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DOE OSTI2024

Anticipating how rain-on-snow events will change through the 21st century: lessons from the 1997 new year’s flood event

The California-Nevada 1997 New Year’s flood was an atmospheric river (AR)-driven rain-on-snow (RoS) event and remains the costliest in their history. The joint occurrence of saturated soils, rainfall, and snowmelt generated inundation throughout northern California-Nevada. Although AR RoS events are projected to occur more frequently with climate change, the warming sensitivity of their flood drivers across scales remains understudied. We leverage the regionally refined mesh capabilities of the Energy Exascale Earth System Model (RRM-E3SM) to recreate the 1997 New Year’s flood with horizontal grid spacings of 3.5 km across California, with forecast lead times of up to 4 days, and across six warming levels ranging from pre-industrial conditions to +3.5° C. We describe the sensitivity of the flood drivers to warming including AR duration and intensity, precipitation phase, intensity and efficiency, snowpack mass and energy changes, and runoff efficiency. Our findings indicate current levels of climate change negligibly influence the flood drivers. At warming levels ≥ 1.7° C, AR hazard potential increases, snowpack nonlinearly decreases, antecedent soil moisture decreases (except where the snowline retreats), and runoff decreases (except in the southern Sierra Nevada where antecedent snowpack persists). Storm total precipitation increases, but at rates below warming-induced increases in saturation-specific humidity. Warming intensifies short-duration, high-intensity rainfall, particularly where snowfall-to-rainfall transitions occur. This study highlights the nonlinear tradeoffs in 21st-century RoS flood hazards with warming and provides water management and infrastructure investment adaptation considerations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Hydrologic investigations of radar-rainfall error propagation to rainfall-runoff model hydrographs

Rainfall is arguably the most important yet most variable input for rainfall-runoff hydrologic models. In this study, the authors search for the characteristics of radar-rainfall estimates that are most important for skillful streamflow predictions. They perform comprehensive hydrologic investigations of radar-rainfall characteristics, including spatiotemporal resolution, radar range visibility, statistical characterization of rainfall variability, all vis-a-vis basin characteristics such as size and river network topology. Since the true rainfall fields are unknown, the authors exploit a paradigm of using two independently constructed radar-rainfall products i.e., Multi-Radar Multi-Sensor and IFC-ZR used operationally by the Iowa Flood Center (IFC). Using the distributed hydrologic model called the Hillslope-Link Model for the domain of the state of Iowa, they evaluate streamflow prediction at 140 USGS gauge stations that monitor rivers in Iowa. Through spatial and temporal rainfall aggregation experiments, the authors show that the impact of spatial and temporal resolution of rainfall is significant typically for smaller basins while starts reducing significantly for basins larger than 1,000 km 2 . Other rainfall characteristics they explored do not reveal a strong signature in the relationship of rainfall differences between the two products and hydrograph errors. However, exploring the product similarities rather than differences reveals that the basin-wide rainfall volume has the most significant effect on streamflow prediction. The results from this study are generalizable for all rainfall observing systems.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Amplified Extreme Floods and Shifting Flood Mechanisms in the Delaware River Basin in Future Climates

Abstract Historical records in the Delaware River Basin reveal complex and spatially diverse flood generating mechanisms influenced by the region's mountains‐to‐plains gradients. This study focuses on predicting future flood hazards and understanding the underlying drivers of changes across the region. Using a process‐based hydrological model, we analyzed the hydrometeorological condition of each historical and future flood event. For each event, at the subbasin scale, we identified the dominant flood generating mechanism, including snowmelt, rain‐on‐snow, short‐duration rain, and long‐duration rain. The rain‐induced floods are further categorized based on the soil's Antecedent Moisture Condition (AMC) before the event, whether dry, normal, or wet. Our historical analysis suggests that rain‐on‐snow is the primary flood mechanism of the Upper Basin. Although most frequent, the magnitude of rain‐on‐snow floods is often less severe than short rain floods. In contrast, historical floods in the Lower Basin are primarily caused by short rain under normal AMC. Given the uncertainties in climate projections, we used an ensemble of future climate scenarios for flood projections. Despite variations in regional climate projections, coherent perspectives emerge: the region will shift toward a warmer, wetter climate, with a projected intensification of extreme floods. The Upper Basin is projected to experience a marked decrease in rain‐on‐snow floods, but a substantial increase in short rain floods with wet AMC. The largest increase in flood magnitude will be driven by short rains with wet AMC in the Upper Basin and by short rains with normal AMC in the Lower Basin.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Capturing Sub‐Kilometer Flood Inundation Dynamics During the California Rain‐on‐Snow Events of 2017

The severe impacts of rain‐on‐snow (ROS) extreme events have been widely recognized and studied. However, unlike hydrological processes, flood inundation dynamics and the relative contribution of rainfall and snowmelt during ROS events remain under‐investigated. We diagnosed and documented sub‐kilometer spatio‐temporal dynamics of flood inundation during the 2017 California ROS events, simulated by a 2‐dimensional hydrodynamic model, River Dynamical Core (RDycore). RDycore shows good performance in capturing fine‐scale flood inundation dynamics against gauge measurements (with a median correlation coefficient of 0.81) and satellite observations. On top of rainfall, snowmelt not only increases the mean maximum inundation depth (12.0%–25.1%), but also expands the total flooded area (19.9%–31.9%) and prolongs the mean flood duration (3.4%–7.1%) across the events. Our findings offer an explicit and accurate picture of when and where ROS flooding could occur and how snowmelt increases flood hazard, valuable for risk assessment and infrastructure planning.

Flood inundation↗

DOE OSTI2025

Hydraulic constraints to stomatal conductance in flooded trees

Stomatal closure is a pervasive response among trees exposed to flooded soil. We tested whether this response is caused by reduced hydraulic conductance in the soil-to-leaf hydraulic continuum (k total ), and particularly by reduced root hydraulic conductance (k root ), which has been widely hypothesized. We tracked stomatal conductance at the leaf level (g s ) and canopy scale (G s ) along with physiological conditions in two temperate tree species, Magnolia grandiflora and Quercus virginiana, that were subjected to flood and control conditions in a greenhouse experiment. Flooding reduced g s , G s , k root and k total . Path analysis showed strong support for direct effects of k total on g s and for flood duration on k total , but not k root on k total . A process-based model that accounted for the k total reduction predicted the timeseries of G s in flood and control treatment trees reasonably well (predicted versus observed G s R 2 = 0.80 and 0.51 for M. grandiflora and Q. virginiana, respectively). However, accounting only for k root reduction in flooded trees was insufficient for predicting observed G s reduction. Together, these results suggest that hydraulic constraints were not limited to roots and highlight the need to account for flooding effects on k total when projecting forest ecosystem function using process-based models.

Plant stress↗

DOE OSTI2020

Conceptual and Mathematical Foundation for the FE/NETL CO 2 Prophet Model for Simulating CO 2 Enhanced Oil Recovery, Version 2

The United States (U.S.) Department of Energy (DOE) Office of Fossil Energy (FE) at the National Energy Technology Laboratory (NETL) has developed the FE/NETL CO 2 Prophet Model, which is Version 2 of CO 2 Prophet. This document describes the mathematical foundation for the FE/NETL CO 2 Prophet Model. CO 2 Prophet was originally developed in the 1990s by Texaco Exploration and Production and Technology Department for DOE. The FE/NETL CO 2 Prophet Model is an oil reservoir simulator that is suitable for simulating water floods and supercritical carbon dioxide (CO 2 ) enhanced oil recovery (EOR). The FE/NETL CO 2 Prophet Model uses a number of assumptions to simplify the equations describing the flow of oil, water (or brine), and CO 2 in the oil reservoir.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2020

User’s Manual for StrmtbFlow, the Stream Tube Multiphase Flow Part of the FE/NETL CO 2 Prophet Model, Version 2

The United States (U.S.) Department of Energy (DOE) Office of Fossil Energy (FE) at the National Energy Technology Laboratory (NETL) has developed the FE/NETL CO 2 Prophet Model, which is an updated version of the CO 2 Prophet. This document is a user’s manual for StrmtbFlow, which is one part of the FE/NETL CO 2 Prophet Model. CO 2 Prophet was originally developed in the 1990s by Texaco Exploration and Production Technology Department for DOE. The FE/NETL CO 2 Prophet Model is an oil reservoir simulator that is suitable for simulating water floods and supercritical carbon dioxide (CO 2 ) enhanced oil recovery (EOR). The FE/NETL CO 2 Prophet Model uses a number of assumptions to simplify the equations describing the flow of oil, water (or brine), and CO 2 in the oil reservoir.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2020

User’s Manual for StrmtbGen, the Stream Tube Generating Part of the FE/NETL CO 2 Prophet Model, Version 2

The United States (U.S.) Department of Energy (DOE) Office of Fossil Energy (FE) at the National Energy Technology Laboratory (NETL) has developed the FE/NETL CO 2 Prophet Model, which is Version 2 of CO 2 Prophet. This document is a User’s Manual for StrmtbGen, which is one part of the FE/NETL CO 2 Prophet Model. CO 2 Prophet was originally developed in the 1990s by Texaco Exploration and Production Technology Department for DOE. The FE/NETL CO 2 Prophet Model is an oil reservoir simulator that is suitable for simulating water floods and supercritical carbon dioxide (CO 2 ) enhanced oil recovery (EOR). The FE/NETL CO 2 Prophet Model uses a number of assumptions to simplify the equations describing the flow of oil, water (or brine), and CO 2 in the oil reservoir.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

Floods and Heavy Precipitation at the Global Scale: 100‐Year Analysis and 180‐Year Reconstruction

Floods and heavy precipitation have disruptive impacts worldwide, but their historical variability remains only partially understood at the global scale. This article aims at reducing this knowledge gap by jointly analyzing seasonal maxima of streamflow and precipitation at more than 3,000 stations over a 100‐year period. The analysis is based on Hidden Climate Indices (HCIs). Like standard climate indices (e.g., Nino 3.4, NAO), HCIs are used as covariates explaining the temporal variability of data, but unlike them, HCIs are estimated from the data. In this work, a distinction is made between common HCIs, that affect both heavy precipitation and floods, and specific HCIs, that exclusively affect one or the other. Overall, HCIs do not show noticeable autocorrelation, but some are affected by noticeable trends. In particular, strong and wide‐ranging trends are identified in precipitation‐specific HCIs, while trends affecting flood‐specific HCIs are weaker and have more localized effects. A probabilistic model is then derived to link HCIs and large‐scale atmospheric variables (pressure, wind, temperature) and to reconstruct HCIs since 1836 using the 20CRv3 reanalysis. In turn this allows estimating the probability of occurrence of floods and heavy precipitation at the global scale. This 180‐year reconstruction highlights flood hot‐spots and hot‐moments in the distant past, well before the establishment of perennial monitoring networks. Finally, the approach presented in this study is generic and paves the way for an improved characterization of historical variability by making a better use of long but highly irregular station data sets.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Storm surges and extreme sea levels: Review, establishment of model intercomparison and coordination of surge climate projection efforts (SurgeMIP).

Coastal flood damage is primarily the result of extreme sea levels. Climate change is expected to drive an increase in these extremes. While proper estimation of changes in storm surges is essential to estimate changes in extreme sea levels, there remains low confidence in future trends of surge contribution to extreme sea levels. Alerting local populations of imminent extreme sea levels is also critical to protecting coastal populations. Both predicting and projecting extreme sea levels require reliable numerical prediction systems. The SurgeMIP (surge model intercomparison) community has been established to tackle such challenges. Efforts to intercompare storm surge prediction systems and coordinate the community 's prediction and projection efforts are introduced. An overview of past and recent advances in storm surge science such as physical processes to consider and the recent development of global forecasting systems are briefly introduced. Selected historical events and drivers behind fast increasing service and knowledge requirements for emergency response to adaptation considerations are also discussed. The community 's initial plans and recent progress are introduced. These include the establishment of an intercomparison project, the identification of research and development gaps, and the introduction of efforts to coordinate projections that span multiple climate scenarios.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Improving Short Term Predictability of Hydrologic Models with Deep Learning

Focal Area: Focal Area 2. Predictive modeling through the use of AI techniques and AI-derived model components; the use of AI and other tools to design a prediction system comprising of a hierarchy of models (e.g., AI driven model/component/parameterization selection). Science Challenge: A major challenge exists in the lack of reliable predictive modeling of water-cycle extremes using macro-scale hydrologic models that are driven by atmospheric climate data. This causes a critical knowledge gap in understanding the magnitudes, probabilities, and severity of droughts, rainfall, and flooding. Improved understanding of these extreme events requires more accurate modeling at high spatial and temporal resolutions. This shortcoming is especially apparent when complex couplings between atmospheric quantities and engineered systems emerge, such as during extreme precipitation or drought events and at intersections of atmospheric-land-fluvial-ocean systems. Added complexity around representing operations of engineered infrastructure leads to a limited capability to analyze the temporal and spatial implications of compounding extreme events across inland and coastal regions. This results in profound challenges for water and power systems operators, agriculture production, and regional infrastructure planning. The science challenge can be summarized as How can we use AI/ML to improve short term predictability of extreme water-cycle events and associated risk, especially compounding events and extreme rainfall patterns that result in flooding, to inland and coastal communities under different climate scenarios?

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Microreactor Assembly Transportation Cask Model Description for Criticality Safety Validation Basis Assessment

Criticality safety analyses are completed on a transportation cask used for microreactor assembly shipment to provide an example of model and analysis to industry for reproducing this type of study on their microreactor fuel shipment. The fuel assembly considered is based on a gas-cooled microreactor (GC-MR), which utilizes HALEU fuel in the form of TRISO particles and utilizes various design options considered in industry designs. Various versions of this GC-MR assembly were studied, with and without YH2 moderator, providing similar conclusions. The shipment cask design is revised based on an existing design ES-3100, developed by Y-12 for the transport of highly enriched uranium (HEU), but is enlarged to hold the GC-MR fuel assembly. Criticality safety analysis for the cask/GC-MR fuel assembly package was performed using the CSAS6 sequence of SCALE6.3.2, utilizing the ENDF/B-VII.1 based continuous energy neutron library, and the analysis strictly follows the guideline from NRC reference reports. Different scenarios, e.g. normal operation, undamaged cask with water flooded, damaged cask with optimal water moderation, have been analyzed and it could be concluded the package would always have a large margin of subcriticality even packed in an infinite array. Sensitivity and similarity analyses are also performed using the TSUNAMI sequence of SCALE6.3.2, and the similarity analysis uses all the experiments from the ICSBEP Handbook with Intermediate and Mixed Enriched Uranium (IEU) and Low Enriched Uranium (LEU) systems together with additional ones that are sponsored by the DNCSH program. These similarity analyses indicate that dry cases have no similar benchmark experiments (ck values greater than 0.8), which may become problematic if more assemblies are shipped together (or a fully loaded core is shipped) and margin to criticality is reduced. However, the damaged cask models with flooded assemblies exhibited similarities to many experiments with ck values greater than 0.8.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Physics–Informed Neural Networks of the Saint–Venant Equations for Downscaling a Large–Scale River Model

Large-scale river models are being refined over coastal regions to improve the scientific understanding of coastal processes, hazards and responses to climate change. However, coarse mesh resolutions and approximations in physical representations of tidal rivers limit the performance of such models at resolving the complex flow dynamics near the river-ocean interface, resulting in inaccurate simulations of flood inundation. In this research, we propose a machine learning (ML) framework based on the state-of-the-art physics-informed neural network (PINN) to simulate the downscaled flow at the subgrid scale. First, we demonstrate that PINN is able to assimilate observations of various types and solve the one-dimensional (1-D) Saint-Venant equations (SVE) directly. We perform the flow simulations over a floodplain and along an open channel in several synthetic case studies. The PINN performance is evaluated against analytical solutions and numerical models. Our results indicate that the PINN solutions of water depth have satisfactory accuracy with limited observations assimilated. In the case of flood wave propagation induced by storm surge and tide, a new neural network architecture is proposed based on Fourier feature embeddings that seamlessly encodes the periodic tidal boundary condition in the PINN's formulation. Furthermore, we show that the PINN-based downscaling can produce more reasonable subgrid solutions of the along-channel water depth by assimilating observational data. The PINN solution outperforms the simple linear interpolation in resolving the topography and dynamic flow regimes at the subgrid scale. This study provides a promising path towards improving emulation capabilities in large-scale models to characterize fine-scale coastal processes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Flood Estimation under Snowmelt and Rain-on-Snow Processes in Alaska: A Military Installation Perspective

Accurate flood estimation in snow-dominated and high-latitude regions remains challenging due to complex interactions among rainfall, snowmelt, and rain-on-snow (ROS) processes, which are not captured in conventional precipitation-based intensity-duration-frequency (PREC-IDF) curves. This study evaluates the Next-Generation IDF (NG-IDF) framework, an extension of PREC-IDF that incorporates total water available for runoff (precipitation minus changes in snow water equivalent), in two contrasting Alaskan watersheds of Department of Defense (DoD) significance: the Little Chena River Basin (LCRB) in interior Alaska, a tributary of the Chena River that flows through Fort Wainwright and near Eielson Air Force Base, and the Upper Ship Creek Basin (USCB), which drains Joint Base Elmendorf-Richardson near Anchorage. Using long-term SNOTEL observations and event-based rainfall-runoff modeling, NG-IDF and PREC-IDF flood estimates were compared against observation-based flood frequency analyses. Results show that NG-IDF consistently reduces flood-estimation bias by 15–20% relative to PREC-IDF, particularly for snowmelt- and ROS-dominated events. In the interior LCRB, permafrost conditions can substantially amplify flood responses during snowmelt events, an effect not explicitly represented in standard design tools. These findings demonstrate that NG-IDF provides a more physically consistent and transferable framework for flood estimation in cold regions, with potential relevance to mission-critical DoD installation resilience. Projected increases in ROS frequency and permafrost degradation across Alaska further emphasize the need to integrate physics-based hydrologic models that explicitly represent snow and permafrost processes to enhance design resilience and operational readiness for military and other critical infrastructure.

Yan, Hongxiang (ORCID:000000022387403X)↗

DOE OSTI2022

Coreflood Tests to Evaluate Enhanced Oil Recovery Potential of Wettability-Altering Surfactants for Oil-Wet Heterogeneous Carbonate Reservoirs

Summary Oil-wetness and heterogeneity are two main factors that result in low oil recovery (OR) by waterflood in carbonate reservoirs. The injected water is likely to flow through high-permeability regions and bypass the oil in the low-permeability matrix. In this study, systematic coreflood tests were carried out in both “homogeneous” cores and “heterogeneous” cores with a wettability-altering surfactant. The homogeneous coreflood tests were conducted to evaluate surfactant retention, as well as to compare tertiary surfactant flooding with secondary surfactant flooding. The heterogeneous coreflood test was proposed to model bypassing in low-permeability matrix during waterfloods, and dynamic imbibition of surfactant into the low-permeability matrix. Surfactant retention results suggest that retention increases as initial oil saturation decreases. The retention of selected surfactant in the target reservoir cores was measured to be within a range of 0.07–0.12 mg/g-rock, which is economically acceptable. The results of homogeneous coreflood tests showed that both secondary waterflood and secondary surfactant flood can achieve high OR (>50%) from relatively homogeneous oil-wet cores. A shut-in phase after the surfactant injection resulted in a surge in oil production, which suggests that enough time should be given for wettability alteration by surfactants. The results of heterogeneous coreflood tests showed that more oil is bypassed in the tighter matrix by waterflood if the permeability is higher in the flooded layer and this bypassed oil is the target for the wettability-altering surfactant floods. Slow wettability-altering surfactant injection leads to imbibition into bypassed regions. When the oil-wet carbonate reservoirs have large unswept regions after waterflood, wettability-altering surfactants can significantly improve OR if enough time is given for imbibition.

Engineering↗

DOE OSTI2026

Microreactor Assembly Transportation Cask Model Description for Criticality Safety Validation Basis Assessment (Rev. 3)

Criticality safety analyses are completed on a transportation cask used for microreactor assembly shipment to provide an example of model and analysis to industry for reproducing this type of study on their microreactor fuel shipment. The fuel assembly considered is based on a gas-cooled microreactor (GC-MR), which utilizes HALEU fuel in the form of TRISO particles and utilizes various design options considered in industry designs. Various versions of this GC-MR assembly were studied, with and without YH 2 moderator, providing similar conclusions. The shipment cask design is revised based on an existing ES-3100 design, developed by Y-12 for the transport of highly enriched uranium (HEU), but is enlarged to hold the GC-MR fuel assembly. Criticality safety analysis for the cask/GC-MR fuel assembly package was performed using the CSAS6 sequence of SCALE6.3.2, utilizing the ENDF/B-VII.1 based continuous energy neutron library, and the analysis strictly follows the guideline from NRC reference reports. Different scenarios, e.g. normal operation, undamaged cask with water flooded, damaged cask with optimal water moderation, have been analyzed and it could be concluded the package would always have a large margin of subcriticality even packed in an infinite array. Sensitivity and similarity analyses are also performed using the TSUNAMI sequence of SCALE6.3.2, and the similarity analysis uses all the experiments from the ICSBEP Handbook with Highly Enriched Uranium (HEU), Intermediate and Mixed Enriched Uranium (IEU) and Low Enriched Uranium (LEU) systems, together with additional ones that are sponsored by the DNCSH program, and selected IRPhEP experiments using TRISO fuel and graphite moderator. These similarity analyses indicate that the dry nominal design has no similar benchmark experiments (ck values greater than 0.8), which may become problematic if more assemblies are shipped together (or a fully loaded core is shipped) and margin to criticality is reduced. However, the cask models with flooded assemblies exhibited similarities to many experiments with c k values greater than 0.8.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Validation of MCNP Critical Benchmark Models of PU-MET-FAST-016

A new centralized repository of high-quality MCNP models of critical benchmark experiments is currently under development at Los Alamos National Laboratory (LANL). The repository is the combined effort of the Nuclear Criticality Safety, Nuclear Data, and Monte Carlo code development/application organizations at LANL. The initial set of benchmark models in the repository are derived from the Whisper Suite provided with MCNP6.2 and are evaluated against the benchmark experiments described in the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook. The goal is to build a single LANL benchmark collection that is up to date with the latest ICSBEP revision, has a formal review and revision process, is contained in an open-source repository, and utilizes new Python tools for improved input and output file review. This paper describes the validation of the models associated with PU-MET-FAST-016, “Flooded 3X3X3 Arrays of 3-kg Plutonium (Pu) Metal Cylinders – Phase I”. In this critical experiment, twenty-seven 3-kg Pu metal cylinders with a height of 46.33 ± 0.15 mm and diameter of 65.25 ± 0.05 mm were arranged in a cubic array. The Pu cylinders were sealed in aluminum cans, and three cans were placed in each of nine perforated aluminum sleeves, as shown in Fig. 1. The nine sleeves were supported by an aluminum frame that allowed for control of the lateral spacing of the cylinders, both in the X and Y directions. The benchmark experiment measured thirteen configurations. Of these configurations, six were modeled using MCNP.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

A Numerical Analysis of The Pool Boiling Process in Flooded Evaporators Using Different Refrigerants

The pool boiling process can be observed in several energy conversion processes including commercial and industrial refrigeration, industrial air-cooling operations, and power generation. The process becomes more involved when pool boiling in a tube bundle is considered. In the current study, a numerical model is developed to predict the key performance parameters of a flooded evaporator while considering a range of working fluids. A kettle reboiler configuration was considered, and a performance model was developed to account for boiling on individual tubes, merging of vapor bubbles, and movement under gravity. A volume of fluid (VOF) model was used to deal with the different phases in the simulation. Various fluids were considered in this study including HFE-7000, HFE-7300, and water. The trajectories of the bubbles were tracked, and the resulting information has been summarized in physical measurable quantities.

Zhang, Mingkan↗