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At least 1,369 records · Page 76
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Large-eddy simulation of an atmospheric bore and associated gravity wave effects on wind farm performance in the southern Great Plains

Gravity waves are a common occurrence in the atmosphere, with a variety of generation mechanisms. Their impact on wind farms has only recently gained attention, with most studies focused on wind farm-induced gravity waves. In this study, the interaction between a wind farm and gravity waves generated by an atmospheric bore event is assessed using multiscale large-eddy simulations. The atmospheric bore is created by a thunderstorm downdraft from a nocturnal mesoscale convective system (MCS). The associated gravity waves impact the wind resource and power production at a nearby wind farm during the American Wake Experiment (AWAKEN) in the US southern Great Plains. A two-domain nested setup (Δx=300 and 20 m) is used in the Weather Research and Forecasting (WRF) model, forced with data from the High-Resolution Rapid Refresh model, to capture both the formation of the bore and its interaction with individual wind turbines. The MCS is resolved on the large outer domain, where the structure of the bore and the associated gravity waves are found to be especially sensitive to parameterized microphysics processes. On the finer inner domain, gravity wave interactions with individual wind turbines are resolved; wake dynamics are captured using a generalized actuator disk parameterization in WRF. The gravity waves are found to have a strong effect on the atmosphere above the wind farm; however, the effect of the waves is more nuanced closer to the surface where there is additional turbulence, both ambient and wake-generated. Notably, the gravity waves modulate the mesoscale environment by weakening and dissipating the preexisting low-level jet, which reduces hub-height wind speed and hence the simulated power output, which is confirmed by the observed supervisory control and data acquisition (SCADA) power data. Additionally, the gravity waves induce local wind direction variations correlated with fluctuations in pressure, which lead to fluctuations in the simulated power output as various turbines within the farm are subjected to waking from nearby turbines.

17 WIND ENERGY↗
DOE OSTI2025

Assessing time-dependent temperature profile predictions using reduced transport models for high performing NSTX plasmas

Time-dependent, predictive simulations were performed with the 1.5D tokamak integrated modeling code TRANSP on a large set of well-analyzed, high performing discharges from the National Spherical Torus Experiment (NSTX) in order to evaluate how well modern reduced transport models can reproduce experimentally observed temperature profiles in spherical tokamaks. Overall, it is found that simulations using the Multi-Mode Model (MMM) more consistently agree with the NSTX observations than those using the Trapped Gyro-Landau Fluid (TGLF) model, despite TGLF requiring orders of magnitude greater computational cost. When considering all examined discharges, MMM has median overpredictions of electron temperature (T e ) and ion temperature (T i ) profiles of 28% and 27%, respectively, relative to the experiment. TGLF overpredicts T e by 46%, with much larger variance than MMM, and underpredicts T i by 25%. As the ratio of kinetic to magnetic field pressure (β) is increased across NSTX discharges, TGLF predicts lower T e and significant flattening of the T i profile, conflicting with NSTX observations. When using an electrostatic version of TGLF, both T e and T i are substantially overpredicted, underscoring the importance of electromagnetic turbulence in the high β spherical tokamak regime. Additionally, calculations with neural net surrogate models for TGLF were performed outside of TRANSP with a time slice flux matching transport solver, finding better agreement with experiment than the TRANSP simulations, highlighting the impact of different transport solvers and simulation techniques. Furthermore, the reasonable agreement with experiment of temperature profiles predicted by MMM motivates a more detailed examination of the sensitivities of the TRANSP simulations with MMM to different NSTX plasma regimes in a companion paper (Lestz et al Plasma Phys. Control. Fusion 67 105030), in preparation for self-consistent, time-dependent predictive modeling of NSTX-U scenarios.

Lestz, J. B. [General Atomics, San Diego, CA (Unit↗
DOE OSTI2023

Electron heating in kinetic-Alfvén-wave turbulence

We report analytical and numerical investigations of subion-scale turbulence in low-beta plasmas using a rigorous reduced kinetic model. We show that efficient electron heating occurs and is primarily due to Landau damping of kinetic Alfvén waves, as opposed to Ohmic dissipation. This collisionless damping is facilitated by the local weakening of advective nonlinearities and the ensuing unimpeded phase mixing near intermittent current sheets, where free energy concentrates. The linearly damped energy of electromagnetic fluctuations at each scale explains the steepening of their energy spectrum with respect to a fluid model where such damping is excluded (i.e., a model that imposes an isothermal electron closure). In conclusion, the use of a Hermite polynomial representation to express the velocity-space dependence of the electron distribution function enables us to obtain an analytical, lowest-order solution for the Hermite moments of the distribution, which is borne out by numerical simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Predicting the impact of particle-particle collisions on turbophoresis with a reduced number of computational particles

A common feature of wall-bounded turbulent particle-laden flows is enhanced particle concentrations in a thin layer near the wall due to a phenomenon known as turbophoresis. Even at relatively low bulk volume fractions, particle-particle collisions regulate turbophoresis in a critical way, making simulations sensitive to collisional effects. Lagrangian tracking of every particle in the flow can become computationally expensive when the physical number of particles in the system is large. Artificially reducing the number of particles in the simulation can mitigate the computational cost. When particle-particle collisions are an important aspect determining the simulation outcome, as in the case when turbophoresis plays an active role, simply reducing the number of particles in the simulation significantly alters the computed particle statistics. This paper introduces a computational particle treatment for particle-particle collisions which reproduces the results of a full simulation with a reduced number of particles. This is accomplished by artificially enhancing the particle collision radius based on scaling laws for the collision rates. The proposed method retains the use of deterministic collision models and is applicable for both low and high Stokes number regimes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

A New Hybrid Mass-Flux/High-Order Turbulence Closure for Ocean Vertical Mixing

While various parameterizations of vertical turbulent fluxes at different levels of complexity have been proposed, each has its own limitations. For example, simple first-order closure schemes such as the K-Profile Parameterization (KPP) lack energetic constraints; two-equation models $k-ε$ like directly solve an equation for the turbulent kinetic energy but do not account for non-diffusive fluxes, and high-order closures that include the high-order transport terms are computationally expensive. To address these, we extend the Assumed-Distribution Higher-Order Closure (ADC) framework originally proposed for the atmospheric boundary layer and apply it to the ocean surface boundary layer. By assuming a probability distribution function relationship between the vertical velocity and tracers, all second-order and higher-order moments are exactly constructed and turbulence closure is achieved in the ADC scheme. In addition, this ADC parameterization has full energetic constraints and includes non-diffusive fluxes without the computational cost of a full higher-order closure scheme. We have tested the ADC scheme against a combination of large eddy simulation (LES), KPP, and $k-ε$ for surface buoyancy-driven convective mixing and found that the ADC scheme is robust with different vertical resolutions and compares well to the LES results.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Deep learning interfacial momentum closures in coarse-mesh CFD two-phase flow simulation using validation data

Multiphase flow phenomena have been widely observed in the industrial applications while it remains a challenging yet unsolved problems. Three-dimensional computational fluid dynamics (CFD) approaches resolve the flow fields on a finer special and temporal scales which can complement the dedicated experimental study. However, closures have to be introduced to reflect the underlying physics in multiphase flow. Among them, the interfacial forces, including drag, lift, turbulent dispersion and wall lubrication forces, play in important role on the bubble’s distribution and migration in liquid-vapor two-phase flow. Development of those closures traditionally rely on the experimental data and analytical derivation with simplified assumptions which usually cannot deliver a universal solution across wide range of flow conditions. In this paper, a data-driven approach, named as Feature Similarity Measurement (FSM), is developed and applied to improve the simulation capability of two-phase flow with coarse-mesh CFD approach. Interfacial momentum transfer in adiabatic bubbly flow serves as the focus of the present study. Both a mature and a simplified set of interfacial closures are taken as the low fidelity data. Experimental data and fine mesh CFD simulations results are adopted as high-fidelity data. Qualitative and quantitative analysis are performed in this paper which reveals that FSM can substantially improve the prediction of coarse mesh CFD model regardless of the choice of interfacial closures and it provides scalability and consistency across discontinuous flow regimes. Furthermore, it demonstrates that data-driven method can aid the multiphase flow modeling by exploring the connections between local physical features and simulation errors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Aeroacoustics Noise Model of OpenFAST

The report describes theory and application of a newly released module of OpenFAST to simulate the aeroacoustic noise generated by the rotor of an arbitrary wind turbine. OpenFAST is a fully open-source publicly available wind turbine analysis tool actively developed at the National Renewable Energy Laboratory. The aeroacoustic module, which is also fully open-source and publicly available, is based on work performed over the past three decades. Frequency-based models for turbulent inflow, turbulent boundary layer – trailing edge, laminar boundary layer – vortex shedding, tip vortex, and trailing edge bluntness – vortex shedding noise mechanisms are included. A simple directivity model is also included. The appendices of this report describe in detail the inputs to the module and how to find them in the input files of OpenFAST. The noise models are exercised simulating the aeroacoustic noise emissions of the IEA Wind Task 37 land-based reference wind turbine. A code-to-code comparison between the implementation presented here and the implementation available at the Wind Energy Institute of the Technical University of Munich, Germany, is also presented.

17 WIND ENERGY↗
DOE OSTI2024

Visualization of post-detonation fireball flowfields and comparison to CFD modeling

Visualization of flow structures within post-detonation fireballs has been performed for benchmark validation of numerical simulations. Custom pressed PETN explosives with a 12-mm diameter hemispherical form factor were used to produce a spherically symmetric post-detonation flow with low soot yield. Hydroxyl-radical planar laser induce fluorescence (OH-PLIF) was employed to visualize the structure ranging from approximately 10 μs to 35 μs after shock breakout from the explosive pellet. Fireball simulations were performed using the HyBurn Computational Fluid Dynamics (CFD) package. Experimental OH-PLIF results were compared to synthetic OH-PLIF from post-processing of CFD simulations. From the comparison of experimental and synthetic OH-PLIF images, CFD is shown to replicate much of the flow structure observed in the experiments, revealing potential differences in turbulent length scales and OH kinetics. Furthermore, results provide significant advancement in experimental resolution of these harsh turbulent combustion environments and validate physical models thereof.

Detonator↗
DOE OSTI2020

Enlarged Nonclosure of Surface Energy Balance With Increasing Atmospheric Instabilities Linked to Changes in Coherent Structures

The nonclosure of surface energy balance remains an outstanding problem in eddy covariance (EC) measurements of land-surface fluxes of heat, water vapor, and CO 2 . Our data collected from an EC tower over a semiarid sagebrush ecosystem indicate that under unstable atmospheric conditions, the nonclosure becomes increased with increasing instability, consistent with many other studies. It is demonstrated that the increased nonclosure is not caused by the inadequate sampling of large-scale turbulent motions using a 30-min averaging interval, though the scales of turbulent motions dominating sensible and latent heat fluxes become enlarged with increasing instability. Quadrant analysis is then used to reveal that the flux contributions from ejections remain nearly constant with increasing instability, whereas the flux contributions from sweeps are reduced and their time fractions increase. Our results imply that the increased nonclosure of surface energy balance is associated with changes in turbulent structures including their dominant time scales and flux contributions of ejections and sweeps as the atmospheric instability increases, which require further studies using vertically distributed observations and/or large eddy simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

The theoretical study on intermittency and propagation of geodesic acoustic mode in L-mode discharge near tokamak edge

Abstract Through a systematically developed theory, we demonstrate that the motion of Instanton identified in Zhang et al (2017 Phys. Plasmas 24 122304) is highly correlated to the intermittent excitation and propagation of geodesic acoustic mode (GAM) that is observed in tokamaks. While many numerical simulations have observed the phenomena, it is the first theory that reveals the physical mechanism behind GAM intermittent excitation and propagation. The preceding work is based on the micro-turbulence associated with toroidal ion temperature gradient mode, and slab-based phenomenological model of zonal flow. When full toroidal effect is introduced into the system, two branches of zonal flow emerge: the torus-modified low frequency zonal flow (TLFZF), and GAM, necessitating a unified exploration of GAM and TLFZF. Indeed, we observe that the transition from the Caviton to Instanton is triggered by a rapid zero-crossing of radial group velocity of drift wave and is found to be strongly correlated with the GAM onset. Many features peculiar to intermittent GAMs, observed in real machines, are thus identified in the numerical experiment. The results will be displayed in figures and in a movie; first for single central rational surface, and then with coupled multiple central rational surfaces. The periodic bursting first shown disappears as being replaced by irregular one, more similar to the intermittent characteristics observed in GAM experiments.

Physics↗
DOE OSTI2024

ATom (Acoustic Tomography Processing Suite) [SWR-24-120]

Acoustic tomography seeks the best-fit fluctuating velocity and temperature fields that explain a collection of signal travel times in a region of interest. This codebase defines an end-to-end framework for executing turbulent field retrievals from acoustic signals, acoustic signal design and processing tools for the physical array, and analysis tool that leverage virtual acoustic tomography arrays based on large-eddy simulations of the atmospheric boundary layer.

Hamilton, Nicholas↗
DOE OSTI2023

Biomass-burning smoke's properties and its interactions with marine stratocumulus clouds in WRF-CAM5 and southeastern Atlantic field campaigns

Abstract. A large part of the uncertainty in climate projections comes from uncertain aerosol properties and aerosol–cloud interactions as well as the difficulty in remotely sensing them. The southeastern Atlantic functions as a natural laboratory to study biomass-burning smoke and to constrain this uncertainty. We address these gaps by comparing the Weather Research and Forecasting with Chemistry Community Atmosphere Model (WRF-CAM5) to the multi-campaign observations ORACLES (ObseRvations of Aerosols above CLouds and their intEractionS), CLARIFY (CLoud–Aerosol–Radiation Interaction and Forcing), and LASIC (Layered Atlantic Smoke Interactions with Clouds) in the southeastern Atlantic in August 2017 to evaluate a large range of the model's aerosol chemical properties, size distributions, processes, and transport, as well as aerosol–cloud interactions. Overall, while WRF-CAM5 is able to represent smoke properties and transport, some key discrepancies highlight the need for further analysis. Observations of smoke composition show an overall decrease in aerosol mean diameter as smoke ages over 4–12 d, while the model lacks this trend. A decrease in the mass ratio of organic aerosol (OA) to black carbon (BC), OA:BC, and the OA mass to carbon monoxide (CO) mixing ratio, OA:CO, suggests that the model is missing processes that selectively remove OA from the particle phase, such as photolysis and heterogeneous aerosol chemistry. A large (factor of ∼2.5) enhancement in sulfate from the free troposphere (FT) to the boundary layer (BL) in observations is not present in the model, pointing to the importance of properly representing secondary sulfate aerosol formation from marine dimethyl sulfide and gaseous SO2 smoke emissions. The model shows a persistent overprediction of aerosols in the marine boundary layer (MBL), especially for clean conditions, which multiple pieces of evidence link to weaker aerosol removal in the modeled MBL than reality. This evidence includes several model features, such as not representing observed shifts towards smaller aerosol diameters, inaccurate concentration ratios of carbon monoxide and black carbon, underprediction of heavy rain events, and little evidence of persistent biases in modeled entrainment. The average below-cloud aerosol activation fraction (NCLD/NAER) remains relatively constant in WRF-CAM5 between field campaigns (∼0.65), while it decreases substantially in observations from ORACLES (∼0.78) to CLARIFY (∼0.5), which could be due to the model misrepresentation of clean aerosol conditions. WRF-CAM5 also overshoots an observed upper limit on liquid cloud droplet concentration around NCLD= 400–500 cm−3 and overpredicts the spread in NCLD. This could be related to the model often drastically overestimating the strength of boundary layer vertical turbulence by up to a factor of 10. We expect these results to motivate similar evaluations of other modeling systems and promote model development to reduce critical uncertainties in climate simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Pressure–Strain Interaction as the Energy Dissipation Estimate in Collisionless Plasma

The dissipative mechanism in weakly collisional plasma is a topic that pervades decades of studies without a consensus solution. We compare several energy dissipation estimates based on energy transfer processes in plasma turbulence and provide justification for the pressure–strain interaction as a direct estimate of the energy dissipation rate. The global and scale-by-scale energy balances are examined in 2.5D and 3D kinetic simulations. We show that the global internal energy increase and the temperature enhancement of each species are directly tracked by the pressure–strain interaction. The incompressive part of the pressure–strain interaction dominates over its compressive part in all simulations considered. The scale-by-scale energy balance is quantified by scale filtered Vlasov–Maxwell equations, a kinetic plasma approach, and the lag dependent von Kármán–Howarth equation, an approach based on fluid models. We find that the energy balance is exactly satisfied across all scales, but the lack of a well-defined inertial range influences the distribution of the energy budget among different terms in the inertial range. Therefore, the widespread use of the Yaglom relation in estimating the dissipation rate is questionable in some cases, especially when the scale separation in the system is not clearly defined. In contrast, the pressure–strain interaction balances exactly the dissipation rate at kinetic scales regardless of the scale separation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Logarithmic profile of temperature in sheared and unstably stratified atmospheric boundary layers

The impact of buoyancy on the mean velocity, temperature, and scalar concentration profiles in the lower atmosphere is typically investigated within the framework of Monin-Obukhov similarity theory (MOST). MOST is the theoretical foundation for parametrizing surface-atmosphere exchanges in nearly all weather, climate, and hydrological models.According to MOST, the classic logarithmic profiles of mean velocity and temperature break down as the buoyancy effects become important. However, recent studies on turbulent Rayleigh-Bénard convection and natural convection along vertical walls suggest that the mean temperature in the near-surface region still follows a logarithmic profile.Motivated by these new results, we study the mean potential temperature profile in sheared and unstably stratified atmospheric boundary layers using direct numerical simulations and field observations. We find that the mean potential temperature profile remains logarithmic across a wide range of stability parameters, which characterizes the relative importance of buoyancy versus shear effects. Compared to MOST, our results suggest that the buoyancy force does not modify the logarithmic nature of the mean potential temperature profile, but instead modulates its slope, which is no longer universal and differs from 1/κ,whereκisthe von Kármán constant. Furthermore, this study provides another perspective on scalar turbulence in the atmospheric boundary layer

58 GEOSCIENCES↗
DOE OSTI2023

Stratospheric temperature measurements from nanosatellite stellar occultation observations of refractive bending

Abstract. Stellar occultation observations from space can probe the stratosphere and mesosphere at a fine vertical scale around the globe. Unlike other measurement techniques like radiosondes and aircraft, stellar occultation has the potential to observe the atmosphere above 30 km, and unlike radio occultation, stellar occultation probes fine-scale phenomena with potential to observe atmospheric turbulence. We imaged the refractive bending angle of a star centroid for a series of occultations by the atmosphere. Atmospheric refractivity, density, and then temperature are retrieved from the bending observations with the Abel transformation and Edlén's law, the hydrostatic equation, and the ideal gas law. The retrieval technique is applied to data collected by two nanosatellites operated by Terran Orbital. Measurements were primarily taken by the GEOStare SV2 mission, with a dedicated imaging telescope, supplemented with images captured by spacecraft bus sensors, namely the star trackers on other Terran Orbital missions. The bending angle noise floor is 10 and 30 arcsec for the star tracker and GEOStare SV2 data, respectively. The most significant sources of uncertainty are due to centroiding errors due to the fairly low-resolution stellar images and telescope pointing knowledge derived from noisy satellite attitude sensors. The former mainly affects the star tracker data, while the latter limits the GEOStare SV2 accuracy, with both providing low vertical resolution. This translates to a temperature profile retrieval up to roughly 20 km for both star tracker and GEOStare SV2 datasets. In preparation of an upcoming 2023 mission designed to correct these deficiencies, SOHIP, we simulated bending angle measurements with varying magnitudes of error. The expected maximum altitude of retrieved temperature is 41 km on average for these simulated measurements with a noise floor of 0.39 arcsec. Our work highlights the capabilities of stellar occultation observations from nanosatellites for atmospheric sounding. Future work will investigate high-frequency observations of atmospheric gravity waves and turbulence, mitigating the major uncertainties observed in these datasets.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Radiation GRMHD simulations of M87: funnel properties and prospects for gap acceleration

Here, we use the public code EBHLIGHT to carry out 3D radiative general relativistic magnetohydrodynamics (GRMHD) simulations of accretion on to the supermassive black hole in M87. The simulations self-consistently evolve a frequency-dependent Monte Carlo description of the radiation field produced by the accretion flow. We explore two limits of accumulated magnetic flux at the black hole (SANE and MAD), each coupled to several subgrid prescriptions for electron heating that are motivated by models of turbulence and magnetic reconnection. We present convergence studies for the radiation field and study its properties. We find that the near-horizon photon energy density is an order of magnitude higher than is predicted by simple isotropic estimates from the observed luminosity. The radially dependent photon momentum distribution is anisotropic and can be modeled by a set of point-sources near the equatorial plane. We draw properties of the radiation and magnetic field from the simulation and feed them into an analytic model of gap acceleration to estimate the very high energy (VHE) γ-ray luminosity from the magnetized jet funnel, assuming that a gap is able to form. We find luminosities of $\rm \sim 10^{41} \, erg \, s^{-1}$ for MAD models and $\rm \sim 2\times 10^{40} \, erg \, s^{-1}$ for SANE models, which are comparable to measurements of M87’s VHE flares. The time-dependence seen in our calculations is insufficient to explain the flaring behaviour. Our results provide a step towards bridging theoretical models of near-horizon properties seen in black hole images with the VHE activity of M87.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Physics-driven Explosions of Stripped High-mass Stars: Synthetic Light Curves and Spectra of Stripped-envelope Supernovae with Broad Light Curves

Stripped-envelope supernovae (SESNe) represent a significant fraction of core-collapse supernovae, arising from massive stars that have shed their hydrogen and, in some cases, helium envelopes. The origins and explosion mechanisms of SESNe remain a topic of active investigation. In this work, we employ radiative-transfer simulations to model the light curves and spectra of a set of explosions of single, solar-metallicity, massive Wolf–Rayet stars with ejecta masses ranging from 4 to 11 M ⊙ , which were computed from a turbulence-aided and neutrino-driven explosion mechanism. We analyze these synthetic observables to explore the impact of varying ejecta mass and helium content on observable features. We find that the light curve shape of these progenitors with high ejecta masses is consistent with observed SESNe with broad light curves but not the peak luminosities. The commonly used analytic formula based on rising bolometric light curves overestimates the ejecta mass of these high-initial-mass progenitor explosions by a factor of up to 2.6. In contrast, the calibrated method by Haynie et al., which relies on late-time decay tails, reduces uncertainties to an average of 20% within the calibrated ejecta mass range. Spectroscopically, the He I 1.083 μm line remains prominent even in models with as little as 0.02 M ⊙ of helium. However, the strength of the optical He I lines is not directly proportional to the helium mass but instead depends on a complex interplay of factors such as the 56 Ni distribution, composition, and radiation field. Thus, producing realistic helium features requires detailed radiative transfer simulations for each new hydrodynamic model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Representation of atmosphere-induced heterogeneity in land–atmosphere interactions in E3SM–MMFv2

In the Energy Exascale Earth System Model (E3SM) Multi-scale Modeling Framework (MMF), where parameterizations of convection and turbulence are replaced by a 2-D cloud-resolving model (CRM), there are multiple options to represent land–atmosphere interactions. Here, we propose three different coupling strategies, namely the (1) coupling of a single land surface model to the global grid (MMF), (2) coupling a single land copy directly to the embedded CRM (SFLX2CRM), and (3) coupling a single copy of land model to each column of the CRM grid (MAML). In the MAML (Multi-Atmosphere Multi-Land) framework, a land model is coupled to CRM at the CRM-grid scale by coupling an individual copy of a land model to each CRM grid. Therefore, we can represent intra-CRM heterogeneity in the land–atmosphere interaction processes. There are 5-year global simulations run using these three coupling strategies, and we find some regional differences but overall small changes with respect to whether a land model is coupled to CRM or a global atmosphere. In MAML, the spatial heterogeneity within CRM induces stronger turbulence, which leads to the changes in soil moisture, surface heat fluxes, and precipitation. However, the differences in the MAML from the other two cases are rather weak, suggesting that the impact of using MAML does not justify the increase in cost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗