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Methodology for assessing the safety of Hydrogen Systems: HyRAM 1.0 technical reference manual

The HyRAM software toolkit provides a basis for conducting quantitative risk assessment and consequence modeling for hydrogen infrastructure and transportation systems. HyRAM is designed to facilitate the use of state-of-the-art science and engineering models to conduct robust, repeatable assessments of hydrogen safety, hazards, and risk. HyRAM is envisioned as a unifying platform combining validated, analytical models of hydrogen behavior, a standardized, transparent QRA approach, and engineering models and generic data for hydrogen installations. HyRAM is being developed at Sandia National Laboratories for the U. S. Department of Energy to increase access to technical data about hydrogen safety and to enable the use of that data to support development and revision of national and international codes and standards. This document provides a description of the methodology and models contained in the HyRAM version 1.0. HyRAM 1.0 includes generic probabilities for hydrogen equipment failures, probabilistic models for the impact of heat flux on humans and structures, and computationally and experimentally validated analytical and first order models of hydrogen release and flame physics. HyRAM 1.0 integrates deterministic and probabilistic models for quantifying accident scenarios, predicting physical effects, and characterizing hydrogen hazards (thermal effects from jet fires, overpressure effects from deflagrations), and assessing impact on people and structures. HyRAM is a prototype software in active development and thus the models and data may change. This report will be updated at appropriate developmental intervals.

08 HYDROGEN↗

Sensor Development for Liquid Water Detection in Dry Storage Casks: FY 2023 Status

Modeling efforts were undertaken in fiscal year (FY) 2023 to evaluate the feasibility and capability for sensing of liquid water inside canister-based dry cask storage systems (DCSSs). The focus was on the development of full-scale finite element models (FEMs) of ultrasound propagation through DCSS canister components. For these initial investigations, simulation of the baseplate component was targeted, envisioning water collection at the bottom of a vertically oriented canister. The effects of internal canister components (i.e., fuel basket, fuel assemblies) on ultrasound propagation in the baseplate component were evaluated in these efforts. The environment inside a DCSS confinement is intended to be inert and free of water to prevent potential corrosion of used fuel cladding or other internal hardware. Spent fuel assemblies are dried, after storage in water pools, to make sure water has been removed from assembly cavities. However, there is some uncertainty about the amount of residual water potentially left behind in a DCSS after drying processes, because water can become trapped in cavities or other small crevices in the surfaces formed by the fuel cladding, fuel assemblies, and other internal hardware components. Considering the complex space- and time-dependent temperature profiles in DCSSs, water may be in a liquid or gas phase depending on its location in the cask and how long the cask has been in storage. Evacuating most water and oxidizing agents contained within a canister is recommended by NUREG-1536 (NRC 2010), which covers DCSSs. As summarized by Salazar et al. (2020), existing guidance typically relies on achievable vacuum pumping pressures sustained over a hold period as a signal of dryness and water removal. However, time series data about water removal from full-scale commercial drying procedures are lacking (Hanson and Alsaed 2019). A review of drying specifications from several vendors led to the conclusion that if the specifications are followed correctly, the residual moisture in DCSSs should present an insignificant risk of cladding degradation (Knoll and Gilbert 1987). A more recent analysis concluded that much larger quantities of residual water could remain in DCSSs, but the amount would still not be expected to lead to significant corrosion of fuel cladding or other internal components (Jung et al. 2013). Industry drying procedures are mostly prescriptive in nature, and operational issues arising during the process could result in incomplete drying. A summary of operational issues and potential negative effects of residual water is provided by Salazar et al. (2019). Experimental efforts are ongoing to validate the extent of water removal in a DCSS based on drying procedures used at nuclear power plants through well-designed investigations of drying process efficacy and water retention (Durbin et al. 2021; Pulido et al. 2022a, Pulido et al. 2022b). This has been approached by simulating limited portions of a DCSS internal volume and fuel assemblies. So far, these efforts have focused on the effects of potential water trapping in the dashpot region of control rod guide tubes but are expected to be expanded to include the effects of other internal hardware features and failed fuel rod cladding. A method for detection and measurement of liquid water (Meyer et al. 2022; Meyer et al. 2021), in tandem with the drying information gained through experimental investigations, provides comprehensive bases for understanding the internal conditions of DCSSs and provides technical information to support licensing decisions.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Experimental and numerical validation of an ultrasonic visualization system for nuclear reactor application

This paper deals with the design of ultrasonic imaging systems for the next generation of nuclear reactors cooled by liquid metal. Indeed, a generation IV research nuclear reactor is being developed by the Belgian Nuclear Research Center (SCK-CEN) in the frame of the MYRRHA project (for Multipurpose hYbrid Research Reactor for High-tech Applications). This sub-critical/critical reactor is cooled by Lead-Bismuth Eutectic (LBE). The opacity of this liquid metal requires the development of an ultrasonic visualization system for internal inspection and object detection. But due to the peculiar conditions met in the core of the reactor, velocity as well as temperature gradients are expected and are likely to affect directly the ultrasonic propagation. The objective of this work is to validate the ultrasonic imaging strategy by tests performed in a dedicated test rig and by numerical simulations using a ray-tracing method. The experimental investigations have been performed on a specific water facility reproducing conditions similar to those encountered in the core of the MYRRHA reactor. These conditions include the propagation over large distance, and the presence of temperature and velocity gradients. In the MYRRHA reactor application, the distance to be travelled by the acoustic waves of the visualization system is about 5 m, including a reflection. The acoustic absorption, the scattering losses, the beam divergence and the transmitted energy during reflection have been determined as a function of the travelled distance. The experimental values are compared with the literature for validation. The presence of temperature and velocity gradients in the core of the reactor is due to the coolant circulation. These gradients are about 5 K over 0.1 m and 1 m/s over 0.2 m, respectively, and are reproduced in the facility for investigating their influence on the propagation of ultrasounds. The experimental data are used for improving and validating a ray-tracing algorithm. This algorithm is then applied to the full scale application for validating the ultrasonic visualization system for nuclear reactor application. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Protection System Validation with Machine Learning Anomaly Classification

A poster for the Early Career Poster Session. Power system protection devices have transitioned over the past few decades from mechanical to analog devices, then to solid state and finally digital. Relays and their associated critical network of equipment have significantly increased in complexity. Even internally, relays have gained significant intricacy, with relatively simple overcurrent or differential functions now being assisted by a myriad of other functions. This is necessary as the grid becomes more complex, but it brings increased difficulty in monitoring and upkeep. Misoperation caused by improper relay settings or malicious actions is a constant challenge faced by all utilities. These improper settings can be difficult to identify and may require exhaustive post-mortem analysis, typically after a major outage event has already occurred. A mechanism is needed for monitoring the behavior of protection systems to validate that they act and perform as expected. This work presents a concept for a machine learning (ML) system capable of validating the performance of protection systems by classifying anomalous events and characterizing protection system responses based solely on available current and voltage measurements. As a first step in its development, an experimental dataset is generated, and a random forest model is implemented with high accuracy in distinguishing four power system scenarios.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

Horizon: A Proposal for Large Aperture, Active Optics in Geosynchronous Orbit

In 1999, NASA's New Millennium Program called for proposals to validate new technology in high-earth orbit for the Earth Observing-3 (NMP EO3) mission to fly in 2003. In response, we proposed to test a large aperture, active optics telescope in geosynchronous orbit. This would flight-qualify new technologies for both Earth and Space science: 1) a future instrument with LANDSAT image resolution and radiometric quality watching continuously from geosynchronous station, and 2) the Next Generation Space Telescope (NGST) for deep space imaging. Six enabling technologies were to be flight-qualified: 1) a 3-meter, lightweight segmented primary mirror, 2) mirror actuators and mechanisms, 3) a deformable mirror, 4) coarse phasing techniques, 5) phase retrieval for wavefront control during stellar viewing, and 6) phase diversity for wavefront control during Earth viewing. Three enhancing technologies were to be flight- validated: 1) mirror deployment and latching mechanisms, 2) an advanced microcontroller, and 3) GPS at GEO. In particular, two wavefront sensing algorithms, phase retrieval by JPL and phase diversity by ERIM International, were to sense optical system alignment and focus errors, and to correct them using high-precision mirror mechanisms. Active corrections based on Earth scenes are challenging because phase diversity images must be collected from extended, dynamically changing scenes. In addition, an Earth-facing telescope in GEO orbit is subject to a powerful diurnal thermal and radiometric cycle not experienced by deep-space astronomy. The Horizon proposal was a bare-bones design for a lightweight large-aperture, active optical system that is a practical blend of science requirements, emerging technologies, budget constraints, launch vehicle considerations, orbital mechanics, optical hardware, phase-determination algorithms, communication strategy, computational burdens, and first-rate cooperation among earth and space scientists, engineers and managers. This manuscript presents excerpts from the Horizon proposal's sections that describe the Earth science requirements, the structural -thermal-optical design, the wavefront sensing and control, and the on-orbit validation.

Chesters, Dennis↗

The role of global cloud climatologies in validating numerical models

The net upward longwave surface radiation is exceedingly difficult to measure from space. A hybrid method using General Circulation Model (GCM) simulations and satellite data from the Earth Radiation Budget Experiment (ERBE) and the International Satellite Cloud Climatology Project (ISCCP) was used to produce global maps of this quantity over oceanic areas. An advantage of this technique is that no independent knowledge or assumptions regarding cloud cover for a particular month are required. The only information required is a relationship between the cloud radiation forcing (CRF) at the top of the atmosphere and that at the surface, which is obtained from the GCM simulation. A flow diagram of the technique and results are given.

HARSHVARDHAN↗

New Pulsed Neutron Die-Away Experiments in Light Water

Thermal neutron scattering laws are important data for many nuclear science and engineering applications, especially criticality safety. Recently, pulsed-neutron die-away experiments have been proposed and used as an experiment to validate thermal neutron scattering laws. These experiments involve irradiating a target moderating material with pulses of neutrons from a neutron generator. The physics of thermal scattering greatly affect how the neutron population in the target exponentially decays via absorption and leakage. Herein, we present experimental results from a new pulsed-neutron die-away experiment of light water that was performed at Lawrence Livermore National Laboratory. The experiments were done with cylindrical targets of varying dimensions to modulate the experiment’s sensitivity to thermal scattering and to absorption. We compare the measured integral parameter of the experiment to simulations with MCNP6.2 ® and to past experiments in literature. The integral parameters that were more sensitive to TSLs showed a larger bias. This validation study is known to have errors because the model of the experiment lacks key features about the detectors and neutron generator. These features will be included in the final benchmark evaluation of the experiment which will be submitted to the International Criticality Safety Benchmark Evaluation Project.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Intracellular distribution of TM4SF1 and internalization of TM4SF1-antibody complex in vascular endothelial cells

Transmembrane-4 L-six family member-1 (TM4SF1) is a small plasma membrane-associated glycoprotein that is highly and selectively expressed on the plasma membranes of tumor cells, cultured endothelial cells, and, in vivo, on tumor-associated endothelium. Immunofluorescence microscopy also demonstrated TM4SF1 in cytoplasm and, tentatively, within nuclei. With monoclonal antibody 8G4, and the finer resolution afforded by immuno-nanogold transmission electron microscopy, we now demonstrate TM4SF1 in uncoated cytoplasmic vesicles, nuclear pores and nucleoplasm. Because of its prominent surface location on tumor cells and tumor-associated endothelium, TM4SF1 has potential as a dual therapeutic target using an antibody drug conjugate (ADC) approach. For ADC to be successful, antibodies reacting with cell surface antigens must be internalized for delivery of associated toxins to intracellular targets. We now report that 8G4 is efficiently taken up into cultured endothelial cells by uncoated vesicles in a dynamin-dependent, clathrin-independent manner. It is then transported along microtubules through the cytoplasm and passes through nuclear pores into the nucleus. These findings validate TM4SF1 as an attractive candidate for cancer therapy with antibody-bound toxins that have the capacity to react with either cytoplasmic or nuclear targets in tumor cells or tumor-associated vascular endothelium. - Highlights: • Anti-TM4SF1 antibody 8G4 was efficiently taken up by cultured endothelial cells. • TM4SF1–8G4 internalization is dynamin-dependent but clathrin-independent. • TM4SF1–8G4 complexes internalize along microtubules to reach the perinuclear region. • Internalized TM4SF1–8G4 complexes pass through nuclear pores into the nucleus. • TM4SF1 is an attractive candidate for ADC cancer therapy.

60 APPLIED LIFE SCIENCES↗

Characterizing the seismic response of a molten salt nuclear reactor

Abstract One Generation IV nuclear reactor, which uses a fluoride salt as a coolant, graphite reflector blocks as a moderator, and circulating buoyant TRISO pebbles as fuel is at an advanced stage of development. To characterize the seismic behavior of components of this reactor, validate numerical models for analysis, and develop recommendations for design, a set of earthquake‐simulator experiments on a scaled model of the reactor vessel and its internals was executed on a six‐degree‐of‐freedom earthquake simulator. The model was seismically isolated at its base using two types of spherical sliding bearings. The scaled model involved representations of the prototype reactor vessel, core barrel, reflector blocks, coolant, and spherical fuel pebbles. The material and geometric properties of different test components were selected based on a dynamic similitude scaling analysis and an approximate length scale of 0.4. Four sets of three‐component earthquake motions were used as inputs for testing. Instrumentation on the test specimen recorded the dynamic responses of the outer vessel, core barrel, and reflector‐block assembly, the hydrodynamic responses (sloshing and hydrodynamic pressure) of the liquid coolant, pebble consolidation under earthquake shaking, and the behavior of the isolation systems. This paper describes the design of the experiments and presents key results from the tests. The dynamic responses of the outer vessel, core barrel, and the reflector blocks revealed that the components responded as a unit for the intense shaking used in the experiments. The sloshing response of the fluid in a thin annulus near the perimeter of the vessel was heavily damped. The change in the packing fraction of the pebble bed under repeated, intense 3D earthquake shaking was less than 3%. Seismically isolating the vessel substantially reduced demands on its internal components.

Engineering↗

A constitutive model for glass–ceramic materials

Glass–ceramics have received recent attention for use in glass–ceramic to metal hermetic seals. Due to their heterogeneous microstructure, these materials exhibit a number of advantageous responses over conventional glass based seals. Key amongst them is the possibility of a controllable thermal strain response and apparent coefficient of thermal expansion which may be used to minimize thermally induced residual stresses for aforementioned seals. Furthermore, these behaviors result from an inorganic glass matrix and variety of crystalline ceramic phases including silica polymorph(s) that may undergo reversible solid-to-solid transformations with associated inelastic strain. Correspondingly, these materials exhibit complex thermomechanical responses associated with multiple inelastic mechanisms (viscoelasticity and phase transformation). While modeling these behaviors is essential for developing and analyzing the corresponding applications, no such model exists. Therefore, in this work a three-dimensional continuum constitutive model for glass–ceramic materials combining these various inelastic mechanisms is developed via an internal state variable approach. A corresponding fully implicit three dimensional numerical formulation is also proposed and implemented. The model is used to simulate existing experiments and validate the proposed formalism. As an example, the simple seal problem of a glass–ceramic seal inside a concentric metal shell is explored. Finally, the impact of the cooling rates, viscoelastic shift factors, and inelastic strain on final residual stress state are all investigated and the differing contributions highlighted.

36 MATERIALS SCIENCE↗

Pronghorn

Pronghorn is designed as a multi-dimensional coarse-mesh conjugate heat transfer simulator (tightly coupled fluid and solid phase heat transfer) for nuclear reactor core applications. Pronghorn’s design philosophy of is that: 1. The tool will be agnostic of reactor concept, including VHTRs, SFRs, FHRs, and LWRs. 2. Must be higher fidelity than traditional nuclear systems/safety analysis (0D-1D). 3. Avoid lower-length scale phenomena, such as boundary layer theory, i.e., rely on closure relations. 4. Apply mixture theory (homogenization) wherever possible. 5. Conserve mass and energy (solve all physics on single mesh). 6. Must be easily coupled to both MOOSE-based and external physics applications. 7. Does not require a super computer. Thus, Pronghorn’s algorithmic philosophy is to resolve large scale flow features and model lower-length scale phenomena, such as boundary layers. The coarse mesh approach for lower-length scale modeling is to develop a multi-component multi-phase homogenization of solid and liquid phases into a mixture formulation inside a finite element. For example, a pebble bed core is represented as a two-phase mixture of coolant and fuel pebbles, where the fuel phase is stationary. Thus, the solid phase exerts a drag force on the fluid phase, composed of form and viscous drag, and both phases exchange internal energy through conduction and convective heat transfer. For Pronghorn, the volume fraction of fluid can vary in space, but not in time. Pronghorn has been validated against the VHTR PBMR400 benchmark problems, used for rod ejection simulations have been conducted for thermal-fluids/neutronics for both pebble-bed and prismatic gas-cooled reactors and simple thermal-neutronics coupled LWR benchmark problems. Pronghorn flow models cover a wide range of transient and steady flow conditions, including, porous fluid flow, compressible flow, and nearly incompressible, thermally expansive flow. The physics can be solved in three-dimensional Cartesian coordinates and two-dimensional cylindrical (r-z) coordinates.

Martineau, RichardC.↗

Computationally efficient evaluation of optimum homogeneous charge compression ignition operating range with accelerated multizone engine cycle simulation

The very intensive calculations necessary to define a performance map requiring evaluation of over a hundred individual operating points can be efficiently conducted with accelerated multizone for engine cycle simulation, leading to a definition of regions of acceptable and optimum homogeneous charge compression ignition operation. Accelerated multizone for engine cycle simulation has the virtue of enabling accurate evaluation of many operating conditions based on thermal stratification data from a single fluid mechanics run at motored conditions. This is possible because thermal stratification is more sensitive to engine geometry than to operating conditions. In this article, accuracy of accelerated multizone for engine cycle simulation is demonstrated by comparison with experimental data for iso-octane homogeneous charge compression ignition operation over a broad range of lean equivalence ratios (0.14–0.28). The validated accelerated multizone for engine cycle simulation model is then applied to generating a performance map for an engine controlled by appropriately adjusting equivalence ratio and internal exhaust gas recirculation. Regions of acceptable and optimum combustion are identified. It is finally demonstrated that while indicated mean effective pressure remains low for optimum homogeneous charge compression ignition operation (1–4 bar), this is sufficient for a large fraction of typical driving in light-duty vehicles. Much driving including idle can therefore be done in homogeneous charge compression ignition mode at high efficiency and low (essentially zero) NOx and particulate matter emissions.

30 DIRECT ENERGY CONVERSION↗

Transverse beam dynamics in non-linear Fixed Field Alternating Gradient accelerators

In this paper, we present some aspects of the transverse beam dynamics in Fixed Field Ring Accelerators (FFRA): we start from the basic principles in order to derive the linearized transverse particle equations of motion for FFRA, essentially FFAGs and cyclotrons are considered here. This is a simple extension of a previous work valid for linear lattices that we generalized by including the bending terms to ensure its correctness for FFAG lattice. The space charge term (contribution of the internal coulombian forces of the beam) is contained as well, although it is not discussed here. The emphasis is on the scaling FFAG type: a collaboration work is undertaken in view of better understanding the properties of the 150 MeV scaling FFAG at KURRI in Japan, and progress towards high intensity operation. Some results of the benchmarking work between different codes are presented. Analysis of certain type of field imperfections revealed some interesting features about this machine that explain some of the experimental results and generalize the concept of a scaling FFAG to a non-scaling one for which the tune variations obey a well-defined law.

43 PARTICLE ACCELERATORS↗

Robust Explanations using Diverse Adversarially Trained Ensembles, Multi-Modal Contrastive Learning, and Attribution-based Confidence Metrics

The primary objective of this project is to strengthen the trustworthiness of AI systems by designing algorithms that make their internal decision-making processes more understandable to human users. This involves creating clear, interpretable explanations for AI decisions and developing metrics to assess these explanations' validity and reliability. Significant progress has been achieved through (i) developing symbolic explanations, (ii) generating meaningful interpretive insights, (iii) establishing accuracy and confidence metrics, and (iv) devising methods to evaluate the knowledge boundaries of AI models. To date, the research findings have been shared in peer-reviewed publications, with accompanying scientific and technical information (STI) detailed below.

97 MATHEMATICS AND COMPUTING↗

Solar Radiation Research Laboratory (SRRL) Core Project Final Report: Fiscal Years 2022-2024

The Solar Radiation Research Laboratory (SRRL) at the National Laboratory of the Rockies (NLR) is a world-leading solar calibration and measurement facility and maintains and disseminates the World Radiation Reference (essentially the W/m2) for the United States that is essential for traceable and accurate measurements of solar radiation at all solar generation facilities. SRRL operates two calibration facilities that meet International Standards Organization-17025 (ISO-17025) standards and provide unique high-quality calibrations to NREL and other U.S. Department of Energy laboratories. The Baseline Measurement System (BMS) at SRRL provides a high-quality record of solar irradiance and surface meteorological conditions. SRRL capabilities are used to develop (1) improved methods for the calibration of solar radiometers; (2) new standards through the ISO, the International Electrotechnical Commission (IEC), and the American Standards for Testing of Materials (ASTM) International; (c) solar radiation and meteorological models; and (d) advanced instrumentation and methods for operating solar measurement stations. The SRRL datasets are also critical for the validation of new models and datasets, such as the National Solar Radiation Database (NSRDB). The research and development of solar radiation measurement systems and resource modeling techniques are essential for advancing the scientific basis for producing reliable resource data. Specifically, the spatial, temporal, and spectral (wavelength dependency) characteristics of the solar resource are required in several different time frames for various project phases.

14 SOLAR ENERGY↗

Origin of low-frequency (intraseasonal) oscillations in the tropical atmosphere. I - Basic theory

A theory for the origin of intraseasonal oscillations of the tropical atmosphere is presented. The theoretical background for and main features of the intraseasonal variability of the tropical atmosphere are discussed. The theory is validated for the 40-50 day oscillation using a simple model. The transient response of the tropical atmosphere to a local oscillating heat source and an internally forced heat source is studied. The structure and mechanism of the eastward propagation are examined. It is noted that the eastward propagation of low-frequency oscillation is the result of the interaction between convection and dynamics via the mobile wave-CISK mechanism. It is suggested that the low-frequency oscillations are an intrinisic atmospheric phenomena that exist without a dynamically interactive ocean.

Lau, K.-M.↗

Knowledge-based system verification and validation

The objective of this task is to develop and evaluate a methodology for verification and validation (V&V) of knowledge-based systems (KBS) for space station applications with high reliability requirements. The approach consists of three interrelated tasks. The first task is to evaluate the effectiveness of various validation methods for space station applications. The second task is to recommend requirements for KBS V&V for Space Station Freedom (SSF). The third task is to recommend modifications to the SSF to support the development of KBS using effectiveness software engineering and validation techniques. To accomplish the first task, three complementary techniques will be evaluated: (1) Sensitivity Analysis (Worchester Polytechnic Institute); (2) Formal Verification of Safety Properties (SRI International); and (3) Consistency and Completeness Checking (Lockheed AI Center). During FY89 and FY90, each contractor will independently demonstrate the user of his technique on the fault detection, isolation, and reconfiguration (FDIR) KBS or the manned maneuvering unit (MMU), a rule-based system implemented in LISP. During FY91, the application of each of the techniques to other knowledge representations and KBS architectures will be addressed. After evaluation of the results of the first task and examination of Space Station Freedom V&V requirements for conventional software, a comprehensive KBS V&V methodology will be developed and documented. Development of highly reliable KBS's cannot be accomplished without effective software engineering methods. Using the results of current in-house research to develop and assess software engineering methods for KBS's as well as assessment of techniques being developed elsewhere, an effective software engineering methodology for space station KBS's will be developed, and modification of the SSF to support these tools and methods will be addressed.

Johnson, Sally C.↗

Vertical Profiles of Latent Heating in TRMM: Validation and Assimilation in the GEOS Data Assimilation System

I have derived the vertical profiles of apparent heating Q and Q2 by using 3-hourly balloon sounding data from the ARM SGP sounding array for three IOPs in 2000. These IOPs cover the periods from 3/1 to 3/22, from 9/25 to 10/8, and from 11/27 to 12/22. These heating profiles will be collocated with the TRMM heating profiles for validation studies once the TRMM profiles become available to the investigators. I have also produced the objective analyses of Q1, Q2 and forcing fields for the international GCSS Case 3 Intercomparison project. The GSFC CRM participated in study, based on which TRMM heating profiles are derived. I have also studied to assimilate the vertical heating profile by constraining the cloud-base mass flux in the cumulus convection scheme using the CCM3. I first derive the vertical heating profile for each convective plume of unit cloud-base mass flux. The observed heating profile form ARM is then de-convoluted to derive the cloud base mass fluxes of all individual plumes. These fluxes are compared with those derived from the quasi-equilibrium hypothesis. They are shown to improve many other aspects of the model behavior.

Zhang, Ming-Hua↗