Results for “Long Time Integration” — Page 10

NASA NTRS1990

Small gain robustness issues in the p-integrator repetitive controller

The basic theory of the digital p-integrator controller is utilized to modify the command to a stable analog feedback control system in order to produce zero tracking error of a repetitive command. Mapping of continuous time poles and zeros to the images in the discrete time domain is performed. It is shown that for a pole excess of one, with p odd, the p-integrator learning controller will often produce a stable learning process, even for relatively large sample times. For a pole excess of two, a stable learning process can often be achieved for any p as long as the sample time is kept sufficiently short. Therefore, when the pole excess is zero and one utilizes the proper p-integrator controller with p odd, stable performance is often produced, even for relatively large sample times.

Longman, Richard W.↗

DOE OSTI2022

Gamma-Ray Imaging to Monitor Accumulating Holdup

Over time, nuclear materials can accumulate in process equipment and keeping track of such material is of interest to many stakeholder communities including safeguards, process monitoring, criticality safety, and radiological safety. Passive gamma-ray imaging provides a visual and quantitative tool that can be applied to this problem, allowing one to determine the amount of material present from the images. In this work we emulate the accumulation of highly enriched uranium (HEU) in a large rectangular stainless-steel duct by stacking 5, 27 × 50 cm2 cards, each of which has approximately 11 g of 235U in oxide form distributed across its surface, behind each other. A series of images were collected using a coded-aperture gamma-ray imager, starting with a single card, adding a second card, etc. Long integrations were collected to allow evaluating the performance of the approach as a function of integration time. The images are analyzed using first principles to determine the amount of material in each image. The results are compared to the known amount of material in each configuration, and as a function of time. The analysis includes a first-principles error propagation and to further evaluate the uncertainty, a boot-strap sampling approach is also applied to the data. The work offers a proof of concept for unattended monitoring of uranium holdup with a quantitative gamma-ray imaging technique.

Ziock, Klaus-Peter↗

DOE OSTI2022

Quantum wake dynamics in Heisenberg antiferromagnetic chains

Traditional spectroscopy, by its very nature, characterizes physical system properties in the momentum and frequency domains. However, the most interesting and potentially practically useful quantum many-body effects emerge from local, short-time correlations. Here, using inelastic neutron scattering and methods of integrability, we experimentally observe and theoretically describe a local, coherent, long-lived, quasiperiodically oscillating magnetic state emerging out of the distillation of propagating excitations following a local quantum quench in a Heisenberg antiferromagnetic chain. This “quantum wake” displays similarities to Floquet states, discrete time crystals and nonlinear Luttinger liquids. We also show how this technique reveals the non-commutativity of spin operators, and is thus a model-agnostic measure of a magnetic system’s “quantumness.”

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRSDate not supplied

Gateway Integrated ECLSS Model Analysis of Intermodule Ventilation Failures

The Gateway Integrated ECLSS Model (GIEM) is a set of two independent models, made in Aspen Custom Modeler (ACM) and Thermal Desktop (TD), of the Gateway stack and each modules' associated environment control and life support system (ECLSS). The GIEM utilizes the 41-Node Metabolic Man (METMAN) to simulate crew inside the Gateway consuming O2 and producing CO2, H2O, and heat for the ECLSS to remove. The modules and visiting vehicles all have different levels of ECLSS capabilities and may rely on other modules and Intermodular Ventilation (IMV), which is used to exchange gas between the modules, to ensure the entire Gateway environment is controlled. If IMV were to fail or be turned off, some vehicles may have limited access to necessary ECLSS functions. This analysis focuses on evaluating O2, CO2, and H2O levels when crew are in vehicles without their own life support and IMV has failed to evaluate how long before the atmosphere is unsafe for the crew. This analysis uses the integrated nature of the GIEM to look at time to effect for O2 depletion and CO2 and H2O buildup when crew are working in vehicles that have been cut off from the ECLSS-active portion of the stack. This information is used to inform for how long crew can safely continue working in the ECLSS-inactive vehicles before experiencing a requirement violation or physical limitation and can be referenced when developing maintenance and emergency response concept of operations (ConOps).

Lawrence Barrett↗

DOE OSTI2024

Research Reactors Division Infrastructure Investment Plan for the High Flux Isotope Reactor

The High Flux Isotope Reactor (HFIR) is a unique national asset. Operational for nearly 60 years, continued investment into the aging infrastructure is necessary to ensure operation for another 6 decades. Additionally, growing missions require HFIR as well as important upgrades. Consequently, carefully integrated planning is required to ensure that infrastructure investments are timely executed to ensure long-term, reliable operation of HFIR. Concerns about challenges to the operational reliability of HFIR resulted in a recommendation from the 2023 Operations Review by the US Department of Energy (DOE) Office of Basic Energy Sciences that a HFIR management strategy be developed to address the infrastructure needs. This report defines the investment needs, which are evolving as new upgrade efforts are better defined. HFIR is part of the three-source strategy within the Neutron Sciences Directorate (NScD) and contributes to the five strategic science areas outlined in the NScD 10 Year Strategic Science Plan: quantum materials, soft matter, materials and engineering, chemistry, and biosciences. Fundamental to this strategy are three core values: operational excellence, responsible stewardship, and servant leadership. These values guide our mission of safe and reliable operation of the reactor and require a strong and just nuclear safety culture, a solemn respect for responsible care of the facility, good workforce development, robust procedures and processes, an effective communication strategy, world-class asset management, a determined customer focus, and a commitment to protecting the environment, the safety and health of the public and our people, and the quality of work performed within our facility. These principles are all essential to operate HFIR at a world-class level. The Research Reactors Division (RRD) will lead a new era of neutron science and isotope production at HFIR through responsible and purposeful leadership and unwavering support of the science community. The approach outlined in this plan highlights the direction leadership is taking to ensure that HFIR is ready to support the science challenges and national needs of the future and that the United States maintains world leadership in neutron sciences. The plan is in alignment with the DOE’s desire to continue operating HFIR and with the NScD strategic science goals for the future. HFIR is an aging facility with numerous infrastructure challenges and needs. It has an aging workforce in relation to the general population of Oak Ridge National Laboratory (ORNL), with many expected retirements over the next 5–10 years. With an increase in work scope caused by changing national priorities and science goals, several critical hires have been identified. To manage HFIR’s infrastructure needs, a prioritized list of equipment upgrades has been identified along with an analysis of future staffing requirements. A desire to operate HFIR at eight cycles per year will necessarily require some significant changes to procedures and processes currently in place as well as targeted staffing additions. Many of the equipment upgrades identified in this plan will significantly increase the reliability of the plant, thus contributing to the effort to reach the goal of safely operating eight cycles per year. A plan to attain eight-cycle operation is being prepared in parallel with the activities identified in this plan, although the actions identified to satisfy both plans will overlap. This plan identifies new infrastructure needs—for both plant equipment and staffing—thus necessitating formulation of future budget requests to fund the increased work scope and improvement activities. Some activities are currently being scheduled with the expectation that funding will be received. Any delays to funding or reductions of funding from the identified cost estimations will directly and negatively affect the plan’s implementation.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS1986

Predicting Failures of Composite, Spherical Pressure Vessels

Long-term viscoelastic effects computed to predict bursts. Spherical pressure vessels commonly made of filamentary composites for applications they must light in weight. Program developed for predicting failure of such vessel over long time span. Short-term failure pressures (bursting points) predicted, but long-term structual integrity of laminated vessels studied only now.

Dozier, J. D.↗

NASA NTRS2003

Quasi-Equilibria of the Rotunno-Emanuel Tropical Cyclone Model

Long-term integrations using the Rotunno-Emanuel (RE) model demonstrate that given sufficient elapsed time the weak initial vortex specified by R E can also lead to tropical cyclogenesis, albeit at a slower growth rate. Thus the RE notion of the finite-amplitude nature of tropical cyclogenesis is valid only if the period of examination is limited to the first eight days. These results also show that, if initial vortex as specified by RE is used, prior to cyclogenesis the model state does not resemble the observed pre-genesis disturbances in the sense that there is no precipitation in the center of the disturbance. Another experiment using the same model but with the initial vortex replaced by a disturbance with a different structure shows that a state resembling the observed pre-genesis disturbances can be simulated and this state can lead to spontaneous cyclogenesis, a rapid transition between two quasi-equilibria. This spontaneous cyclogenesis is associated with the generation of a new convective region at large radius and its subsequent contraction, which reminds one of the observed eye-wall replacement, but the distinction from the latter is obvious.

Chao, Winston C.↗

NASA NTRS1995

Scale-dependent Ocean Wave Turbulence

Wave turbulence is a common feature of nonlinear wave motions observed when external forcing acts during a long period of time, resulting in developed spectral cascades of energy, momentum, and other conserved integrals. In the ocean, wave turbulence occurs on various scales from capillary ripples, and those of baroclinic inertia-gravity, to Rossby waves. Oceanic wave motions are discussed.

ocean waves wave turbulence wave motions wave ener↗

NASA NTRS2008

Thermostable Shelf Life Study

The objective of this project is to determine the shelf life end-point of various food items by means of actual measurement or mathematical projection. The primary goal of the Advanced Food Technology Project in these long duration exploratory missions is to provide the crew with a palatable, nutritious and safe food system while minimizing volume, mass, and waste. The Mars missions could be as long as 2.5 years with the potential of the food being positioned prior to the crew arrival. Therefore, it is anticipated that foods that are used during the Mars missions will require a 5 year shelf life. Shelf life criteria are safety, nutrition, and acceptability. Any of these criteria can be the limiting factor in determining the food's shelf life. Due to the heat sterilization process used for the thermostabilized food items, safety will be preserved as long as the integrity of the package is maintained. Nutrition and acceptability will change over time. Since the food can be the sole source of nutrition to the crew, a significant loss in nutrition may determine when the shelf life endpoint has occurred. Shelf life can be defined when the food item is no longer acceptable. Acceptability can be defined in terms of appearance, flavor, texture, or aroma. Results from shelf life studies of the thermostabilized food items suggest that the shelf life of the foods range from 0 months to 8 years, depending on formulation.

Perchonok, M. H.↗

NASA NTRS2009

Thermostabilized Shelf Life Study

The objective of this project is to determine the shelf life end-point of various food items by means of actual measurement or mathematical projection. The primary goal of the Advanced Food Technology Project in these long duration exploratory missions is to provide the crew with a palatable, nutritious and safe food system while minimizing volume, mass, and waste. The Mars missions could be as long as 2.5 years with the potential of the food being positioned prior to the crew arrival. Therefore, it is anticipated that foods that are used during the Mars missions will require a 5 year shelf life. Shelf life criteria are safety, nutrition, and acceptability. Any of these criteria can be the limiting factor in determining the food's shelf life. Due to the heat sterilization process used for the thermostabilized food items, safety will be preserved as long as the integrity of the package is maintained. Nutrition and acceptability will change over time. Since the food can be the sole source of nutrition to the crew, a significant loss in nutrition may determine when the shelf life endpoint has occurred. Shelf life can be defined when the food item is no longer acceptable. Acceptability can be defined in terms of appearance, flavor, texture, or aroma. Results from shelf life studies of the thermostabilized food items suggest that the shelf life of the foods range from 0 months to 8 years, depending on formulation.

Perchonok, Michele H.↗

NASA NTRS2020

Integrated Demand Management: Annotated Bibliography

NASA has developed the Integrated Demand Management (IDM) concept over a five-year long project lifespan. During that time period, IDM researchers, both at NASA and outside organizations funded by NASA, published approximately forty conference papers and other technical publications associated with the IDM concept. In this document, these publications are cited and annotated for their content and their relevance to the IDM concept development.

IDM↗

DOE OSTI2023

On the convergence of statistics in simulations of stationary incompressible turbulent flows

When reporting statistics from simulations of statistically stationary chaotic phenomenon, it is important to verify that the simulations are time-converged. This condition is connected with the statistical error or number of digits with which statistics can be reliably reported. In this work we consider numerical experiments of low Reynolds number incompressible homogeneous and isotropic turbulence as a model problem to investigate statistical convergence over finite simulation times. Specifically, we investigate the time integration requirements that allow meaningful reporting of the statistical error associated with finiteness of the temporal domain. We address two key questions: (1) How long should a simulation be performed in terms of large eddy time, and (2) How should the simulation time be divided among temporal windows over which a quantity of interest is estimated so that its statistical error could be reliably reported? We find that reliable reporting of statistical errors requires simulations on the order of 10 4 large eddy times, which is orders of magnitude longer than typically performed. Additionally, data post-processing should employ windows of at least ten times the large eddy time scale, with the most robust computation of statistical error of the mean requiring window sizes of an additional factor of ten. For practical simulations, we demonstrate that it is possible to estimate the statistical error within a factor of two under a less stringent condition in which a minimum of four windows with size at least ten large eddy times are used. In conclusion, our observations for homogeneous isotropic turbulence are also shown to hold in turbulent channel flow.

42 ENGINEERING↗

NASA NTRS2009

Acute Hemodynamic Effects of the Braslet-M Device on the International Space Station

The Braslet-M occlusion device is prescribed for cosmonauts as a countermeasure for early phases of spaceflight to temporarily alleviate symptoms associated with the cephalad fluid shift. Using a multipurpose ultrasound (US) device onboard, we assessed the acute hemodynamic effects of the Bracelet-M device on a long duration International Space Station (ISS) crewmember. Methods A combination of just-in-time training and real-time remote expert assistance was used to conduct the imaging procedures. An HDI-5000 imager (Philips, Bothell, WA) was used, provided by the ISS Human Research Facility. Superficial femoral artery (SFA), femoral vein (FV) flow spectra were obtained at mid-thigh level. Left ventricle was imaged through the apical 4-chamber view, with Color M-Mode to measure propagation velocity (V (p)). After 10 minutes of Bracelet-M use, data collection was repeated. All data were transmitted in DICOM format to ground for analysis. Results With Braslet-M, cardiac V(p) slope decreased (56ms to 42ms). A stagnation signature in the FV was seen suggesting impeded flow (rouleaux formation, too-low-to-measure velocity, and increase in diameter). Quadri-phasic flow in SFA was seen both before and after Braslet-M application. Velocities in the SFA decreased with Braslet-M (65cm/sec to 52cm/sec) and so did the time velocity integrals (16.97 to 12.4); the flow pattern spoke of resistivity increase in the vascular bed. Conclusion In the long duration ISS crewmember we observed effects of lower extremity venous occlusion through both central and peripheral indicators. A part of circulating volume transferred to peripheral potential vascular space. Impediment to venous outflow was demonstrated objectively, with a commensurate change in the flow pattern of the main feeding artery. Central volume reduction caused lower V(p). Additional studies are warranted to determine the time course of the changes and the dynamics in interstitial fluid sequestration, as well as the safe levels and duration of the compression forces.

Hamilton, Douglas R.↗

NASA NTRS2016

MarCO: Interplanetary Mission Development on a CubeSat Scale

Shortly after JPL’s Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight) mission launches, separates, and commences its cruise phase, two CubeSats will deploy from the launch vehicle’s upper stage and begin independent flight to Mars (Fig. 1). During InSight’s entry, descent, and landing (EDL) sequence, these twin Mars Cube One (MarCO) spacecraft will fly 3,500 km above the Martian surface, recording and relaying InSight UHF radio data to the Deep Space Network (DSN) on Earth1. MarCO is a twin CubeSat mission developed by the NASA Jet Propulsion Laboratory (JPL) to accompany the InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) Mars mission lander. MarCO's primary mission objective is to launch with InSight and independently fly to Mars to serve as a communications relay during InSight's entry, descent, and landing (EDL) phase. MarCO represents a new type of deep space mission: CubeSats at Mars. Building on the development of JPL's first interplanetary CubeSat project, the Interplanetary Nano-Spacecraft Pathfinder in Relevant Environment (INSPIRE), MarCO further refined the approach to hardware, software, and ground architecture development to solve the challenges of quickly building low-budget spacecraft to fly to Mars. The greatest constraint, beyond others typical of CubeSat missions, was time. The duration between MarCO's conception to completion of spacecraft assembly was less than two years - an unprecedented schedule for any planetary mission to date. Through necessity, MarCO has built on previous experience, procedures, systems, and development methodologies, defining a new niche for supporting larger primary missions. The MarCO spacecraft are poised to write a new chapter in deep space exploration. Originally slated to launch and reach Mars in 2016, the InSight mission schedule subsequently slipped to 2018. During the original landing of InSight, Earth would not be in view, and no orbiter around Mars would have been in position to both receive UHF EDL data and simultaneously relay it back to Earth. It was from this obstacle that MarCO was conceived. Regardless of any changes to InSight’s 2018 EDL configuration geometry, MarCO is still expected to fly and serve in the same capacity as originally designed: the first CubeSat mission to Mars. CubeSats have historically been firmly in the domain of universities and small companies. As first conceived, they served as a platform upon which to teach all aspects of the space mission lifecycle. JPL took on this mission type with Interplanetary Nano-Spacecraft Pathfinder in Relevant Environment2 (INSPIRE), moving the concept into a new domain: deep space. Building from the INSPIRE platform and lessons learned, MarCO addressed new challenges in the domain of planetary missions: independent interplanetary flight and navigation, integration with a large-scale mission, long-distance and long-delay communication, short development time, and a small development team. Of these, the greatest constraint was schedule: only 18 months passed from conception of mission concept until delivery of fully assembled and tested flight hardware. Careful selection of mission team, along with extensive use of off-the-shelf equipment, and streamlining automated processes, was essential. This achievement represents the next step in the evolution of CubeSats beyond low-Earth orbit.

Werne, Thomas↗

NASA NTRSDate not supplied

Integral Channel Nozzles and Heat Exchangers using Additive Manufacturing Directed Energy Deposition NASA HR-1 Alloy

Heat exchangers for use in propulsion applications are very critical components because they must be efficient, compact and light and often operate with working fluids at extreme temperatures or pressures or both. Various components and systems use heat exchangers such as combustion chambers of gas turbines and internal combustion engines, fuel cells (air supply and thermal management), electric batteries (thermal management), evaporators and recuperators of waste-heat-to-power systems, and rocket engines. Even if the results are more generally applicable, the heat exchangers applications to which this study is more closely related are regeneratively cooled rocket nozzles and chambers, and repressurization systems for the launch vehicles. These components are often thin-walled and contain pressurized fluids, like propellants at cryogenic or elevated temperatures. Given that the environments that these propulsion components must endure are challenging, the manufacturing to meet these specifications often require long lead times due to specialty processes and unique tooling associated with the combined thin-wall integral channel and large-scale structures. Additive manufacturing (AM) offers programmatic advantages for reduction in processing time and cost in addition to various technical advantages, including the possibility to achieve enhanced hardware complexity targeted to superior performance, part consolidation, and the capability of processing of novel alloys. While AM is already being utilized for heat exchanger components in propulsion applications, almost all these AM components are made by means of Laser Powder Bed Fusion (L-PBF). L-PBF allows for fine features but is rather limited with respect to the overall size of the components that can be manufactured. Recent developments are maturing the Laser Powder Directed Energy Deposition (LP-DED) process which may be used, for example, to make integral channel thin-wall regeneratively-cooled rocket nozzles with diameters greater than 1 m. This paper highlights some integral channel heat exchanger demonstrator hardware applications of LP-DED, as well as the characterization of this process in combination with the use of the NASA HR-1 alloy. To properly utilize LP-DED for heat exchanger manufacturing, various aspects are being characterized such as geometry limitations, measurement of surface texture and geometric angled surfaces, surface enhancements for internal channels, and material evaluation. NASA HR-1 (FeNi-Cr) is a high strength hydrogen resistant superalloy developed for use in aerospace applications, such as heat exchangers. Some aspects and considerations about the design of heat exchangers are summarized together with data relevant to LP-DED manufacturing in combination with the NASA HR-1 alloy. Microchannels were successful deposited down to 2.54 mm and 1 mm wall thickness, wall angles of 30°, both with high reproducibility. It was also found that the areal surface roughness is highly dependent on the size of the powder feedstock used for deposition. The characterization of these LP-DED features is critical for fluid flow and heat transfer predictions as it can be exploited to enhance heat transfer at the cost of increased pressure drop.

Additive Manufacturing↗

NASA NTRSDate not supplied

Integral Channel Nozzles and Heat Exchangers using Additive Manufacturing Directed Energy Deposition NASA HR-1 Alloy

Heat exchangers for use in propulsion applications are very critical components because they must be efficient, compact and light and often operate with working fluids at extreme temperatures or pressures or both. Various components and systems use heat exchangers such as combustion chambers of gas turbines and internal combustion engines, fuel cells (air supply and thermal management), electric batteries (thermal management), evaporators and recuperators of waste-heat-to-power systems, and rocket engines. Even if the results are more generally applicable, the heat exchangers applications to which this study is more closely related are regeneratively cooled rocket nozzles and chambers, and repressurization systems for the launch vehicles. These components are often thin-walled and contain pressurized fluids, like propellants at cryogenic or elevated temperatures. Given that the environments that these propulsion components must endure are challenging, the manufacturing to meet these specifications often require long lead times due to specialty processes and unique tooling associated with the combined thin-wall integral channel and large-scale structures. Additive manufacturing (AM) offers programmatic advantages for reduction in processing time and cost in addition to various technical advantages, including the possibility to achieve enhanced hardware complexity targeted to superior performance, part consolidation, and the capability of processing of novel alloys. While AM is already being utilized for heat exchanger components in propulsion applications, almost all these AM components are made by means of Laser Powder Bed Fusion (L-PBF). L-PBF allows for fine features but is rather limited with respect to the overall size of the components that can be manufactured. Recent developments are maturing the Laser Powder Directed Energy Deposition (LP-DED) process which may be used, for example, to make integral channel thin-wall regeneratively-cooled rocket nozzles with diameters greater than 1 m. This paper highlights some integral channel heat exchanger demonstrator hardware applications of LP-DED, as well as the characterization of this process in combination with the use of the NASA HR-1 alloy. To properly utilize LP-DED for heat exchanger manufacturing, various aspects are being characterized such as geometry limitations, measurement of surface texture and geometric angled surfaces, surface enhancements for internal channels, and material evaluation. NASA HR-1 (FeNi-Cr) is a high strength hydrogen resistant superalloy developed for use in aerospace applications, such as heat exchangers. Some aspects and considerations about the design of heat exchangers are summarized together with data relevant to LP-DED manufacturing in combination with the NASA HR-1 alloy. Microchannels were successful deposited down to 2.54 mm and 1 mm wall thickness, wall angles of 30°, both with high reproducibility. It was also found that the areal surface roughness is highly dependent on the size of the powder feedstock used for deposition. The characterization of these LP-DED features is critical for fluid flow and heat transfer predictions as it can be exploited to enhance heat transfer at the cost of increased pressure drop.

additive manufacturing↗

NASA NTRS2004

Integrating Ground System Tools From Multiple Technologies Into a Single System Environment

With rapid technology changes and new and improved development techniques, it becomes extremely difficult to try to add capabilities to existing ground systems without wanting to replace the entire system. Replacing entire systems is not usually cost effective so there is a need to be able to slowly improve systems without long development times that introduce risk due to large amounts of change. The Marshall Space Flight Center s (MSFC) Payload Operations Integration Center (POIC) ground system provides command, telemetry, and payload planning systems in support of the International Space Station. Our systems have continuously evolved with technology changes due to hardware end of life issues, and also due to user requirement changes. As changes have been implemented, we have tried to take advantage of some of the latest technologies while at the same time maintaining certain legacy capabilities that are not cost affective to replace. One of our biggest challenges is to integrate all of these implementations into a single system that is usable, maintainable, and scalable. Another challenge is to provide access to our tools in such a way that users are not aware of all the various implementation methods and tools being used. This approach not only makes our system much more usable, it allows us to continue to migrate capabilities and to add capabilities without impacting system usability. This paper will give an overview of the tools used for MSFC ISS payload operations and show an approach for integrating various technologies into a single environment that is maintainable, flexible, usable, cost effective, and that meets user needs.

Ritter, George H.↗

DOE OSTI2021

Learning Forecasts of Rare Stratospheric Transitions from Short Simulations

Abstract Rare events arising in nonlinear atmospheric dynamics remain hard to predict and attribute. We address the problem of forecasting rare events in a prototypical example, sudden stratospheric warmings (SSWs). Approximately once every other winter, the boreal stratospheric polar vortex rapidly breaks down, shifting midlatitude surface weather patterns for months. We focus on two key quantities of interest: the probability of an SSW occurring, and the expected lead time if it does occur, as functions of initial condition. These optimal forecasts concretely measure the event’s progress. Direct numerical simulation can estimate them in principle but is prohibitively expensive in practice: each rare event requires a long integration to observe, and the cost of each integration grows with model complexity. We describe an alternative approach using integrations that are short compared to the time scale of the warming event. We compute the probability and lead time efficiently by solving equations involving the transition operator, which encodes all information about the dynamics. We relate these optimal forecasts to a small number of interpretable physical variables, suggesting optimal measurements for forecasting. We illustrate the methodology on a prototype SSW model developed by Holton and Mass and modified by stochastic forcing. While highly idealized, this model captures the essential nonlinear dynamics of SSWs and exhibits the key forecasting challenge: the dramatic separation in time scales between a single event and the return time between successive events. Our methodology is designed to fully exploit high-dimensional data from models and observations, and has the potential to identify detailed predictors of many complex rare events in meteorology.

Finkel, Justin↗