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At least 559 records · Page 31

A Remote Sensing-Based Tool for Assessing Rainfall-Driven Hazards

RainyDay is a Python-based platform that couples rainfall remote sensing data with Stochastic Storm Transposition (SST) for modeling rainfall-driven hazards such as floods and landslides. SST effectively lengthens the extreme rainfall record through temporal resampling and spatial transposition of observed storms from the surrounding region to create many extreme rainfall scenarios. Intensity-Duration-Frequency (IDF) curves are often used for hazard modeling but require long records to describe the distribution of rainfall depth and duration and do not provide information regarding rainfall space-time structure, limiting their usefulness to small scales. In contrast, Rainy Day can be used for many hazard applications with 1-2 decades of data, and output rainfall scenarios incorporate detailed space-time structure from remote sensing. Thanks to global satellite coverage, Rainy Day can be used in inaccessible areas and developing countries lacking ground measurements, though results are impacted by remote sensing errors. Rainy Day can be useful for hazard modeling under nonstationary conditions.

Daniel B Wright↗

Computational Model Prediction and Biological Validation Using Simplified Mixed Field Exposures for the Development of a GCR Reference Field

The yield of chromosomal aberrations has been shown to increase in the lymphocytes of astronauts after long-duration missions of several months in space. Chromosome exchanges, especially translocations, are positively correlated with many cancers and are therefore a potential biomarker of cancer risk associated with radiation exposure. Although extensive studies have been carried out on the induction of chromosomal aberrations by low- and high-LET radiation in human lymphocytes, fibroblasts, and epithelial cells exposed in vitro, there is a lack of data on chromosome aberrations induced by low dose-rate chronic exposure and mixed field beams such as those expected in space. Chromosome aberration studies at NSRL will provide the biological validation needed to extend the computational models over a broader range of experimental conditions (more complicated mixed fields leading up to the galactic cosmic rays (GCR) simulator), helping to reduce uncertainties in radiation quality effects and dose-rate dependence in cancer risk models. These models can then be used to answer some of the open questions regarding requirements for a full GCR reference field, including particle type and number, energy, dose rate, and delivery order. In this study, we designed a simplified mixed field beam with a combination of proton, helium, oxygen, and iron ions with shielding or proton, helium, oxygen, and titanium without shielding. Human fibroblasts cells were irradiated with these mixed field beam as well as each single beam with acute and chronic dose rate, and chromosome aberrations (CA) were measured with 3-color fluorescent in situ hybridization (FISH) chromosome painting methods. Frequency and type of CA induced with acute dose rate and chronic dose rates with single and mixed field beam will be discussed. A computational chromosome and radiation-induced DNA damage model, BDSTRACKS (Biological Damage by Stochastic Tracks), was updated to simulate various types of CA induced by acute exposures of the mixed field beams used for the experiments. The chromosomes were simulated by a polymer random walk algorithm with restrictions to their respective domains in the nucleus [1]. The stochastic dose to the nucleus was calculated with the code RITRACKS [2]. Irradiation of a target volume by a mixed field of ions was implemented within RITRACKs, and the fields of ions can be delivered over specific periods of time, allowing the simulation of dose-rate effects. Similarly, particles of various types and energies extracted from a pre-calculated spectra of galactic cosmic rays (GCR) can be used in RITRACKS. The number and spatial location of DSBs (DNA double-strand breaks) were calculated in BDSTRACKS using the simulated chromosomes and local (voxel) dose. Assuming that DSBs led to chromosome breaks, and simulating the rejoining of damaged chromosomes occurring during repair, BDSTRACKS produces the yield of various types of chromosome aberrations as a function of time (only final yields are presented). A comparison between experimental and simulation results will be shown.

Hada, M.↗

Fokker-Planck response of stochastic satellites

The present investigation is concerned with the effects of stochastic geometry and random environmental torques on the pointing accuracy of spinning and three-axis stabilized satellites. The study of pointing accuracies requires a knowledge of the rates of error growth over and above any criteria for the asymptotic stability of the satellites. For this reason the investigation is oriented toward the determination of the statistical properties of the responses of the satellites. The geometries of the satellites are considered stochastic so as to have a phenomenological model of the motions of the flexible structural elements of the satellites. A widely used method of solving stochastic equations is the Fokker-Planck approach where the equations are assumed to define a Markoff process and the transition probability densities of the responses are computed directly as a function of time. The Fokker-Planck formulation is used to analyze the response vector of a rigid satellite.

Huang, T. C.↗

Stochastic acceleration of electrons in solar flares

The generation of lower-hybrid waves by cross-field currents is applied to reconnection processes proposed for solar flares. Recent observations on fragmentation of energy release and acceleration, and on hard X-ray (HXR) spectra are taken into account to develop a model for electron acceleration by resonant stochastic interactions with lower-hybrid turbulence. The continuity of the velocity distribution is solved including collisions and escape from the turbulence region. It describes acceleration as a diffusion process in velocity space. The result indicates two regimes that are determined by the energy of the accelerating electrons which may explain the double power-law often observed in HXR spectra. The model further predicts an anticorrelation between HXR flux and spectral index in agreement with observations.

Benz, A. O.↗

NASA Radiation Track Image GUI for Assessing Space Radiation Biological Effects

The high-charge high-energy (HZE) ion components of the galactic cosmic rays when compared to terrestrial forms of radiations present unique challenges to biological systems. In this paper we present a deoxyribonucleic acid (DNA) breakage model to visualize and analyze the impact of chromatin domains and DNA loops on clustering of DNA damage from X rays, protons, and HZE ions. Our model of DNA breakage is based on a stochastic process of DNA double-strand break (DSB) formulation that includes the amorphous model of the radiation track and a polymer model of DNA packed in the cell nucleus. Our model is a Monte-Carlo simulation based on a randomly located DSB cluster formulation that accomodates both high- and low-linear energy transfer radiations. We demonstrate that HZE ions have a strong impact on DSB clustering, both along the chromosome length and in the nucleus volume. The effects of chromosomal domains and DNA loops on the DSB fragment-size distribution and the spatial distribution of DSB in the nucleus were studied. We compare our model predictions with the spatial distribution of DSB obtained from experiments. The implications of our model predictions for radiation protection are discussed.

Ponomarev, Artem L.↗

Performability evaluation of the SIFT computer

The paper deals with the models, techniques, and evaluation methods that were successfully used to test the performance of the SIFT degradable computing system. The performance of the computer plus its air transport mission environment is modeled as a random variable, taking values in a set of 'accomplishment level'. The levels are defined in terms of four attributes of total system (computer plus environment) behavior, namely safety, no change in mission profile, no operational penalties, and no economic penalties. The base model of the total system is a stochastic process, whose states describe the internal structure of SIFT and the relevant conditions of its computational environment. Base model state trajectories are related to accomplishment levels via a special function, and solution methods are then used to determine the performability of the total system for various parameters of the computer and environment.

Meyer, J. F.↗

Guidance and Control strategies for aerospace vehicles

A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions.

Hibey, J. L.↗

Complexity of life via collective mind

e mind is introduced as a set of simple intelligent units (say, neurons, or interacting agents), which can communicate by exchange of information without explicit global control. Incomplete information is compensated by a sequence of random guesses symmetrically distributed around expectations with prescribed variances. Both the expectations and variances are the invariants characterizing the whole class of agents. These invariants are stored as parameters of the collective mind, while they contribute into dynamical formalism of the agents' evolution, and in particular, into the reflective chains of their nested abstract images of the selves and non-selves. The proposed model consists of the system of stochastic differential equations in the Langevin form representing the motor dynamics, and the corresponding Fokker-Planck equation representing the mental dynamics (Motor dynamics describes the motion in physical space, while mental dynamics simulates the evolution of initial errors in terms of the probability density). The main departure of this model from Newtonian and statistical physics is due to a feedback from the mental to the motor dynamics which makes the Fokker-Planck equation nonlinear. Interpretation of this model from mathematical and physical viewpoints, as well as possible interpretation from biological, psychological, and social viewpoints are discussed. The model is illustrated by the dynamics of a dialog.

collective intelligence↗

The stochastic evolution of asteroidal regoliths and the origin of brecciated and gas-rich meteorites

A model is constructed which views regolith evolution on asteroids as a stochastic process. Average values are shown to be poor descriptors of regolith depth. The utility of the average depth is not significantly increased by avoiding large craters or thick ejecta deposits, a procedure adopted in previous regolith studies. The statistical uncertainty associated with regolith depth severely limits the power of regolith models in predicting parent-body size for brecciated meteorites. A Monte Carlo algorithm was used to simulate the random walks and corresponding charged-particle irradiation histories of grains in regoliths. On rocky asteroids, only about 20 percent of the grains was exposed to solar cosmic ray ions. Results based on present-day conditions in the asteroid belt agree well with irradiation features observed in gas-rich meteorites. An origin during epochs of early solar system evolution is not required.

Housen, K. R.↗

Stochastic three-wave interaction in flaring solar loops

A model is proposed for the dynamic structure of high-frequency microwave bursts. The dynamic component is attributed to beams of precipitating electrons which generate electrostatic waves in the upper hybrid branch. Coherent upconversion of the electrostatic waves to electromagnetic waves produces an intrinsically stochastic emission component which is superposed on the gyrosynchrotron continuum generated by stably trapped electron fluxes. The role of the density and temperature of the ambient plasma in the wave growth and the transition of the three wave upconversion to stochastic, despite the stationarity of the energy source, are discussed in detail. The model appears to reproduce the observational features for reasonable parameters of the solar flare plasma.

Vlahos, L.↗

A stochastic approach to robust broadband structural control

Viewgraphs on a stochastic approach to robust broadband structural control are presented. Topics covered include: travelling wave model; dereverberated mobility model; computation of dereverberated mobility; power flow; impedance matching; stochastic systems; control problem; control of stochastic systems; using cost functional; Bernoulli-Euler beam example; compensator design; 'power' dual variables; dereverberation of complex structure; and dereverberated transfer function.

Macmartin, Douglas G.↗

The Effect of Stochastic Acceleration on the Dynamics of Solar Energetic Particles in the Heliosphere

Solar Energetic Particles (SEPs) are crucial in space weather phenomena, impacting space-based technologies and human activities in space. Understanding the dynamics of SEPs, including their acceleration and transport mechanisms, is essential for improving predictive models and mitigating adverse effects. This study investigates the impact of stochastic acceleration (SA) on the dynamics of SEPs within the heliosphere. By integrating stochastic acceleration into a SEP transport model, we assess its impact relative to diffusive shock acceleration (DSA). The investigation utilizes the Adaptive Mesh Particle Simulator (AMPS) within the Space Weather Modeling Framework (SWMF) to simulate SEP dynamics, incorporating solar wind parameters and turbulence from the Alfven Wave Solar Model (AWSoM). To do this, we solve the focused transport equation to model the propagation of SEPs along magnetic field lines, extending these lines to 5 AU to incorporate the potential effects of pitch angle scattering beyond 1 AU. This aspect could notably impact the decay phase of a SEP event. Modeling the transport of SEPs is coupled with the simulation of solar wind dynamics, the interplanetary magnetic field, and the characteristics of Alfven wave turbulence. This presentation covers the modeling approach used in this research, the characterization of the impact of the stochastic acceleration, and the role of pitch angle scattering at various heliocentric distances on the dynamics of the SEP events' decay phase.

SEP↗

Computer Modeling of Sand Transport on Mars Using a Compart-Mentalized Fluids Algorithm (CFA)

It has been postulated that aeolian transport on Mars may be significantly different from that on Earth. From laboratory experiments simulating martian grain transport [2], it has been observed that (saltating) grains striking the bed can cause hundreds of secondary reptation trajectories when impact occurs at speeds postulated for Mars. Some of the ballistically induced trajectories "die ouf' and effectively join the ranks on the creep population that is merely nudged along by impact. Many of the induced reptation trajectories, however, are sufficiently high for the grains to become part of the saltation load (it is irrelevant to the boundary layer how a grain attained its initial lift force). When these grains, in turn, strike the surface, they too are capable of inducing more reptating grains. This cascading effect has been discussed in connection with terrestrial aeolian transport in an attempt to dispel the notion that sand motion is divisible only into creep and saltation loads. On Earth, only a few grains are splashed by impact. On Mars, it may be hundreds. We developed a computer model to address this phenomenon because there are some important ramifications: First, this ratio may mean that martian aeolian transport is dominated by reptation flux rather than saltation. On Earth, the flux would be a roughly balanced mixture between reptation/creep and saltation. On Venus, there would be no transport other than by saltation. In other words, an understanding of planetary aeolian processes may not be necessarily understood by extrapolating from the "Earth case", with only gravity and atmospheric density/viscosity being considered as variables. Second, the reptation flux on Mars may be self sustaining, so that little input is required by the wind once transport has been initiated. The number of grains saturating the boundary layer near the bed may mean that average grain speed on Mars might conceivably be less than that on Earth. This would say much for models of sand comminution on Mars. A multiple-grain transport model using just the equations of grain motion describing lift and drag is impossible to develop owing to stochastic effects --the very effects we wish to model. Also, unless we were to employ supercomputing techniques and extremely complex computer codes that could deal with millions of grains simultaneously, it would also be difficult to model grain transport if we attempted to consider every grain in motion. No existing computer models were found that satisfactorily used the equations of motion to arrive at transport flux numbers for the different populations of saltation and reptation. Modeling all the grains in a transport system was an intractable problem within our resources, and thus we developed what we believe to be a new modeling approach to simulating grain transport. The CFA deals with grain populations, but considers them to belong to various compartmentalized fluid units in the boundary layer. In this way, the model circumvents the multigrain problem by dealing primarily with the consequences of grain transport --momentum transfer between air and grains, which is the physical essence of a dynamic grain-fluid mixture. We thus chose to model the aeolian transport process as a superposition of fluids. These fluids include the air as well as particle populations of various properties. The prime property distinguishing these fluids is upward and downward grain motion. In a normal saltation trajectory, a grain's downwind velocity increases with time, so a rising grain will have a smaller downwind velocity than a failing grain. Because of this disparity in rising and falling grain proper-ties, it seemed appropriate to track these as two separate grain populations within the same physical space. The air itself can be considered a separate fluid superimposed within and interacting with the various grain-cloud "fluids". Additional informaiton is contained in the original.

Marshall, J.↗

AMOC Stability in GISS-E2-1-G: A Case of Stochastic Bifurcation

A 10-member ensemble simulation using the NASA GISS-E2-1-G climate model shows a clear bifurcation in the Atlantic Meridional Overturning Circulation (AMOC) strength under the SSP2-4.5 future scenario, leading to 8 stable AMOC-on and 2 stable AMOC-off climate states after 400 years of integration, despite identical forcing of each ensemble member. Ocean models have previously shown a tipping point where sufficient forcing (e.g. by freshwater inputs) can shut down the AMOC. A variety of fully coupled models have demonstrated this, either through hosing experiments or increased precipitation and warming at high latitudes due to increased concentrations of greenhouse gases. In the GISS simulations, there are no external freshwater perturbations. The bifurcation arises freely in the coupled system and is the result of stochastic variability associated with sea-ice transport and melting in the Irminger Sea following a slowing of the GHG concentration increase at the end of the twenty-first century. We believe this is the first time that a CMIP-class model has shown such a bifurcation across an initial condition ensemble.

GISS ModelE2.1↗

Stochastic Reconstruction of Thermal Protection Material Properties from Arc-Jet Experiments

Material response models are used to assess reliability using variances in the bond-line temperature predictions based on uncertainties in trajectory, aerothermal environment, and material properties. A key deficiency in the current approach is that input uncertainties are too often subjective, empirical, or ad-hoc, and are not rigorously linked to the arc-jet test data used to develop the TPS material model. While materials such as PICA are well understood, future missions may require more novel materials such as HEEET where unknown uncertainties have real consequences on the ability to assess reliability. A quantifiable estimate of reliability requires an iterative methodology where the parameters driving the variance in bond-line temperature (for example) are systematically identified. A test campaign to collect data or develop new models can then be identified to reduce those input uncertainties. A Bayesian inference loop defines these connections mathematically, i.e., prior knowledge about uncertainty is updated based on observation. While these concepts are well known (and often applied intuitively in a non-rigorous approach), only recent advances in reduced-order modelling have made them computationally viable methods for engineering. By replacing deterministic inverse methods with stochastic approaches, the hope is new materials proposed for future missions can more rapidly be developed with a greater understanding of the TPS material reliability. Two additional steps for the analysis of arc jet test data are discussed. The first is ability to construct a reduced-order model using material response simulations (Icarus/US3D) of the arc-jet test articles, and the second is the inclusion of this surrogate model in the Bayesian inversion process. Both capabilities will be demonstrated using prior PICA arc-jet test data. The quality of a surrogate model will be investigated and the variances on the calibrated material properties will be compared to our current understanding of the PICA material model.

Material response↗

Autonomous Ocean World Exploration: Advancement of a Virtual Testbed

The search for life (extinct or extant) and potentially habitable bodies in our solar system and beyond is one of the 12 priority science questions outlined in the National Acadamies’ 2022 decadal survey [5]. Extraterrestrial destinations containing liquid water present an opportunity to search for life as we know it, and in recent years an increasing number of such locations have been discovered within our solar system. Several Jovian moons—Europa, Ganymede, and Callisto [10]—and the Saturnian moons Enceladus [8] and Titan [9] are known or suspected to harbor massive subsurface oceans. Of these "ocean worlds", Europa is the focus of at least one planned NASA orbiter mission, Europa Clipper [4], and an early lander mission concept, the Europa Lander [2, 3]. Whereas most robotic missions to the Moon and Mars (e.g. orbiters, rovers, landers) to date have had ground controllers on Earth tightly involved in mission operations, missions to more distant worlds will require a high degree of onboard autonomy due to long communication lags and blackouts, harsh environments (radiation, cold), and more limited battery and hardware life. The past decade has seen great advances in both AI technologies and computing scalability and performance that offer promising solutions for spacecraft autonomy and motivate the software system and research programs described in this paper. The Ocean Worlds Autonomy Testbed for Exploration, Research, and Simulation (OceanWATERS) [1], which has been in development at the NASA Ames Research Center since 2018, is a virtual environment for testing lander autonomy solutions. It is built on the Robot Operating System (ROS), runs on consumer-grade Linux workstations, and was released as open source in 2020. OceanWATERS provides a physical and visual simulation of a prototypical lander in a Europa-like environment (Figure 1). The lander was modeled after requirements and specifications made in JPL’s Europa Lander Study of 2016 [3]. Simulated lander systems include stereo cameras and spotlights mounted on an antenna mast that pans and tilts, a 6 degrees of freedom (DoF) robotic arm with a force-torque sensor and two interchangeable end effectors, and a battery pack power system. The environment consists of multiple terrain models including a highly detailed model sourced from the FROST dataset [11], simulation of surrounding planetary bodies based on an ephemeris model, and lighting from the sun with associated surface illumination, reflectance, and shadows. Operations supported by OceanWATERS include panoramic and directed imaging of the environment and lander workspace, Cartesian and joint-level arm commanding, grinding of the terrain surface (e.g. digging a trench), and scooping of ground material (Figure 2) which can be discarded or collected as science samples in a receptacle that can be emptied (science operations themselves are not simulated). These operations are realized as ROS Actions and are complimented by a wide selection of telemetry that is continually produced by each lander subsystem. The power system model is driven by the open-source Generic Software Architecture for Prognostics (GSAP) [11] that predicts the battery’s remaining useful life and other characteristics. As a testbed for high-level autonomy, OceanWATERS provides an execution framework based on PLEXIL [12], an open-source plan specification language and execution engine developed largely at Ames. NASA's initial development of OceanWATERS, as well the Ocean Worlds Lander Autonomy Testbed (OWLAT) [6], a complimentary physical testbed developed at JPL, was the first step in a plan for realizing candidate onboard autonomy solutions for such planetary landers. In 2020 NASA solicited applications for its Autonomous Robotics Research for Ocean Worlds (ARROW) program, and in 2021 the similar Concepts for Ocean worlds Life Detection Technology (COLDTech) program. Collectively six research teams, based in universities and companies across the United States, were awarded grants to develop and demonstrate autonomy solutions on OceanWATERS and OWLAT. These 1–2-year projects have now finished or are nearing completion, and a wide variety of autonomy challenges in ocean world surface missions were addressed. Prototyped and demonstrated solutions have included autonomous discovery, response and adaptation to system faults and unexpected environmental events, world model synthesis through perception, plan synthesis using learned models, methods to optimize sample target selection and prioritize science data transmission, extension of PLEXIL for stochastic decision-making, and an integration of a model of JPL’s mission-ready COLDArm [7]. Technologies used in these projects include many forms of machine learning, causal reasoning, automated planning, Markov decision processes, formal methods, and other advanced techniques. A more detailed summary of the ARROW and COLDTech projects is given herein. OceanWATERS has had significant enhancements since its open-source release in 2020. Many of its new features were driven or shaped by feedback from the ARROW and COLDTech teams and requirements of their projects. In support of enabling autonomous adaptation to spacecraft faults (a specific capability solicited by both programs), a fault injection and detection framework was developed that supports a wide and growing range of fault types such as locked joints, image loss, and battery failures. The power system model was completed and integrated into the simulator, starting as a single-cell battery model and later upgraded to a multi-cell model with associated faults such as cell disconnection. Arm/terrain interaction was improved by adding a force-torque sensor and associated faults, and an analytic dig force model based on the Balovnev bucket force equations. Environment fidelity was increased by modeling terrain deformation resulting from digging and scooping; visual improvements were made in textures, lighting, and shadows. To facilitate interoperation with OWLAT, a unified command and telemetry interface between the testbeds was developed at the ROS level, along with a PLEXIL interface. The number of lander operations was greatly expanded (e.g. with Cartesian-based arm and antenna movement), and a framework was designed for users to build their own lander actions. A GUI for PLEXIL plan selection was created (Figure 3), and an expansive set of plans were added, such as those that illustrate patterns for fault handling. This paper provides a self-contained high-level description of OceanWATERS, focusing on more detailed coverage of the aforementioned enhancements. It provides a high-level summary of the projects undertaken by participants in the ARROW and COLDTech programs and how these efforts have helped shape OceanWATERS. Finally, potential future work and directions for the testbed are listed, as likely informed by the recent planetary science decadal survey [5].

K Michael Dalal↗

Comparison of Model Calculations of Biological Damage from Exposure to Heavy Ions with Measurements

The space environment consists of a varying field of radiation particles including high-energy ions, with spacecraft shielding material providing the major protection to astronauts from harmful exposure. Unlike low-LET gamma or X rays, the presence of shielding does not always reduce the radiation risks for energetic charged-particle exposure. Dose delivered by the charged particle increases sharply at the Bragg peak. However, the Bragg curve does not necessarily represent the biological damage along the particle path since biological effects are influenced by the track structures of both primary and secondary particles. Therefore, the ''biological Bragg curve'' is dependent on the energy and the type of the primary particle and may vary for different biological end points. Measurements of the induction of micronuclei (MN) have made across the Bragg curve in human fibroblasts exposed to energetic silicon and iron ions in vitro at two different energies, 300 MeV/nucleon and 1 GeV/nucleon. Although the data did not reveal an increased yield of MN at the location of the Bragg peak, the increased inhibition of cell progression, which is related to cell death, was found at the Bragg peak location. These results are compared to the calculations of biological damage using a stochastic Monte-Carlo track structure model, Galactic Cosmic Ray Event-based Risk Model (GERM) code (Cucinotta, et al., 2011). The GERM code estimates the basic physical properties along the passage of heavy ions in tissue and shielding materials, by which the experimental set-up can be interpreted. The code can also be used to describe the biophysical events of interest in radiobiology, cancer therapy, and space exploration. The calculation has shown that the severely damaged cells at the Bragg peak are more likely to go through reproductive death, the so called "overkill".

Kim, Myung-Hee Y.↗

Advanced data assimilation in strongly nonlinear dynamical systems

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Miller, Robert N.↗