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DOE OSTI2025

Determination of Intermolecular Distances in Dilute Solutions of Macroions and Their Direct Correlations with Self-Assembly and Macrophase Transitions

Here, this work demonstrates new attempts to determine the intermolecular distances between charged macroionic solutes in their dilute solutions, which regulate the solute’s microphase (self-assembly) and macrophase transitions. Small-angle X-ray scattering (SAXS) and analytical ultracentrifuge (AUC) techniques were applied to determine the intermolecular distances for the 2.42 nm-sized, spherical uranyl peroxide molecular cluster {U 60 } in their self-assembled states in dilute aqueous solution and concentrated phases, respectively. The counterion-mediated attraction among {U 60 } leads to characteristic, inter-{U 60 } distances in solutions, which increase gradually with decreasing the strength of introduced counterions (e.g., lower valency). The gradual increment of inter-{U 60 } distance demonstrates a nice correlation with the macroscopic phase transitions of {U 60 }, from single crystals to concentrated fluids containing rigid 2-D sheets, then to dilute solutions containing a small amount of standalone, floating 2-D sheets of {U 60 }, and finally to dilute solutions containing a limited amount of self-assembled single-layered, spherical blackberry structures of different sizes from the bending of more flexible 2-D sheets.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Li + (ionophore) nanoclusters engineered aqueous/non-aqueous biphasic electrolyte solutions for high-potential lithium-based batteries

The use of aqueous/non-aqueous biphasic electrolyte solutions in Li-based battery systems circumvents the limitations of poor reductive stability of aqueous electrolyte solutions, broadening their electrochemical stability window. However, aqueous/non-aqueous electrolytes suffer from biphasic mixing and high impedance when Li ions cross the biphasic interface. Here we propose the use of 12-crown-4 (12C4) and tetraglyme (G4) as lithium ionophores to form Li + (ionophore) nanoclusters in both non-aqueous and aqueous phases to overcome the interface challenges in biphasic electrolytes. The Li + (ionophore) nanoclusters have the H 2 O-excluding inner Li + solvation structure in non-polar 1,1,2,2-tetrafluoroethyl 2,2,3,3-tetrafluoropropyl ether (TTE), allowing fast charge transport across the biphasic interface without solvent mixing or water shuttling. Further, a tailored electrolyte formulation comprising the lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt, 12C4, TTE and H 2 O solvents (labelled LiTFSI-12C4@TTE/H 2 O) demonstrates low impedance (2.7 Ω cm -2 ) at the TTE/H 2 O interface and enabling 2,000 cycles of prelithiated graphite||LiFePO 4 coin cells at 850 mA g -1 with an average Coulombic efficiency of 99.8%. Single-layer 22.5 mAh Li||LiMn 2 O 4 pouch cells using LiTFSI-12C4@TTE/H 2 O electrolyte with G4 delivered a stable discharge capacity of about 1.3 mAh cm -2 for 80 cycles at 0.5 mA cm -2 .

25 ENERGY STORAGE↗

DOE OSTI2025

Positron stopping in multilayer materials

Positron annihilation spectroscopy provides a sensitive toolset for defect characterization. In beam based studies of single-layer targets, the form of implantation profiles is well established, depending on the kinetic energy and angle of incident positrons relative to the target surface and the density and average atomic number of the target. For multilayer systems, the difference in density and across the layers makes derivation of an analytical form difficult. To date, the determination of positron stopping profiles in multilayer targets has primarily involved Monte Carlo simulations. We present here an alternative approach that estimates the energy distribution dN/dE of those positrons transmitted past each layer boundary, by fitting the remaining tail of the stopping profile after each layer with a basis set comprised of calculated stopping profiles in the same material they are transmitted through. The stopping profile in the next layer is then found by summing a series of stopping profiles in the new medium in proportion to the determined distribution dN/dE. The results of our model are compared with simulation results in a system of alternating layers of Al and Au and find reasonable agreement in the predicted profile and excellent agreement in the predicted mean implantation depth. Finally, we derived a simple formula-based approach for the calculation of the mean implantation depth in two-layer systems that provides results in excellent agreement with the full model.

Jones, A. C. L. [Arizona State University, Tempe, ↗

DOE OSTI2026

Improving protonic ceramic electrochemical cell performance via a dual-phase reaction-sintered bilayer electrolyte

Protonic ceramic electrochemical cells (PCCs) are promising energy conversion devices, but their fabrication remains challenging. In particular, the typical electrolytes for PCCs such as BaCe 0.7 Zr 0.1 Y 0.1 Yb 0.1 O 3−δ (7111) and BaCe 0.4 Zr 0.4 Y 0.1 Yb 0.1 O 3−δ (4411) suffer from intrinsic barium evaporation issues during high-temperature sintering. This tendency towards barium loss, combined with their highly refractory nature, leads to a tradeoff between sinterability and chemical stability. To address this tradeoff, we propose a bilayer electrolyte combining layers of 4411 and 7111 materials that is designed to enhance sinterability and conductivity through dual-phase reactive sintering. Our findings demonstrate that the bilayer structure exhibits shrinkage behavior closely matched to that of the fuel electrode substrate, with a higher shrinkage compared to a single-layer 4411 electrolyte. Utilizing this bilayer electrolyte structure, our PCCs achieve a peak power density of 637 mW∙cm −2 in fuel-cell mode and a current density of 1060 mA∙cm −2 at 1.3 V in electrolysis mode at 600 °C. Our PCCs demonstrate high Faradaic efficiency of 83% at 1.3 V and 500 °C. Hybrid distribution of relaxation times (DRT) polarization mapping further reveals that the bilayer structure reduces Ohmic and polarization resistance in both fuel-cell and electrolysis modes.

ceramic processing↗

DOE OSTI2026

Viability of perturbative expansion for quantum field theories on neurons

Neural Network (NN) architectures that break statistical independence of parameters have been proposed as a new approach for simulating local quantum field theories (QFTs) [1]. In the infinite neuron number limit, single-layer NNs can exactly reproduce QFT results. This paper examines the viability of this architecture for perturbative calculations of local QFTs for finite neuron number N using scalar ϕ 4 theory in d Euclidean dimensions as an example. We find that the renormalized O(1/N ) corrections to two-and four-point correlators yield perturbative series which are sensitive to the UV cut-off and therefore have a weak convergence. We propose a modification to the architecture to improve this convergence and discuss constraints on the parameters of the theory and the scaling of N which allow us to extract accurate field theory results.

Sen, Srimoyee [Iowa State University, Ames, IA (Un↗

DOE OSTI2025

Quantitative surface studies of moiré intercalated Pb structures under Gr/SiC

Quantitative growth studies using surface diffraction and scanning tunneling microscopy are carried out to determine the intercalation conditions for Pb under Gr/SiC, with initial phase a mixture of buffer-layer and single-layer graphene. Intercalation is a kinetically complex, multistage process with intercalated Pb moving between different subsurface locations with annealing, eventually to the location of higher stability. The transfer is determined by monitoring the difference of a given spot intensity from its clean value, as a function of growth parameters. In addition, a broad, low-intensity (10×10) gr moiré phase is observed exclusively originating from intercalated Pb. Well-defined growth conditions are identified for the moiré spot to be observed reversibly. The (10×10) gr phase follows changes of the Pb(10) spot during growth and annealing experiments, instead of changes of the other Gr/SiC spots indicating preferred nucleation of Pb islands on the (10×10) gr domains. These structural results are discussed in connection to different models proposed for the (10×10) gr supercell and the subsurface Pb coverage. In conclusion, mass transport of subsurface Pb is unusually high, possibly because of the very high compression of the intercalated Pb, when compared to metallic Pb(111).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Time-Domain Extreme-Ultraviolet Diffuse Scattering Spectroscopy of Nanoscale Surface Phonons

Here, we report the observation of dynamic fringe patterns in the diffuse scattering of extreme ultraviolet light from surfaces, following femtosecond optical excitation. At each point on the detector, the diffuse scattering intensity exhibits oscillations at well-defined frequencies that correspond to surface phonons with wave vectors determined by the scattering geometry, indicating that the optical excitation generates coherent surface phonons propagating in all directions and spanning a wavelength range from 60 to 300 nm. This phenomenon is observed on a variety of samples, including single-layer and multilayer metal films, as well as bulk semiconductors. The measured surface phonon dispersions show good agreement with theoretical calculations. By comparing signal amplitudes from samples with different surface morphologies, we find that the excitation mechanism is linked to the natural surface roughness of the samples. However, the signal is still detectable on extremely smooth surfaces with subnanometer roughness. Our findings demonstrate a simple and effective method for optically exciting coherent surface phonons with nanoscale wavelengths on a wide range of solid samples and establish a foundation for surface phonon spectroscopy in a wave vector range well beyond the limit of conventional surface Brillouin scattering.

Capotondi, F. [Elettra-Sincrotrone Trieste (Italy)↗

DOE OSTI2025

Surface acoustic waves and lattice vibrations in two-dimensional Ti 3 ⁢C 2 ⁢𝑇 𝑥 (𝑇 =O, F) MXene films

We investigated surface acoustic wave (SAW) propagation and lattice vibrations in two-dimensional (2D) titanium carbide (Ti 3 ⁢C 2 ⁢𝑇 x ) MXene films as a function of surface termination and layer stacking, using atomistic simulations. We found that SAW propagation velocity is highly sensitive to both single-layer properties and interlayer bonding. Surface terminations significantly modulate wave behavior, with oxygen and fluorine terminations producing distinct effects on wave propagation, with oxygen-terminated monolayers exhibiting 20% higher wave speeds than fluorine counterparts due to strengthened intralayer bonds. Key observations include the transition from one to two layers causing wave speed variations, and the development of interlayer modes that generate more dispersed lattice vibrations. As the film layer thickness increases, SAW propagation becomes predominantly confined to the upper surface, with coherence of vibrational modes diminishing in multilayer structures. These findings suggest MXene terminations and layer stacking are crucial parameters for controlling SAW behavior, offering promising avenues for novel acoustic wave device applications.

2-dimensional systems↗

DOE OSTI2025

Collective Modes in Multilayer Graphene/𝛼−RuCl 3 Heterostructures

Collective modes in multilayer graphene, such as plasmons and phonons, exhibit sensitivity to displacement fields and interlayer coupling, distinguishing them from their counterparts in single-layer graphene. Here, we engineer collective modes in charge-transfer heterostructures composed of multilayer graphene and 𝛼−RuCl 3 . In heterostructures with a single 𝛼−RuCl 3 interface, the charge transfer generates displacement fields up to 7 V/nm at the interface between 𝛼−RuCl 3 and the adjacent graphene layer—the highest value achieved through charge-transfer methods. As a result of the broken inversion symmetry, we discover enhanced nonlinear optical response and modified phonon selection rules. Conversely, we find that multilayer graphene sandwiched between two 𝛼−RuCl 3 flakes causes displacement fields to cancel. There, we achieve carrier densities as high as 8 ×10 13 cm −2 in multilayer graphene and restore the phonon selection rules to their unperturbed state. Meanwhile, we demonstrate that plasmonic properties derive from the depletion of multiple valence bands. As a result of the quasilinear band dispersion, these “Dirac multiband plasmons” are relatively unaffected by displacement fields. On the other hand, the inverted heterostructure sequence—two multilayer graphene sheets encapsulating 𝛼−RuCl 3 —activates significant alteration of the plasmons via interlayer plasmon-plasmon coupling. Hence, multilayer graphene and 𝛼−RuCl 3 heterostructures offer a gate-free platform for engineering collective modes derived from inversion symmetry and interlayer coupling.

Moore, Samuel L. [Columbia University, New York, N↗

DOE OSTI2026

Enhanced two-dimensional ferromagnetism in van der Waals β-UTe 3 monolayers

The discovery of local-moment magnetism in van der Waals (vdW) semiconductors down to the single-layer limit has led to a paradigm shift in the understanding of two-dimensional (2D) magnets. The incorporation of strong electronic and magnetic correlations in 2D vdW metals remains a sought-after platform to enable control of emergent quantum phases and to achieve more theoretically tractable microscopic models of complex materials. To date, however, there is limited success in the discovery of such metallic vdW platforms, and f-electron monolayers remain out of reach. Here, we demonstrate that strongly correlated β–uranium tritelluride (β-UTe 3 ) can be exfoliated to the monolayer limit. Unexpectedly, β-UTe 3 remains ferromagnetic in this limit with an enhanced ordering temperature of 35 kelvin, a factor of two larger than its bulk counterpart. Our work establishes β-UTe 3 as a materials platform for investigating and modeling correlated behavior in the monolayer limit and opens numerous avenues for quantum control with, e.g., strain engineering.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Computational Analysis of Anode and Cathode Structuring Effects on Charge and Discharge in Graphite|LiNi 0.6 Mn 0.2 Co 0.2 O 2 Batteries

Structured electrodes (SEs) improve the rate capability of Lithium-ion batteries by engineering micrometer-scale electrolyte regions into the electrode, promoting rapid ionic transport. Prior research has focused on structuring one electrode (anode or cathode) with an analysis on either the charge or discharge performance. We present a holistic study using three-dimensional models to investigate the isolated effects of structuring either electrode and the combined effects of structuring both electrodes on the charge and discharge capacity of single-layer cells at 4 C and 6 C. Volumetric and gravimetric discharge energy density (Wh/L stack and Wh/kg stack ) and charge capacity (Ah/kg stack and Ah/L stack ) are evaluated for multi-layer pouch cell stacks. Pairing SE anodes with SE cathodes demonstrated improvements up to 15% in discharge Wh/kg stack and up to 33% in charge Ah/kg stack over a conventional cell; Energy required to charge per Ah/kg stack was improved by 13%–14%. SE cathodes paired with a conventional anode exhibited improvements of 0.3%–22% across all performance metrics evaluated. Conversely, pairing a SE anode with a conventional cathode demonstrated improved charge capacity up to 13% but showed a 2%–23% lower discharge energy density. The importance of aligning SEs in a cell from a performance and manufacturing perspective is also analyzed.

25 ENERGY STORAGE↗

DOE OSTI2026

Nanosecond dual-wavelength irradiation effects on laser-induced damage in hafnia coatings

Nanosecond dual-wavelength laser-induced damage was investigated at 1064 nm (1ω) and 355 nm (3ω) on ion-beam-sputtered hafnia single-layer coatings. Single-wavelength 1-on-1 tests were first conducted to establish reference onset fluences. Dual-wavelength tests combined a primary beam with variable fluence at one wavelength and a background, secondary wavelength beam with fixed fluences set to several percentages of the corresponding onset fluence. When 1ω was used as the background irradiation, the perceived damage resistance at 3ω decreased gradually. Here, in contrast, 3ω background irradiation at as little as 10% of the onset fluence led to an ≈ 50% abrupt reduction in the perceived 1ω damage resistance, followed by modest changes upon further increases in 3ω background fluences. Scanning electron microscopy and conversion ratios indicate that 3ω light is the primary driver of damage onset in the case of dual wavelength irradiation. A two-step precursor generation and activation model reproduces the 3ω behavior (1ω as background), but not the strong initial 1ω reduction (3ω as background), suggesting additional 3ω-induced precursors that saturate at low fluence.

Optics and optical instruments↗

DOE OSTI2025

An Investigation of Thermal Properties of 2D Materials [Dissertation]

Studying the thermal conductivity of 2D materials is important due to the applications of 2D materials in fields such as thermal management, thermoelectricity, renewable energy, and sensors. As such, measurements of the thermal conductivity of these 2D materials become important to measure. Thermal conductivity is often difficult to measure for 2D materials due to their atomically thin nature and many experimental methods for doing so requiring contact with the sample, which can alter the thermal properties. A non-contact method for calculating the thermal conductivity of 2D materials supported on substrates in order to model the thermal conductivity of 2D materials for devices, is proposed and experimentally performed in this dissertation. The optothermal Raman technique is a useful non-contact diagnostic technique useful in determining the thermal conductivity of 2D materials. The optothermal Raman typically does not account for heat losses due to convection or radiation or substrate resistance, which are shown to be important factors to consider when developing an optothermal Raman model. Additionally, the calculation of the interfacial thermal conductance between the bottom surface of the sample and the top surface of the substrate, plays an important role in determining the final value of the thermal conductivity of a supported sample, and will yield differing results based on whether or not the conductance is calculated using an approach such as the Diffuse Mismatch Model (DMM) or calculated directly by varying the laser heating profile (usually done by changing the laser objective). This is shown to be the case for both graphene on Ni, graphene on Cu, and SnSe 2 on Cu. In addition to experimentally calculating the thermal conductivity of a 2D material with the optothermal Raman technique, the thermal conductivity of 2D materials can also be calculated using computational methods. The three-phonon method is a method which can be used to simulate phonon scattering processes and determine the thermal conductivity of semiconductors, wherein phonon scattering is the dominant mechanism which determines the thermal conductivity. The three-phonon method uses relaxation times for phonon scattering with other phonons, electrons, and other material system elements, such as isotopes or material defects, in order to create a single-mode relaxation time approximation (SMRTA), which is used to calculate the final value of the thermal conductivity. An important consideration when determining the thermal conductivity of a 2D material using this method is the device geometry, which is reflected in this work as the phonon-boundary scattering relaxation time. This inclusion is important along with the inclusion of phonon-electron scattering in accurately determining the thermal conductivity of a 2D material. In both the optothermal Raman experiments and the three-phonon method computations, strain is shown to have a demonstrable effect on the thermal conductivity of 2D materials. When a 1.1% strain was applied to the mechanical properties of SnSe, the three-phonon processes yielded a lower thermal conductivity than the no-strain case. For the optothermal Raman experiments, the strain induced in the Cu substrate and transferred to a single-layer graphene (SLG) sample yields a trend where the thermal conductivity of the SLG decreases with respect to strain applied. In the case where the interfacial thermal conductance was calculated directly, the conductance increased with respect to strain applied. This presents strain as a reliable and viable method for tuning the thermal properties of 2D materials for device applications.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Mesoscale Organization in Cumulus-Coupled Stratocumulus

Marine cloud systems cover a substantial portion of the world’s oceans. Most of these clouds form relatively close to the ocean surface, typically within one to two kilometers, a region referred to by meteorologists as the marine boundary layer. They are composed predominantly of liquid water, although ice particles can occur in mid- and high-latitude marine clouds during winter. In satellite imagery, these clouds appear bright against the darker ocean surface below, reflecting a large fraction of incoming sunlight back into space that would otherwise warm the ocean. Because marine boundary layer clouds cover such an extensive area of the ocean, they exert a significant influence on Earth’s overall transfer of solar energy absorbed by the surface and thermal energy emitted to space, a balance known as the planetary radiation budget. Marine boundary layer clouds are typically thin, and their formation and dissipation depend on a delicate balance between processes acting at the ocean surface below and the warm, dry air above. They are notoriously difficult to simulate accurately in weather forecast models, which often produce too few marine low clouds in midlatitudes and clouds in tropical regions that are excessively bright, meaning they reflect too much solar radiation. The marine boundary layer is frequently characterized by widespread overcast cloud cover that often transitions from a continuous, single-layer deck to more broken cloud fields toward the tropics. These transitions typically proceed through an intermediate stage in which shallow, broken clouds form beneath the overlying stratiform cloud deck. Once broken clouds develop below the overcast, they frequently self-organize into cloud clusters known as marine boundary layer convective complexes (MBLCCs), although the mechanisms governing the formation and organization of MBLCCs remain poorly understood. Accurately representing these transitions in long-range weather forecast models is essential because they influence the properties of air masses advected over the continental United States and Europe, and they become increasingly important for forecasts on seasonal and longer timescales. We employed two complementary approaches to investigate the processes controlling MBLCCs and their impact on marine cloud cover. Long-term observations from the U.S. Department of Energy’s Eastern North Atlantic (ENA) Observatory provided a unique dataset that allowed us to characterize fundamental properties of MBLCCs, including their typical size and frequency of occurrence. These observations were combined with high-resolution numerical simulations performed on supercomputers to examine the evolution of MBLCCs during cold-air outbreaks over the ENA region.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Radiative Cooling Paints: Application on Warehouses and Integration with Phase Change Materials

Despite extensive research on radiative cooling (RC), researchers are still working to understand its best implementation strategy and potential benefits. Understanding this could be an instrumental part of reducing building energy costs and combating climate change. In this work, we introduce two concepts to achieve this goal and broaden the application of RC paints. While building energy simulations for RC are common, most studies focus on single-layer paints in residential settings. Limited research exists on warehouses, and no literature has conducted multi-climate zone analyses or included RC technologies with >90% reflectance. As RC technology advances in efficiency, versatility, and affordability, large-scale simulations across diverse climates are crucial, particularly for warehouses as a passive indoor temperature control solution. Here, a TRNSYS-modeled single-story warehouse assesses the energy impact of BaSO4-based RC paints. Another under-explored RC application is its integration with phase change materials (PCMs), which provide thermal regulation via latent heat storage. Though RC and PCMs have been combined by placing PCMs atop, beneath, or within RC layers, studies focus on either experiments or modeling, with no validation between the two. Here, we develop a simple RC+PCM experimental and modeling setup, placing RC paint atop an aluminum cell filled with a Rubitherm PCM.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2025

Marine Boundary Layer Cloud Boundaries and Phase Estimation Using Airborne Radar and In Situ Measurements During the SOCRATES Campaign over Southern Ocean

The Southern Ocean Clouds, Radiation, Aerosol Transport Experimental Study (SOCRATES) was an aircraft-based campaign (15 January–26 February 2018) that deployed in situ probes and remote sensors to investigate low-level clouds over the Southern Ocean (SO). A novel methodology was developed to identify cloud boundaries and classify cloud phases in single-layer, low-level marine boundary layer (MBL) clouds below 3 km using the HIAPER Cloud Radar (HCR) and in situ measurements. The cloud base and top heights derived from HCR reflectivity, Doppler velocity, and spectrum width measurements agreed well with corresponding lidar-based and in situ estimates of cloud boundaries, with mean differences below 100 m. A liquid water content–reflectivity (LWC-Z) relationship, LWC = 0.70Z0.29, was derived to retrieve the LWC and liquid water path (LWP) from HCR profiles. The cloud phase was classified using HCR measurements, temperature, and LWP, yielding 40.6% liquid, 18.3% mixed-phase, and 5.1% ice samples, along with drizzle (29.1%), rain (3.2%), and snow (3.7%) for drizzling cloud cases. The classification algorithm demonstrates good consistency with established methods. This study provides a framework for the boundary and phase detection of MBL clouds, offering insights into SO cloud microphysics and supporting future efforts in satellite retrievals and climate model evaluation.

MBL clouds over Southern Ocean↗

DOE OSTI2026

Occurrence of seeding multi-layer clouds in the Arctic from ground-based observations

Studies of Arctic clouds often focus on low-level single-layer clouds (SLCs). Here, we use combined observations of soundings and cloud radar during the MOSAiC, ACSE, and AO2018 research cruises as well as from long-term observations at Ny-Ålesund, Svalbard and Utqiagvik, Alaska to investigate the occurrence of SLCs and multi-layer clouds (MLCs) in the Arctic and to assess the rate of ice-crystal seeding in cold MLCs. MOSAiC observations show cloudy conditions in between 70 % and 90 % of sounding-radar cases. SLCs show occurrence rates of 30 % to 40 % with the highest value of 45 % during October. Cold MLCs are most abundant from November to June (40 % to 55 % of cases). Seeding occurs in about half to two thirds of the identified cold MLCs during MOSAiC for which the sub-saturated layer extends between 100 and 1000 m. The seeding rate increases by as much as 20 percentage points as the assumed size of the falling ice crystals is increased from 100 to 400 µm. The observations reveal a stable rate of cloud-free conditions of around 20 % over the covered latitude range. Cloud occurrence during MOSAiC and at Ny-Ålesund in July, when the geographical distance between observations was minimal, shows reasonable agreement. Comparisons of MOSAiC and other research cruises to the central Arctic also indicate consistent occurrence rates of different cloud types despite the likely effect of year-to-year variability. The comparison of data from ship campaigns and land sites suggests that the latter are not necessarily a good indicator of cloud occurrence in the high Arctic.

Achtert, Peggy [Leipzig Univ. (Germany); Meteorolo↗

DOE OSTI2025

Urban weather modeling using WRF: linking physical assumptions, code implementation, and observational needs

The Weather Research and Forecasting (WRF) model includes urban schemes that simulate the influence of urban surfaces on the atmosphere using parameterizations for flux, and radiative exchanges. Three core schemes – the Bulk urban parameterization, Single-Layer Urban Canopy Model (SLUCM), and Multi-Layer Urban Canopy Model (MLUCM) – represent increasing levels of complexity. Although the parameterizations within these urban schemes are described in the literature, their specific implementation remains poorly documented, thus slowing down model development efforts. This manuscript provides a roadmap to the three urban schemes in WRF version 4.5.2, presenting equations using the same symbols as in the model code, along with references to code lines, and including graphics and explanations that connect the code to its physical foundations. Our thorough review of the urban parameterizations implemented in WRF version 4.5.2 highlighted a handful of parameters that may introduce discontinuities in simulations: (i) in the SLUCM, a 1 mm h −1 rain rate threshold is employed to switch between two minimum moisture availability parameterizations, thus impacting latent heat flux calculations; (ii) in the SLUCM a threshold is used to partition shortwave radiation into direct and diffuse components; (iii) in all three urban schemes, the bulk Richardson number is employed to select the similarity function, which influences the vertical distribution of heat and momentum. We also identified a highly simplified treatment of the radiative balance on roof surfaces. The implications of these simplifications can be assessed through targeted observations across relevant conditions, including varying precipitation rates, cloud cover, and transitions between stability regimes. Furthermore, the widespread application of the Monin-Obukhov similarity theory in these urban schemes warrants model evaluation under highly stable and unstable conditions and in heterogeneous urban settings with variable land cover and building heights on scales finer than model resolution. To address these challenges, we offer guidance on observational strategies, emphasizing the need for multi-parametric measurements to capture potential compensating biases and multi-height measurements that align with the levels where quantities are diagnostic and prognosed in the model (i.e., the lowest atmospheric level of the WRF model). Finally, our inspection of the code revealed implementation bugs that have now been corrected in WRF versions 4.6.0 and 4.6.1. Sensitivity tests over the Atlanta urban area show that these corrections affect surface temperatures, underscoring the importance of performing rigorous documentation and verification of the implementation of parameterizations in model code.

54 ENVIRONMENTAL SCIENCES↗