent radiobiological experiments suggest the need for new approaches to risk assessment that include time-dependent biological events due to the signaling times for activation and relaxation of biological processes in cells and tissue. Thus, the tracking of the temporal and spatial distribution of events in tissue is a major goal of the GERMcode in support of the simulation of biological processes important in GCR risk assessments. In order to validate our approach, basic radiobiological responses such as cell survival curves, mutation, chromosomal aberrations, and representative mouse tumor induction curves are implemented into the GERMcode. Extension of these descriptions to other endpoints related to non-targeted effects and biochemical pathway responses will be discussed.

Kim, Myung-Hee Y.↗

Impact of Scattering Model on Disdrometer Derived Attenuation Scaling

NASA Glenn Research Center (GRC), the Air Force Research Laboratory (AFRL), and the Politecnico di Milano (POLIMI) are currently entering the third year of a joint propagation study in Milan, Italy utilizing the 20 and 40 GHz beacons of the Alphasat TDP5 Aldo Paraboni scientific payload. The Ka- and Q-band beacon receivers were installed at the POLIMI campus in June of 2014 and provide direct measurements of signal attenuation at each frequency. Collocated weather instrumentation provides concurrent measurement of atmospheric conditions at the receiver; included among these weather instruments is a Thies Clima Laser Precipitation Monitor (optical disdrometer) which records droplet size distributions (DSD) and droplet velocity distributions (DVD) during precipitation events. This information can be used to derive the specific attenuation at frequencies of interest and thereby scale measured attenuation data from one frequency to another. Given the ability to both predict the 40 GHz attenuation from the disdrometer and the 20 GHz timeseries as well as to directly measure the 40 GHz attenuation with the beacon receiver, the Milan terminal is uniquely able to assess these scaling techniques and refine the methods used to infer attenuation from disdrometer data.In order to derive specific attenuation from the DSD, the forward scattering coefficient must be computed. In previous work, this has been done using the Mie scattering model, however, this assumes a spherical droplet shape. The primary goal of this analysis is to assess the impact of the scattering model and droplet shape on disdrometer derived attenuation predictions by comparing the use of the Mie scattering model to the use of the T-matrix method, which does not assume a spherical droplet. In particular, this paper will investigate the impact of these two scattering approaches on the error of the resulting predictions as well as on the relationship between prediction error and rain rate.

statistics↗