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At least 109 records · Page 6

The Role of Atmospheric Aerosol Concentration on Deep Convective Precipitation: Cloud-resolving Model Simulations

Aerosols and especially their effect on clouds are one of the key components of the climate system and the hydrological cycle [Ramanathan et al., 20011. Yet, the aerosol effect on clouds remains largely unknown and the processes involved not well understood. A recent report published by the National Academy of Science states "The greatest uncertainty about the aerosol climate forcing - indeed, the largest of all the uncertainties about global climate forcing - is probably the indirect effect of aerosols on clouds NRC [2001]." The aerosol effect on clouds is often categorized into the traditional "first indirect (i.e., Twomey)" effect on the cloud droplet sizes for a constant liquid water path and the "semi-direct" effect on cloud coverage. The aerosol effect on precipitation processes, also known as the second type of aerosol indirect effect, is even more complex, especially for mixed-phase convective clouds. ln this paper, a cloud-resolving model (CRM) with detailed spectral-bin microphysics was used to examine the effect of aerosols on three different deep convective cloud systems that developed in different geographic locations: South Florida, Oklahoma and the Central Pacific. In all three cases, rain reaches the ground earlier for the low CCN (clean) case. Rain suppression is also evident in all three cases with high CCN (dirty) case. However, this suppression only occurs during the first hour of the simulations. During the mature stages of the simulations, the effects of increasing aerosol concentration range from rain suppression in the Oklahoma case, to almost no effect in the Florida case, to rain enhancement in the Pacific case. These results show the complexity of aerosol interactions with convection.

Tao, W.-K.↗

The Role of Atmospheric Aerosol Concentration on Deep Convective Precipitation: Cloud-Resolving Model Simulations

Aerosols and especially their effect on clouds are one of the key components of the climate system and the hydrological cycle [Ramanathan et al., 2001]. Yet, the aerosol effect on clouds remains largely unknown and the processes involved not well understood. A recent report published by the National Academy of Science states "The greatest uncertainty about the aerosol climate forcing - indeed, the largest of all the uncertainties about global climate forcing - is probably the indirect effect of aerosols on clouds NRC [2001]." The aerosol effect on Clouds is often categorized into the traditional "first indirect (i.e., Twomey)" effect on the cloud droplet sizes for a constant liquid water path and the "semi-direct" effect on cloud coverage. The aerosol effect on precipitation processes, also known as the second type of aerosol indirect effect, is even more complex, especially for mixed-phase convective clouds. In this paper, a cloud-resolving model (CRM) with detailed spectral-bin microphysics was used to examine the effect of aerosols on three different deep convective cloud systems that developed in different geographic locations: South Florida, Oklahoma and the Central Pacific, In all three cases, rain reaches the ground earlier for the low CCN (clean) case. Rain suppression is also evident in all three cases with high CCN (dirty) case. However, this suppression only occurs during the first hour of the simulations. During the mature stages of the simulations, the effects of increasing aerosol concentration range from rain suppression in the Oklahoma case, to almost no effect in the Florida case, to rain enhancement in the Pacific case. These results show the complexity of aerosol interactions with convection. The model results suggest that evaporative cooling is a key process in determining whether high CCN reduces or enhances precipitation. Stronger evaporative cooling can produce a stronger cold pool and thus stronger low-level convergence through interactions with the low-level wind shear. Consequently, precipitation processes can be more vigorous. For example,, the evaporative cooling is more than two times stronger in the lower troposphere with high CCN for the Pacific case. Sensitivity tests also suggest that ice processes are crucial for suppressing precipitation in the Oklahoma case with high CCN.

Tao, Wei-Kuo↗

Incremental Learning for Passive Microwave Precipitation Retrievals using Advanced Technology Microwave Sounder

Spaceborne passive microwave (PMW) radiometry is central to global precipitation monitoring, yet retrieval uncertainties remain substantial, particularly for cross-track sounders whose variable footprints and channel configurations are optimized for atmospheric temperature and moisture profiling rather than precipitation. Consequently, existing operational products often exhibit angular-dependent biases, limited effective swath utilization, unrealistic rainfall probability distributions, and systematic misclassification of precipitation phase. These limitations are further compounded by the scarcity of globally accurate and representative precipitation observations, as training data from the Dual-frequency Precipitation Radar (DPR) and the Cloud Profiling Radar (CPR) are spatially sparse, lack uniform global coverage, and exhibit heterogeneous error characteristics across precipitation regimes. To address these challenges, this study presents a supervised retrieval algorithm that incrementally trains an ensemble of extreme gradient-boosted decision trees by augmenting base learners with pre-training on reanalysis data and post-training on coincident DPR and CPR observations matched with the Advanced Technology Microwave Sounder (ATMS). By transferring prior information from reanalysis to posterior constraints from radar observations and adopting a sequential detection–estimation strategy for precipitation phase and rate retrieval, the proposed approach yields retrievals across the full ATMS swath that are largely free from persistent deficiencies in current Global Precipitation Measurement (GPM) passive microwave operational products. In particular, the method resolves bimodal artifacts in rainfall retrievals and mitigates systematic high-latitude snowfall biases, including overestimation across the Arctic and underestimation across the Antarctic. Validation against independent Multi-Radar Multi-Sensor (MRMS) data over the Contiguous United States (CONUS) further demonstrates improved performance in precipitation phase detection and rate estimation relative to both reanalysis and current GPM PMW products.

Mahyar Garshasbi↗

A Risk-Informed Approach to Trustworthiness Assessment in Digital Twins-Based Autonomous Control

In autonomous control systems, digital twins (DTs) are used to perform diagnostic and prognostic functions. The trustworthiness of these DTs is dependent on quality and coverage of the training data, model accuracy and integrity of sensor data. This work introduces a methodology to determine the trustworthiness of a DT system given faulty sensor data using a risk informed approach. Bayesian Belief Networks (BBNs) are used to propagate uncertainties and determine the probability of trustable recommendations. The decision to trust the control action provided by the DT is based on the DT output, expert opinion, and severity of problems. The performance of DTs is reliant on the data they are trained on. When they encounter out of distribution data, the trustworthiness of the recommendations decreases. To address this issue, we include an expert component that provides input on sensor degradation. For this, we utilize a generative artificial intelligence (AI) model, such as Generative Pretrained Transformer (GPT). The GPT functions as an expert with broad knowledge. The GPT is fine-tuned to understand and discriminate sensor degradation scenarios using manufactured data. This methodology is demonstrated through a case study on a Nearly Autonomous Management and Control System (NAMAC) during a steady state scenario. Various sensor degradation types with different severity levels are considered. Degraded sensor data is processed by the DT system and the fine-tuned GPT. Finally, using the BBN, we combine the GPT information and the DT output with its sources of uncertainty. This provides an output regarding the trustworthiness of the DT recommendation.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Communications and tracking - Light and IR will help carry high traffic

The space station currently under consideration by NASA must simultaneously track and communicate with the many vehicles and objects surrounding it in orbit. While the Space Shuttle has 23 antennas, more than 50 will be required by the space station. In addition to Shuttle-compatible equipment at P, L, C, S, and Ku bands, the station system will probably incorporate Ka, W, IR and optical frequency equipment for tracking and communications. A major design challenge is foreseen in the placement of separate antennas, lenses and reflectors over the station's external geometry in order to give both the overlapping fields of view required for spherical coverage and the radiation of unambiguous navigation guide beams and markers. Adaptive distributed element arrays are under consideration. Another approach to spherical coverage involves the use of omnidirectional antennas which both transmit and receive RF energy over a wide range of angles.

Dickinson, R. M.↗

Rotational modulation and flares on RS Canum Venaticorum and BY Draconis stars. 18: Coordinated VLA, ROSAT, and IUE observations of RS CVn binaries

As part of a coordinated program of multi-wavelength observations of RS CVn close binary systems, we observed 15 systems with the Very Large Array (VLA) and 10 systems with IUE, simultaneously or nearly simultaneously with the ROSAT All Sky Survey observations of these stars. Of the 22 systems observed with ROSAT, three were observed both by IUE and the VLA. Radio observations were made at 3.6, 6 and 20 cm. Of the 15 observed RS CVn systems, we detected 11 with greater than 4 sigma confidence at one or more wavelengths. The IUE observations were made within the RIASS (ROSAT-IUE All Sky Survey) program. We present the results of the VLA observations, along with the corresponding subsets of the ROSAT Position Sensitive Proportional Counter (PSPC) X-ray and Wide Field Camera (WFC) XUV survey, and RIASS IUE observations. We obtained an extended VLA/IUE/ROSAT simultaneous coverage of one system, TY Pyx, covering more than one orbital period. These observations reveal that the quiescent radio flux of TY Pyx is relatively constant over time scales of up to 7 hours, but that it did change by a factor of 3 over 24 hours, probably due to a flare on 1990 Nov. 12. The UV, XUV and X-ray fluxes do not show large day-to-day or phase-related variability. The observation of the decay phase of a radio flare on EI Eri, with no accompanying X-ray or XUV flare, suggests that the lack of a strong correlation between X-ray and radio flares previously noted for dMe flare stars holds for RS CVn systems as well. We suggest that the radio flare may have been due to a coherent emission process such as electron cyclotron emission. The simultaneous measurements presented here provide a unique test of the general correlation between radio and soft X-ray luminosities, L(sub radio) approximately L(sub x exp m) (Drake et al. 1989) with a power-law slope close to unity, which was previously derived using data obtained years apart. Our derived slopes are consistent with and thus support the general correlations between coronal and chromospheric/transition region emissions previously derived from nonsimultaneous measurements of a much larger sample of these variable sources. However, the importance of simultaneous measurements for accurate energy balance calculations is stressed.

Fox, David C.↗

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Aerosols and especially their effect on clouds are one of the key components of the climate system and the hydrological cycle [Ramanathan et al., 2001]. Yet, the aerosol effect on clouds remains largely unknown and the processes involved not well understood. A recent report published by the National Academy of Science states "The greatest uncertainty about the aerosol climate forcing - indeed, the largest of all the uncertainties about global climate forcing - is probably the indirect effect of aerosols on clouds [NRC, 2001]." The aerosol effect on clouds is often categorized into the traditional "first indirect (i.e., Twomey)" effect on the cloud droplet sizes for a constant liquid water path [Twomey, 1977] and the "semi-direct" effect on cloud coverage [e.g., Ackerman et al ., 2001]." Enhanced aerosol concentrations can also suppress warm rain processes by producing a narrow droplet spectrum that inhibits collision and coalescence processes [e.g., Squires and Twomey, 1961; Warner and Twomey, 1967; Warner, 1968; Rosenfeld, 19991. The aerosol effect on precipitation processes, also known as the second type of aerosol indirect effect [Albrecht, 1989], is even more complex, especially for mixed-phase convective clouds. Table 1 summarizes the key observational studies identifying the microphysical properties, cloud characteristics, thermodynamics and dynamics associated with cloud systems from high-aerosol continental environments. For example, atmospheric aerosol concentrations can influence cloud droplet size distributions, warm-rain process, cold-rain process, cloud-top height, the depth of the mixed phase region, and occurrence of lightning. In addition, high aerosol concentrations in urban environments could affect precipitation variability by providing an enhanced source of cloud condensation nuclei (CCN). Hypotheses have been developed to explain the effect of urban regions on convection and precipitation [van den Heever and Cotton, 2007 and Shepherd, 2005]. Please see Tao et al. (2007) for more detailed description on aerosol impact on precipitation. Recently, a detailed spectral-bin microphysical scheme was implemented into the Goddard Cumulus Ensemble (GCE) model. Atmospheric aerosols are also described using number density size-distribution functions. A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region and summertime convection over a mid-latitude continent with different concentrations of CCN: a low "clean" concentration and a high "dirty" concentration. The impact of atmospheric aerosol concentration on cloud and precipitation will be investigated.

Tao, Wei-Kuo↗

PRIME: A bottom-up approach to probabilistic rule development

PRIME is a system to be used by an intelligent machine to allow it to operate in an abstract but uncertain (or stochastic) environment. It maintains a model of the effects of the machine's actions in the form of a rule base, which is induced from experience. This bottom-up approach to rule development allows the model to adapt to changes in the environment. Each rule consists of a condition under which the rule is active, an action, the effect of the action on the environment, and an estimate of the probability of this effect occurring. The effect probabilities are used to model the uncertainty in the environment, permitting multiple possible effects for a single action under a particular set of conditions. The objective of the intelligent machine is to satisfy user-specified goals with maximum probability of success. PRIME fulfills this requirement in two ways: it continuously updates the rule base with the most recent information, to ensure the validity of the model; and it generates plans which have the maximum probability of achieving the goals, based on the probability estimates in the rule base. PRIME is composed of three main processes: exploration, generalization, and planning. In exploration, the machine executes various randomly chosen actions, observes the effects on the environment, and updates the rule base accordingly. This process is used to develop the rule base in simulation, as well as to supplement the current knowledge during normal operation. Generalization is the procedure used to induce general rules from experience, which is encoded in the form of specific rules. These general rules extend the machine's knowledge to situations which have not been encountered yet, thereby increasing the capability of the machine to plan effectively. Planning is the process of constructing an optimal sequence of actions to satisfy a goal, using the rule base to predict the effects of these actions and to determine the probability of success of the plan. The rule representation and many other data structures were specifically chosen to maximize the efficiency of these processes. A simulated environment was designed to test the performance of PRIME. The results of experimentation were largely negative. The main problem was that the domain coverage of the rules was inadequate for the number of rules stored in the rule base, due to redundancies in general rules and numerous rules covering ineffective actions. It was determined that a more efficient generalization, and some form of goal-directed exploration, are necessary in order to solve most of the current deficiencies in PRIME.

Miller, Scott A.↗

Trajectory Design for the Europa Clipper Mission Concept

Europa is one of the most scientifically intriguing targets in planetary science due to its potential suitability for extant life. As such, NASA has funded the California Institute of Technology Jet Propulsion Laboratory and the Johns Hopkins University Applied Physics Laboratory to jointly determine and develop the best mission concept to explore Europa in the near future. The result of nearly 4 years of work--the Europa Clipper mission concept--is a multiple Europa flyby mission that could efficiently execute a number of high caliber science investigations to meet Europa science priorities specified in the 2011 NRC Decadal Survey, and is capable of providing reconnaissance data to maximize the probability of both a safe landing and access to surface material of high scientific value for a future Europa lander. This paper will focus on the major enabling component for this mission concept--the trajectory. A representative trajectory, referred to as 13F7-A21, would obtain global-regional coverage of Europa via a complex network of 45 flybys over the course of 3.5 years while also mitigating the effects of the harsh Jovian radiation environment. In addition, 5 Ganymede and 9 Callisto flybys would be used to manipulate the trajectory relative to Europa. The tour would reach a maximum Jovicentric inclination of 20.1 deg. have a deterministic (Delta)V of 164 m/s (post periapsis raise maneuver), and a total ionizing dose of 2.8 Mrad (Si).

orbital mechanics↗

Sorption of Arsenate, Selenate, and Molybdate on the Barite (001) Surface

Interactions of ions with ionically bonded minerals such as barite (BaSO 4 ) influence the fate and transport of the ions, while the factors that control the sorption of toxic oxyanions on barite remain elusive. In this study, the sorption of arsenate, selenate, and molybdate on the barite (001) surface was examined at pH ~5 using in situ crystal truncation rod analysis, resonant anomalous X-ray reflectivity, and atomic force microscopy. The results show that arsenate and selenate mainly incorporate into the top monolayer of barite, while molybdate primarily adsorbs above the surface. The sorption coverage of arsenate is greater (by ~100%) than that of selenate but similar to that of molybdate. The different incorporation coverages between arsenate and selenate can be explained by their different protonation states at pH 5. The incorporated arsenate may be stabilized by hydrogen bonds between arsenate and oxygen atoms of neighboring sulfate compared to selenate, which exists predominantly in the deprotonated state. The adsorption of molybdate above the surface probably stems from a surface-induced oligomerization, as the anion and the oligomer may be too large for incorporation. Our observation of these different sorption mechanisms demonstrates how the physicochemical properties of the anions control the selective uptake of the toxic metals on the dominant surface of the ionically bonded mineral barite.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dynamics of suspended sediment plumes in Lake Ontario

The absence of turbidity plumes during the winter was well documented in an ususually successful sequence of images obtained February 10 - 12, 1974. Useful imagery of the south shore of Lake Ontario was obtained on 3 successive days at a time when sky cover over the area normally approaches complete coverage. Imagery of the Oswego, Genesee, and Niagara rivers failed to detect any plumes, however faint. Despite strong northwest winds on February 11 there was no indication of shoreline erosion generated by wave action. Frozen ground, snow cover, shoreline icing and minimal construction and farm activity without doubt reduces the probability of sediment movement in winter. Thunderstorm activity over the study area is very rare during the cold season so that the erosive energy of rainfall is greatly reduced. Moreover, a fairly high percentage of the winter precipitation is in the form of snow or sleet further reducing the impact of rainfall energy on sediment transport.

Pluhowski, E. J.↗

Evaluation and comparisons of recent geopotential solutions

A statistical evaluation of some of the recent satellite determined gravity models, including some with distinct data base, indicates that the geopotential coefficients of these models are individually meaningful for frequencies with wave numbers n = 2 through 7 certainly and wave numbers n = 8 through 10 probably. Geopotential coefficients in higher frequency ranges while apparently important for computing accurate satellite orbits seem to have little geophysical significance in an individual sense. Differences between various gravity models and those satellite purely between determined geopotential models and their associated combination models show no consistent relationship to surface gravimetric coverage. Additional classical tracking data are important in improving the existing description of the earth's gravity field but their contribution in extending its frequency range beyond what is now available is uncertain.

Khan, M. A.↗

Space telescope optical telescope assembly/scientific instruments. Phase B: Preliminary design and program definition study. Volume 2A(3): Astrometry

Wide field measurements, namely, measurements of relative angular separations between stars over a relatively wide field for parallax and proper motion determinations, were made with the third fine guidance sensor. Narrow field measurements, i.e., double star measurements, are accomplished primarily with the area photometer or faint object camera at f/96. The wavelength range required can be met by the fine guidance sensor which has a spectral coverage from 3000 to 7500 A. The field of view of the fine guidance sensor also exceeds that required for the wide field astrometric instrument. Requirements require a filter wheel for the wide field astrometer, and so one was incorporated into the design of the fine guidance sensor. The filter wheel probably would contain two neutral density filters to extend the dynamic range of the sensor and three spectral filters for narrowing effective double star magnitude difference.

Source record↗

CsO x Nanostructures on Au(111): Morphology- and Size-dependent Activity for the Water–Gas Shift Reaction

Alkali oxides are typically used as promoters of heterogeneous catalysts for the water–gas shift (WGS; H 2 O + CO → H 2 + CO 2 ) reaction. On Au(111), CsO x exhibits diverse nanostructures at varying coverages, as revealed by scanning tunneling microscopy. Clusters of cesium oxide (Cs 2 O 2 ) nucleate at elbow sites of the Au(111) herringbone when θ Cs is less than 0.1 ML. Subsequently, these clusters transform into two-dimensional (2D) islands (Cs 2 O, Cs 2 O 2 , CsO 2 ) as the cesium coverage increases (θ Cs > 0.1 ML). Both types of CsO x nanostructures enable the WGS process on Au(111). The highest activity was seen for the cesium oxide clusters which facilitated the partial dissociation of water and binding of CO. The CO ads and OH ads groups were not strongly bound and probably reacted to yield a short-lived HOCO intermediate that led to gaseous H 2 and CO 2 . The 2D islands of CsO x also enabled the WGS but their efficiency was reduced due to the formation of cesium hydroxide compounds (limiting mobility of OH groups) and the generation of CO 3 and C species (blocking of active centers). The fact that the performance of the CsO x /Au(111) catalysts changed dramatically with variations in the chemical properties of the CsO x nanostructures indicates that the alkali oxide was an integral part of the active phase, playing a central role in the activation and conversion of the reactants. To attach the label of “promoter” to CsO x is a simplification that does not help in the design and optimization of catalysts for C1 chemistry. In conclusion, to achieve a rational design, one must consider the structural and chemical properties of the alkali oxide.

36 MATERIALS SCIENCE↗

Impact of Assimilating Adaptively Thinned AIRS Cloud-Cleared Radiances in the GEOS

This work examines the assimilation of AIRS (Atmospheric Infrared Sounder) radiances from two points of view: the thinning strategy and the use of cloud-cleared radiances as opposed to clear-sky. Previous published work by this team, based on a very large set of Observing System Experiments performed with a 2014 3DVAR version of the GEOS (Goddard Earth Observing System), has shown that the assimilation of adaptively thinned AIRS cloud-cleared radiances (CCRs) improves the representation of tropical cyclones (TCs) without damaging the global forecast skill. The simple adaptive methodology is based on denser AIRS coverage in moving domains centered on TCs, and sparser coverage everywhere else. Subsequent experiments showed that the adaptive methodology produces good results also when applied to clear-sky CrIS (Cross-track Infrared Sounder) and IASI (Infrared Atmospheric Sounding Interferometer) radiances. In addition, the results indicate that the density of all hyperspectral data assimilated over meteorologically inactive areas is excessive, probably because of horizontal error correlation, suggesting that the global thinning should be more aggressive. More recent work focused on the polar regions has shown another positive impact of assimilating cloud-cleared AIRS radiances instead of clear-sky. The results show that high latitude atmospheric dynamics is very sensitive to the representation of the lower tropospheric temperature structure over the Arctic region. Specifically, assimilation of CCRs over areas that are data poor and also affected by broken stratus clouds, and as such minimally observed by AIRS clear-sky radiances, changes substantially the temperature structure over the Arctic low troposphere. Ingestion of CCRs over the region propagates, through hydrostatic adjustments, to mid-tropospheric geopotential height, allowing for better prediction of mid-latitude waves. In addition, adaptively thinned CCRs also improve the representation of mesoscale convective cyclones at high latitudes. An example of an Antarctic low is provided. Finally, recent ongoing work with the hybrid 4DenVAR GEOS, investigating the 2017 boreal TC season, has confirmed the previous results: namely that aggressively thinned cloud-cleared radiances improve TC structure with no loss of global skill.

CCR↗

Surface features of Phobos and Deimos

Viking Orbiter images have provided nearly complete coverage of the two satellites of Mars and have been used to construct maps of the surface features of Phobos and Deimos. The satellites have radically different appearances although nearly all features on both objects were formed directly or indirectly by impact cratering. Phobos has an extensive network of linear depressions (grooves) that probably were formed indirectly by the largest impact recorded on Phobos. Deimos lacks grooves as well as the large number of ridges that occur on Phobos. Craters on Deimos have substantial sediment fill; those on Phobos have none. Evidence of downslope movement of debris is prominent on Deimos but is rare on Phobos. Many of the differences between Phobos and Deimos may be caused by modest differences in mechanical properties. However, the lack of a very large crater on Deimos may be responsible for its lack of grooves.

Thomas, P.↗

Assessment of the Advanced Very High Resolution Radiometer (AVHRR) for Snowfall Retrieval in High Latitudes Using CloudSat and Machine Learning

Precipitation retrieval is a challenging topic, especially in high latitudes (HL), and current precipitation products face ample challenges over these regions. This study investigates the potential of the Advanced Very High Resolution Radiometer (AVHRR) for snowfall retrieval in HL using CloudSat radar information and machine learning (ML). With all the known limitations, AVHRR observations should be considered for HL snowfall retrieval because 1) AVHRR data have been continuously collected for about four decades on multiple platforms with global coverage, and similar observations will likely continue in the future; 2) current passive microwave satellite precipitation products have several issues over snow and ice surfaces; and 3) good coincident observations between AVHRR and CloudSat are available for training ML algorithms. Using ML, snowfall rate was retrieved from AVHRR’s brightness temperature and cloud probability, as well as auxiliary information provided by numerical reanalysis. The results indicate that the ML-based retrieval algorithm is capable of detection and estimation of snowfall with comparable or better statistical scores than those obtained from the Atmospheric Infrared Sounder (AIRS) and two passive microwave sensors contributing to the Global Precipitation Measurement (GPM) mission constellation. The outcomes also suggest that AVHRR-based snowfall retrievals are spatially and temporally reasonable and can be considered as a quantitatively useful input to the merged precipitation products that require frequent sampling or long-term records.

Mohammad Reza↗

An error bound for instantaneous coverage

An error bound is derived for a reliability model approximation method. The approximation method is appropriate for the semi-Markov models of reconfigurable systems that are designed to achieve extremely high reliability. The semi-Markov models of these system are complex, and a significant amount of their complexity arises from the detailed descriptions of the reconfiguration processes. The reliability model approximation method consists of replacing a detailed description of a reconfiguration process with the probabilities of the possible outcomes of the reconfiguration process. These probabilities are included in the model as instantaneous jumps from the fault-occurrence state. Since little time is spent in the reconfiguration states, instantaneous jumps are a close approximation to the original model. This approximation procedure is shown to produce an overestimation for the probability of system failure, and an error bound is derived for this overestimation.

White, Allan L.↗