We present the development of the adjoint of a physically based cirrus formation parameterization that computes the sensitivity of formed crystal number concentration to numerous model variables (e.g., updraft velocity, soluble aerosol geometric mean diameter and number concentration, insoluble aerosol geometric mean diameter and number concentration, and ice deposition coefficient). The adjoint is demonstrated in the CESM Community Atmosphere Model Version 5.1, where sensitivity information is computed and used to quantify which variables are most responsible for modeled variability in formed crystal number concentration. The sensitivity of formed crystal number concentration to updraft velocity is positive and largest over the tropics where regions of deep convection are collocated with large sulfate number concentrations. Sensitivity to sulfate number concentration is largest over the tropics where updraft cooling is sufficient and sulfate number concentration is low, pointing to a sulfate limited regime. Outside of the tropics, crystal production is dominated by heterogeneous freezing; unexpectedly, sensitivities to insoluble aerosol number concentration for accumulation and coarse mode dust, black carbon, and organic carbon are negative in sign here. This is a result of infrequent, anomalously high updraft velocity events causing shifts in the dominant modes of freezing which act to bias sensitivity information when annually averaged. Updraft velocity is responsible for ~95% of the variability in formed crystal number concentration in the high latitudes of the Northern Hemisphere. In the tropics, sulfate number concentration controls variability in formed crystal number concentration since crystal production here is sulfate limited. Insoluble aerosol species play a secondary role in influencing the variability of crystal concentrations; coarse mode dust is the largest contributor to crystal number variability at nearly 60%, although the spatial extent of this influence is small and concentrated over highly localized dust events. When globally averaged, nearly 90% of the variability in crystal number concentration can be described by only updraft velocity, sulfate number, temperature, and coarse mode dust number concentration. Although these results depend on parameter assumptions, the robustness of the underlying physics of the cirrus formation parameterization used throughout this work suggests that this approach can be a powerful method for efficiently identifying the origin of microphysical dependencies within large scale atmospheric simulations.

This thesis is concerned with a very broad aspect of adjoint equations. It is not my intention to treat the solution of adjoint equations but rather to state and prove some of the more interesting theorems. Because of the necessity of so many concepts and definitions,Chapter I is devoted entirely to definitions and basic related concepts. In Chapter II I have attempted to provide most of the fundamental concepts and theorems on inverse operations, as they are needed to treat adjoint equations. Chapter III contains the main body of this thesis, theorems on adjoint equations.

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1947. / Typescript with manuscript equations. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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<p> This thesis addresses recent trends and developments of the adjoint-variable method (AVM) for microwave structures with the time-domain transmission-line modeling (TD-TLM) method. </p> <p> Design sensitivity analysis of high-frequency (HF) structures is concerned with estimating the sensitivity of the response with respect to the design parameters. This information is essential at different stages of the design cycle such as the optimization, tolerance analysis, and yield analysis. </p> <p> Traditional approaches of sensitivity calculations involve estimating the sensitivities thought fmite-difference approximations. They suffer from formidable simulation time, as the full-wave analysis of practical HF structure requires extensive computational time. For a structure with N design parameters, at least N+l system analyses are required to extract the design response and its sensitivities. The adjoint variable method, on the other hand, supplies the sensitivity information in a very efficient way. Using at most two system analysis, the algorithm provides the design responses and its sensitivities, regardless of the number of the design parameters. </p> <p> In this thesis two contributions have been achieved which aims at enhancing the efficiency of the TLM-A VM framework. The first contribution is a reformulation of the AVM. This reformulation results in casting both the original and the adjoint systems in mathematically identical forms. It is shown that both systems can thus be modeled using a single TLM simulator with the only difference in the excitation. The second contribution focuses on generalizing the A VM algorithm by employing it for more advanced TLM nodes. The compatibility of the symmetrical condensed node (SCN) with the AVM algorithm has been verified in previous work for a general 3-D problem. Here, this is extended to include the hybrid symmetrical condensed node (HSCN), which is more efficient in terms of memory saving and simulation time. The new approaches are all illustrated through sensitivity estimation of different waveguide structures. </p> / Thesis / Master of Applied Science (MASc)

This work evaluates whether the branch of Reynolds Averaging in Computational Fluid Dynamics can be used to, based on real field measurements, find the source of the measured gas in question. The method to do this is via the adjoint to the Reynolds Averaged Scalar Transport equation, explained and derived herein. Since the Inverse is only as good as the main equation, forward runs are made to evaluate the turbulence model. Reynolds Averaged Navier Stokes is solved in a domain containing 4 cubes in a 2x2 grid, generating a velocity field for said domain. The turbulence model in question is a union of two modifications to the standard two equation k-ε model in order to capture blunt body turbulence but also to model the atmospheric boundary layer. This field is then inserted into the Reynolds Averaged Scalar Transport equation and the simulation is compared to data from the Environmental Flow wind tunnel in Surrey. Finally the adjoint scalar transport is solved, both for synthetic data that was generated in the forward run, but also for the data from EnFlo. It was discovered that the turbulent Schmidt number plays a major role in capturing the dispersed gas, three different Schmidt numbers were tested, the standard 0.7, the unconventional 0.3 and a height dependent Schmidt number. The widely accepted value of 0.7 did not capture the dispersion at all and gave a huge model error. As such the adjoint scalar transport was solved for 0.3 and a height dependent Schmidt number. The interaction between measurements, the real source strength (which is not used in the adjoint equation, but needed to find the source) and the location of the source is intricate indeed. Over estimation and under estimation of the forward model may cancel out in order to find the correct source, with the correct strength. It is found that Reynolds Averaged Computational fluid dynamics may prove useful in source term estimation. / Detta arbete utvärderar hurvida Reynolds medelvärdesmodellering inom flödessimuleringar kan användas till att finna källan till en viss gas baserat på verkliga mätningar ute i fält. Metoden går ut på att använda den adjungerade ekvationen till Reynolds tidsmedlade skalära transportekvationen, beskriven och härledd häri. Då bakåtmodellen bygger på framåtmodellen, måste såleds framåtmodellen utvärderas först. Navier-Stokes ekvationer med en turbulensmodell löses i en domän, innehållandes 4 kuber i en 2x2 orientering, för vilken en hastighetsprofil erhålles. Turbulensmodellen som användes är en union av två olika k-ε modeller, där den ena fångar turbulens runt tröga objekt och den andra som modellerar atmosfäriska gränsskiktet. Detta fält används sedan i framåtmodellen av skalära transportekvationen, som sedan jämförs med körningar från EnFlo windtunneln i Surrey. Slutligen testkörs även den adjungerade ekvationen, både för syntetiskt data genererat i framåtkörningen men även för data från EnFlo tunneln. Då det visade sig att det turbulenta Schmidttalet spelar stor roll inom spridning i det atmosfäriska gränsskiktet, gjordes testkörningar med tre olika Schmidttal, det normala 0.7, det väldigt låga talet 0.3 samt ett höjdberoende Schmidttal. Det visade sig att det vanligtvis använda talet 0.7 inte alls lyckas fånga spridningen tillfredställande och gav ett stort modellfel. Därför löstes den adjungerade ekvationen för 0.3 samt för ett höjdberoende Schmidttal. Interaktionen mellan mätningar, den riktiga källstyrkan (som är okänd i den adjungerade ekvationen) samt källpositionen är onekligen intrikat. Över- samt underestimationer av framåtmodellen kan ta ut varandra i bakåtmodellen för att finna rätt källa, med rätt källstyrka. Det ter sig som Reynolds turbulensmodellering mycket möjligt kan användas inom källtermsuppskattning.

Post-seismic deformation and glacial isostatic adjustment are two processes by which the Earth deforms viscoelastically. In both cases, the details of the deformation depend on the rheological structure of the Earth as well as the forcing, which is the earthquake and further movement on the fault in the case of post-seismic deformation, and the change in load on the surface of the Earth due to the redistribution of water and ice mass in the case of glacial isostatic adjustment. It is therefore possible to learn about the Earth's rheological structure and the processes' respective forcings from measurements of the deformation. In order to use measurements in this way, it is first necessary to have a method of forward modelling the processes, that is, calculating the deformation due to a given forcing and in an earth model with a given structure. Given this, a way of calculating derivatives of measurements of the deformation with respect to the parameters of interest is then desirable. In this dissertation, the adjoint method is used. This, for the first time, enables efficient calculation of continuous derivatives, which have many potential applications. Firstly, they can be used within a gradient-based optimisation method to find a model which minimises some data misfit function. The derivatives can also be used to quantify the uncertainty in such a model and hence to provide understanding of which parts of the model are well constrained. Finally, they enable construction of measurements which provide sensitivity to a particular part of the model space. In this dissertation, new methods for forward modelling both post-seismic deformation and glacial isostatic adjustment are presented. The adjoint method is also applied to both problems. Numerical examples are presented in spherically symmetric earth models and, in the case of glacial isostatic adjustment, models with laterally varying rheological structure. Such examples are used to illustrate the potential applications of the developments made within this dissertation.

Radiation portal monitors are being deployed at border crossings throughout the world to prevent the smuggling of nuclear and radiological materials; however, a tension exists between security and the free-flow of commerce. Delays at ports-of-entry have major economic implications, so it is imperative to minimize portal monitor screening time. We have developed an algorithm to locate a radioactive source using a distributed array of detectors, specifically for use at border crossings. To locate the source, we formulated an optimization problem where the objective function describes the least-squares difference between the actual and predicted detector measurements. The predicted measurements are calculated by solving the 3-D deterministic neutron transport equation given an estimated source position. The source position is updated using the steepest descent method, where the gradient of the objective function with respect to the source position is calculated using adjoint transport calculations. If the objective function is smaller than a predetermined convergence criterion, then the source position has been identified. To test the algorithm, we first verified that the 3-D forward transport solver was working correctly by comparing to the code PARTISN (Parallel Time-Dependent SN). Then, we developed a baseline scenario to represent a typical border crossing. Test cases were run for various source positions within each vehicle and convergence criteria, which showed that the algorithm performed well in situations where we have perfect knowledge of parameters such as the material properties of the vehicles. We also ran a sensitivity analysis to determine how uncertainty in various parameters-the optical thickness of the vehicles, the fill level in the gas tank, the physical size of the vehicles, and the detector efficiencies-affects the results. We found that algorithm is most sensitive to the optical thickness of the vehicles. Finally, we tested the simplifying assumption of one energy group by using measurements obtained from MCNPX (Monte Carlo N-Particle Extended). These results showed that the one-energy-group assumption will not be sufficient if the code is deployed in a real-world scenario. While this work describes the application of the algorithm to a land border crossing, it has potential for use in a wide array of nuclear security problems.

The growing concern regarding regulation and accountability of plutonium and SNM produced in commercial and research nuclear reactor fuel has driven the need for new spent nuclear fuel characterization methods to enable quantification and qualification of radioisotopes contained in used fuel in a reliable, quick, and inexpensive manner, with little to no impact on normal reactor operating procedures. This research aims to meet these objectives by employing advanced computational radiation transport methods incorporated into an algorithm to post process scintillator detector data gathered from used nuclear fuel in a spent fuel pool or in air. An existing, novel post processing algorithm, SmartID, has been updated to extract and identify unique photopeaks represented in the underwater environment for pool cooled used fuel. The resulting spectral data will be post-processed using an updated SmartID algorithm folded with deterministic adjoint results to render both qualitative and quantitative fuel content and irradiation estimates. This work has much significance to the nuclear power industry, safeguards, and forensics communities, since it yields this information at room temperature for a relatively low cost.