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NASA NTRS2020

The NASA MODIS-VIIRS Continuity Cloud Optical Properties Products

The NASA Aqua MODIS and Suomi National Polar-Orbiting Partnership (SNPP) Visible Infrared Imaging Radiometer Suite (VIIRS) climate data record continuity cloud properties products (CLDPROP) were publicly released in April 2019 with an update later that year (Version 1.1). These cloud products, having heritage with the NASA Moderate-resolution Imaging Spectroradiometer (MODIS) MOD06 cloud optical properties product and the NOAA GOES-R Algorithm Working Group (AWG) Cloud Height Algorithm (ACHA), represent an effort to bridge the multispectral imager records of NASA’s Earth Observing System (EOS) and NOAA’s current generation of operational weather satellites to achieve a continuous, multi-decadal climate data record for clouds that can extend well into the 2030s. CLDPROP offers a “continuity of approach,” applying common algorithms and ancillary datasets to both MODIS and VIIRS, including utilizing only a subset of spectral channels available on both sensors to help mitigate instrument differences. The initial release of the CLDPROP_MODIS and CLDPROP_VIIRS data records spans the SNPP observational record (2012-present). Here, we present an overview of the algorithms and an evaluation of the intersensor continuity of the core CLDPROP_MODIS and CLDPROP_VIIRS cloud optical property datasets, i.e., cloud thermodynamic phase, optical thickness, effective particle size, and derived water path. The evaluation includes analyses of pixel-level MODIS/VIIRS co-locations as well as spatial and temporal aggregated statistics, with a focus on identifying and understanding the root causes of individual dataset discontinuities. The results of this evaluation will inform future updates to the CLDPROP products and help scientific users determine the appropriate use of the product datasets for their specific needs.

satellite remote sensing↗

NASA NTRS2005

Biomimetic Models for An Ecological Approach to Massively-Deployed Sensor Networks

Promises of ubiquitous control of the physical environment by massively-deployed wireless sensor networks open avenues for new applications that will redefine the way we live and work. Due to small size and low cost of sensor devices, visionaries promise systems enabled by deployment of massive numbers of sensors ubiquitous throughout our environment working in concert. Recent research has concentrated on developing techniques for performing relatively simple tasks with minimal energy expense, assuming some form of centralized control. Unfortunately, centralized control is not conducive to parallel activities and does not scale to massive size networks. Execution of simple tasks in sparse networks will not lead to the sophisticated applications predicted. We propose a new way of looking at massively-deployed sensor networks, motivated by lessons learned from the way biological ecosystems are organized. We demonstrate that in such a model, fully distributed data aggregation can be performed in a scalable fashion in massively deployed sensor networks, where motes operate on local information, making local decisions that are aggregated across the network to achieve globally-meaningful effects. We show that such architectures may be used to facilitate communication and synchronization in a fault-tolerant manner, while balancing workload and required energy expenditure throughout the network.

Jones, Kennie H.↗

DOE OSTI2025

Revealing the roles of the solid–electrolyte interphase in designing stable, fast-charging, low-temperature Li-ion batteries

Designing the solid–electrolyte interphase (SEI) is critical for stable, fast-charging, low-temperature Li-ion batteries. Fostering a “fluorinated interphase,” SEI enriched with LiF, has become a popular design strategy. Although LiF possesses low Li-ion conductivity, many studies have reported favorable battery performance with fluorinated SEIs. Such a contradiction suggests that optimizing SEI must extend beyond chemical composition design to consider spatial distributions of different chemical species. In this work, we demonstrate that the impact of a fluorinated SEI on battery performance should be evaluated on a case-by-case basis. Sufficiently passivating the anode surface without impeding Li-ion transport is key. We reveal that a fluorinated SEI containing excessive and dense LiF severely impedes Li-ion transport. In contrast, a fluorinated SEI with well-dispersed LiF (i.e., small LiF aggregates well mixed with other SEI components) is advantageous, presumably due to the enhanced Li-ion transport across heterointerfaces between LiF and other SEI components. An electrolyte, 1 M LiPF 6 in 2-methyl tetrahydrofuran (2MeTHF), yields a fluorinated SEI with dispersed LiF. This electrolyte allows anodes of graphite, μSi/graphite composite, and pure Si to all deliver a stable Coulombic efficiency of 99.9% and excellent rate capability at low temperatures. Pouch cells containing layered cathodes also demonstrate impressive cycling stability over 1,000 cycles and exceptional rate capability down to −20 °C. Through experiments and theoretical modeling, we have identified a balanced SEI-based approach that achieves stable, fast-charging, low-temperature Li-ion batteries.

25 ENERGY STORAGE↗

DOE OSTI2021

Energy Efficiency: What Has Research Delivered in the Last 40 Years?

This article presents a critical assessment of 40 years of research that may be brought under the umbrella of energy efficiency, spanning different aggregations and domains—from individual producing and consuming agents to economy-wide effects to the role of innovation to the influence of policy. After 40 years of research, energy efficiency initiatives are generally perceived as highly effective. Innovation has contributed to lowering energy technology costs and increasing energy productivity. Energy efficiency programs in many cases have reduced energy use per unit of economic output and have been associated with net improvements in welfare, emission reductions, or both. Rebound effects at the macro level still warrant careful policy attention, as they may be nontrivial. Complexity of energy efficiency dynamics calls for further methodological and empirical advances, multidisciplinary approaches, and granular data at the service level for research in this field to be of greatest societal benefit.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Induced seismicity red-light thresholds for enhanced geothermal prospects in the Netherlands

Prospects for geothermal energy in the Netherlands have renewed concerns around induced earthquakes. Risks from induced earthquakes are managed by traffic light protocols (TLPs), where the red-light is chosen as the stop-point before exceeding a tolerance to risk. Here, we simulate post-shut-in earthquake scenarios based on realistic information for the Netherlands. We focus on three risk metrics: aggregates like nuisance and damage impacts and also local personal risk (LPR) – a likelihood of building collapse fatality for an individual. Our results show that the severity of these risks varies spatially by orders of magnitude. Prior induced seismicity (e.g., the 2012 Huizinge event) provides a reference baseline to calibrate the Dutch earthquake risk tolerances. We find that these calibrated risk tolerances are similar to those observed in North America, suggesting an underlying sociological ‘license to operate.’ Furthermore, the use of calibrated risk tolerances results in nuisance concerns completely eclipsing the other two metrics. We compare our results to a hypothetical Groningen geothermal operation and find that our approach sets red-light thresholds approximately one magnitude unit below the ML 3.6 Huizinge event. Overall, our results provide a first-order recommendation for red-light thresholds and proactive management of Dutch enhanced geothermal induced seismicity.

15 GEOTHERMAL ENERGY↗

DOE OSTI2021

Rapid preparation of nanodiscs for biophysical studies

Nanodiscs, which are disc-shaped entities that contain a central lipid bilayer encased by an annulus of amphipathic helices, have emerged as a leading native-like membrane mimic. The current approach for the formation of nanodiscs involves the creation of a mixed-micellar solution containing membrane scaffold protein, lipid, and detergent followed by a time consuming process (3–12 h) of dialysis and/or incubation with sorptive beads to remove the detergent molecules from the sample. In contrast, the methodology described herein provides a facile and rapid procedure for the preparation of nanodiscs in a matter of minutes (<15 min) using Sephadex® G-25 resin to remove the detergent from the sample. A panoply of biophysical techniques including analytical ultracentrifugation, dynamic light scattering, gel filtration chromatography, circular dichroism spectroscopy, and cryogenic electron microscopy were employed to unequivocally confirm that aggregates formed by this method are indeed nanodiscs. We believe that this method will be attractive for time-sensitive and high-throughput experiments.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

MOSIQS: Persistent Memory Object Storage With Metadata Indexing and Querying for Scientific Computing

Scientific applications often require high-bandwidth shared storage to perform joint simulations and collaborative data analytics. Shared memory pools provide a chance to satisfy such needs. Recently, a high-speed network such as Gen-Z utilizing persistent memory (PM) offers an opportunity to create a shared memory pool connected to compute nodes. However, there are several challenges to use scientific applications on the shared memory pool directly such as scalability, failure-atomicity, and lack of scientific metadata-based search and query. In this paper, we propose MOSIQS, a persistent memory object storage framework with metadata indexing and querying for scientific computing. We design MOSIQS based on the key idea that memory objects on PM pool can live beyond the application lifetime and can become the sharing currency for applications and scientists. MOSIQS provides an aggregate memory pool atop an array of persistent memory devices to store and access memory objects to accelerate scientific computing. MOSIQS uses a lightweight persistent memory key-value store to manage the metadata of memory objects, which enables memory object sharing. To facilitate metadata search and query over millions of memory objects resident on memory pool, we introduce Group Split and Merge (GSM), a novel persistent index data structure designed primarily for scientific datasets. GSM splits and merges dynamically to minimize the query search space and maintains low query processing time while overcoming the index storage overhead. MOSIQS is implemented on top of PMDK. We evaluate the proposed approach on many-core server with an array of real PM devices. Experimental results show that MOSIQS gains a 100% write performance improvement and executes multi-attribute queries efficiently with 2.7× less index storage overhead offering significant potential to speed up scientific computing applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Game Theory Approaches for System-level Incentive Design

This report presents a generalized Stackelberg game framework for designing and evaluating financial incentives that enhance power system resilience through strategic deployment of distributed energy resources(DERs) under various contingencies. The proposed approach addresses the challenge of coordinating individual community investment decisions to meet system-wide resilience objectives. The framework is demonstrated in a three-community test system subjected to two transmission contingency scenarios: inter-community line failure (Case 1) and complete main grid disconnection (Case 2). In both cases, three incentive levels are compared: a Base case with no financial incentives, and low and high incentive cases. In Case 1, the Base case (no incentives) results in a total installed DER capacity of 217.2 MW, with no load shedding due to alternative routing, but community costs remain high. Increasing incentives raises DER deployment to 286.9 MW, lowers aggregate community costs by $22M annually, and completely avoids the need for costly new transmission line construction. In Case 2, the Base case results in 24.3 MWh of unserved load; introducing incentives eliminates all load shedding and ensures up to 89 MWh of battery storage is available for emergency reserve. These results demonstrate that targeted incentives can dramatically improve grid resilience and cost-effectiveness. The framework thus offers policymakers and system planners a robust tool to quantify and compare the effectiveness of incentive programs for multi-community transmission networks behavior, system resilience, and economic efficiency.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

A Kinetic Monte Carlo Approach for Simulating Cascading Transmission Line Failure

In this work, cascading transmission line failures are studied through a dynamical model of the power system operating under fixed conditions. The power grid is modeled as a stochastic dynamical system where first-principles electromechanical dynamics are excited by small Gaussian disturbances in demand and generation around a specified operating point. In this context, a single line failure is interpreted in a large deviation context as a first escape event across a surface in phase space defined by line security constraints. The resulting system of stochastic differential equations admits a transverse decomposition of the drift, which leads to considerable simplification in evaluating the quasipotential (rate function) and, consequently, computation of exit rates. Tractable expressions for the rate of transmission line failure in a restricted network are derived from large deviation theory arguments and validated against numerical simulations. Extensions to realistic settings are considered, and individual line failure models are aggregated into a Markov model of cascading failure inspired by chemical kinetics. Cascades are generated by traversing a graph composed of weighted edges representing transitions to degraded network topologies. Numerical results indicate that the Markov model can produce cascades with qualitative power-law properties similar to those observed in empirical cascades.

Kinetic Monte Carlo, rare events, Cascading Failur↗

DOE OSTI2021

Structural Reorganization of Noncellulosic Polymers Observed In Situ during Dilute Acid Pretreatment by Small-Angle Neutron Scattering

Production of second-generation bioethanol from lignocellulosic biomass requires pretreatment to open the plant cell wall structure and improve enzyme access. Many different thermochemical pretreatments have been extensively developed and employed, but the exact nature of plant cell wall recalcitrance and the most efficient and economical approach to alter plant cell wall structure via pretreatment still remain elusive. In order to understand the role of noncellulosic switchgrass polymers on the overall efficiency of pretreatment, the structural evolution of the noncellulosic polymers of the plant cell wall were investigated during dilute acid pretreatment (DAP) by employing in-situ small-angle neutron scattering (in-situ SANS). In this study, we observed real-time structural changes not possible to observe by any other technique. To deconvolute the structural evolution of lignin and hemicellulose polymers during DAP, native switchgrass (NATV), and isolated holocellulose (HOLO) and cellulose (CELL) fractions from NATV were studied. Our results show that aggregate particles first appear around 80 °C for NATV and HOLO samples. Further, due to the low temperature and pretreatment severity condition, these particles are likely derived from hemicellulose. The formations of much larger aggregate particles, only observed in the NATV sample, were attributed to lignin. For the HOLO sample, as the temperature and pretreatment severity condition increased, hemicellulose-derived aggregate particle sizes increased, suggesting this process was the nucleation and early stage formation of pseudolignin particles. Consistent with our interpretation of structural evolutions in NATV and HOLO samples, no formation of aggregate particles was observed in CELL samples for the entire duration of the pretreatment. These results suggest that not only lignin but also hemicellulose can form aggregate particles within plant cell walls during pretreatment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Elucidating the formation mechanisms of zeolites using data-driven modelling and in-situ characterization

Zeolites are the main solid catalysts used by the chemical industry. The use of zeolites in separations and as shape selective catalysts requires control of the width and connectivity of their pores. 235 distinct zeolite frameworks have been synthesized to date, of over 2 million that have been proposed. Recent work indicates that the limitation is in large part kinetic: new synthetic pathways are required to access new zeolites. Organic cations are used to direct the synthesis towards specific zeolites. However, the molecular mechanisms by which cations direct the nucleation towards specific zeolites is not known. Elucidating these mechanisms is key to realize new zeolites for catalysis and separations, and is the focus of this project. This project developed and implemented a synergistic, data-driven computational and experimental approach to resolve the molecular pathways of nucleation, growth, and polymorph selection of zeolites and the role of organic cations in directing their formation. The project developed computationally efficient and accurate models for the study of the nucleation and growth of pure silica zeolites in molecular simulations, using machine learning with data from experiments. Simulations with these models were integrated with scanning tunneling electron microscopy, computer vision, and deep learning to unveil the molecular pathways of formation of a zeolite. Of particular interest in this project was to elucidate the role of amorphous precursors in the nucleation of the zeolite. Previous experiments indicate that zeolites are born within non-crystalline aggregates in which the silicates and organic cations have local and medium range order similar to that of the zeolite. The organic cations that direct the formation of zeolites and those that direct the formation of ordered mesoporous silicas are similar. We hypothesized that the frustrated attraction that for large organic cations leads to the formation of stable mesophases that direct the synthesis of mesoporous silicas, could promote the formation of metastable mesophases that can assist in the nucleation and polymorph selection of zeolites. The simulations resolved how structure directing agents build crystalline order and showed that mesoscopic pre-ordering occurs is not required to facilitate the nucleation of zeolites, because the synthesis occurs at high driving forces, where the barriers for nucleation are negligible. This project unveiled that polymorph selection in zeolite synthesis occurs after nucleation, opening a distinct area of control through the kinetics of growth and not through nucleation barriers.

36 MATERIALS SCIENCE↗

DOE OSTI2020

High-temperature 2D ferromagnetism in conjugated microporous porphyrin-type polymers

The need for magnetic 2D materials that are stable to the enviroment and have high Curie temperatures is very important for various electronic and spintronic applications. We have found that two-dimensional porphyrin-type aza-conjugated microporous polymer crystals are such a material (Fe-aza-CMPs). Fe-aza-CMPs are stable to CO, CO 2 , and O 2 atmospheres and show unusual adsorption, electronic, and magnetic properties. Indeed, they are semiconductors with small energy band gaps ranging from 0.27 eV to 0.626 eV. CO, CO 2 , and O 2 molecules can be attached in three different ways where single, double, or triple molecules are bound to iron atoms in Fe-aza-CMPs. For different attachment configurations we find that for CO and CO 2 a uniform distribution of the molecules is most energetically favorable while for O 2 molecules aggregation is most energetically preferable. The magnetic moments decrease from 4 to 2 to 0 for singly, doubly, triply occupied configurations for all gasses respectively. The most interesting magnetic properties are found for O 2 molecules attached to the Fe-aza-CMP. For a single attachment configuration we find that an antiferromagnetic state is favorable. When two O 2 molecules are attached, the calculations show the highest exchange integral with a value of J = 1071 μeV. This value has been verified by two independent methods where in the first method J is calculated by the energy difference between ferromagnetic and anitferromagnetic configurations. The second method is based on the frozen magnon approach where the magnon dispersion curve has been fitted by the Ising model. Finally, for the second method J has been estimated at J = 1100 μeV in excellent agreement with the first method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2006

Attenuating Stereo Pixel-Locking via Affine Window Adaptation

For real-time stereo vision systems, the standard method for estimating sub-pixel stereo disparity given an initial integer disparity map involves fitting parabolas to a matching cost function aggregated over rectangular windows. This results in a phenomenon known as 'pixel-locking,' which produces artificially-peaked histograms of sub-pixel disparity. These peaks correspond to the introduction of erroneous ripples or waves in the 3D reconstruction of truly Rat surfaces. Since stereo vision is a common input modality for autonomous vehicles, these inaccuracies can pose a problem for safe, reliable navigation. This paper proposes a new method for sub-pixel stereo disparity estimation, based on ideas from Lucas-Kanade tracking and optical flow, which substantially reduces the pixel-locking effect. In addition, it has the ability to correct much larger initial disparity errors than previous approaches and is more general as it applies not only to the ground plane.

pixel locking effect↗

DOE OSTI2020

A Customizable Metric to Provide a Comprehensive Picture of the Mobility Potential of a Location

Accessibility in a geo-spatial context refers to the ease of reaching a variety of opportunities from a given location. Accessibility theories (and resulting metrics) have traditionally focused on quantifying access to specific opportunities (such as jobs), or focused on specific modes (such as car, bike, etc.). Such approaches often fall short of providing a comprehensive picture of the true accessibility potential of a location as a combination of multiple modes to multiple types of destinations. Addressing this drawback, a novel metric labeled the ‘Mobility Energy Productivity (MEP) Metric’ was developed at the National Renewable Energy Laboratory to quantify the mobility potential of a location to connect people to goods, services, and employment using a variety of modes, while accounting for time, energy, and affordability. The MEP metric has been integrated with advance travel behavior models to compute the changes in mobility potential for various future scenarios, such as introduction of automated vehicles, and/or electric vehicles—but does so at the aggregate, or average-citizen level. The MEP in its initial iteration is not customized to the particular socio-economic contingents, or even to an individual whose modal availability or pattern of trip making may substantially differ from the average. Addressing this gap, this research effort extends the MEP framework from a static state to a more tailored and dynamic state, one in which an individual, or group can customize the metric for their unique characteristics, such as modes, activity patterns, and time-of-day preferences. The extended MEP metric framework can now be integrated to assess the customized mobility energy productivity of an individual.

ADVANCED PROPULSION SYSTEMS,ENERGY PLANNING, POLIC↗

DOE OSTI2020

The Cost of Saving Electricity: A Multi-Program Cost Curve for Programs Funded by U.S. Utility Customers

This study analyzed the cost performance of electricity efficiency programs implemented by 116 investor-owned utilities between 2009 and 2015 in 41 states, representing about three-quarters of the total spending on U.S. efficiency programs. We applied our typology to characterize efficiency programs along several dimensions (market sector, technology, delivery approach, and intervention strategy) and report the costs incurred by utilities and other program administrators to achieve electricity savings as a result of the programs. Such cost performance data can be used to compare relative costs of different types of efficiency programs, evaluate efficiency options alongside other electricity resources, benchmark local efficiency programs against regional and national cost estimates, and assess the costs of meeting state efficiency policies. The savings-weighted average cost of saved electricity for the period was $0.025/kilowatt-hour (kWh). The cost of saved electricity for programs that targeted residential customers was $0.021/kWh, compared to $0.025/kWh for programs for commercial and industrial customers. Ultimately, we developed an aggregate program savings “cost curve” for the actual electricity efficiency resource during the period that provides insights into the relative costs of various types of efficiency programs and the savings contribution of each program type to the efficiency resource at a national level.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Simulation of PV Variability as a Function of PV Generation and Plant Size: Preprint

The deployment of photovoltaic (PV) systems continues to show significant expansion; however, this growth has brought added attention to issues around the variability of the solar resource. Both spatial and temporal variability exist. Temporal scales can range from the sub-second to multiyear, whereas spatial scales can range from a few meters to tens of kilometers. There are multiple methods described in the literature to quantify PV variability at various spatial and temporal scales. This study focuses on short-term temporal variability and uses similar approaches with the addition of PV plant size a parameter to quantify variability. The method employed here incorporates the normalization of clear- and cloudy-sky conditions and PV plant size to quantify nominal variability metrics. The distribution and fluctuations of these metrics provide relevant information that is useful for system operations. The National Solar Radiation Database (NSRDB) is used to simulate PV variability as a function of PV generation and plant size. Hypothetical but realistic system information at 33 locations is used to model PV generation by feeding NSRDB solar irradiance data to the National Renewable Energy Laboratory’s System Advisor Model (SAM). Over the selected region, it is found that the aggregated ramp rates for the 1-minute data are associated with standard deviations ranging from 0.002–0.055 on a daily basis; however, hourly intervals induce higher aggregated ramp rates than the other timescales. Even though minute-to-minute variations are significant for the 1-minute timescale, the standard deviation aggregated into a daily metric is smaller because of the cancellation of values.

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2021

Simulation of PV Variability as a Function of PV Generation and Plant Size

The deployment of photovoltaic (PV) systems continues to show significant expansion; however, this growth has brought added attention to issues around the variability of the solar resource. Both spatial and temporal variability exist. Temporal scales can range from the sub-second to multiyear, whereas spatial scales can range from a few meters to tens of kilometers. There are multiple methods described in the literature to quantify PV variability at various spatial and temporal scales. This study focuses on short-term temporal variability and uses similar approaches with the addition of PV plant size a parameter to quantify variability. The method employed here incorporates the normalization of clear-and cloudy-sky conditions and PV plant size to quantify nominal variability metrics. The distribution and fluctuations of these metrics provide relevant information that is useful for system operations. The National Solar Radiation Database (NSRDB) is used to simulate PV variability as a function of PV generation and plant size. Hypothetical but realistic system information at 33 locations is used to model PV generation by feeding NSRDB solar irradiance data to the National Renewable Energy Laboratory’s System Advisor Model (SAM). Over the selected region, it is found that the aggregated ramp rates for the 1-minute data are associated with standard deviations ranging from 0.002–0.055 on a daily basis; however, hourly intervals induce higher aggregated ramp rates than the other timescales. Even though minute-to-minute variations are significant for the 1-minute time-scale, the standard deviation aggregated into a daily metric is smaller because of the cancellation of values.

irradiance↗

NASA NTRS1986

An optimization model for the US Air-Traffic System

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function.

Mulvey, J. M.↗