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Inversion of Gravity Fields From the Spacecraft Orbital Data Using an Adjoint Operator Approach

In perturbation approximation, the forward problem of orbital dynamics (equations with initial conditions) is linear with respect to variations of coordinates and/or velocities of the spacecraft and to corresponding variations of the gravity field in the models used. The linear operator adjoint to the linear operator of such forward problem turns out to be instrumental in inversion of differences between observed and predicted coordinates/velocities in terms of the updates of harmonics in the initial gravity field model. Based on this approach, the solution of resulting adjoint problem of orbital dynamics can be used to directly evaluate the matrix of partial derivatives of observable differences with respect to the gravity field harmonics. General discussion of the adjoint problem of orbital dynamics is given and an example of a mathematical formalism for the practical retrieval algorithm is presented.

Ustinov, E. A.

Comparison of the Tangent Linear Properties of Tracer Transport Schemes Applied to Geophysical Problems.

A number of geophysical applications require the use of the linearized version of the full model. One such example is in numerical weather prediction, where the tangent linear and adjoint versions of the atmospheric model are required for the 4DVAR inverse problem. The part of the model that represents the resolved scale processes of the atmosphere is known as the dynamical core. Advection, or transport, is performed by the dynamical core. It is a central process in many geophysical applications and is a process that often has a quasi-linear underlying behavior. However, over the decades since the advent of numerical modelling, significant effort has gone into developing many flavors of high-order, shape preserving, nonoscillatory, positive definite advection schemes. These schemes are excellent in terms of transporting the quantities of interest in the dynamical core, but they introduce nonlinearity through the use of nonlinear limiters. The linearity of the transport schemes used in Goddard Earth Observing System version 5 (GEOS-5), as well as a number of other schemes, is analyzed using a simple 1D setup. The linearized version of GEOS-5 is then tested using a linear third order scheme in the tangent linear version.

4DVAR

Shielding Considerations for CubeSat Structures During Solar Maximum

The purpose of this lessons learned is to communicate the utility of shielding in small spacecraft planning for the support of mission assurance and reliability. Numerous SmallSats have been flying in polar low earth orbit for scientific, communications, technology demonstrations, and imaging with academic, commercial, and government interests. Shielding has been part of mission assurance and reliability from the advent of long duration spacecraft missions. The Shields-1 CubeSat has been operating in polar low earth orbit since 16 December 2018 with atomic number (Z)-grade radiation shielding and demonstrates shielding effectiveness. Shields-1 has collected a representative example of solar minimum data in 2019 with 8 Teledyne dosimeters over varying shielding effectiveness. It serves as current experimental data and has been compared with NOVICE Shielding estimates using the AP8 –AE8 trapped radiation model with the Shields-1 CAD and generic CubeSat 3 unit (U) models. Using NOVICE model radiation analysis coding, the shielding effectiveness's, based on a generic CubeSat 3U structure with 4 electronic boards, were estimated for aluminum wall thicknesses ranging from 0.204 cmto4.44 cm (0.550 g/cm2–12.0 g/cm2) thick aluminum. For modeled polar orbiting spacecraft, solar maximum total ionizing dose (TID)increases by nearly a magnitude for thin-walled aluminum 0.550g/cm2-0.686 g/cm2(0.204 cm –0.254 cm) typical CubeSat structures. The shielding effectiveness by NOVICE Sigma estimates, which is a shielding sphere approximation around a detector, showed a linear relationship with wall thickness, which increased over the wall thickness by a ratio of 1.43 determined by linear regression analysis. Using NOVICE Adjoint Monte-Carlo Modeling of solar minimum and solar maximum with the inclusion of a worst-case solar particle event over a one year mission without geomagnetic shielding, the TID for minimum and maximum conditions for a generic 3U with a wall thickness of 0.254 cm is 158 RAD and 1540 RAD, respectively. The modeled total solar maximum TID is over estimated, because at low orbital latitudes a spacecraft will have shielding from Earth's magnetic field. However, TID will still be significant at high latitudes over the poles, where a spacecraft is exposed in a solar particle event. In contrast, to a thin walled generic 3U CubeSat, Shields-1 electronics enclosure has a shielding effectiveness of 21.3 g/cm2from NOVICE Sigma modeling and is expected to show reduced total ionizing dose increases during the present active Solar Cycle 25 period. Because solar particle events during solar maximum increase TID on electronic parts with thin-walled shielding in short periods of time, it is a mission assurance and reliability consideration on the spacecraft’s mission value versus adding shielding for risk reduction of premature spacecraft or instrument payload loss. Since the volumes of many instruments and system electronics have reduced with small spacecraft, shielding material costs and weight penalties have diminished. A small spacecraft project budget and schedule may limit traditional radiation-hardened part use and radiation testing requirements, where shielding can contribute to mission assurance and reliability with reduced costs.

Shields-1

Shielding Considerations for CubeSat Structures During Solar Maximum

The purpose of this lessons learned paper is to communicate the utility of shielding in small spacecraft planning for the support of mission assurance and reliability. Numerous SmallSats have been flying in polar low Earth orbit for science, communications, technology demonstrations, and imaging with academic, commercial, and government interests. Shielding has been part of mission assurance and reliability from the advent of long duration spacecraft missions. The Shields-1 CubeSat has been operating in polar low Earth orbit since 16 December 2018 with atomic number (Z)-grade radiation shielding and demonstrates shielding effectiveness. Shields-1 has collected a representative example of solar minimum data in 2019 with eight Teledyne µDosimeters over varying shielding effectivenesses. It serves as current experimental data and has been compared with NOVICE Shielding estimates using the AP8 – AE8 trapped radiation model with the Shields-1 CAD and generic CubeSat three unit (3U) models. Using NOVICE model radiation analysis coding, the shielding effectivenesses, based on a generic CubeSat 3U structure with four electronic boards, were estimated for aluminum wall thicknesses ranging from 0.204 cm to 4.44 cm (0.550 g/cm 2 to 12.0 g/cm 2 ). For modeled polar orbiting spacecraft, solar maximum total ionizing dose (TID) increases by nearly a magnitude for thin-walled aluminum 0.550-g/cm 2 - 0.686-g/cm 2 (0.204-cm – 0.254-cm) typical CubeSat structures. The shielding effectiveness estimated by NOVICE Sigma, which is a shielding sphere approximation around a detector, showed a linear relationship with wall thickness, which increased over the wall thickness by a ratio of 1.43 determined by linear regression analysis. Using NOVICE Adjoint Monte-Carlo Modeling of solar minimum and solar maximum with the inclusion of a worst-case solar particle event over a one-year mission without geomagnetic shielding, the TID for minimum and maximum conditions for a generic 3U with a wall thickness of 0.254 cm is 158 RAD and 1540 RAD, respectively. The modeled total solar maximum TID is over estimated, because at low orbital latitudes a spacecraft will have shielding from the Earth’s magnetic field. However, TID will still be significant at high latitudes over the poles, where a spacecraft is exposed in a solar particle event. In contrast to a thin-walled generic 3U CubeSat, the Shields-1 electronics enclosure has a shielding effectiveness of 21.3 g/cm 2 from NOVICE Sigma modeling and is expected to show reduced total ionizing dose increases during the present active Solar Cycle 25 period. Because solar particle events during solar maximum increase TID on electronic parts with thin-walled shielding in short periods of time, it is a mission assurance and reliability consideration on the mission value of the spacecraft versus adding shielding for risk reduction of premature spacecraft or instrument payload loss. Since the volumes of many instruments and system electronics have reduced with small spacecraft, shielding material costs and weight penalties have diminished. A small spacecraft project budget and schedule may limit traditional radiation-hardened part use and radiation testing requirements, where shielding can contribute to mission assurance and reliability with reduced costs.

Shields-1

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

Introduction to Data Assimilation

Atmospheric data assimilation is a class of techniques used for producing descriptions of fields of air temperature, pressure, humidity, wind, etc. on a spatial grid or in terms of a finite functional representation. These are then used to initialize numerical weather forecasts or to analyze the atmosphere for other purposes. The techniques combine past, present, and even future observations in an approximate statistically optimal way. Various types of statistical or physically-based models and their corresponding adjoints are employed to relate diverse fields in both time and space and to relate what is observed to what is being analyzed. Computationally, the problem is very demanding and onstraining on the techniques that can be employed on a routine basis.

Atmospheric data assimilation

Supercurrents and (partial) supersymmetry in adjoint QCD 2 and its generalizations

1 + 1-dimensional SU(N) gauge theory coupled to an adjoint Majorana fermion, also known as adjoint QCD 2 , has the surprising feature that at fermion mass $\sqrt{\frac{g^2N}{2\pi }}$ it exhibits supersymmetry. In this paper, we obtain a deeper insight into how the supersymmetry works by constructing the gauge invariant, Lorentz covariant supercurrent j μA . Its conservation relies crucially on the presence of a quantum anomaly. We generalize this construction to a class of models where, in addition to an adjoint Majorana fermion of an appropriate mass, the gauge theory is coupled to some collection of massless fermions (SU(N) may be replaced by a more general gauge group). In general, these models have a supersymmetric massive sector and a non-supersymmetric CFT sector [1], but there are cases in which both sectors are supersymmetric. An example of such a gapless, fully supersymmetric model is SU(N) gauge theory coupled to three adjoint Majorana fermions, of which two are massless and the third has mass $\sqrt{\frac{3{g}^2N}{2\pi }}$.

anomalies in field and string theories

Adjoint methods for aerodynamic wing design

A model inverse design problem is used to investigate the effect of flow discontinuities on the optimization process. The optimization involves finding the cross-sectional area distribution of a duct that produces velocities that closely match a targeted velocity distribution. Quasi-one-dimensional flow theory is used, and the target is chosen to have a shock wave in its distribution. The objective function which quantifies the difference between the targeted and calculated velocity distributions may become non-smooth due to the interaction between the shock and the discretization of the flowfield. This paper offers two techniques to resolve the resulting problems for the optimization algorithms. The first, shock-fitting, involves careful integration of the objective function through the shock wave. The second, coordinate straining with shock penalty, uses a coordinate transformation to align the calculated shock with the target and then adds a penalty proportional to the square of the distance between the shocks. The techniques are tested using several popular sensitivity and optimization methods, including finite-differences, and direct and adjoint discrete sensitivity methods. Two optimization strategies, Gauss-Newton and sequential quadratic programming (SQP), are used to drive the objective function to a minimum.

Grossman, Bernard

Analyzing Carbon Dioxide and Methane Emissions in California Using Airborne Measurements and Model Simulations

Greenhouse gas (GHG) concentrations have increased over the past decades and are linked to global temperature increases and climate change. These changes in climate have been suggested to have varying effects, and uncertain consequences, on agriculture, water supply, weather, sea-level rise, the economy, and energy. To counteract the trend of increasing atmospheric concentrations of GHGs, the state of California has passed the California Global Warming Act of 2006 (AB-32). This requires that by the year 2020, GHG (e.g., carbon dioxide (CO2) and methane (CH4)) emissions will be reduced to 1990 levels. To quantify GHG fluxes, emission inventories are routinely compiled for the State of California (e.g., CH4 emissions from the California Greenhouse Gas Emissions Measurement (CALGEM) Project). The major sources of CO2 and CH4 in the state of California are: transportation, electricity production, oil and gas extraction, cement plants, agriculture, landfills/waste, livestock, and wetlands. However, uncertainties remain in these emission inventories because many factors contributing to these processes are poorly quantified. To alleviate these uncertainties, a synergistic approach of applying air-borne measurements and chemical transport modeling (CTM) efforts to provide a method of quantifying local and regional GHG emissions will be performed during this study. Additionally, in order to further understand the temporal and spatial distributions of GHG fluxes in California and the impact these species have on regional climate, CTM simulations of daily variations and seasonality of total column CO2 and CH4 will be analyzed. To assess the magnitude and spatial variation of GHG emissions and to identify local “hot spots”, airborne measurements of CH4 and CO2 were made by the Alpha Jet Atmospheric eXperiment (AJAX) over the San Francisco Bay Area (SFBA) and San Joaquin Valley (SJV) in January and February 2013 during the Discover-AQ-CA study. High mixing ratios of GHGs were observed in-flight with a high degree of spatial variability. To provide an additional method to quantify GHG emissions, and analyze AJAX measurement data, the GEOS-Chem CTM is used to simulate SFBA/SJV GHG measurements. A nested-grid version of GEOS-Chem will be applied and utilizes varying emission inventories and model parameterizations to simulate GHG fluxes/emissions. The model considers CO2 fluxes from fossil fuel use, biomass/biofuel burning, terrestrial and oceanic biosphere exchanges, shipping and aviation, and production from the oxidation of carbon monoxide, CH4, and non-methane volatile organic carbons. The major sources of CH4 simulated in GEOS-Chem are domesticated animals, rice fields, natural gas leakage, natural gas venting/flaring (oil production), coal mining, wetlands, and biomass burning. Preliminary results from the comparison between available observations (e.g., AJAX and CALGEM CH4 emission maps) and GEOS-Chem results will be presented, along with a discussion of CO2 and CH4 source apportionment and the use of the GEOS-Chem-adjoint to perform inverse GHG modeling.

Johnson, Matthew S.

Evaluation of the DAO Retrospective Data Assimilation System

We have developed and implemented a retrospective data assimilation system (RDAS) as an upgrade to the operational DAO/Terra data assimilation system. This formulation aims at improving analysis over filter analysis by the dynamically consistent incorporation of observation information past a given analysis time. The current implementation of the RDAS uses the adjoint of the tangent linear model of a simplified version of the Terra general circulation model and extensions to the physical-space statistical analysis system to propagate observation information back in time. The RDAS adopts the same assumptions of the regular data assimilation system, particularly, no explicit propagation of error covariances are involved therefore rendering a procedure that is computationally affordable. In this study, we show results of experiments conducted to investigate the performance of the 6-hour (lag-1) RDAS. Statistical results obtained over one month during a winter season indicate that the RDAS represents considerable improvement over the regular assimilation. Plans for implementation of the RDAS capability in our new finite-volume data assimilation system will also be presented at the time of the conference.

Zhu, Yanqiu

Lessons Learned from Inlet Integration Analysis of NASA's Low Boom Flight Demonstrator

In 2016, NASA's Aeronautics Research Mission Directorate announced the New Aviation Horizons Initiative with a goal of designing/building several X-Planes, including a Low Boom Flight Demonstrator (LBFD). That same year, NASA awarded a contract to Lockheed Martin (LM) to advance the LBFD concept through preliminary design. Several configurations of the LBFD aircraft were analyzed by both LM engineers and NASA researchers. This presentation focuses on some of the CFD simulations that were run by NASA Glenn researchers. NASA's FUN3D V13.1 code was used for all adjoint-based grid refinement studies and Spalart-Allmaras turbulence model was used during adaptation. It was found that adjoint-based grid adaptation did not accurately capture inlet performance for high speed top-aft-mounted propulsion.

Adjoint-based Grid Adaptatio

Under-Track CFD-Based Shape Optimization for a Low-Boom Demonstrator Concept

The detailed outer mold line shaping of a Mach 1.6, demonstrator-sized low-boom concept is presented. Cruise trim is incorporated a priori as part of the shaping objective, using an equivalent-area-based approach. Design work is performed using a gradient-driven optimization framework that incorporates a three-dimensional, nonlinear flow solver, a parametric geometry modeler, and sensitivities derived using the adjoint method. The shaping effort is focused on reducing the under-track sonic boom level using an inverse design approach, while simultaneously satisfying the trim requirement. Conceptual-level geometric constraints are incorporated in the optimization process, including the internal layout of fuel tanks, landing gear, engine, and crew station. Details of the model parameterization and design process are documented for both flow-through and powered states, and the performance of these optimized vehicles presented in terms of inviscid L/D, trim state, pressures in the near-field and at the ground, and predicted sonic boom loudness.

Wintzer, Mathias

ISSM: Ice Sheet System Model

In order to have the capability to use satellite data from its own missions to inform future sea-level rise projections, JPL needed a full-fledged ice-sheet/iceshelf flow model, capable of modeling the mass balance of Antarctica and Greenland into the near future. ISSM was developed with such a goal in mind, as a massively parallelized, multi-purpose finite-element framework dedicated to ice-sheet modeling. ISSM features unstructured meshes (Tria in 2D, and Penta in 3D) along with corresponding finite elements for both types of meshes. Each finite element can carry out diagnostic, prognostic, transient, thermal 3D, surface, and bed slope simulations. Anisotropic meshing enables adaptation of meshes to a certain metric, and the 2D Shelfy-Stream, 3D Blatter/Pattyn, and 3D Full-Stokes formulations capture the bulk of the ice-flow physics. These elements can be coupled together, based on the Arlequin method, so that on a large scale model such as Antarctica, each type of finite element is used in the most efficient manner. For each finite element referenced above, ISSM implements an adjoint. This adjoint can be used to carry out model inversions of unknown model parameters, typically ice rheology and basal drag at the ice/bedrock interface, using a metric such as the observed InSAR surface velocity. This data assimilation capability is crucial to allow spinning up of ice flow models using available satellite data. ISSM relies on the PETSc library for its vectors, matrices, and solvers. This allows ISSM to run efficiently on any parallel platform, whether shared or distrib- ISSM: Ice Sheet System Model NASA's Jet Propulsion Laboratory, Pasadena, California uted. It can run on the largest clusters, and is fully scalable. This allows ISSM to tackle models the size of continents. ISSM is embedded into MATLAB and Python, both open scientific platforms. This improves its outreach within the science community. It is entirely written in C/C++, which gives it flexibility in its design, and the power/speed that C/C++ allows. ISSM is svn (subversion) hosted, on a JPL repository, to facilitate its development and maintenance. ISSM can also model propagation of rifts using contact mechanics and mesh splitting, and can interface to the Dakota software. To carry out sensitivity analysis, mesh partitioning algorithms are available, based on the Scotch, Chaco, and Metis partitioners that ensure equal area mesh partitions can be done, which are then usable for sampling and local reliability methods.

Larour, Eric

The DAO Retrospective Data Assimilation System

The fixed-lag Kalman smoother of Cohn et al. (1994), or a version of a more computationally feasible approximation of it developed by Todling et al. (1998), is under implementation at the Data Assimilation Office (DAO) to build a retrospective data assimilation system (RDAS). The initial version of the RDAS uses the physical-space statistical analysis system and a modification of the incremental analysis update (IAU) procedure of Bloom et al. (1996); a follow up version of the RDAS Nill require the use of the adjoint of the DAO general circulation model (developed by Y. Yang and M Navon). The retrospective procedure is designed to produce improved analyses as well as improved assimilated fields consequently providing an improved climate representation through data assimilation.

Todling, Richardo

Improved Earthquake Source Parameters with 3D Wavespeed Models in California and Nevada

Seismic tomography harnesses earthquake data to explore the inaccessible structure of the Earth. Adjoint waveform tomography (AWT), a method of seismic tomography, updates the tomographic model by optimizing the fit between observed earthquake data and synthetic waveforms. The synthetic data are calculated by solving the wave equation through a given 3D model. An important requirement to calculating synthetics is the source information (location, centroid time, depth, and moment tensor). Errors in source information affect the quality of the synthetics produced, which in turn can limit how structure can be inferred in the AWT workflow. Here, to test the effect of updating source information, we used MTTime (Chiang, 2020), a time-domain full-waveform moment tensor inversion code, to calculate the moment tensors and depths of 118 earthquakes that occurred in California and Nevada over a 20-yr period. We calculated 3D Green’s functions using a 3D seismic wavespeed model of California and Nevada (Doody et al., 2023b). We show that the inverted solutions provide better waveform fits than the Global Centroid Moment Tensor catalog and increase usable, well-correlated data by up to 7%. Therefore, we argue that recalculating source parameters should be considered in AWT workflows, particularly for smaller magnitude events (⁠M w > 5.0).

58 GEOSCIENCES

Adjoint-Operator Learning For A Neural Network

Electronic neural networks made to synthesize initially unknown mathematical models of time-dependent phenomena or to learn temporally evolving patterns by use of algorithms based on adjoint operators. Algorithms less complicated, involve less computation and solve learning equations forward in time possibly simultaneously with equations of evolution of neural network, thereby both increasing computational efficiency and making real-time applications possible.

Barhen, Jacob

An Adjoint-Based Analysis of the Sampling Footprints of Tall Tower, Aircraft and Potential Future Lidar Observations of CO2

A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future CO2 levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an 'inverse problem', where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from longterm surface and aircraft monitoring stations with data from intensive field campaigns and with proposed future satellite observations. We have recently developed an adjoint for the GSFC 3-D Parameterized Chemistry and Transport Model (PCTM). Here, we will present results from a PCTM Adjoint study comparing the sampling footprints of tall tower, aircraft and potential future lidar observations of CO2. The vertical resolution and extent of the profiles and the observation frequency will be considered for several sites in North America.

Andrews, Arlyn