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DOE OSTI2022

Comparing the shock sensitivity of insensitive energetic materials

We present a tabletop method to study the shock sensitivity of plastic-bonded explosives that are considered shock insensitive using high dynamic range optical emission spectroscopy with laser-launched km/s flyer plate impacts (2, 3, and 4 km/s), which measures the spectral radiance (the emission spectrum vs a calibrated intensity standard) every 0.8 ns in the nanosecond and microsecond regimes. The explosives were TATB (1,3,5 trinitro, 2,4,6 triamino benzene), FOX-7 (1,1-diamino-2,2-dinitroethylene), LLM-105 (2,6-diamino-3,5-dinitropyrazine-1-oxide), and NTO (nitrotriazolone), all with 20% Sylgard 182 binder. Time resolving emission from shocked explosives produces a unique fingerprint at each shock pressure, and the emission temporal profile can be used to understand each material's shock response and the underlying mechanisms within the framework of the well-known shock ignition and growth models. Ignition was characterized by the emission intensity during nanosecond hot spot ignition. The growth process, which occurs after the shock has unloaded, was characterized by the time derivative of microsecond emission intensity. Singular-value decomposition was used to determine a characteristic spectral radiance over the entire time range, and this radiance was fit to a graybody model to determine a characteristic temperature Tc. Even though these insensitive explosives have similar shock sensitivities, our method can clearly distinguish their shock response. FOX-7 and NTO were the most sensitive, with FOX-7 having the greatest shock ignition sensitivity, growth rate, and Tc. LLM-105 was much less sensitive than FOX-7 and NTO, and TATB consistently showed the lowest sensitivity by any measure.

Akhtar, Meysam (ORCID:0000000243897837)↗

DOE OSTI2025

Heterogeneous energetic material damage simulator (HEDS): A deep learning approach to simulate damage–sensitivity linkages

Damage in the microstructures of energetic materials (EMs), such as propellants and plastic bonded explosives (PBXs), can significantly alter their response to external loads. Both sensitization and desensitization can occur, causing concerns with safety and performance in the field; predictive models that connect damage and the sensitivity of EMs can enable design and provide confidence in their robustness and reliability. However, modeling of damage evolution is challenging for real microstructures of EMs; samples of damaged EMs are difficult to obtain, thereby hindering experiments and direct numerical simulations to determine the sensitivity of EMs at various stages of damage. Here, we develop an approach to generate synthetic, i.e., in silico produced, damaged microstructures for use in simulations to connect damage levels to sensitivity. The development of the present workflow to generate and impose varying levels of damage in microstructures, known as HEDS (Heterogeneous Energetic Material Damage Simulator), begins with a small set of images of damaged PBXs and combines a collection of deep neural network techniques to generate microstructures with varying levels of damage. By making the synthetic microstructures conform closely to those observed in available real, imaged microstructures, we develop an ensemble of damaged microstructures that can be used for in silico shock experiments. HEDS develops these microstructure ensembles as level set fields, which are directly employed in a sharp interface Eulerian hydrocode where shock simulations are performed to quantify the energy release rate from hotspot fields generated in the microstructure. These capabilities can be useful for the analysis and assessment of changes in the sensitivity of EMs and to design formulations that are less susceptible to damage-induced changes in sensitivity and performance.

Fang, Irene (ORCID:0009000844557122)↗

DOE OSTI2014

Un-collimated single-photon imaging system for high-sensitivity small animal and plant imaging

In preclinical single-photon emission computed tomography (SPECT) system development the primary objective has been to improve spatial resolution by using novel parallel-hole or multi-pinhole collimator geometries. Furthermore, such high-resolution systems have relatively poor sensitivity (typically 0.01% to 0.1%). In contrast, a system that does not use collimators can achieve very high-sensitivity. Here we present a high-sensitivity un-collimated detector single-photon imaging (UCD-SPI) system for the imaging of both small animals and plants. This scanner consists of two thin, closely spaced, pixelated scintillator detectors that use NaI(Tl), CsI(Na), or BGO. The performance of the system has been characterized by measuring sensitivity, spatial resolution, linearity, detection limits, and uniformity. With 99m Tc (140 keV) at the center of the field of view (20 mm scintillator separation), the sensitivity was measured to be 31.8% using the NaI(Tl) detectors and 40.2% with CsI(Na). The best spatial resolution (FWHM when the image formed as the geometric mean of the two detector heads, 20 mm scintillator separation) was 19.0 mm for NaI(Tl) and 11.9 mm for CsI(Na) at 140 keV, and 19.5 mm for BGO at 1116 keV, which is somewhat degraded compared to the cm-scale resolution obtained with only one detector head and a close source. The quantitative accuracy of the system’s linearity is better than 2% with detection down to activity levels of 100 nCi. Two in vivo animal studies (a renal scan using 99m Tc MAG-3 and a thyroid scan with 123 I) and one plant study (a 99m TcO 4 - xylem transport study) highlight the unique capabilities of this UCD-SPI system. From the renal scan, we observe approximately a one thousand-fold increase in sensitivity compared to the Siemens Inveon SPECT/CT scanner. In conclusion, UCD-SPI is useful for many imaging tasks that do not require excellent spatial resolution, such as high-throughput screening applications, simple radiotracer uptake studies in tumor xenografts, dynamic studies where very good temporal resolution is critical, or in planta imaging of radioisotopes at low concentrations.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2015

Low Insertion Loss and Highly Sensitive SH-SAW Sensors Based on 36° YX LiTaO 3 Through the Incorporation of Filled Microcavities

Reduction in power consumption and improvement in mass sensitivity are important considerations for surface acoustic wave (SAW) devices used in various sensing applications. Detection of minute quantities of a particular species (clinical sensing) and power requirements (wireless sensing) are two key metrics that must be optimized. In this paper, a 3-D finite element model (FEM) was employed to compare insertion loss (IL) and mass sensitivity of SAW sensors having microcavities filled with ZnO and nanocrystalline diamond to a standard two-port SAW design. Initial simulation results show that ZnO filled cavities (depth = 5 mu m) were most effective at reducing power loss Delta IL = (6.03 dB) by increasing particle displacement (acousto-electric to mechanical transduction) at the output transducer. A 100-pg/cm(2) load was applied to the sensing area of each device to evaluate mass sensitivity. Our simulations suggest that ZnO filled cavities with shallow depth (2.5 mu m) have the greatest sensitivity. The FEM simulations are used to understand the acoustic wave propagation in microcavity-based SAW sensors. The observed enhancement in mass sensitivity and power transfer is attributed to waveguiding effects and constructive interference of the scattered acoustic waves from the microcavities. Devices fabricated with microcavities similar to 1 mu m deep decreased IL by 3.306 dB compared with a standard SAW device. Additional simulations were conducted for each device configuration using the same depth in order to make a direct comparison between measured and simulated results. Our findings offer encouraging prospects for designing low IL highly sensitive microcavity-based SAW biosensors.

36 MATERIALS SCIENCE↗

DOE OSTI2015

SENSITIVITY EVALUATION OF THE DAILY THERMAL PREDICTIONS OF THE AGR-2 EXPERIMENT IN THE ADVANCED TEST REACTOR

A temperature sensitivity evaluation has been performed for the AGR-2 fuel experiment on an individual capsule. A series of cases were compared to a base case by varying different input parameters into the ABAQUS finite element thermal model. These input parameters were varied by ±10% to show the temperature sensitivity to each parameter. The most sensitive parameters are the outer control gap distance, heat rate in the fuel compacts, and neon gas fraction. Thermal conductivity of the fuel compacts and thermal conductivity of the graphite holder were in the middle of the list for sensitivity. The smallest effects were for the emissivities of the stainless steel and graphite, along with gamma heat rate in the non-fueled components. Sensitivity calculations were also performed varying with fast neutron fluence, showing a general temperature rise with an increase in fast neutron fluence. This is a result of the control gas gap becoming larger due to the graphite holder shrinkage with neutron damage. A smaller sensitivity is due to the thermal conductivity of the fuel compacts and graphite holder decreasing with fast neutron fluence.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2018

A Functional Response Metric for the Temperature Sensitivity of Tropical Ecosystems

Abstract Earth system models (ESMs) simulate a large spread in carbon cycle feedbacks to climate change, particularly in their prediction of cumulative changes in terrestrial carbon storage. Evaluating the performance of ESMs against observations and assessing the likelihood of long-term climate predictions are crucial for model development. Here, we assessed the use of atmospheric growth rate variations to evaluate the sensitivity of tropical ecosystem carbon fluxes to interannual temperature variations. We found that the temperature sensitivity of the observed growth rate depended on the time scales over which atmospheric observations were averaged. The temperature sensitivity of the growth rate during Northern Hemisphere winter is most directly related to the tropical carbon flux sensitivity since winter variations in Northern Hemisphere carbon fluxes are relatively small. This metric can be used to test the fidelity of interactions between the physical climate system and terrestrial ecosystems within ESMs, which is especially important since the short-term relationship between ecosystem fluxes and temperature stress may be related to the long-term feedbacks between ecosystems and climate. If the interannual temperature sensitivity is used to constrain long-term temperature responses, the inferred sensitivity may be biased by 20%, unless the seasonality of the relationship between the observed growth rate and tropical fluxes is taken into account. These results suggest that atmospheric data can be used directly to evaluate regional land fluxes from ESMs, but underscore that the interaction between the time scales for land surface processes and those for atmospheric processes must be considered.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Sensitivity-based Similarity Metrics for New Experiment Design Optimization

The nuclear data used in advanced reactor simulations requires validation. Data from nuclear criticality experiments can provide this validation. New nuclear criticality experiment design requires extensive knowledge and expert judgement such that the experimental design parameters are selected in such a way to keep the experiment subcritical. To aide in this experimental design process, professionals can utilize sensitivity and uncertainty analysis. Sensitivity and uncertainty analysis relies on matching new application experiments with currently existing benchmark experiments. Currently, there is functionality in the Whisper 1.1 software package to calculate a similarity metric based on neutron multiplication factor sensitivity coefficients between a new application designed by the user and existing International Criticality Safety Benchmark Experiment Project (ICSBEP) benchmarks. The Whisper 1.1 software package is included in Monte Carlo N-Particle ® Code Version 6.21 (MCNP ® 6.2). This work is geared toward expanding this capability to new similarity metrics based on beta-effective sensitivity coefficients and reactivity coefficient sensitivity coefficients. While the investigation of these sensitivity coefficients is presented in detail in separate works at this same conference, this work will be primarily focused on studying the similarity metrics in more detail. These similarity metrics will then be incorporated into the optimization algorithms used for experiment design in EUCLID (Experiments Underpinned by Computational Learning for Improvements in nuclear Data), which is a Los Alamos National Laboratory (LANL) project designed to constrain nuclear data of interest, such that adjustments can be made to possible inaccuracies. A more detailed optimization can be subsequently performed by breaking down these similarity metrics by isotope, reaction, and energy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Hyper-Differential Sensitivity Analysis of Uncertain Parameters in PDE-Constrained Optimization

Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional complexity, namely, uncertain parameters in the PDEs. Uncertainty quantification (UQ) is necessary to characterize, prioritize, and study the influence of these uncertain parameters. Sensitivity analysis, a classical tool in UQ, is frequently used to study the sensitivity of a model to uncertain parameters. In this article, we introduce "hyper-differential sensitivity analysis" which considers the sensitivity of the solution of a PDE-constrained optimization problem to uncertain parameters. Our approach is a goal-oriented analysis which may be viewed as a tool to complement other UQ methods in the service of decision making and robust design. We formally define hyper-differential sensitivity indices and highlight their relationship to the existing optimization and sensitivity analysis literatures. Assuming the presence of low rank structure in the parameter space, computational efficiency is achieved by leveraging a generalized singular value decomposition in conjunction with a randomized solver which converts the computational bottleneck of the algorithm into an embarrassingly parallel loop. Two multi-physics examples, consisting of nonlinear steady state control and transient linear inversion, demonstrate efficient identification of the uncertain parameters which have the greatest influence on the optimal solution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Sensitivity Analysis of Salt Storage Cavern Mechanical Integrity Test Parameters

This report examines the sensitivity of salt cavern Mechanical Integrity Tests (MIT) to uncertainties in key test parameters. MIT's are used by cavern operators to detect and quantify leak rates in access wells in underground salt storage caverns and involve a suite of measured and assumed parameters that have a direct impact on the sensitivity of the testing to detect actual leaks from the cavern storage system. Determining the sensitivity of the testing to these different parameters provides a basis for understanding the results from, and informing the design criteria for, this type of testing. Without fully understanding the sensitivity of the test to the testing parameters, it is possible that the test results may not accurately reflect the integrity of the cavern system; an actual leak may be missed, or an intact system may be interpreted as leaking. This report reviews the main parameters included in MITs and examines how selected changes in their values can impact test results. The deviations used in the sensitivity analyses were designed to be within the ranges believed to be similar to those which may be encountered during testing. The results show that small, plausible fluctuations in some of the parameters measured values can have a significant impact on the testing results. Of the parameters studied here, the sensitivity analyses showed the order of importance to be (from highest to lowest): nitrogen-oil interface depth measurement, well bore temperature, well head pressure, and finally the internal geometry of the testing interval.

42 ENGINEERING↗

DOE OSTI2020

An updated estimate of the Mu2e experiment sensitivity

The Mu2e experiment at Fermilab will search for the conversion of a negative muon into an electron inside the field of a nucleus. This process does not conserve charged-lepton flavour and is heavily suppressed in the Standard Model (SM), with a branching ratio < 10-50. Any evidence of it would be an undeniable evidence of new physics beyond the SM. The project sets out to achieve a single event sensitivity of $\sim 3 × 10^{-17}$ on the ratio between the probability for a conversion of a negative muon into an electron and the one for a muon capture by the nucleus. Such a sensitivity would represent a 4 orders of magnitude improvement on the previous upper limit for the process, making possible to test predictions of different extensions of the SM. Mu2e uses three superconducting solenoids to produce and measure the muon conversions. In the first solenoid, the Production Solenoid, pions and kaons are produced, together with other secondary products, by 8 GeV kinetic energy proton interactions in a tungsten target. A gradient magnetic field is specifically designed to direct low momentum particles into the Transport Solenoid, an S-shaped magnet that filters out particles with unwanted charge and momentum. Muons, produced by pion and kaon decays, finally reach the aluminum Stopping Target in the Detector Solenoid, where they eventually stop and convert. The result of the conversion process is a monochromatic electron of ~105 MeV/c momentum. The Detector Solenoid also hosts the two main detectors: a straw tube tracker and two CsI calorimeter disks, both providing measurement of event kinematics. A germanium detector and a LaBr crystal are located downstream of the Detector Solenoid to measure the X and gamma rays produced by the muon captures in the Stopping Target. A veto system of scintillators covering the Detector Solenoid and half of the Transport Solenoid is used to identify and reject cosmic rays interactions. With respect to the initial project, the Mu2e running plan has evolved to a staged configuration with 2 years at reduced intensity before the 2025 accelerator shutdown for the neutrino beam upgrade and 2 or 3 years at full intensity after that. This, together with geometry changes and a better knowledge of detector performances obtained by the first slice tests, has required a full revision of the signal over background selection that is the subject of this thesis. In order to achieve a new estimate of Mu2e sensitivity, the simulation of the data corresponding to the first 2 years of data acquisition has been performed. This includes both conversion electrons (CE) and the main sources of background: cosmics, decay-in orbits (DIO), radiative pion captures (RPC) and antiprotons. The characteristics of the signal and of the main backgrounds have been studied to define the best selection variables for CE. A special effort has been devoted to the evaluation of the antiproton background. The lack of experimental data for antiproton production cross section makes the systematic uncertainty on this background significant. A new parameterization of the cross section has been developed to fit the existing data and to provide a more reliable estimate of the systematic uncertainty by comparing the results of the old and the new model. A special effort has been devoted to the optimization of the antiprotons Monte Carlo generator. This study has also revealed that the dominant component within this background is represented by antiprotons produced in the opposite direction with respect to the Transport Solenoid entrance and then redirected to it by back-scattering processes in the Production Target. This ultimately highlights the sensitivity of the background estimate to the G4 handling of antiproton interactions in the 1 to 3 GeV/c momentum range. Finally, the final experimental sensitivity has been studied. The momentum and time selection have been optimized to obtain the 5-sigma discovery reach or, in case of no signal, the upper limit on conversion probability. The results confirm that, in the firs t two years of data taking, Mu2e will be able to improve the current experimental sensitivity for muon-to-electron conversion in an atomic field by more than 3 order of magnitudes.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

A Spatially Explicit Individual-Based Modeling Approach to Evaluate the Cumulative Effects of Wind Energy Development on the Greater Sage-Grouse: Sensitivity Analysis and Validation of Key Parameters

To address the need for an approach to evaluate cumulative ecological impacts of wind energy development, particularly those on critical wildlife habitats and species, the authors developed a proof-of-concept, landscape-based, spatially explicit individual-based modeling (IBM) framework for populations of the greater sage-grouse (Centrocercus urophasianus) in Albany County, Wyoming, based on published and other available information on the life history of the species. This sage-grouse IBM estimates the spatial and temporal movements of sage-grouse based on modeled effects of habitat characteristics and developments on sage-grouse condition, survivorship, and reproduction. After completing the initial version of the model, we conducted a series of sensitivity analyses of key model parameters and validation of lek occurrences and spatial distributions to better understand performance of the model relative to observed values of important life history characteristics. The parameter sensitivity analysis was conducted as a series of one-factor-at-a-time tests in which the values of selected parameters were individually varied to evaluate the corresponding effects on model output. We examined the model’s response to changes in parameter values to gain insight into the overall robustness of the model, identify key driver parameters, and initiate qualitative validation. Five functions selected for sensitivity analyses were (1) the rate of change in body condition in relationship to habitat suitability index (HSI) of occupied habitat (condition change rate), (2) the effect of competition between individuals with overlapping home ranges expressed as a percentage reduction in HSI (competition factor), (3) value of condition at which survivorship probability is equal to zero (zero survivorship condition), (4) the relationship between female body condition and clutch size, and (5) the relationship between female body condition and nest success. We varied the parameter values to be tested for the sensitivity analysis around the original value used in the model (i.e., tested values were higher and lower than the model’s original value) to examine the effect of this variation on the predicted output of the model. Model outputs evaluated in the sensitivity analysis included (1) predicted age-class distribution (as measured by the percentage of immature individuals within the population); (2) predicted sex ratio; (3) predicted age-sex class distribution (percent of population in each of six age-sex classes, i.e., male and female juveniles, yearlings, and adults); (4) lifespan; (5) population size; and (6) spatial distribution. Of the five parameters analyzed, condition change rate, survivorship, clutch size, and nest success did not substantially affect any of the evaluated model outputs. For the predicted age-class distribution, the percentage of immature individuals predicted by the model for these four parameters ranged from 61.9% to 65.0%, which was reasonable with respect to the reference values of 51.4 to 57.8% in published studies. The ratio of females to males ranged from 1.09 to 1.14, which was comparable to the reference values of 1.2 to 3.0 presented in an existing study. The predicted mean lifespan ranged from 1.62 to 1.74 years, which appears to be reasonable with respect to the reference values of 0.9 to 1.1 years for sharp-tail grouse and greater prairie chickens presented by published studies. The predicted population size ranged from 1,877 to 3,140. This prediction would be reasonable with respect to our estimate of 5,000 yearlings and adults, which was based on the USFWS estimate for the state of Wyoming scaled to the number of leks in the county. The predicted spatial distribution was not substantially affected by the parameter values examined. In our sensitivity analyses, the only tested parameter that had a noticeable effect on model output was competition factor. Over the range of values tested for this parameter, predicted population size exhibited the largest range (from 1,833 to 4,737) of all parameters tested. As the competition factor increased, the predicted population size decreased. This reflects the effect competition had on the number of individuals that could co occur in high-quality habitat patches. Despite this apparently significant effect, the range of values appears to be reasonable with respect to our estimate of 5,000 yearlings and adults, which was based on the USFWS estimate for the state of Wyoming scaled to the number of leks in the county.

17 WIND ENERGY↗

DOE OSTI2022

Impact of Increased Latent Generations on Sensitivity Calculations with SCALE [Slides]

Depending on the system, energy, and/or nuclide, altering the number of latent generations can significantly impact generated sensitivity coefficients. In general, as the number of latent generations increases, the accuracy of the generated sensitivity value compared with the DP value increases and there is a significant increase in the uncertainty with generated sensitivity values. IFP generated sensitivities appear to be more stable than those with CLUTCH. Complex systems, even with IFP and increased latent generations can still produce poor results (i.e., MPC- 32). This reiterates the importance of performing DPs to confirm sensitivities. IFP-Shift and CLUTCH can take advantage of parallel computing abilities. Work continues in this area as additional parameters and calculational methods are examined to provide analysts insights to successfully generating sensitivity coefficients for confirmatory analyses and validation efforts.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Development of Decay Heat Sensitivity Analysis Capability in SCALE/ORIGEN

In this work, a decay heat sensitivity analysis capability was developed and implemented in the ORIGEN code of the SCALE nuclear modeling and simulation suite. This capability introduces improved numerical integration schemes, which overcome the challenges associated with accurately modeling the behavior of adjoint nuclide amounts during coarse time steps for both nuclide amount and decay heat sensitivity calculations. This capability significantly improves the accuracy of calculations without compromising computational efficiency compared to the existing method. Extensive verification was conducted for various benchmark problems, including a 238 Pu decay and an irradiation problem involving 135 Xe, evaluated with both coarse and fine time grids. The results show excellent agreement with reference direct perturbation solutions, reaffirming the computational accuracy of the newly proposed numerical integration methods. Furthermore, sensitivity analyses were performed for fission product inventories ( 147 Sm, 150 Sm, 155 Gd) in pressurized water reactor UO 2 and MOX fuel assemblies. These analyses demonstrated that the ORIGEN sensitivity analysis capability can capture detailed sensitivity coefficients and underlying physics in real applications. Additionally, a decay heat sensitivity analysis for high-assay low-enriched uranium fuel, including various initial 235 U enrichment and burnup points, highlights the extended capabilities of SCALE/ORIGEN in comprehensively assessing the factors influencing total decay heat. These advancements in ORIGEN offer valuable insights for reactor analysis, fuel design, and safety assessments, especially in the context of advanced nuclear fuel development and design changes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Sensitivity Studies of Premixed Flame Response to Transverse, High Frequency Disturbances

This study analyzes the response of premixed flames to high frequency transverse acoustic disturbances. A significant body of experiment, modeling and simulation efforts has been performed to understand the response of the spatially integrated heat release of premixed flames to low-frequency disturbances. These studies quantified this sensitivity through the Flame Transfer Function (FTF), as the global heat release is the key quantity influencing thermoacoustic stability for acoustically compact flames. Recent efforts have expanded these models to consider high-frequency acoustic disturbances, and the sensitivity of premixed flames through the Rayleigh integral (RI). The full Rayleigh Integral, as opposed to simply the spatially integrated heat release, must be considered in these cases where the flame is not acoustically compact. Prior modeling studies considered several effects - stability of axisymmetric flames centered in a cylindrical combustion chamber and the effect of flame offset from the combustor axis and the effect of mean flame asymmetries in the flame centered in the combustor. These studies showed that the flame's stability was sensitive to all these parameters, as well as to the transverse mode in question. In this paper, we quantify these different parametric sensitivities of premixed flame stability in the presence of high-frequency transverse acoustic modes - specifically sensitivity to flame length and nozzle location within the acoustic mode shape for 2 different transverse modes. The sensitivity of the RI to these control parameters provides an improved understanding of which flame parameters are critical to improve the overall thermoacoustic stability of the system.

Acharya, Vishal S.↗

DOE OSTI2020

Environmental sensitivities of shallow-cumulus dilution – Part 1: Selected thermodynamic conditions

Cumulus entrainment, and its consequent dilution of buoyant cloud cores, strongly regulates the life cycle of shallow cumuli yet remains poorly understood. Herein, new insights into this problem are obtained through large-eddy simulations that systematically investigate the sensitivity of shallow-cumulus dilution to cloud-layer relative humidity (RH), cloud- and subcloud-layer depths, and continentality (i.e., the land–ocean contrast). The simulated cloud-core dilution is found to be strongly sensitive to continentality, with fractional dilution rates twice as large over the ocean as over land. Using a similarity theory based on the turbulent-kinetic-energy (TKE) budget, the reduced cloud-core dilution over land is attributed to larger cloud-base mass flux (mb), driven by stronger surface heating and subcloud turbulence. As mb increases, the fractional dilution rate must decrease to maintain energetic equilibrium. A positive sensitivity is also found to cloud-layer RH, with the core dilution increasing by 25 %–50 % for a 10 % enhancement in RH. This sensitivity is interpreted using the buoyancy-sorting hypothesis, in that mixtures of cloud and environmental air are more likely to become negatively buoyant and detrain (rather than diluting the cloud core) in drier cloud layers. By contrast, the sensitivities of (marine) shallow-cumulus dilution to cloud- and subcloud-layer depths are weak, with a 3 % decrease for a doubling for the former and a 4 % reduction in dilution for a 50 % deeper subcloud layer. These surprisingly weak sensitivities are readily explained by offsetting effects in the TKE similarity theory. Altogether, these experimental findings provide useful, though still incomplete, guidance for flow-dependent shallow-cumulus entrainment formulations in large-scale models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1981

Sensitivity of optimum solutions to problem parameters

In an aircraft configuration optimization, the information of interest is the sensitivity of optimal block fuel consumption and wing aspect ratio and area, to variations of required range and payload. The objectives of this study are: (1) to show how the equations capable of yielding the sensitivity derivatives (the sensitivity equations) can be obtained for a constrained optimum regardless of the type of optimization algorithm that was used to arrive at the optimum point, (2) to review the solvability of the sensitivity equations and (3) to report on applications on structural optimization. Numerical examples, which demonstrate the sensitivity analysis, include a tubular column and a three-bar truss for which closed form solutions are obtained, a ten-bar truss that requires the use of a finite element analysis, and a thin-walled beam characterized by strongly nonlinear constraints for local buckling. It is concluded that a practically significant extrapolation accuracy may be obtained for a reasonably broad range of parameter changes; and that accuracy does not depend strongly on the degree of convergence of the optimum solution from which the sensitivity derivatives are obtained.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1982

Climate studies with a multi-layer energy balance model. I - Model description and sensitivity to the solar constant. II - The role of feedback mechanisms in the CO2 problem

A nine-layer zonally averaged, steady-state model, based upon thermal energy balance, is developed for use in climate sensitivity studies and includes an accurate treatment of radiative transfer, parameterized meridional and vertical energy transport, and thermodynamic interaction between the surface and the atmosphere. A high degree of nonlinearity is exhibited by the model in a study of sensitivity to changes in the solar constant. The change in the hemispheric mean surface temperature is +3.1 C in response to a 2% increase in the solar constant and -4.3 C in response to a 2% decrease in the solar constant. The sensitivity varies with latitude, and the response of atmospheric temperature varies with height. In addition, the model is used to study the sensitivity of climate to a doubling of the atmospheric CO2 content. It is found that the tropospheric temperature lapse rate decreases at low latitudes but increases at high latitudes in response to a doubled CO2 content. Averaged over the Northern Hemisphere, the change is +2.3 C in the surface temperature and +0.47 C in the earth's brightness temperature. The effects of some feedback mechanisms on the climate sensitivity to a doubled CO2 content show that the sensitivity of surface temperature approximately doubles at all latitudes due to the change in water vapor content.

Peng, L.↗

NASA NTRS1987

Investigation, development and application of optimal output feedback theory. Vol. 4: Measures of eigenvalue/eigenvector sensitivity to system parameters and unmodeled dynamics

Some measures of eigenvalue and eigenvector sensitivity applicable to both continuous and discrete linear systems are developed and investigated. An infinite series representation is developed for the eigenvalues and eigenvectors of a system. The coefficients of the series are coupled, but can be obtained recursively using a nonlinear coupled vector difference equation. A new sensitivity measure is developed by considering the effects of unmodeled dynamics. It is shown that the sensitivity is high when any unmodeled eigenvalue is near a modeled eigenvalue. Using a simple example where the sensor dynamics have been neglected, it is shown that high feedback gains produce high eigenvalue/eigenvector sensitivity. The smallest singular value of the return difference is shown not to reflect eigenvalue sensitivity since it increases with the feedback gains. Using an upper bound obtained from the infinite series, a procedure to evaluate whether the sensitivity to parameter variations is within given acceptable bounds is developed and demonstrated by an example.

Halyo, Nesim↗