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DOE OSTI2025

Understanding Model Inadequacy in TRISO Nuclear Fuel Fission Products Release Models: Empirical and Mechanistic Approaches

The increasing use of tristructural isotropic (TRISO) particle fuel in both advanced and existing reactors necessitates a thorough evaluation of uncertainties and shortcomings in TRISO fission product release models. These inadequacies arise from the simplifications made in computational models compared to experimental data. Utilizing the BISON fuel performance code and experimental data from the Advanced Gas Reactor (AGR) program provides a unique chance to rigorously assess these inadequacies within a Bayesian uncertainty quantification (UQ) framework. This study contrasts the standard Bayesian framework with the Kennedy-O'Hagan (KOH) framework, which explicitly accounts for modeling inadequacies, in the context of UQ for TRISO silver release models. It examines both the traditional Arrhenius equation and a more advanced lower-length-scale (LLS)-informed model that incorporates microstructure information. The inverse UQ process applied to AGR-2 and AGR-3/4 datasets identified modeling inadequacy as the primary source of uncertainty, with experimental noise also being significant, while model parameter uncertainty was minimal. Both the Arrhenius and LLS-informed models showed similar levels of modeling inadequacy. For forward predictive UQ using the AGR-1 dataset, the KOH framework enhanced the accuracy and quality of quantified uncertainties by approximately 30% and 40%, respectively, compared to the standard Bayesian framework. This improvement was observed for both the Arrhenius and LLS-informed models. At the engineering scale, both models performed similarly, but the LLS-informed model outperformed the Arrhenius equation at the mesoscale. These findings underscore the importance of explicitly considering modeling inadequacy in the UQ process and highlight the need for ongoing refinement of physics-based models to address these shortcomings.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2007

GPS-Based Reduced Dynamic Orbit Determination Using Accelerometer Data

Currently two gravity field satellite missions, CHAMP and GRACE, are equipped with high sensitivity electrostatic accelerometers, measuring the non-conservative forces acting on the spacecraft in three orthogonal directions. During the gravity field recovery these measurements help to separate gravitational and non-gravitational contributions in the observed orbit perturbations. For precise orbit determination purposes all these missions have a dual-frequency GPS receiver on board. The reduced dynamic technique combines the dense and accurate GPS observations with physical models of the forces acting on the spacecraft, complemented by empirical accelerations, which are stochastic parameters adjusted in the orbit determination process. When the spacecraft carries an accelerometer, these measured accelerations can be used to replace the models of the non-conservative forces, such as air drag and solar radiation pressure. This approach is implemented in a batch least-squares estimator of the GPS High Precision Orbit Determination Software Tools (GHOST), developed at DLR/GSOC and DEOS. It is extensively tested with data of the CHAMP and GRACE satellites. As accelerometer observations typically can be affected by an unknown scale factor and bias in each measurement direction, they require calibration during processing. Therefore the estimated state vector is augmented with six parameters: a scale and bias factor for the three axes. In order to converge efficiently to a good solution, reasonable a priori values for the bias factor are necessary. These are calculated by combining the mean value of the accelerometer observations with the mean value of the non-conservative force models and empirical accelerations, estimated when using these models. When replacing the non-conservative force models with accelerometer observations and still estimating empirical accelerations, a good orbit precision is achieved. 100 days of GRACE B data processing results in a mean orbit fit of a few centimeters with respect to high-quality JPL reference orbits. This shows a slightly better consistency compared to the case when using force models. A purely dynamic orbit, without estimating empirical accelerations thus only adjusting six state parameters and the bias and scale factors, gives an orbit fit for the GRACE B test case below the decimeter level. The in orbit calibrated accelerometer observations can be used to validate the modelled accelerations and estimated empirical accelerations computed with the GHOST tools. In along track direction they show the best resemblance, with a mean correlation coefficient of 93% for the same period. In radial and normal direction the correlation is smaller. During days of high solar activity the benefit of using accelerometer observations is clearly visible. The observations during these days show fluctuations which the modelled and empirical accelerations can not follow.

VanHelleputte, Tom↗

NASA NTRS2013

The Ocean Colour Climate Change Initiative: III. A Round-Robin Comparison on In-Water Bio-Optical Algorithms

Satellite-derived remote-sensing reflectance (Rrs) can be used for mapping biogeochemically relevant variables, such as the chlorophyll concentration and the Inherent Optical Properties (IOPs) of the water, at global scale for use in climate-change studies. Prior to generating such products, suitable algorithms have to be selected that are appropriate for the purpose. Algorithm selection needs to account for both qualitative and quantitative requirements. In this paper we develop an objective methodology designed to rank the quantitative performance of a suite of bio-optical models. The objective classification is applied using the NASA bio-Optical Marine Algorithm Dataset (NOMAD). Using in situ Rrs as input to the models, the performance of eleven semianalytical models, as well as five empirical chlorophyll algorithms and an empirical diffuse attenuation coefficient algorithm, is ranked for spectrally-resolved IOPs, chlorophyll concentration and the diffuse attenuation coefficient at 489 nm. The sensitivity of the objective classification and the uncertainty in the ranking are tested using a Monte-Carlo approach (bootstrapping). Results indicate that the performance of the semi-analytical models varies depending on the product and wavelength of interest. For chlorophyll retrieval, empirical algorithms perform better than semi-analytical models, in general. The performance of these empirical models reflects either their immunity to scale errors or instrument noise in Rrs data, or simply that the data used for model parameterisation were not independent of NOMAD. Nonetheless, uncertainty in the classification suggests that the performance of some semi-analytical algorithms at retrieving chlorophyll is comparable with the empirical algorithms. For phytoplankton absorption at 443 nm, some semi-analytical models also perform with similar accuracy to an empirical model. We discuss the potential biases, limitations and uncertainty in the approach, as well as additional qualitative considerations for algorithm selection for climate-change studies. Our classification has the potential to be routinely implemented, such that the performance of emerging algorithms can be compared with existing algorithms as they become available. In the long-term, such an approach will further aid algorithm development for ocean-colour studies.

Phytoplankton↗

DOE OSTI2024

Feasibility of Formulating Ecosystem Biogeochemical Models From Established Physical Rules

Abstract To improve the predictive capability of ecosystem biogeochemical models (EBMs), we discuss the feasibility of formulating biogeochemical processes using physical rules that have underpinned the many successes in computational physics and chemistry. We argue that the currently popular empirically based approaches, such as multiplicative empirical response functions and the law of the minimum, will not lead to EBM formulations that can be continuously refined to incorporate improved mechanistic understanding and empirical observations of biogeochemical processes. Instead, we propose that EBM parameterizations, as a lossy data compression problem, can be better formulated using established physical rules widely used in computational physics and chemistry, and different biogeochemical processes can be more robustly integrated within a reactive‐transport framework. Through several examples, we demonstrate how mathematical representations derived from physical rules can improve understanding of relevant biogeochemical processes and enable more effective communication between modelers, observationalists, and experimentalists regarding essential questions, such as what measurements are needed to meaningfully inform models and how can models generate new process‐level hypotheses to test in empirical studies. Finally, while empirical models with more parameters are often less robust, physical rules‐based models can be more robust and show lower predictive equifinality, stemming from their enhanced consistency in representations of processes, interactions and spatial scaling.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Deep potential molecular dynamics simulations of low-temperature plasma-surface interactions

Machine learning approaches to potential generation for molecular dynamics (MD) simulations of low-temperature plasma-surface interactions could greatly extend the range of chemical systems that can be modeled. Empirical potentials are difficult to generalize to complex combinations of multiple elements with interactions that might include covalent, ionic, and metallic bonds. This work demonstrates that a specific machine learning approach, Deep Potential Molecular Dynamics (DeepMD), can generate potentials that provide a good model of plasma etching in the Si-Cl-Ar system. Comparisons are made between MD results using DeepMD models and empirical potentials, as well as experimental measurements. Pure Si properties predicted by the DeepMD model are in reasonable agreement with experimental results. Simulations of Si bombardment by Ar + ions demonstrate the ability of the DeepMD method to predict sputtering yields as well as the depth of the amorphous-crystalline interface. Etch yields as a function of flux ratio and ion energy for simultaneous Cl 2 and Ar + impacts are in good agreement with previous simulation results and experiment. Predictions of etch yields and etch products during plasma-assisted atomic layer etching of Si-Cl 2 -Ar are shown to be in good agreement with MD predictions using empirical potentials and with experiment. Finally, good agreement was also seen with measurements for the spontaneous etching of Si by Cl atoms at 300 K. Further, the demonstration that DeepMD can reproduce results from MD simulations using empirical potentials is a necessary condition to future efforts to extend the method to a much wider range of systems for which empirical potentials may be difficult or impossible to obtain.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

A Design Method for Low-Pressure Venturi Nozzles

The purpose of this work is to provide empirical design models for low-pressure, subsonic Venturi nozzles. Experimentally validated simulations were used to determine the effect of nozzle geometry and operating conditions on the suction ratio (ratio of suction mass flow rate to motive mass flow rate) of low-pressure, subsonic Venturi nozzles, over a wide range of geometries and operating conditions, through a parametric study. The results of the parametric study were used to develop seven empirical models, each with a different range of applicability or calculating a different indicator of nozzle performance (i.e., suction ratio, momentum ratio, or dynamic pressure ratio), of the Venturi nozzles using a constrained multi-variable global optimization method. Of the seven empirical models, the best models were found to be those for low- (less than one) and high-suction ratios (greater than one), with mean absolute percentage errors of 5% and 18%, respectively. These empirical models provide a design tool for subsonic, low-pressure Venturi nozzles that is more than an order of magnitude more accurate than a governing equation approach or conventional flow head calculations. These newly-developed empirical models can be applied for initial nozzle design when precise suction ratios are required.

O’Hern, Hannah↗

NASA NTRS1994

Modeling jets in cross flow

Various approaches to the modeling of jets in cross flow are reviewed. These are grouped into four classes, namely: empirical models, integral models, perturbation models, and numerical models. Empirical models depend largely on the correlation of experimental data and are mostly useful for first-order estimates of global properties such as jet trajectory and velocity and temperature decay rates. Integral models are based on some ordinary-differential form of the conservation laws, but require substantial empirical calibration. They allow more details of the flow field to be obtained; simpler versions have to assume similarity of velocity and temperature profiles, but more sophisticated ones can actually calculate these profiles. Perturbation models require little empirical input, but the need for small parameters to ensure convergent expansions limits their application to either the near-field or the far-field. Therefore, they are mostly useful for the study of flow physics. Numerical models are based on conservation laws in partial-differential form. They require little empirical input and have the widest range of applicability. They also require the most computational resources. Although many qualitative and quantitative features of jets in cross flow have been predicted with numerical models, many issues affecting accuracy such as grid resolution and turbulence model are not completely resolved.

Demuren, A. O.↗

NASA NTRS1995

Study of tropospheric correction for intercontinental GPS common-view time transfer

Current practice is to incorporate general empirical models of the troposphere, which depend only on the station height and the elevation of the satellite, in GPS time receivers used for common-view time transfer. Comparisons of these models with a semi-empirical model based on weather measurements show differences of several nanoseconds. This paper reports on a study of tropospheric correction during GPS common-view time transfer over a short baseline of about 700 km, and three long baselines of 6400 km, 9000 km and 9600 km. It is shown that the use of a general empirical model of the troposphere within a region where the climate is similar does not affect time transfer by more than a few hundreds of picoseconds. For the long distance links, differences between the use of a general empirical model and the use of a semi-empirical model reach several nanoseconds.

Lewandowski, Wlodzimierz W.↗

NASA NTRS1995

High latitude ion composition

A data base comprised of all available ionosphere satellite ion composition measurements - the Goddard Comprehensive Ionosphere Data Base (GCID) - has been set upon optical disks for convenient merging and accessing of data from different satellites. This data has recentely been expanded to include all accessible satellite electron density and plasma temperature measurements. This paper demonstrates with a couple examples, the potential of GCID as an alternative to empirical models for undertanding ionsophere physics and chemistry. Through binning techniques GCID provdes a tool that complements and improves on the International Reference Ionosphere model (IRI) in delineating the topology of high latitude ion composition. GCID provides at a glance a measure of the local statistical variabilty of the ion compostions that is not in empirical models such as IRI. Furthermusing the data to determine the spatial and geophysical parameter range over which the minor ion species are approximately in chemical equilibrium, the number of data points available for empirical ion composition models can be increased by using the statiscally more reliable neutral and electron empirical models to derive ions composition. Currently available empirical models are not capable of adequately defining the comples high latitude distribution - a measure of the variablity is needed.

Grebowsky, J. M.↗

NASA NTRS2010

An Attempt to Derive the epsilon Equation from a Two-Point Closure

The goal of this paper is to derive the equation for the turbulence dissipation rate epsilon for a shear-driven flow. In 1961, Davydov used a one-point closure model to derive the epsilon equation from first principles but the final result contained undetermined terms and thus lacked predictive power. Both in 1987 and in 2001, attempts were made to derive the epsilon equation from first principles using a two-point closure, but their methods relied on a phenomenological assumption. The standard practice has thus been to employ a heuristic form of the equation that contains three empirical ingredients: two constants, c(sub 1 epsilon), and c(sub 2 epsilon), and a diffusion term D(sub epsilon) In this work, a two-point closure is employed, yielding the following results: 1) the empirical constants get replaced by c(sub 1), c(sub 2), which are now functions of Kappa and epsilon; 2) c(sub 1) and c(sub 2) are not independent because a general relation between the two that are valid for any Kappa and epsilon are derived; 3) c(sub 1), c(sub 2) become constant with values close to the empirical values c(sub 1 epsilon), c(sub epsilon 2), (i.e., homogenous flows); and 4) the empirical form of the diffusion term D(sub epsilon) is no longer needed because it gets substituted by the Kappa-epsilon dependence of c(sub 1), c(sub 2), which plays the role of the diffusion, together with the diffusion of the turbulent kinetic energy D(sub Kappa), which now enters the new equation (i.e., inhomogeneous flows). Thus, the three empirical ingredients c(sub 1 epsilon), c(sub epsilon 2), D (sub epsilon)are replaced by a single function c(sub 1)(Kappa, epsilon ) or c(sub 2)(Kappa, epsilon ), plus a D(sub Kappa)term. Three tests of the new equation for epsilon are presented: one concerning channel flow and two concerning the shear-driven planetary boundary layer (PBL).

Canuto, V. M.↗

NASA NTRS2018

Parametric Analysis of Aircraft WingWeight Using Low-Order Physics-Based Analysis

In the conceptual aircraft design phase, prediction of the empty weight typically relies on empirically-based regression equations which execute quickly and require little detailed information about the internal structural layout. Since they are based on existing aircraft, however, empirical methods can lose their validity for newer technologies and unconventional configurations. Designers can transition to higher-order, physics-based analysis methods to improve the accuracy of the weight prediction, but at the cost of complex model setup and increased computational time. This paper describes a methodology for low-order aero-structural analysis of conceptual aircraft configurations that increases the use of physics-based analysis in conceptual design, but is less complex and time-consuming than higher-order methods such as finite-element analysis. The methodology uses Vehicle Sketch Pad (OpenVSP) to model the aircraft geometry, and ASWING to perform the aero-structural analysis. The internal forces and moments from the ASWING analysis are post-processed to calculate the resulting direct and shear stresses in the structure, and the thickness distributions of the aircraft components are varied to match the maximum von Mises stress at each cross section to the material allowable. To offset the increased computational time relative to empirical weight equations, a process is studied which uses parametric variation to develop a regression equation relating the weight of the aircraft wing to major design variables. This new weight equation is similar to existing empirical equations, but is built using the more physics-based methodology; the new equation could be used to augment or replace portions of the empirical database to improve the validity of the wing weight prediction for unconventional configurations and advanced technologies.

Olson, Erik D.↗

DOE OSTI2021

A Nonstationary and Non-Gaussian Moving Average Model for Solar Irradiance

Historically, power has flowed from large power plants to customers. Increasing penetration of distributed energy resources such as solar power from rooftop photovoltaic has made the distribution network a two-way-street with power being generated at the customer level. The incorporation of renewables introduces additional uncertainty and variability into the power grid. Distribution network operation studies are being adapted to include renewables; however, such studies require high quality solar irradiance data that adequately reflect realistic meteorological variability. Data from satellite-based products are spatially complete, but temporally coarse, whereas solar irradiances exhibit high frequency variation at very fine timescales. We propose a new stochastic method for temporally downscaling global horizontal irradiance (GHI) to 1 min resolution, but we do not consider the spatial aspect due to limited availability of the in situ irradiance measurements. Solar irradiance's first and second-order structures vary diurnally and seasonally, and our model adapts to such nonstationarity. Empirical irradiance data exhibits highly non-Gaussian behavior; we develop a nonstationary and non-Gaussian moving average model that is shown to capture realistic solar variability at multiple timescales. We also propose a new estimation scheme based on Cholesky factors of empirical autocovariance matrices, bypassing difficult and inaccessible likelihood-based approaches. The model is demonstrated for a case study of three locations that are located in diverse climates through the United States. The model is compared against competitors from the literature and is shown to provide better uncertainty and variability quantification on testing data.

Cholesky factor↗

DOE OSTI2022

Model for determining rupture area in Zircaloy cladding under LOCA conditions

The dispersal of nuclear fuel through a cladding rupture opening during a transient event is the primary safety concern preventing the United States nuclear industry from extending burnup beyond a peak rod average burnup of 62 GWd/tU. The majority of research thus far has prioritized understanding, or at a minimum prioritized quantifying, fuel fragmentation and pulverization as a function of burnup and to a lesser extent onset temperature. Early high burnup loss-of-coolant accident tests performed at the Halden Boiling Water Reactor evaluated the impact of relocation on cladding temperature, whereas historical and recent cladding burst tests focused primarily on generating data related to cladding balloon and burst timing. However, very little effort has been put forth to develop a relationship for determining the rupture opening dimensions for Zircaloy cladding tubes bursting during a simulated light water reactor loss-of-coolant accident. This is significant because high burnup loss-of-coolant accident data suggest dispersal could be limited by the size of the rupture opening or rupture dimensions, thereby minimizing the safety concern. Therefore, the purpose of this research is to build a database composed of all simulated loss-of-coolant accident data to develop an empirical model that conservatively captures the rupture opening dimensions and translates those dimensions to rupture area. Analysis of the experimental data indicates the rupture dimensions are strongly correlated to the peak balloon strain. This relationship is leveraged to develop a rupture length empirical correlation as a function of peak balloon strain and a rupture width empirical correlation as a function of rupture length. Outliers in the experimental data are identified and discussed. Finally, the rupture opening empirical model is presented in such a way for general implementation into high fidelity fuel performance codes or fuel performance codes used for safety analyses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Enhancing high-fidelity neural network potentials through low-fidelity sampling

The efficacy of neural network potentials (NNPs) critically depends on the quality of the configurational datasets used for training. Prior research using empirical potentials has shown that well-selected liquid–solid transitional configurations of a metallic system can be translated to other metallic systems. This study demonstrates that such validated configurations can be relabeled using density functional theory (DFT) calculations, thereby enhancing the development of high-fidelity NNPs. Training strategies and sampling approaches are efficiently assessed using empirical potentials and subsequently relabeled via DFT in a highly parallelized fashion for high-fidelity NNP training. Our results reveal that relying solely on energy and force for NNP training is inadequate to prevent overfitting, highlighting the necessity of incorporating stress terms into the loss functions. To optimize training involving force and stress terms, we propose employing transfer learning to fine-tune the weights, ensuring that the potential surface is smooth for these quantities composed of energy derivatives. This approach markedly improves the accuracy of elastic constants derived from simulations in both empirical potential-based NNPs and relabeled DFT-based NNPs. Overall, this study offers significant insights into leveraging empirical potentials to expedite the development of reliable and robust NNPs at the DFT level.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Calculating the space-charge-limited current density for nonplanar geometries by simulating the charge-free electric field

Calculating the space-charge-limited-current density (SCLCD) for a complicated diode geometry often requires computationally expensive particle-in-cell (PIC) codes. Here, this paper addresses this issue by using the charge-free electric field $E_0$ calculated using COMSOL Multiphysics to determine local and global SCLCD. The SCLCD obtained by using the surface average of $|E_0|^2$ on the cathode recovers theoretical results for one-dimensional (1D) planar, cylindrical, and tip-to-tip geometries in appropriate limits. We next compared tip-to-tip calculations with the SCLCD obtained using the PIC code Empire. The SCLCD calculated using COMSOL agreed well with Empire for flatter 1D tip-to-tip geometries and diverged with increasing sharpness. Physically, Empire predicts lower SCLCD than COMSOL because the electrons spread due to concentrated space-charge at the tip, whereas theory assumes that the electrons follow the charge-free electric field lines. We further assess the behavior of the SCLCD for tips protruding from the centers of flat, circular plates of various areas. Larger plate areas with constant tip size recover the 1D planar SCLCD globally and 1D tip-to-tip SCLCD locally, while reducing the difference between Empire and COMSOL calculations since larger plates capture more of the emitted electrons, reducing SCLCD suppression due to beam spreading. These results show that charge-free electric field simulations can be used to determine the SCLCD without needing to simulate particle dynamics in PIC.

Wright, Jack K. [Purdue Univ., West Lafayette, IN ↗

DOE OSTI2024

Parametric description of intermittent probability distribution functions in solar wind and magnetohydrodynamic turbulence

ABSTRACT In this work, we find empirical evidence that the scale-dependent statistical properties of solar wind and magnetohydrodynamic (MHD) turbulence can be described in terms of a family of parametric probability distribution functions (PDFs) known as Normal Inverse Gaussian (NIG). Understanding these PDFs is one of the most important goals in turbulence theory, as they are inherently connected to the intermittent properties of solar wind turbulence. We investigate the properties of PDFs of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics on a 23-yr-long sample of WIND data near 1 au and high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a $2048^3$ mesh are used to construct scale-dependent PDFs. The empirical PDFs are fitted to NIG distributions, which depend on four free parameters. Our analysis shows that NIG distributions accurately capture the evolution of the PDFs, with scale-dependent parameters, from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. We also show that empirically-measured NIG parameters exhibit well-defined scaling properties that are similar across the three empirical data sets, which may be indicative of universal behaviour.

Astronomy & Astrophysics↗

DOE OSTI2020

Physically based correction of systematic errors of Rotating Shadowband Irradiometers

Accurate measurements of direct normal, diffuse horizontal and global horizontal irradiance (DNI, DHI and GHI) are needed for meteorological studies and are essential for the solar resource assessment at potential solar power plant sites. Often, these potential sites are remote and hence require robust sensors that require minimal maintenance that are not affected strongly by soiling. Therefore, Rotating Shadowband Irradiometers (RSI) are widely used for resource assessment. To achieve the required accuracy, corrections for the raw values of RSIs depending on systematic temperature, incidence angle and spectral errors must be used, and a thorough calibration of the sensor head must be applied. The existing correction functions are derived from comparisons of RSIs to thermopile radiometers at selected sites and therefore empirical. Their accuracy is considered to be site dependent. In this work a new correction and calibration method is presented that removes the systematic errors using a physical approach. It is based on information of the sensor properties as well as measurements of its directional response, and incorporates the atmospheric conditions at the measurement site. In this case, no empiric relations obtained from a specific site are required. The method requires estimates of the current DHI and GHI spectra during each measurement of the RSI. Based on these spectra, a spectral correction, which includes a spectrum dependent temperature correction, can be made without employing empirical relationships. The new physical calibration and correction method is tested at three sites and reaches similar results compared to the empirical functions. This is already achieved with rudimentary estimations of the GHI and DHI spectra and we expect that these estimations can be improved in the future. The results indicate that the physical approach reduces the problematic location dependence of the current calibration and correction methods. The physical correction and calibration method show promise for a further improvement of the RSI accuracy.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

The diurnal cycle of entrainment and detrainment in LES of the Southern Ocean driven by observed surface fluxes and waves

Empirical rules for both entrainment and detrainment are developed from LES of the Southern Ocean boundary layer when the turbulence, stratification, and shear cannot be assumed to be in equilibrium with diurnal variability in surface flux and wave (Stokes drift) forcing. A major consequence is the failure of downgradient eddy viscosity, which becomes more serious with Stokes drift and is overcome by relating the angle between the stress and shear vectors to the orientations of Lagrangian shear to the surface and of local Eulerian shear over 5 m. Thus, the momentum flux can be parameterized as a stress magnitude and this empirical direction. In addition, the response of a deep boundary layer to sufficiently strong diurnal heating includes boundary layer collapse and the subsequent growth of a morning boundary layer, whose depth is empirically related to the time history of the forcing, as are both morning detrainment and afternoon entrainment into weak diurnal stratification. Below the boundary layer, detrainment rules give the maximum buoyancy flux and its depth, as well a specific stress direction. Another rule relates both afternoon and nighttime entrainment depth and buoyancy flux to surface layer turbulent kinetic energy production integrals. These empirical relationships are combined with rules for boundary layer transport to formulate two parameterizations; one based on eddy diffusivity and viscosity profiles and another on flux profiles of buoyancy and of stress magnitude. Evaluations against LES fluxes show the flux profiles to be more representative of the diurnal cycle, especially with Stokes drift.

54 ENVIRONMENTAL SCIENCES↗