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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Dependence of Cloud Macrophysical Properties and Phase Distributions on Environmental Conditions Over the North Atlantic and Southern Ocean: Results From COMBLE and MARCUS

The accurate representation of Cold Air Outbreaks (CAOs) and affiliated mixed-phase boundary layer (BL) clouds in models is challenging. How BL cloud properties evolve during CAOs and their dependence on meteorological conditions is not well understood but is important for the simulation of Earth's energy budgets. Here the properties of polar BL clouds over the North Atlantic (NA) and Southern Ocean (SO) are compared using observations from the Measurements of Aerosol Radiation and CloUds over the SO (MARCUS) and CAOs in the Marine BL Experiment (COMBLE) conducted over the NA. MARCUS observations show a stronger BL inversion than COMBLE, with a higher mean EIS (estimated inversion strength)/LTS (lower tropospheric stability) of -0.03 K/13 K compared to COMBLE’s -3.2 K/9.3 K. 39% of CAOs observed during COMBLE were intense with M > 5 K, while MARCUS only had 1.3%. 78%/72% of clouds sampled in CAOs during COMBLE/MARCUS had cloud top heights <4 km. The mean BL cloud top height was over 400 m higher, and the BL was over 500 m deeper for M of 10 K compared to 0 K for both regions. MARCUS observed a 27% moister BL structure than COMBLE when M > 5 K due to stronger BL inversion trapping more moisture within the BL. Under the same LTS, EIS, and M conditions, MARCUS observed a 12% drier BL structure, and clouds were 46% more turbulent than COMBLE. During CAOs, 54% of single-layer BL clouds sampled during MARCUS had liquid-dominated bases compared to 39% during COMBLE.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1986

Why do interstellar grains exist?

There exists a discrepancy between calculated destruction rates of grains in the interstellar medium and postulated sources of new grains. This problem was examined by modelling the global life cycle of grains in the galaxy. The model includes: grain destruction due to supernovae shock waves; grain injection from cool stars, planetary nebulae, star formation, novae, and supernovae; grain growth by accretion in dark clouds; and a mixing scheme between phases of the interstellar medium. Grain growth in molecular clouds is considered as a mechanism or increasing the formation rate. To decrease the shock destruction rate, several new physical processes, such as partial vaporization effects in grain-grain collisions, breakdown of the small Larmor radius approximation for betatron acceleration, and relaxation of the steady-state shock assumption are included.

Seab, C. G.↗
NASA NTRS2010

Characteristics of Precipitation, Cloud, and Latent Heating Associated with the Madden-Julian Oscillation

This study investigates the evolution of cloud and rainfall structures associated with Madden Julian oscillation (MJO) using Tropical Rainfall Measuring Mission (TRMM) data. Two complementary indices are used to define MJO phases. Joint probability distribution functions (PDFs) of cloud-top temperature and radar echo-top height are constructed for each of the eight MJO phases. The genesis stage of MJO convection over the western Pacific (phases 1 and 2) features a bottom-heavy PDF, characterized by abundant warm rain, low clouds, suppressed deep convection, and higher sea surface temperature (SST). As MJO convection develops (phases 3 and 4), a transition from the bottom-heavy to top-heavy PDF occurs. The latter is associated with the development of mixed-phase rain and middle-to-high clouds, coupled with rapid SST cooling. At the MJO convection peak (phase 5), a top-heavy PDF contributed by deep convection with mixed-phase and ice-phase rain and high echo-top heights (greater than 5 km) dominates. The decaying stage (phases 6 and 7) is characterized by suppressed SST, reduced total rain, increased contribution from stratiform rain, and increased nonraining high clouds. Phase 7, in particular, signals the beginning of a return to higher SST and increased warm rain. Phase 8 completes the MJO cycle, returning to a bottom-heavy PDF and SST conditions similar to phase 1. The structural changes in rain and clouds at different phases of MJO are consistent with corresponding changes in derived latent heating profiles, suggesting the importance of a diverse mix of warm, mixed-phase, and ice-phase rain associated with low-level, congestus, and high clouds in constituting the life cycle and the time scales of MJO.

Lau, K-M.↗
NASA NTRSDate not supplied

TPSAS-NF1676L-23557-DND

The Cloud-Aerosol LIdar with Orthogonal Polarization (CALIOP) measures both parallel and perpendicular backscatter of linearly polarized 532 nm light from cloud particles in the atmosphere. The perpendicular component of the return signal allows differentiation between cloud layers consisting of spherical water droplets from those with non-spherical ice particles. A two-way distribution of layer-integrated 532 nm total backscatter and the layer-integrated 532 nm depolarization ratio further differentiates between water cloud layers with significant multiple scattering, horizontally-oriented ice particles that cause specular reflections, and randomly-oriented ice particles, as described in Hu et al., 2009. The cloud phase algorithm functions well for the majority of clouds, but there have been some recent changes and improvements that are described in this poster. The impact of the CALIOP viewing angle change from near-nadir (0.3 degrees) to slightly tilted (3.0 degrees) on the optical properties of the various CALIOP cloud particle phases is also shown. A major improvement to the phase algorithm is the limitation of a spatial coherence test for horizontally-oriented ice to cloud layers that have sufficient integrated attenuated backscatter to likely contain HOI. This change reduces a "striping" effect caused by noisiness in the spatial coherence test for thin cloud layers. Additional temperature tests are considered, and the regional and vertical distribution of cloud layers with the various CALIOP cloud phases is shown. Only one cloud particle phase is allowed for each 5 km portion of a cloud layer that is considered by the cloud phase algorithm, so we use in situ aircraft and CloudSat observations to determine how the CALIOP cloud phase algorithm is treating optically and thermally thick clouds, which may be mixed-phase.

Melody Avery↗
NASA NTRS1999

Lightning and 85-GHz MCSs in the Global Tropics

Numerous observations of tropical convection show that tropical continental mesoscale convective systems (MCSs) are much more prolific lightning producers than their oceanic counterparts. Satellite-based climatologies using 85-GHz passive microwave ice-scattering signatures from the Special Sensor Microwave/Imager (SSM/I) indicate that MCSs of various size and intensity are found throughout the global tropics. In contrast, global lightning distributions show a strong land bias with an order of magnitude difference between land and ocean lightning. This is somewhat puzzling, since 85-GHz ice-scattering and the charge separation processes that lead to lightning are both thought to depend upon the existence of large graupel particles. The fact that low 85-GHz brightness temperatures are observed in tropical oceanic MCSs containing virtually no lightning leads to the postulate that tropical oceanic and tropical continental MCSs have fundamentally different hydrometeor profiles through the mixed phase region of the cloud (0 C <= T <= 20 C). Until recently, validation of this postulate has not been practicable on a global scale. Recent deployment of the Tropical Rainfall Measuring Mission (TRMM) satellite presents a unique opportunity for MCS studies. The multi-sensor instrument ensemble aboard TRMM, including a multi-channel microwave radiometer, the Lightning Imaging Sensor (LIS), and the first space-borne radar, facilitates high-resolution case studies of MCS structure throughout the global tropics. An important precursor, however, is to better understand the distribution of MCSs and lightning in the tropics. With that objective in mind, this research undertakes a systematic comparison of 85-GHz-defined MCSs and lightning over the global tropics for a full year, as an initial step toward quantifying differences between land and ocean convective systems.

Toracinta, E. Richard↗
NASA NTRS2001

TRMM Precipitation Radar and Microwave Imager Observations of Convective and Stratiform Rain and Their Theoretical Implications

Theoretical models of radiative transfer are developed to simulate the 85 GHz brightness temperature, T85, observed by the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) radiometer as a function of rain rate. These simulations are performed separately over regions of convective and stratiform rain. For the purpose of constructing vertical profiles of hydrometeors in these regions, guidance is taken from TRMM Precipitation Radar (PR) observations, and from recent investigations of LDR and Z(sub DR) measurements made by land-based polarimetric radars. We find that for a given rain rate, the extinction in 85 GHz due to hydrometeors above the freezing level is relatively weak in convective regions compared to that in stratiform regions. The hydrometeor profile above the freezing level responsible for this weak extinction in convective regions is inferred, from LDR and Z(sub DR) observations and theoretical considerations, to contain two layers: 1) a layer of two km thickness with mixed phase particles, liquid drops and graupel, directly above the freezing level, and 2) a layer of graupel extending from the top of the mixed-phase layer to the cloud top. Strong extinction in the stratiform regions is inferred to result from slowly-falling, low-density ice aggregates (snow) above the freezing level. These theoretical results are consistent with T85 measured by TMI and the rain rate deduced from PR for convective and stratiform rain regions. On the basis of this study we infer that the accuracy of the rain rate sensed by TMI depends critically on the specification of the convective or stratiform nature of the rain.

Prabhakara, C.↗
DOE OSTI2025

Search for a Cloud Phase Feedback in the Arctic Climate System

This project was motivated by a hypothesis involving the transition in lower troposphere temperatures across the freezing point of water. Specifically, at temperatures just below to about ten degrees below freezing, Arctic clouds should be in a mixed-phase, with strong influences from secondary ice production (e.g., the Hallett-Mossop process). At temperatures just above freezing, clouds should become entirely deglaciated. We hypothesized that, with multiple years of ARM data, a statistically significant change could be detected in cloud radiative properties and surface radiative fluxes that could be directly attributed to this phase change. Furthermore, in a gradually warming climate, these phase change-related responses in surface radiation would represent a cloud phase feedback as part of Arctic amplification. We designed this research project to coincide with a new ARM Arctic cloud radar product developed by Ed Luke and collaborators at BNL (Luke et al., 2021: PNAS, doi:10.1073/pnas.2021387118) that explicitly contains SIP cloud properties retrieved from radar data. This research project has successfully concluded after analysis of a much larger North Slope of Alaska (NSA) data sample than originally anticipated, and the results are quite different than originally hypothesized.

58 GEOSCIENCES↗
DOE OSTI2025

Investigation of Arctic Cloud Properties and Surface Radiation Based on MOSAiC Shipborne Observations

The Arctic is rapidly changing due to changes of the Earth system. This study investigates cloud fraction, phase partition, cloud type, and their relationships with surface radiation based on yearlong shipborne observations in the Arctic regions. The Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) campaign provided lidar and radar observations of cloud microphysical properties and surface shortwave (SW) and longwave (LW) radiation. Cloud and radiative properties were examined at daily and monthly resolutions in four seasons. Low clouds were found to be most prevalent throughout the year, followed by deep clouds. The ice phase is the dominant phase except for summer (June–August). Liquid and mixed phases show more significant monthly and annual mean radiative effects in SW and LW than the ice phase. The clouds show net warming effects due to LW heating in most months, while the SW cooling effects of clouds become more dominant for July and August. The cloud and radiation observations from MOSAiC were used to evaluate simulations of the atmospheric component of the Energy Exascale Earth System Model version 2. The simulations show large overestimations of the liquid and mixed phases in the Arctic regions from February to September. The simulations also underestimate the percentages of low clouds and overestimate the percentages of deep clouds throughout the year. Altogether, this work provides a unique analysis of cloud and radiation properties based on high-resolution shipborne observations, which can be used to assist future model evaluation and development.

58 GEOSCIENCES↗
NASA NTRS2004

Thermodynamic Conditions Favorable to Superlative Thunderstorm Updraft, Mixed Phase Microphysics and Lightning Flash Rate

Satellite observations of lightning flash rate have been merged with proximal surface station thermodynamic observations toward improving the understanding of the response of the updraft and lightning activity in the tropical atmosphere to temperature. The tropical results have led in turn to an examination of thermodynamic climatology over the continental United States in summertime and its comparison with exceptional electrical conditions documented in earlier studies. The tropical and mid-latitude results taken together support an important role for cloud base height in regulating the transfer of Convective Available Potential Energy (CAPE) to updraft kinetic energy in thunderstorms. In the tropics, cloud base height is dominated by the dry bulb temperature over the wet bulb temperature as the lightning-regulating temperature in regions characterized by moist convection. In the extratropics, an elevated cloud base height may enable larger cloud water concentrations in the mixed phase region, a favorable condition for the positive charging of large ice particles that may result in thunderclouds with a reversed polarity of the main cloud dipole. The combined requirements of instability and cloud base height serve to confine the region of superlative electrification to the vicinity of the ridge in moist entropy in the western Great Plains.

Williams, E.↗
DOE OSTI2025

ARM Thermodynamic Cloud Phase (THERMOCLDPHASE) Value-Added Product Report

The U.S. Department of Energy Atmospheric Radiation Measurement (ARM) User Facility’s Thermodynamic Cloud Phase (THERMOCLDPHASE) Value-Added Product (VAP) provides vertically resolved thermodynamic cloud phase classifications (Zhang and Levin 2024). This VAP applies the multi-sensor methodology introduced by Shupe (2007) to identify cloud phase at the pixel level as liquid, drizzle, liquid + drizzle, rain, ice, snow, or mixed-phase. In addition, the VAP determines the overall cloud layer phase—classified as liquid, mixed-phase, or ice—based on the fraction of ice-containing pixels within the entire layer.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2013

Sensitivity of warm-frontal processes to cloud-nucleating aerosol concentrations

An extratropical cyclone that crossed the United States on 9-11 April 2009 was successfully simulated at high resolution (3-km horizontal grid spacing) using the Colorado State University Regional Atmospheric Modeling System. The sensitivity of the associated warm front to increasing pollution levels was then explored by conducting the same experiment with three different background profiles of cloud-nucleating aerosol concentration. To the authors' knowledge, no study has examined the indirect effects of aerosols on warm fronts. The budgets of ice, cloud water, and rain in the simulation with the lowest aerosol concentrations were examined. The ice mass was found to be produced in equal amounts through vapor deposition and riming, and the melting of ice produced approximately 75% of the total rain. Conversion of cloud water to rain accounted for the other 25%. When cloud-nucleating aerosol concentrations were increased, significant changes were seen in the budget terms, but total precipitation remained relatively constant. Vapor deposition onto ice increased, but riming of cloud water decreased such that there was only a small change in the total ice production and hence there was no significant change in melting. These responses can be understood in terms of a buffering effect in which smaller cloud droplets in the mixed-phase region lead to both an enhanced vapor deposition and decreased riming efficiency with increasing aerosol concentrations. Overall, while large changes were seen in the microphysical structure of the frontal cloud, cloud-nucleating aerosols had little impact on the precipitation production of the warm front.

ice↗
NASA NTRS2007

Liquid Water Oceans in Ice Giants

Aptly named, ice giants such as Uranus and Neptune contain significant amounts of water. While this water cannot be present near the cloud tops, it must be abundant in the deep interior. We investigate the likelihood of a liquid water ocean existing in the hydrogen-rich region between the cloud tops and deep interior. Starting from an assumed temperature at a given upper tropospheric pressure (the photosphere), we follow a moist adiabat downward. The mixing ratio of water to hydrogen in the gas phase is small in the photosphere and increases with depth. The mixing ratio in the condensed phase is near unity in the photosphere and decreases with depth; this gives two possible outcomes. If at some pressure level the mixing ratio of water in the gas phase is equal to that in the deep interior, then that level is the cloud base. The gas below the cloud base has constant mixing ratio. Alternately, if the mixing ratio of water in the condensed phase reaches that in the deep interior, then the surface of a liquid ocean will occur. Below this ocean surface, the mixing ratio of water will be constant. A cloud base occurs when the photospheric temperature is high. For a family of ice giants with different photospheric temperatures, the cooler ice giants will have warmer cloud bases. For an ice giant with a cool enough photospheric temperature, the cloud base will exist at the critical temperature. For still cooler ice giants, ocean surfaces will result. A high mixing ratio of water in the deep interior favors a liquid ocean. We find that Neptune is both too warm (photospheric temperature too high) and too dry (mixing ratio of water in the deep interior too low) for liquid oceans to exist at present. To have a liquid ocean, Neptune s deep interior water to gas ratio would have to be higher than current models allow, and the density at 19 kbar would have to be approx. equal to 0.8 g/cu cm. Such a high density is inconsistent with gravitational data obtained during the Voyager flyby. In our model, Neptune s water cloud base occurs around 660 K and 11 kbar, and the density there is consistent with Voyager gravitational data. As Neptune cools, the probability of a liquid ocean increases. Extrasolar "hot Neptunes," which presumably migrate inward toward their parent stars, cannot harbor liquid water oceans unless they have lost almost all of the hydrogen and helium from their deep interiors.

Wiktorowicz, Sloane J.↗
DOE OSTI2025

University of Miami G-band Vapor Radiometer Calibration (UMGVR_CAL) Field Campaign Report

Cold-air outbreak (CAO) clouds in the Arctic are commonly mixed-phase (MP); however, the partitioning of the amount of ice and water in CAO clouds and precipitation is not always well observed. Understanding how cloud phases partition as a function of cloud life cycle is important for predicting snowfall rates, convective life cycle, and intensity at weather timescales. The partitioning into liquid versus ice also has radiative impacts that are consequential for climate. These concerns motivated the incorporation of an airborne G-band vapor radiometer (GVR) into an National Science Foundation-supported aircraft campaign named the Cold Air outbreak Experiment in the Sub-Arctic Region (CAESAR). The GVR is an upward-pointing passive microwave radiometer using four frequencies centered around the 183.31 GHz water vapor absorption line, displaced by +- 1, 3, 7, and 14 GHz. For context, The U.S. Department of Energy (DOE)’s Atmospheric Radiation Measurement (ARM) user facility operates a surface-based GVR at its North Slope of Alaska (NSA) site. The same GVR has been used previously for a field campaign in the southeast Pacific, where an offset was noticed between brightness temperatures (Tbs) measured under clear skies compared to those calculated from a radiative transfer model. To account for any calibration offsets to the Tbs, a request was made to DOE to allow the GVR to operate at ARM’s Southern Great Plains (SGP) observatory and enable comparisons between its measurements and those available at SGP. This request was granted, titled ‘UMGVR_CAL’, short for ‘UMGVR_Calibration’. From October 30 to November 10, 2023, the GVR was deployed to the ARM SGP site to take advantage of their regular, nearby radiosonde launches under clear-sky conditions. The latter were determined using the SGP total sky imagery data. The GVR brightness temperatures in these clear-sky conditions were compared to those calculated by a radiative transfer code (PAMTRA) based on the SGP radiosondes. During the campaign, four suitable clear-sky episodes could be used for the GVR calibration. While few in number, these proved to be enough to satisfy our goal.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Preserving Tracer Correlations in Moment-Based Atmospheric Transport Models

A linear non-diffusive algorithm for advective transport is developed that greatly improves the detail at which aerosols and clouds can be represented in atmospheric models. Linear advection schemes preserve tracer correlations but the most basic linear scheme is rarely used by atmospheric modelers on account of its excessive numerical diffusion. Higher-order schemes are in widespread use, but these present new problems as nonlinear adjustments are required to avoid occurrences of negative concentrations, spurious oscillations, and other non-physical effects. Generally successful at reducing numerical diffusion during the advection of individual tracers, for example, particle number or mass, the higher-order schemes fail to preserve even the simplest of correlations between interrelated tracers. As a result, important attributes of aerosol and cloud populations including radial moments of particle size distributions, molecular precursors related through chemical equilibria, aerosol mixing state, and distribution of cloud phase are poorly represented. We introduce a new transport scheme, minVAR, that is both non-diffusive and preservative of tracer correlations, thereby combining the best features of the basic and higher-order schemes while enabling new features such as the tracking of sub-grid information at arbitrarily fine scales with high computational efficiency.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2004

Possible NASA Contributions to HEAT

A four-year experiment (HEAT) has been proposed (one summer in the field, 2005) to determine the sources and causes for the enhanced cloud-to-ground lightning over Houston, Texas, in association with simultaneous experiments by the Environmental Protection Agency (EPA) and the Texas Natural Resource Conservation Commission (TNRCC). Houston is the third most populous city in the United States and the region contains 50% of the petroleum refining capacity of the United States. Recent studies covering the period 1989-2000 document a 50% increase of cloud-to-ground lightning in the Houston area as compared to background values, which is second in flash density only to the Tampa Bay, Florida area. It is suggested that the elevated flash densities could result from several factors, including, 1) the convergence due to the urban heat island effect and complex sea breeze, and 2) the increasing levels of air pollution from anthropogenic sources producing numerous small droplets and thereby suppressing mean droplet size. The latter effect would enable more cloud water to reach the mixed phase region where it is involved in the formation of precipitation and the separation of electric charge, leading to an enhancement of lightning. The primary goals of HEAT are to examine the effects of (1) pollution, (2) the urban heat island, and (3) the complex coastline, on storms and lightning characteristics in the Houston area. The project is a multi- agency effort and will employ numerous observing capabilities and expertise. Dr. Shepherd has been asked to serve as a possible co- investigator to contribute expertise in areas related to urban impacts on precipitation variability. Dr. Shepherd is also a key NASA representative in the interagency effort. This presentation will provide an overview of recent NASA research focused on urban rainfall in Houston and offer potential NASA capabilities that could contribute to HEAT.

Shepherd, J. M.↗
NASA NTRS2006

Optically Thin Liquid Water Clouds: Their Importance and Our Challenge

Many of the clouds important to the Earth's energy balance, from the tropics to the Arctic, are optically thin and contain liquid water. Longwave and shortwave radiative fluxes are very sensitive to small perturbations of the cloud liquid water path (LWP) when the liquid water path is small (i.e., < g/sq m) and, thus, the radiative properties of these clouds must be well understood to capture them correctly in climate models. We review the importance of these thin clouds to the Earth's energy balance, and explain the difficulties in observing them. In particular, because these clouds are optically thin, potentially mixed-phase, and often (i.e., have large 3-D variability), it is challenging to retrieve their microphysical properties accurately. We describe a retrieval algorithm intercomparison that was conducted to evaluate the issues involved. The intercomparison included eighteen different algorithms to evaluate their retrieved LWP, optical depth, and effective radii. Surprisingly, evaluation of the simplest case, a single-layer overcast cloud, revealed that huge discrepancies exist among the various techniques, even among different algorithms that are in the same general classification. This suggests that, despite considerable advances that have occurred in the field, much more work must be done, and we discuss potential avenues for future work.

Turner, D. D.↗
NASA NTRS2000

A Melting Layer Model for Passive/Active Microwave Remote Sensing Applications: Simulation of TRMM Observations - Part 2

The one-dimensional, steady-state melting layer model developed in Part I of this study is used to calculate both the microphysical and radiative properties of melting precipitation, based upon the computed concentrations of snow and graupel just above the freezing level at applicable horizontal gridpoints of 3-dimensional cloud resolving model simulations. The modified 3-dimensional distributions of precipitation properties serve as input to radiative transfer calculations of upwelling radiances and radar extinction/reflectivities at the TRMM Microwave Imager (TMI) and Precipitation Radar (PR) frequencies, respectively. At the resolution of the cloud resolving model grids (approx. 1 km), upwelling radiances generally increase if mixed-phase precipitation is included in the model atmosphere. The magnitude of the increase depends upon the optical thickness of the cloud and precipitation, as well as the scattering characteristics of ice-phase precipitation aloft. Over the set of cloud resolving model simulations utilized in this study, maximum radiance increases of 43, 28, 18, and 10 K are simulated at 10.65, 19.35 GHz, 37.0, and 85.5 GHz, respectively. The impact of melting on TMI-measured radiances is determined not only by the physics of the melting particles but also by the horizontal extent of the melting precipitation, since the lower-frequency channels have footprints that extend over 10''s of kilometers. At TMI resolution, the maximum radiance increases are 16, 15, 12, and 9 K at the same frequencies. Simulated PR extinction and reflectivities in the melting layer can increase dramatically if mixed-phase precipitation is included, a result consistent with previous studies. Maximum increases of 0.46 (-2 dB) in extinction optical depth and 5 dBZ in reflectivity are simulated based upon the set of cloud resolving model simulations.

Olson, William S.↗
DOE OSTI2025

Oscillate and renormalize: Fast phonons reshape the Kondo effect in flat-band systems

Here, we examine the interplay between electron correlations and phonons in an Anderson-Holstein impurity model with an Einstein phonon. When the phonons are slow compared to charge fluctuations (frequency 𝜔 0 ≪ 𝑈/2, the onsite Coulomb scale 𝑈/2), we demonstrate analytically that the expected phonon-mediated reduction of interactions is completely suppressed, even in the strong-coupling regime. This suppression arises from the oscillator's inability to respond to rapid charge fluctuations, manifested as a compensation effect between the polaronic cloud and the excited-state phonons associated with valence fluctuations. We identify a frozen mixed valence phase, above a threshold dimensionless electron-phonon coupling 𝛼* when the phonons are slow, where the static phonon cloud locks the impurity into specific valence configurations, potentially explaining the puzzling coexistence of mixed valence behavior and insulating properties in materials like rust. Conversely, when the phonon is fast (𝜔 0 ≳ 𝑈/2), the system exhibits conventional polaronic behavior with renormalized onsite interactions effectively 𝑈 eff due to phonon-mediated attraction, with additional satellite features in the local spectral function due to phonon excitations. Using numerical renormalization group calculations, a fully dynamic renormalization technique, we confirm these behaviors in both regimes. These findings have important implications for strongly correlated systems where phonon energy scales may be comparable to the Coulomb scale, such as in twisted bilayer graphene, necessitating careful consideration of interaction renormalizations in theoretical models.

Anderson impurity model↗