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A finite element based method for solution of optimal control problems

A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

Bless, Robert R.↗

Partitioning uncertainty in projections of Arctic sea ice

Abstract Improved knowledge of the contributing sources of uncertainty in projections of Arctic sea ice over the 21st century is essential for evaluating impacts of a changing Arctic environment. Here, we consider the role of internal variability, model structure and emissions scenario in projections of Arctic sea-ice area (SIA) by using six single model initial-condition large ensembles and a suite of models participating in Phase 5 of the Coupled Model Intercomparison Project. For projections of September Arctic SIA change, internal variability accounts for as much as 40%–60% of the total uncertainty in the next decade, while emissions scenario dominates uncertainty toward the end of the century. Model structure accounts for 60%–70% of the total uncertainty by mid-century and declines to 30% at the end of the 21st century in the summer months. For projections of wintertime Arctic SIA change, internal variability contributes as much as 50%–60% of the total uncertainty in the next decade and impacts total uncertainty at longer lead times when compared to the summertime. In winter, there exists a considerable scenario dependence of model uncertainty with relatively larger model uncertainty under strong forcing compared to weak forcing. At regional scales, the contribution of internal variability can vary widely and strongly depends on the calendar month and region. For wintertime SIA change in the Greenland-Iceland-Norwegian and Barents Seas, internal variability contributes 60%–70% to the total uncertainty over the coming decades and remains important much longer than in other regions. We further find that the relative contribution of internal variability to total uncertainty is state-dependent and increases as sea ice volume declines. These results demonstrate that internal variability is a significant source of uncertainty in projections of Arctic sea ice.

Bonan, David B. (ORCID:0000000338676009)↗

Shadow Lagrangian dynamics for superfluidity

Motivated by a similar approach for Born-Oppenheimer molecular dynamics, this paper proposes an extended "shadow" Lagrangian density for quantum states of superfluids. The extended Lagrangian contains an additional field variable that is forced to follow the wave function of the quantum state through a rapidly oscillating extended harmonic oscillator. By considering the adiabatic limit for large frequencies of the harmonic oscillator, we can derive the two equations of motions, a Schrödinger-type equation for the quantum state and a wave equation for the extended field variable. The equations are coupled in a nonlinear way, but each equation individually is linear with respect to the variable that it defines. The computational advantage of this new system is that it can be easily discretized using linear time stepping methods, where we propose to use a Crank-Nicolson-type approach for the Schrödinger equation and an extended leapfrog scheme for the wave equation. Furthermore, the difference between the quantum state and the extended field variable defines a consistency error that should go to zero if the frequency tends to infinity. By coupling the time-step size in our discretization to the frequency of the harmonic oscillator we can extract an easily computable consistency error indicator that can be used to estimate the numerical error without additional costs. The findings are illustrated in numerical experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Lower-Stratospheric Control of the Frequency of Sudden Stratospheric Warming Events

The sensitivity of stratospheric polar vortex variability to the basic-state stratospheric temperature profile is investigated by performing a parameter sweep experiment with a dry dynamical core general circulation model where the equilibrium temperature profiles in the polar lower and upper stratosphere are systematically varied. It is found that stratospheric variability is more sensitive to the temperature distribution in the lower stratosphere than in the upper stratosphere. In particular, a cold lower stratosphere favors a strong time-mean polar vortex with a large daily variability, promoting frequent sudden stratospheric warming events in the model runs forced with both wavenumber-1 and wavenumber-2 topographies. This sensitivity is explained by the control exerted by the lower-stratospheric basic state onto fluxes of planetary-scale wave activity from the troposphere to the stratosphere, confirming that the lower stratosphere can act like a valve for the upward propagation of wave activity. It is further shown that with optimal model parameters, stratospheric polar vortex climatology and variability mimicking Southern and Northern Hemisphere conditions are obtained with both wavenumber-1 and wavenumber-2 topographies.

54 ENVIRONMENTAL SCIENCES↗

National Prevalence of Caprine Prion Protein Genetic Variability at Codons 146, 211, and 222 in Goat Herds in the United States

Scrapie is a neurodegenerative disease that impacts sheep and goats, characterized by gradual and progressive changes in neurological function. Recent research shows that the scrapie incubation period is significantly influenced by specific variations in amino acids within the prion protein gene (PRNP). The objective of this study was to estimate the national prevalence of caprine PRNP genetic variability at codons 146, 211, and 222 in goat populations across the United States. A total of 3052 blood, ear tissue, and brain tissue samples were collected from goats from 50 states. The participating states were categorized into four Veterinary Service (VS) district regions. The samples underwent DNA extraction, and the PRNP variants corresponding to codons 146, 211, and 222 were amplified and sequenced. The analysis of PRNP variants, when compared to the PRNP reference sequence, revealed seven alleles in twelve genotypes. The homozygous 146NN, 211RR, and 222QQ alleles, which have been linked to an increased risk of scrapie, were found to be the most prevalent among all the goats. The heterozygous 222QK, 211RQ, 146SD, 146ND, and 146NS alleles and the homozygous 222KK, 146SS, and 146DD alleles, known to be associated with reduced scrapie susceptibility and a prolonged incubation period after experimental challenge, were found in 1.098% (222QK), 2.33% (211RQ), 0.58% (146SD), 3.13% (146ND), 20.68% (146NS), 0.005% (222KK), 3.31% (146SS), and 0.67% (146DD) of goats, respectively. The 222QK allele was found most frequently in goats tested from the east (VS District 1, 1.59%) and southwest (VS District 4, 1.08%) regions, whereas the 211RQ allele was found most often in goats tested from the Midwest (VS District 2, 8.03%) and east (VS District 1, 6.53%) regions. The 146NS allele was found most frequently in goats tested from the northwest (VS District 3, 29.02%) and southwest (VS District 4, 20.69%) regions. Our results showed that the prevalence of less susceptible genotypes at PRNP codon 146 may be sufficient to use genetic susceptibility testing in some herds. This may reduce the number of goats removed as part of a herd clean-up plan and may promote the selective breeding goats for less susceptible alleles in high-risk herds at the national level.

59 BASIC BIOLOGICAL SCIENCES↗

Joint Synoptic and Cloud Variability over the Northeast Atlantic near the Azores

Abstract Marine boundary layer clouds are modified by processes at different spatial and temporal scales. To isolate the processes governing aerosol–cloud–precipitation interactions, multiday synoptic variability of the environment must be accounted for. Information on the location of low clouds relative to the ridge–trough pattern gives insight into how cloud properties vary as a function of environmental subsidence and stability. The technique of self-organizing maps (SOMs) is employed to objectively classify the 500-hPa geopotential height patterns for 33 years of reanalysis fields (ERA-Interim) into pretrough, trough, posttrough, ridge, and zonal-flow categories. The SOM technique is applied to a region of prevalent marine low cloudiness over the eastern North Atlantic Ocean that is centered on the Azores island chain, the location of a long-term U.S. Department of Energy observation site. The Azores consistently lie in an area of substantial variability in synoptic configuration, thermodynamic environment, and cloud properties. The SOM method was run in two ways to emphasize multiday and seasonal variability separately. Over and near the Azores, there is an east-to-west sloshing back and forth of the western edge of marine low clouds associated with different synoptic states. The different synoptic states also exhibit substantial north–south variability in the position of high clouds. For any given month of the year, there is large year-to-year variability in the occurrence of different synoptic states. Hence, estimating the climatological behavior of clouds from short-term field campaigns has large uncertainties. This SOM approach is a robust method that is broadly applicable to characterizing synoptic regimes for any location.

54 ENVIRONMENTAL SCIENCES↗

Manganese concentration influences nitrogen cycling in agricultural soil

Manganese (Mn) can modulate nitrogen (N) transformations in soil, yet its role in agroecosystems remains understudied. We conducted a 51-day microcosm incubation with agricultural soils differing in long-term N history (N 0 , no added N; N 1 , added 225 kg N ha −1 for a duration of 27 years) and amended with soluble Mn at 0 (M 0 ), 50 (M 1 ), or 250 (M 2 ) mg kg −1 and Glyceria striata (Lam.) residue. In N 1 soils, Mn additions (both M 1 and M 2 ) lowered total mineral N by 25 % relative to N 1 M 0 at day 51 and reduced 51-day cumulative N₂O by 32 % (N 1 M 1 ) and 42 % (N 1 M 2 ) vs. N 1 M 0 , whereas effects in N 0 were negligible. Mn also depressed ammonia-oxidizing bacterial amoA gene transcripts at day 15 in N 1 M 2 vs. N 1 M 0 (2.5 fold change). This reduction was likely due to increased N loss via complete denitrification to N₂ through microbial pathways such as nitrate/nitrite-dependent manganese oxidation (NDMO), where bacteria directly used the added Mn 2+ to reduce nitrate (NO 3 − ) and nitrite (NO 2 − ) to N 2 or as Mn dependent-ammonia oxidation (Mnammox) where bacteria oxidized ammonium (NH 4 + ) to N 2 , using Mn oxides as electron acceptors that formed from the oxidation of the added Mn. Other contributing mechanisms may include Mn-induced N immobilization, toxicity, and changes in the microbial community. These mechanistic results indicate that background Mn availability and redox dynamics can shape nitrification–denitrification pathways under N-rich conditions. In conclusion, we highlight how native Mn pools and redox state may help explain observed variability in N losses and greenhouse gas production across agricultural soils.

Decomposition↗

The High-resolution Urban Meteorology for Impacts Dataset (HUMID) daily for the Conterminous United States

Many current gridded surface meteorological datasets are inadequate for quantifying near surface spatiotemporal variability because they do not fully represent the impacts of land surface heterogeneity. Of note, explicit representation of the spatial structure and magnitude of local urban warming are usually lacking. Here we enhance the representation of spatial meteorological variability over urban areas in the conterminous United States (CONUS) by employing the High-Resolution Land Data Assimilation System (HRLDAS), which accounts for the fine-scale impacts of spatiotemporally varying land surfaces on weather. We also synthesize in situ meteorological data including local mesonets to create a 1 km grid spacing model-observation fusion product spanning 1981-2018 over the CONUS. Daily maximum, minimum, and mean values for a variety of temperature estimates, humidity, and surface energy budget terms, among others, are included. This High-resolution Urban Meteorology for Impacts Dataset (HUMID) will be useful for studies examining spatial variability of near surface meteorology and the impacts of urban heat islands across many disciplines including epidemiology, ecology, and climatology.

54 ENVIRONMENTAL SCIENCES↗

Reverse thrust performance of the QCSEE variable pitch turbofan engine

Results of steady-state reverse and forward-to-reverse thrust transient performance tests are presented. The original QCSEE 4-segment variable fan nozzle was retested in reverse and compared with a continuous, 30-deg half-angle conical exlet. Data indicated that the significantly more stable, higher pressure recovery flow with the fixed 30-deg exlet resulted in lower engine vibrations, lower fan blade stress and approximately a 20% improvement in reverse thrust. Objective reverse thrust of 35% of takeoff thrust was reached. Thrust response of less than 1.5 sec was achieved for the approach and the takeoff-to-reverse thrust transients.

Samanich, N. E.↗

A Study of Bound States of Systems of Helium and Lithium Using the Method of Discrete-Variable Representation

The systems of particles He{sub 2}, {sup 6}Li–He, {sup 7}Li–He, He{sub 3}, {sup 6}Li–He{sub 2}, and {sup 7}Li–He{sub 2}, the binding energies of which are small and the bound-state wave functions of which are widely distributed in space, are considered. Because the interaction potential is weak and rather localized compared to the characteristic sizes of wave functions of these systems, the problem of an accurate determination of binding energy and wave functions is complicated. Small changes in input parameters or an inaccuracy of calculations can lead to considerable deviations of calculated results from true values. An essential part of the study is the development and application of the discrete-variable representation method. This method is based on the determination of basis functions and the nodes and weights of a quadrature formula in such way that the values of a function are zero at all these nodes but one. With this representation the time required for calculating the Hamiltonianmatrix elements is reduced several times. The binding energies of several systems consisting of helium and lithium atoms were obtained using the method of discrete-variable representation. Thanks to the application of this approach, the calculation time was significantly reduced without loss in accuracy.

74 ATOMIC AND MOLECULAR PHYSICS↗

Projected Changes to Hydroclimate Seasonality in the Continental United States

Abstract Future changes to the hydrological cycle are projected in a warming world, and any shifts in drought risk may prove extremely consequential for natural and human systems. In addition to long‐term moistening, drying, or warming trends, perturbations to the annual cycle of regional hydroclimate variables may also have substantial impacts. We analyze projected changes in several hydroclimate variables across the continental United States, along with shifts in the amplitude and phase of their annual cycles. We find that even in regions where no robust change in the annual mean is expected, coherent changes to the annual cycle are projected. In particular, we identify robust regional phase shifts toward earlier arrival of peak evaporation in the northern regions, and peak runoff and total soil moisture in the western regions. Changes in the amplitude of the annual cycle of total and surface soil moisture are also projected, and reflect changes to the annual cycle in surface water supply and demand. Whether changes become detectable above the background noise of internal variability depends strongly on the future scenario considered, and significant changes to the annual cycle are largely avoided in the lowest‐forcing scenario.

54 ENVIRONMENTAL SCIENCES↗

Projected Changes to Hydroclimate Seasonality in the Continental United States

Future changes to the hydrological cycle are projected in a warming world, and any shifts in drought risk may prove extremely consequential for natural and human systems. In addition to long-term moistening, drying, or warming trends, perturbations to the annual cycle of regional hydroclimate variables may also have substantial impacts. We analyze projected changes in several hydroclimate variables across the continental United States, along with shifts in the amplitude and phase of their annual cycles. We find that even in regions where no robust change in the annual mean is expected, coherent changes to the annual cycle are projected. In particular, we identify robust regional phase shifts toward earlier arrival of peak evaporation in the northern regions, and peak runoff and total soil moisture in the western regions. Changes in the amplitude of the annual cycle of total and surface soil moisture are also projected, and reflect changes to the annual cycle in surface water supply and demand. Whether changes become detectable above the background noise of internal variability depends strongly on the future scenario considered, and significant changes to the annual cycle are largely avoided in the lowest-forcing scenario.

drought↗

A High-Resolution Land Data Assimilation System Optimized for the Western United States

The Western Land Data Assimilation System (WLDAS) is a custom instance of the NASA Land Information System that combines land surface parameters, meteorological forcing data, and satellite products within a land surface model to produce daily estimates of the water and energy budget variables for the western United States. WLDAS was configured through discussions with partners, with the goal of groundwater sustainability planning for the state of California in mind. The publicly available output dataset has a 1-km grid resolution and spans 1979–present, which makes it suitable for water resources assessments. The data are also able to contextualize the recent drought events in California. Assimilation of Leaf Area Index, which is demonstrated herein to improve simulation over agricultural areas in California, specifically in terms of evapotranspiration in irrigation regions, will be included along with other data assimilation in subsequent releases of WLDAS.

land surface modeling↗

Analysis of Soil Freeze/Thaw Signatures During Slapex F/T Campaign

Permanently frozen and seasonally frozen soils occur over a large portion of the Earth's land surface. Changes in the freeze/thaw state of the land surface reflects major changes in thermal and hydraulic properties as well as acting as a "switch" for many ecological processes. In short, soil freeze/thaw state is a fundamental land surface variable in the water and energy cycles, and it connects to the carbon cycle. Surface freeze/thaw state is observable by passive and active microwave sensors. For example, NASA's Soil Moisture Active Passive (SMAP) mission includes a freeze/thaw data product. Such satellite sensing offers routine all-season and all-weather global observations of soil freeze/thaw state with the application of suitable algorithms. We describe early finding from the SLAPex Freeze/Thaw campaign, believed to be the first airborne campaign of its type, focusing on soil freeze/thaw.

SLAPex↗

IM3/HyperFACETS Thermodynamic Global Warming (TGW) Simulation Datasets

Publication For a thorough description of the methods, see the peer-reviewed paper: Jones, A.D., Rastogi, D., Vahmani, P. et al. Continental United States climate projections based on thermodynamic modification of historical weather. Sci Data 10, 664 (2023). https://doi.org/10.1038/s41597-023-02485-5 Overview The IM3 / HyperFACETS climate simulations provide 40-year historical (1980-2019) as well as four 80-year future simulations (2020-2099) over the U.S. The future simulations are split into near (2020-2059) and far future (2060-2099) segments. The future scenarios span a range of plausible changes in future climate (both Global Circulation Model (GCM) and Representative Concentration Pathways/Shared Socioeconomic Pathway (RCP/SSP) dimensions). The simulations provide climate variables with high spatiotemporal resolution (25 hourly variables and 207 3-hourly variables at 12 km2). The datasets are generated using dynamical downscaling with the WRF (Weather Research and Forecasting) model (version 4.2.1) and therefore preserve physical consistency across variables. WRF is a state-of-the-art, fully compressible, non-hydrostatic, mesoscale numerical weather prediction model. WRF is coupled with an urban canopy model (UCM), which resolves urban surfaces. The future scenarios were developed using a thermodynamic global warming approach where past events are replayed under a range of future warming conditions. These scenarios therefore provide a perspective on potential increases in extreme event intensity, geographic scope, and duration, with previously non-extreme conditions potentially crossing new thresholds to be considered extreme by today's standards. This approach is not intended to estimate future changes in extreme event frequency that might result from changes in large-scale atmospheric dynamics. This dataset has NOT been bias corrected. A bias corrected version of selected variables is under development and will be released here when available. Scenarios Files Data for each scenario is provided in weekly NetCDF files. 25 variables are available at hourly resolution, and 207 variables are available at three-hourly resolution. Spatial resolution is 12km and spans the conterminous United States (CONUS), including some areas of Canada and Mexico, resulting in a grid of 424 by 299 cells. The spatial projection is a Lambert Conformal Conic with the following proj-string: "+proj=lcc +lat_0=40.0000076293945 +lon_0=-97 +lat_1=30 +lat_2=45 +x_0=0 +y_0=0 +R=6370000 +units=m +no_defs". The available scenarios and simulation periods are listed below: historical | 1980 - 2019 rcp45cooler | 2020 - 2059 rcp45cooler | 2060 - 2099 rcp45hotter | 2020 - 2059 rcp45hotter | 2060 - 2099 rcp85cooler | 2020 - 2059 rcp85cooler | 2060 - 2099 rcp85hotter | 2020 - 2059 rcp85hotter | 2060 - 2099 * The first year (1979, 2019, and 2059) of data within each scenario represents a model warmup period and should not be used. These are located in the `spinup_files` directory. Historical year 2020 is considered an extra year of data beyond the simulation period and can be found in the `additional_files` directory. For information on specific variables and a more in-depth discussion of methodology, please refer to the data landing page at https://tgw-data.msdlive.org. Delta Warming Files The global and CONUS warming deltas for each scenario are provided in degrees Celsius annually and monthly. Restart Files Yearly restart files are provided for each scenario which can be used to restart the WRF model at a particular point in time. Spinup Files The first year of data within each simulation period represents a model warmup period and should not be used. The files are provided here for the sake of reproducibility. Additional Files Additional years of data are provided as an extension of the historic simulation.

Jones, Andrew D.↗

Application of 'steady' state finite element and transient finite difference theory to sound propagation in a variable duct - A comparison with experiment

Experimental data are presented for sound propagation in a simulated infinite hard wall duct with a large change in duct cross sectional area. The data are conveniently tabulated for further use. The 'steady' state finite element theory of Astley and Eversman (1981) and the transient finite difference theory of White (1981) are in good agreement with the data for both the axial and transverse pressure profiles and the axial phase angle. Therefore, numerical finite difference and finite element theories appear to be ideally suited for handling duct propagation problems which encounter large axial gradients in acoustic parameters. The measured energy reflection coefficient agrees with the values from the Astley-Eversman modal coupling model.

Baumeister, K. J.↗

An Analysis of Terrestrial and Aquatic Environmental Controls of Riverine Dissolved Organic Carbon in the Conterminous United States

Riverine carbon cycling is an important, but insufficiently investigated component of the global carbon cycle. Analyses of environmental controls on riverine carbon cycling are critical for improved understanding of mechanisms regulating carbon processing and storage along the terrestrial-aquatic continuum. Here, we compile and analyze riverine dissolved organic carbon (DOC) concentration data from 1402 United States Geological Survey (USGS) gauge stations to examine the spatial variability and environmental controls of DOC concentrations in the United States (U.S.) surface waters. DOC concentrations exhibit high spatial variability, with an average of 6.42 ± 6.47 mg C/ L (Mean ± Standard Deviation). In general, high DOC concentrations occur in the Upper Mississippi River basin and the Southeastern U.S., while low concentrations are mainly distributed in the Western U.S. Single-factor analysis indicates that slope of drainage areas, wetlands, forests, percentage of first-order streams, and instream nutrients (such as nitrogen and phosphorus) pronouncedly influence DOC concentrations, but the explanatory power of each bivariate model is lower than 35%. Analyses based on the general multi-linear regression models suggest DOC concentrations are jointly impacted by multiple factors. Soil properties mainly show positive correlations with DOC concentrations; forest and shrub lands have positive correlations with DOC concentrations, but urban area and croplands demonstrate negative impacts; total instream phosphorus and dam density correlate positively with DOC concentrations. Notably, the relative importance of these environmental controls varies substantially across major U.S. water resource regions. In addition, DOC concentrations and environmental controls also show significant variability from small streams to large rivers, which may be caused by changing carbon sources and removal rates by river orders. In sum, our results reveal that general multi-linear regression analysis of twenty one terrestrial and aquatic environmental factors can partially explain (56%) the DOC concentration variation. In conclusion, this study highlights the complexity of the interactions among these environmental factors in determining DOC concentrations, thus calls for processes-based, non-linear methodologies to constrain uncertainties in riverine DOC cycling.

54 ENVIRONMENTAL SCIENCES↗

Electrostatic energy harvester

An electrostatic energy harvester broadly comprises an electrical energy storage component, an electrical energy transfer stage, first and second variable capacitors, and a switching control module. The electrical energy transfer stage includes diode-connected transistors and dictates electrical energy transfer between the electrical energy storage component and the variable capacitors. The switching control module timely switches between the first and second variable capacitors according to a state machine. Subsequent electrical energy investments from the electrical energy storage component are less than an initial electrical energy investment due to remnant electrical energy remaining at the previously active one of the first and second variable capacitors from previous electrical energy harvesting.

Wilson, Amy Charlene↗