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DOE OSTI2025

Heterogeneous Mixtures of Dictionary Functions to Approximate Subspace Invariance in Koopman Operators: Why Deep Koopman Operators Work

Abstract Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary . In a widely used algorithm, extended dynamic mode decomposition (EDMD), the dictionary functions are drawn from a fixed class of functions. Deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper, we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Typically, a Koopman dictionary’s nonlinear functions are homogeneous. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm Yeung et al. ( In: 2019 American Control Conference (ACC), 2019). We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves similar accuracy and dimensional scaling to deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.

Johnson, Charles A.↗

DOE OSTI2024

The cosmic-ray positron excess and its imprint in the Galactic gamma-ray sky

Abstract We study the origin of the positron excess observed in the local cosmic-ray spectrum at high energies, and relate it to the cosmic rays and gamma-ray emission across the entire Galaxy. In particular, we explore the hypothesis of a single, dominant source accountable for primary electron-positron pairs. Since we are agnostic about the physical nature of the underlying source population, we consider four models that are representative of young pulsars, old stars (as a tracer of millisecond pulsars), and annihilating dark matter particles. In the dark matter hypothesis, we consider both a cored and a cuspy model for the halo in the Milky Way. Then, we compare the associated gamma-ray sky maps withFermi-LAT data. We find that the emission arising from pulsar wind nebulae is fairly concentrated near the mid plane, and therefore additional cosmic-ray sources must be invoked to explain the emission at the center of the Galaxy. If the local positron excess were mainly due to millisecond pulsars, inverse Compton scattering by the particles injected would naturally account for a non-negligible fraction of the central gamma-ray emission. The same process would lead to a tension for a standard NFW dark matter profile, exceeding the gamma-ray data by almost a factor of 2 in some regions of the Galaxy. Although the results for an isothermal, cored profile are in agreement with these data, the cross section needed in both cases is around 2 orders of magnitude above the thermal cross-section, disfavouring the dark matter interpretation.

Astronomy & Astrophysics↗

DOE OSTI2024

Impact of Self-shielding Minihalos on the Lyα Forest at High Redshift

Abstract Dense gas in minihalos with masses of 10 6 −10 8 M ⊙ can shield themselves from reionization for ∼100 Myr after being exposed to the UV background. These self-shielded systems, often unresolved in cosmological simulations, can introduce strong absorption in quasar spectra. This paper is the first systematic study on the impact of these systems on the Ly α forest. We first derive the H i column density profile of photoevaporating minihalos by conducting 1D radiation–hydrodynamics simulations. We utilize these results to estimate the Ly α opacity from minihalos in a large-scale simulation that cannot resolve self-shielding. When the ionization rate of the background radiation is 0.03 × 10 −12 s −1 , as expected near the end of reionization at z ∼ 5.5, we find that the incidence rate of damped Ly α absorbers increases by a factor of ∼2−4 compared to at z = 4.5. The Ly α flux is, on average, suppressed by ∼3% of its mean due to minihalos. The absorption features enhance the 1D power spectrum up to ∼5% at k ∼ 0.1 h Mpc −1 (or 10 −3 km −1 s), which is comparable to the enhancement caused by inhomogeneous reionization. The flux is particularly suppressed in the vicinity of large halos along the line-of-sight direction at separations of up to 10 h −1 Mpc at r ⊥ ≲ 2 h −1 Mpc. However, these effects become much smaller for higher ionizing rates (≳0.3 × 10 −12 s −1 ) expected in the post-reionization Universe. Our findings highlight the need to consider minihalo absorption when interpreting the Ly α forest at z ≳ 5.5. Moreover, the sensitivity of these quantities to the ionizing background intensity can be exploited to constrain the intensity itself.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

From subsidies to stressors: Positively skewed ecological gradients alter biological responses to nutrients in streams

Abstract Subsidy–stress gradients offer a useful framework for understanding ecological responses to perturbation and may help inform ecological metrics in highly modified systems. Historic, region‐wide shifts from bottomland hardwood forest to row crop agriculture can cause positively skewed impact gradients in alluvial plain ecoregions, resulting in tolerant organisms that typically exhibit a subsidy response (increased abundance in response to environmental stressors) shifting to a stress response (declining abundance at higher concentrations). As a result, observed biological tolerance in modified ecosystems may differ from less modified regions, creating significant challenges for detecting biological responses to restoration efforts. Using the agriculturally dominated Mississippi Alluvial Plain (MAP) ecoregion in Mississippi, USA, as a case study, we tested the hypothesis that macroinvertebrate taxa that typically display a subsidy response to nutrient enrichment in less modified ecoregions (i.e., nutrient‐tolerance) shift to a stress response to increasing nutrients in highly modified watersheds with elevated baseline nutrient conditions (i.e., nutrient intolerance). The abundance and diversity of MAP‐specific intolerant taxa identified with threshold indicator taxa analysis were either unresponsive or exhibited a subsidy response to increasing nutrients in less modified ecoregions in Mississippi with less land alteration and lower nutrient concentrations, but declined at higher concentrations, providing evidence for a stress response to elevated nutrients in the MAP. Additionally, MAP‐specific tolerant and intolerant taxa richness responded to increased nutrients predictably and consistently across space and time within the MAP. However, in MAP streams, elevated specific conductance was predicted to dampen the response of tolerant and intolerant taxa richness to increasing nutrient concentrations, highlighting the importance of considering multistressor interactions when interpreting biological data. Lastly, we demonstrate the efficacy of this approach with sediment bacterial communities characterized with amplicon sequencing, which lack sufficient life history characteristics necessary for the development of multimetric indices. Both macroinvertebrate and bacterial communities responded similarly to increasing nutrient concentrations, suggesting DNA‐based approaches may provide an efficient biological assessment tool for monitoring water quality improvements in highly modified watersheds.

DeVilbiss, Stephen E. [U.S. Geological Survey Lowe↗

DOE OSTI2024

Milky Way-est: Cosmological Zoom-in Simulations with Large Magellanic Cloud and Gaia–Sausage–Enceladus Analogs

Abstract We present Milky Way-est, a suite of 20 cosmological cold-dark-matter-only zoom-in simulations of Milky Way (MW)-like host halos. Milky Way-est hosts are selected such that they (i) are consistent with the MW’s measured halo mass and concentration, (ii) accrete a Large Magellanic Cloud (LMC)-like (≈10 11 M ⊙ ) subhalo within the last 2 Gyr on a realistic orbit, placing them near 50 kpc from the host center at z ≈ 0, and (iii) undergo a >1:5 sub-to-host halo mass ratio merger with a Gaia–Sausage–Enceladus (GSE)-like system at early times (0.67 < z < 3). Hosts satisfying these LMC and GSE constraints constitute <1% of all halos in the MW’s mass range, and their total masses grow rapidly at late times due to LMC analog accretion. Compared to hosts of a similar final halo mass that are not selected to include LMC and GSE analogs, Milky Way-est hosts contain 22% more subhalos with present-day virial masses above 10 8 M ⊙ throughout the virial radius, on average. This enhancement reaches ≈80% in the inner 100 kpc and is largely, if not entirely, due to LMC-associated subhalos. These systems also induce spatial anisotropy in Milky Way-est subhalo populations, with ≈60% of the total subhalo population within 100 kpc found in the current direction of the LMC. Meanwhile, we find that GSE-associated subhalos do not significantly contribute to present-day Milky Way-est subhalo populations. These results provide context for our Galaxy’s dark matter structure and subhalo population and will help interpret a range of measurements that are currently only possible in the MW.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

The Dual Nature of Entrainment-Mixing Signatures Revealed through Large-Eddy Simulations of a Convection-Cloud Chamber

Abstract Entrainment of subsaturated air into a cloud can influence its optical and microphysical properties in various ways, depending on the droplet evaporation and turbulent mixing time scales. Previous experiments in the Pi convection-cloud chamber have revealed that, given a fixed entrained air property, the mixing of entrained subsaturated air results in complete evaporation of some cloud droplets, with the rest remaining unchanged. This is a signature of inhomogeneous mixing. While comparing the results of entrainment with varying air properties, the mixing signature appears as if the subsaturated air is well mixed with the cloud to evenly reduce the droplets’ size. In other words, taken together, the experiments appear to have the signature of homogeneous mixing. To explore these results in a greater depth, we conduct large-eddy simulations combined with a bin microphysics scheme. Our results reproduce the similar signatures of inhomogeneous and homogeneous mixing, implying that LES can resolve the inhomogeneous mixing when the grid spacing is smaller than the entrained air parcel. Additionally, we observe that increasing the aerosol injection rate enhances the signature of inhomogeneous mixing, while coarser grid spacing diminishes it. Finally, the change in wall fluxes in response to various entrained air properties confirms that the homogeneous signature seen in the analysis of an ensemble of simulations is the result of various equilibrium states. This further strengthens the suggestion that the homogeneous mixing signature found in aircraft observations near the cloud top may result from combining entrainment events of different intensities, possibly caused by various-sized eddies. Significance Statement Large-eddy simulation and size-resolved microphysics can resolve time scales for turbulent mixing and evaporation and, therefore, are well suited for reproducing, extending, and interpreting the entrainment experiment in the Pi convection-cloud chamber. Our simulation results confirm (i) the inhomogeneous mixing signature for an individual entrainment event and (ii) the appearance of homogeneous mixing in an ensemble of entrainment episodes. Furthermore, we demonstrate that the inhomogeneous mixing signature is more pronounced in a polluted cloud, but coarser grid spacing in simulations may compromise the accuracy of this signature. Last, the homogeneous mixing signature results from various equilibrium states established for different entrainment intensities and adjusted wall fluxes, which are challenging to measure experimentally but can be easily analyzed in the simulations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Evolution of oxygen and stratification and their relationship in the North Pacific Ocean in CMIP6 Earth system models

Abstract. This study examines the linkages between the upper-ocean (0–200 m) oxygen (O2) content and stratification in the North Pacific Ocean using four Earth system models (ESMs), an ocean hindcast simulation, and an ocean reanalysis. The trends and variability in oceanic O2 content are driven by the imbalance between physical supply and biological demand. Physical supply is primarily controlled by ocean ventilation, which is responsible for the transport of O2-rich surface waters to the subsurface. Isopycnic potential vorticity (IPV), a quasi-conservative tracer proportional to density stratification that can be evaluated from temperature and salinity measurements, is used herein as a dynamical proxy for ocean ventilation. The predictability potential of the IPV field is evaluated through its information entropy. The results highlight a strong O2–IPV connection and somewhat higher (as compared to the rest of the basin) predictability potential for IPV across the tropical Pacific, where the El Niño–Southern Oscillation occurs. This pattern of higher predictability and strong anticorrelation between O2 and stratification is robust across multiple models and datasets. In contrast, IPV at mid-latitudes has low predictability potential and its center of action differs from that of O2. In addition, the locations of extreme events or hotspots may or may not differ between the two fields, with a strong model dependency, which persists in future projections. On the one hand, these results suggest that it may be possible to monitor ocean O2 in the tropical Pacific based on a few observational sites co-located with the more abundant IPV measurements; on the other, they lead us to question the robustness of the IPV–O2 relationship in the extratropics. The proposed framework helps to characterize and interpret O2 variability in relation to physical variability and may be especially useful in the analysis of new observation-based data products derived from the BGC-Argo float array in combination with the traditional but far more abundant Argo data.

Novi, Lyuba↗

DOE OSTI2025

Control Mechanisms for Self‐Sealing in Activated Clay‐Rich Faults Through Controlled Hydraulic Injection Experiment

Abstract In a high‐pressure injection fault activation experiment conducted at the Mont Terri underground research laboratory in Switzerland, the transmissivity of the Opalinus Clay fault significantly increased due to opening and shearing. The fluid injection, spanning a few hours, generated a 10 m radius fault activation patch. Subsequent pressure pulse tests conducted bi‐weekly for a year revealed the gradual return of fault transmissivity to its initial state. The study utilized fluid pressure decay analysis, optical fiber monitoring, continuous active source seismic measurements and borehole displacement sensors for measuring fault displacements. The fault zone exhibited a dilation of approximately 1.4 mm, associated with both normal and tangential movements during activation, resulting in a sudden transmissivity increase from 1 × 10 −12 to 3.2 × 10 −7 m 2 /s. Early post‐activation, transient compaction and the subsequent slow compaction were observed, transitioning to an extension regime. The pressure pulse tests demonstrated a rapid transmissivity drop by more than two orders of magnitude within the first 10 days, followed by a gradual and less pronounced decrease. Plastic shear and compaction dominated the transmissivity evolution until 70 days after injection ended, followed by a period where additional factors, such as clay mineral swelling, influenced the behavior. Extrapolation suggested a sealing process taking at least 50 years after the initial activation. Plain Language Summary A field‐scale fault activation experiment offers valuable insights into the elasto‐plastic processes governing the sealing of shale faults. The experiment reveals a rapid increase in the fault's transmissivity by approximately five orders of magnitude during activation. Subsequent observations show a gradual transmissivity decrease by about three orders of magnitude post‐activation, with slow long‐term plastic shear and compaction of the fault competing against secondary processes, notably clay mineral swelling. All conceptual models employed to interpret these field data converge on the estimation that the fault's return to its initial low transmissivity state would require a minimum of 50 years. Key Points High‐pressure injection fault activation experiment at the Mont Terri underground research laboratory Continuous transmissivity measurements record self‐sealing inside a clay‐rich fault zone Transmissivity undergoes a phase of domination by slow plastic compaction and shearing during the initial post‐activation period, with mineral swelling exerting its influence over the long term

Guglielmi, Yves↗

DOE OSTI2025

Hyperspectral leaf reflectance of grasses varies with evolutionary lineage more than with site

Abstract To predict ecological responses at broad environmental scales, grass species are commonly grouped into two broad functional types based on photosynthetic pathway. However, closely related species may have distinctive anatomical and physiological attributes that influence ecological responses, beyond those related to photosynthetic pathway alone. Hyperspectral leaf reflectance can provide an integrated measure of covarying leaf traits that may result from phylogenetic trait conservatism and/or environmental conditions. Understanding whether spectra‐trait relationships are lineage specific or reflect environmental variation across sites is necessary for using hyperspectral reflectance to predict plant responses to environmental changes across spatial scales. We measured hyperspectral leaf reflectance (400–2400 nm) and 12 structural, biochemical, and physiological leaf traits from five grass‐dominated sites spanning the Great Plains of North America. We assessed if variation in leaf reflectance spectra among grass species is explained more by evolutionary lineage (as captured by tribes or subfamilies), photosynthetic pathway (C 3 or C 4 ), or site differences. We then determined whether leaf spectra can be used to predict leaf traits within and across lineages. Our results using redundancy analysis ordination (RDA) show that grass tribe identity explained more variation in leaf spectra (adjusted R 2 = 0.12) than photosynthetic pathway, which explained little variation in leaf spectra (adjusted R 2 = 0.00). Furthermore, leaf reflectance from the same tribe across multiple sites was more similar than leaf reflectance from the same site across tribes (adjusted R 2 = 0.12 and 0.08, respectively). Across all sites and species, trait predictions based on spectra ranged considerably in predictive accuracies ( R 2 = 0.65 to <0.01), but R 2 was >0.80 for certain lineages and sites. The relationship between Vc max , a measure of photosynthetic capacity, and spectra was particularly promising. Chloridoideae, a lineage more common at drier sites, appears to have distinct spectra‐trait relationships compared with other lineages. Overall, our results show that evolutionary relatedness explains more variation in grass leaf spectra than photosynthetic pathway or site, but consideration of lineage‐ and site‐specific trait relationships is needed to interpret spectral variation across large environmental gradients.

Pau, Stephanie [Department of Geography University↗

DOE OSTI2024

Atmospheric H 2 observations from the NOAA Cooperative Global Air Sampling Network

Abstract. The NOAA Global Monitoring Laboratory (GML) measures atmospheric hydrogen (H2) in grab samples collected weekly as flask pairs at over 50 sites in the Cooperative Global Air Sampling Network. Measurements representative of background air sampling show higher H2 in recent years at all latitudes. The marine boundary layer (MBL) global mean H2 was 552.8 ppb in 2021, 20.2 ± 0.2 ppb higher compared to 2010. A 10 ppb or more increase over the 2010–2021 average annual cycle was detected in 2016 for MBL zonal means in the tropics and in the Southern Hemisphere. Carbon monoxide measurements in the same-air samples suggest large biomass burning events in different regions likely contributed to the observed interannual variability at different latitudes. The NOAA H2 measurements from 2009 to 2021 are now based on the World Meteorological Organization Global Atmospheric Watch (WMO GAW) H2 mole fraction calibration scale, developed and maintained by the Max Planck Institute for Biogeochemistry (MPI-BGC), Jena, Germany. GML maintains eight H2 primary calibration standards to propagate the WMO scale. These are gravimetric hydrogen-in-air mixtures in electropolished stainless steel cylinders (Essex Industries, St. Louis, MO), which are stable for H2. These mixtures were calibrated at the MPI-BGC, the WMO Central Calibration Laboratory (CCL) for H2, in late 2020 and span the range 250–700 ppb. We have used the CCL assignments to propagate the WMO H2 calibration scale to NOAA air measurements performed using gas chromatography and helium pulse discharge detector instruments since 2009. To propagate the scale, NOAA uses a hierarchy of secondary and tertiary standards, which consist of high-pressure whole-air mixtures in aluminum cylinders, calibrated against the primary and secondary standards, respectively. Hydrogen at the parts per billion level has a tendency to increase in aluminum cylinders over time. We fit the calibration histories of these standards with zero-, first-, or second-order polynomial functions of time and use the time-dependent mole fraction assignments on the WMO scale to reprocess all tank air and flask air H2 measurement records. The robustness of the scale propagation over multiple years is evaluated with the regular analysis of target air cylinders and with long-term same-air measurement comparison efforts with WMO GAW partner laboratories. Long-term calibrated, globally distributed, and freely accessible measurements of H2 and other gases and isotopes continue to be essential to track and interpret regional and global changes in the atmosphere composition. The adoption of the WMO H2 calibration scale and subsequent reprocessing of NOAA atmospheric data constitute a significant improvement in the NOAA H2 measurement records.

Pétron, Gabrielle↗

DOE OSTI2025

Baseflow Identification via Explainable AI With Kolmogorov‐Arnold Networks

Abstract Hydrological models often involve constitutive laws that may not be optimal in every application. We propose to replace such laws with the Kolmogorov‐Arnold networks (KANs), a class of neural networks designed to identify symbolic expressions. We demonstrate KAN's potential on the problem of baseflow identification, a notoriously challenging task plagued by significant uncertainty. KAN‐derived functional dependencies of the baseflow components on the aridity index outperform their original counterparts; they demonstrate that water availability, rather than potential evapotranspiration, drives baseflow by constraining actual evapotranspiration under arid conditions. On a test set, they increase the Nash‐Sutcliffe efficiency (NSE) by 65%, decrease the root mean squared error by 29%, and increase the Kling‐Gupta efficiency by 34%. This superior performance is achieved while reducing the number of fitting parameters from three to two. Next, we use data from 378 catchments across the continental United States to refine the water‐balance equation at the mean‐annual scale. The KAN‐derived equations based on the refined water balance outperform both the current aridity index model, with up to a 105% increase in NSE, and the KAN‐derived equations based on the original water balance. While the performance of our model and tree‐based machine learning methods is similar, KANs offer the advantage of simplicity and transparency and require no specific software or computational tools. This case study focuses on the aridity index formulation, but the approach is flexible and transferable to other hydrological processes. Plain Language Summary Equations used in hydrologic model are often suboptimal, resulting in reduced prediction accuracy and efficiency. We implemented Kolmogorov‐Arnold networks (KAN), a machine learning algorithm for deriving symbolic formulations, to estimate groundwater recharge and showed that it outperforms an existing state‐of‐the‐art semi‐empirical formulation. In hydrology, Nash‐Sutcliffe efficiency (NSE), root mean squared error (RMSE), and Kling‐Gupta efficiency (KGE) are commonly used to evaluate model performance. Higher NSE and KGE values indicate better performance, while lower RMSE values are preferable. Our results show that NSE increased by 71%, RMSE decreased by 32%, and KGE improved by 25%. In addition, KAN identifies an optimal functional form and can be used to derive new analytical formulas using the prior knowledge. The KAN‐inspired equation outperformed the original formulation and reduced the fitting parameters. Furthermore, we refined the water‐balance equation at the mean‐annual scale and showed that, based on the new water‐balance equation, KAN can derive new formulations that are superior to the original aridity index formulations (up to 105% increase in NSE) and KAN‐derived equations based on the original water balance. These findings highlight the significant potential of KAN to advance the scientific understanding of a wide range of hydrologic processes. Key Points Kolmogorov‐Arnold networks (KANs) enhance interpretability of machine‐learned hydrological models KAN‐derived symbolic formulations outperform state‐of‐the‐art semi‐empirical aridity indices KAN‐identified functional form yields an analytical index with fewer fitting parameters and improved performance

baseflow↗