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The Method of Finite Averages
The Method of Finite Averages (MoFA) is a rigorous multiscale modeling methodology for efficiently modeling multi-physical phenomena in heterogeneous porous media. The code developed in this project aims to perform the numerical calculations required to formulate, implement, and verify MoFA models for Earth and Energy systems (i.e., model verification refers to performing fully-resolved simulations of the systems and comparing their results to those of the models). In general, MoFA transforms partial differential equations (PDEs) describing the fine-scale physics of a system into coupled ordinary differential equations (ODEs)---in time---that describe the coarse-scale---or "average"---physical behaviors of the system. This transformation significantly expedites system simulation, as the coarse-scale ODEs involve vastly fewer degrees of freedom than the fine-scale PDEs. The code developed under this project will allow users to 1.) generate system geometries and numerical meshes, 2.) solve the PDE and ODE systems required for MoFA model formulation and implementation, 3.) solve the PDE systems required to obtain fully-resolved simulation results for model verification, and 4.) compare and plot results (e.g., the model and fully-resolved simulation solutions, the error between the solutions, etc.).
Evaluation of methods and improvement of predictions for specification properties of petroleum-based and alternative aviation fuels
To support our research and process modeling for liquid fuels, including blends, from petroleum and synthetic sources such as from biomass intermediates, we evaluated composition-based prediction methods and improved predictions for five key specification properties of petroleum-based and alternative aviation fuels, namely distillation temperatures (10 % distilled, t 10 , and final boiling point, t FBP ), density, flash point, net heat of combustion, and freezing point. The types of fuels included were petroleum-based jet fuels, jet-fuel surrogate mixtures, synthetic blending components obtained from different sources, and blends of Jet A with many synthetic blending components. Expanded datasets to update associated parameters allowed significant improvements for one of the prediction methods used in earlier work, namely the Modified Weighted Average method published initially by Shi et al. By considering the importance of lighter compounds for flash points and heavier compounds for freezing points, the revised Modified Weighted Average method was further improved. For liquid density, the revised Modified Weighted Average method gave the best overall results. The revised Modified Weighted Average method, the American Society for Testing and Materials D7215 method, and the D7215 method modified by another group gave comparable results for flash point, while the revised Modified Weighted Average and D3338 methods gave the best results for net heat of combustion. Freezing point was well predicted using the revised Modified Weighted Average method and showed the most significant improvements over current predictions. Distillation temperature t 10 was not well predicted, while t FBP was predicted with a mean absolute error comparable to experimental reproducibility.
Stochastic average model methods
We consider the solution of finite-sum minimization problems, such as those appearing in nonlinear least-squares or general empirical risk minimization problems. We are motivated by problems in which the summand functions are computationally expensive and evaluating all summands on every iteration of an optimization method may be undesirable. Here we present the idea of stochastic average model (SAM) methods, inspired by stochastic average gradient methods. SAM methods sample component functions on each iteration of a trust-region method according to a discrete probability distribution on component functions; the distribution is designed to minimize an upper bound on the variance of the resulting stochastic model. We present promising numerical results concerning an implemented variant extending the derivative-free model-based trust-region solver POUNDERS, which we name SAM-POUNDERS.
A combined ensemble-volume average homogenization method for lattice structures with defects under dynamic and static loading
In the study of lattices structures, both experiments and numerical simulations are often conducted with small samples. Using combined ensemble and volume averaging, this work introduces a method to extract a macroscopic constitutive response of a lattice material from numerical simulations performed in periodic domains. The domain size needed to obtain statistically accurate results is investigated. Similar to molecular dynamics, the concept of the virial stress is introduced after homogenized equations are derived using the ensemble averaging method. Under static conditions, the virial stress is shown to agree with the volume averaged solid stress. Using the homogenization method, constitutive relations for this stress can be obtained from systems with uniform strains. Application of such obtained constitutive relations to more general cases results in an error proportional to the square of the ratio between the lattice length scale and the macroscopic length scale. Taking advantage of this property, numerical simulations are performed in systems with a uniform gradient of the average velocity. The volume average method is then used to accelerate convergence when studying lattices with defects. To avoid the artificial numerical time scale from the size of a representative volume element divided by the wave speed, a numerical scheme is developed to enforce a spatially uniform velocity gradient within the computational domain while allowing fluctuations of the velocity or displacement to develop naturally. To account for probability distribution of lattice defects, the stress is calculated as the ensemble-volume averaged value. For dynamic systems, energy dissipation properties are also studied.
Data for Clumping Index Estimation With 30°-tilted Cameras in Row Crops: Evaluation of Methods and Segment Size Effects
The clumping index (CI) quantifies the spatial distribution of foliage elements and is essential for accurately estimating the plant area index (PAI), canopy radiative transfer, and photosynthesis. Traditionally, the finite-length averaging method (LX), the gap size distribution method (CC), and a combined approach of CC and LX (CLX) have been applied to instruments like TRAC and digital hemispherical photography to estimate CI. However, a comprehensive evaluation of these methods in row crops remains limited, especially regarding the influence of segment size on CI. Meanwhile, digital cameras offer a cost-effective and user-friendly solution for canopy measurements in row crops, yet their application in this context remains underexplored. In this study, we employed a new approach using a 30°-tilted digital camera to estimate CI in corn and soybean fields, applying the LX, CC, and CLX methods. We systematically assessed the performance of these three methods by combining field measurements in real-world fields with simulations using the LESS 3D radiative transfer model. Our results showed that CLX applied to the whole image and 45° segment offered accurate estimation of CI (bias within ±0.1, RMSE < 0.2) and PAI (bias within ±0.4, RMSE < 1) in real-world fields and LESS simulations. The accuracy of the LX method was highly sensitive to segment size, with the best performance observed at the 15° segment (PAI bias within ±0.4). In contrast, the CC method remained stable across different segment sizes, and its performance was generally comparable to that of LX, except at the 15° segment. Across view zenith angles, CI derived from CC generally showed a continuous increase, while those from LX and CLX followed a rising trend at small zenith angles but began to decline at 68°, likely due to an increasing proportion of no-gap segments. Seasonally, LX tended to show decreasing CI during early growth stages but increased as the canopy matured, whereas CC and CLX showed gradually increasing CI before plateauing at peak PAI. The 30°-tilted camera effectively captured CI variations across different angles and growth stages, making it a practical and robust instrument for row crop canopy structure analysis. Applying these CI methods to digital cameras offers a low-cost and accessible CI estimation alternative, improving canopy structure monitoring accuracy in row crops.
Improved uranium isotopic ratio determinations for the liquid sampling-atmospheric pressure glow discharge orbitrap mass spectrometer by use of moving average processing
The liquid sampling-atmospheric pressure glow discharge (LS-APGD) is a versatile combined atomic and molecular (CAM) ionization source capable of ionizing elemental species, small polar compounds, low-polarity polycyclic aromatic hydrocarbons, and proteins. While the LS-APGD has been proven capable of determining the 235U/238U isotope ratio in enriched and natural uranium, recent efforts have strived to reduce the analysis time of individual measurements by employing higher-order data processing techniques, specifically, moving average methods. Additionally, the use of a moving average (of data windows of various widths) improves the precision of the ratio measurements and reduces the number of scans needed to be collected to generate high-precision results. Additionally, use of the moving average minimizes the quantity of sample that needs to be analyzed while reducing the measurement time. These reductions have allowed isotope ratio (IR) determinations to be made using injections instead of direct infusion of the analyte. For example, employing a 40-point window width in the moving average to direct infusion data reduced the percent relative standard deviation (% RSD) of the 235U/238U values from 3.4% to 0.5%. For the injection of a 100 μL aliquot, the % RSD was reduced from 5.3% to 0.7%.
A comparison of the dielectric function for p-point water models
We compute the longitudinal dielectric function ɛl(k) for p-point water models, p = 3 (SPC/E, TIP3P), p = 4 (TIP4P-EW, OPC), and p = 5 (TIP5P-E) from the charge–charge fluctuation function SZZ(k), obtained from two methods: average of the charge in k-space (method:sum) and from the pair distribution function in Fourier space (method:integral). The latter requires a continuation to small k-values, which we thoroughly discuss. We conclude with a detailed comparison of the longitudinal dielectric function for the different p-point models and its main characteristics: small k and large k limits, position of the poles, and its (complex) zeros.
Overview of recent turbulence studies across multiple confinement modes at the ASDEX Upgrade tokamak using the Correlation Electron Cyclotron Emission diagnostic
This work presents an overview of recent and ongoing experimental measurements of core and edge turbulence across multiple confinement regimes using the Correlation Electron Cyclotron Emission (CECE) diagnostic at the ASDEX Upgrade (AUG) tokamak. A common goal among these investigations is to identify how the properties of the turbulent electron temperature fluctuations measured by CECE influence and regulate the unique transport characteristics of each confinement regime, including L-mode, I-mode, ELMy H-mode, and ELM-free H-mode. Optics and signal processing methods to aid in the analysis and interpretation of experimental turbulence results are also presented. These methods, and particularly the down-sampling and ensemble averaging method, are relevant to a wide variety of fusion and non-fusion applications.
Multi-Model and Multi-Scale Global Sensitivity Analysis for Identifying Controlling Processes of Complex Systems
An environmental model consists of multiple process level sub-models, and each sub-model represents a process that is key to the operation of the simulated system. Global sensitivity analysis methods have been widely used to identify important processes for system model development and improvement. The existing methods of global sensitivity analysis only consider parametric uncertainty, and are not capable of handling model uncertainty caused by multiple process models that arise from competing hypotheses about one or more processes. To address this problem, this project develops a new method to probe model output sensitivity to competing process models by integrating model averaging methods with variance-based global sensitivity analysis to address uncertainty in process models and parameters. The new method yields three process sensitivity indices. The first one is called first-order process sensitivity index, and it is derived as a single summary measure of relative process importance. Evaluating the index is computationally expensive, because it relies in a Monte Carlo scheme that requires thousands and even millions of model executions. To reduce computational cost, this project develops a computationally efficient, quasi Monte Carlo method, and this method is presented in Chapter 2 of this report with and a numerical example for demonstration. The numerical example shows that the results of the quasi Monte Carlo method are substantially close to those of the full Monte Carlo method, but the computational cost of the quasi Monte Carlo method is only 0.7% of that of the full Monte Carlo method. The second index is called total-effect process sensitivity index, and it measures interactions between different processes. Therefore, this sensitivity index includes the first-order process sensitivity index, and can be used to identify influential processes. On the other hand, the total-effect process sensitivity index can also be used to screen non-influential processes. This is demonstrated by two numerical examples using the Sobol-G* functions and groundwater flow models that consider recharge process, geological process, and snowmelt process. The numerical examples shows that the total-effect process sensitivity index is more informative than the first-order process sensitivity. The derivation of the process sensitivity index and the numerical examples are discussed in Chapter 3. Chapter 4 presents two computationally efficient methods for screening non-influential processes to exclude them from further investigation. The two methods are the multi-model difference-based sensitivity (MMDS) analysis method, which can be implemented using the Latin Hypercube Sampling. The second one is the implementation of MMDS method using a binning method. The numerical example for the Sobol-G* function indicates the two methods are capable of identifying non-influential models, and the numerical examples for the groundwater flow and reactive transport show that the two methods are effective for groundwater problems. However, it should be noted that the two methods are numerical approximations, and they can only be used for screening non-influential processes, not for ranking importance of system processes. All the sensitivity analysis methods are implemented by developing python codes, and the codes are in a software called SAMMPY: a python package for process sensitivity analysis under multiple models. The SAMMPY design and structure are discussed in Chapter 5, and the package is released to the public for free download.
Clumping index estimation with 30°-tilted cameras in row crops: Evaluation of methods and segment size effects
The clumping index (CI) quantifies the spatial distribution of foliage elements and is essential for accurately estimating the plant area index (PAI), canopy radiative transfer, and photosynthesis. Traditionally, the finite-length averaging method (LX), the gap size distribution method (CC), and a combined approach of CC and LX (CLX) have been applied to instruments like TRAC and digital hemispherical photography to estimate CI. However, a comprehensive evaluation of these methods in row crops remains limited, especially regarding the influence of segment size on CI. Meanwhile, digital cameras offer a cost-effective and user-friendly solution for canopy measurements in row crops, yet their application in this context remains underexplored. In this study, we employed a new approach using a 30°-tilted digital camera to estimate CI in corn and soybean fields, applying the LX, CC, and CLX methods. We systematically assessed the performance of these three methods by combining field measurements in real-world fields with simulations using the LESS 3D radiative transfer model. Our results showed that CLX applied to the whole image and 45° segment offered accurate estimation of CI (bias within ±0.1, RMSE < 0.2) and PAI (bias within ±0.4, RMSE < 1) in real-world fields and LESS simulations. The accuracy of the LX method was highly sensitive to segment size, with the best performance observed at the 15° segment (PAI bias within ±0.4). In contrast, the CC method remained stable across different segment sizes, and its performance was generally comparable to that of LX, except at the 15° segment. Across view zenith angles, CI derived from CC generally showed a continuous increase, while those from LX and CLX followed a rising trend at small zenith angles but began to decline at 68°, likely due to an increasing proportion of no-gap segments. Seasonally, LX tended to show decreasing CI during early growth stages but increased as the canopy matured, whereas CC and CLX showed gradually increasing CI before plateauing at peak PAI. The 30°-tilted camera effectively captured CI variations across different angles and growth stages, making it a practical and robust instrument for row crop canopy structure analysis. Furthermore, applying these CI methods to digital cameras offers a low-cost and accessible CI estimation alternative, improving canopy structure monitoring accuracy in row crops.
Tracking blobs in the turbulent edge plasma of a tokamak fusion device
Abstract The analysis of turbulence in plasmas is fundamental in fusion research. Despite extensive progress in theoretical modeling in the past 15 years, we still lack a complete and consistent understanding of turbulence in magnetic confinement devices, such as tokamaks. Experimental studies are challenging due to the diverse processes that drive the high-speed dynamics of turbulent phenomena. This work presents a novel application of motion tracking to identify and track turbulent filaments in fusion plasmas, called blobs, in a high-frequency video obtained from Gas Puff Imaging diagnostics. We compare four baseline methods (RAFT, Mask R-CNN, GMA, and Flow Walk) trained on synthetic data and then test on synthetic and real-world data obtained from plasmas in the Tokamak à Configuration Variable (TCV). The blob regime identified from an analysis of blob trajectories agrees with state-of-the-art conditional averaging methods for each of the baseline methods employed, giving confidence in the accuracy of these techniques. By making a dataset and benchmark publicly available, we aim to lower the entry barrier to tokamak plasma research, thereby greatly broadening the community of scientists and engineers who might apply their talents to this endeavor.
Uncertainty of SW Cloud Radiative Effect in Atmospheric Models Due to the Parameterization of Liquid Cloud Optical Properties
Clouds are largely responsible for the spread of climate models predictions. Here we focus on the uncertainties in cloud shortwave radiative effect due to the parameterization of liquid cloud single scattering properties (SSPs) from liquid water content (LWC) and droplet number concentration (N), named parameterization of cloud optical properties. Uncertainties arise from not accounting for the droplet size distribution (DSD)—which affects the estimation of the effective radius (r eff ) and modulates the r eff -dependency of the SSPs—and from averaging SSPs over wide spectral bands. To assess these uncertainties a series of r eff -dependent SSPs parameterizations corresponding to various DSDs and spectral averaging methods are derived and implemented in a radiative code. Combined with the DSD-dependent estimation of r eff they are used to compute the bulk radiative properties (reflectance, transmittance, absorptance) of various clouds (defined in terms of LWC and N), including a homogeneous cloud, more realistic case studies, and outputs of a climate model. The results show that the cloud radiative forcing can vary up to 20% depending on the assumed DSD. Likewise, differences up to 20% are obtained for heating rates. The estimation of r eff is the main source of uncertainty, while the SSPs parameterization contributes to around 20% of the total uncertainty. Spectral averaging is less an issue, except for atmospheric absorption. Overall, global shortwave cloud radiative effect can vary by 6 W m –2 depending on the assumed DSD shape, which is about 13% of the best observational estimate.
Estimation of soil classes and their relationship to grapevine vigor in a Bordeaux vineyard: advancing the practical joint use of electromagnetic induction (EMI) and NDVI datasets for precision viticulture
Working within a vineyard in the Pessac Léognan Appellation of Bordeaux, France, this study documents the potential of using simple statistical methods with spatially-resolved and increasingly available electromagnetic induction (EMI) geophysical and normalized difference vegetation index (NDVI) datasets to accurately estimate Bordeaux vineyard soil classes and to quantitatively explore the relationship between vineyard soil types and grapevine vigor. First, co-located electrical tomographic tomography (ERT) and EMI datasets were compared to gain confidence about how the EMI method averaged soil properties over the grapevine rooting depth. Then, EMI data were used with core soil texture and soil-pit based interpretations of Bordeaux soil types (Brunisol, Redoxisol, Colluviosol and Calcosol) to estimate the spatial distribution of geophysically-identified Bordeaux soil classes. A strong relationship (r = 0.75, p < 0.01) was revealed between the geophysically-identified Bordeaux soil classes and NDVI (both 2 m resolution), showing that the highest grapevine vigor was associated with the Bordeaux soil classes having the largest clay fraction. The results suggest that within-block variability of grapevine vigor was largely controlled by variability in soil classes, and that carefully collected EMI and NDVI datasets can be exceedingly helpful for providing quantitative estimates of vineyard soil and vigor variability, as well as their covariation. The method is expected to be transferable to other viticultural regions, providing an approach to use easy-to-acquire, high resolution datasets to guide viticultural practices, including routine management and replanting.
Solar Uncertainty Management and Mitigation for Exceptional Reliability in Grid Operations (SUMMER-GO): Project Final Report
The Solar Uncertainty Management and Mitigation for Exceptional Reliability in Grid Operation (SUMMER-GO) project was recently completed through a collaboration among the National Renewable Energy Laboratory, Maxar, the Electric Reliability Council of Texas (ERCOT), the University of Texas at Dallas, the University of California Berkeley, and the University of Colorado Boulder. The project made significant advances in probabilistic solar power forecasting, both through the development of Bayesian model averaging methods for ensemble forecasting and in bringing these and other advancements into practice with Maxar's delivery of operational forecasts to ERCOT. In addition to creating more reliable solar power forecasts, the project developed methods for their utilization in power system operations. These include the development of risk-aware unit commitment and economic dispatch algorithms and methods to reformulate probabilistic forecasts to be used in these power system operational models. Dynamic power system reserve methods were also developed, which have been shown in silico to create economic savings and reliability improvements on an ERCOT-like system as well as financial savings in the ERCOT system through more granular consideration of the uncertainty associated with solar power forecasts. Finally, a situational awareness tool to help grid operators better understand solar power forecast uncertainty in daily operations was developed and extensively vetted.
Explicit physics-informed neural networks for nonlinear closure: The case of transport in tissues
In upscaling methods, closures for nonlinear problems present a well-known challenge. While a number of theoretical methods have been proposed for handling such closures, nonlinearities still remain a significant obstacle for many problems. In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in multiscale tissues. The classical effectiveness factor model is used to formulate the macroscale reaction kinetics. We train a multilayer perceptron network using training data generated by direct numerical simulations over microscale examples. Once trained, the network is used in an algorithm for numerically solving the upscaled (coarse-grained) differential equation describing mass transport and reaction in two example tissues. The network is described as being explicit in the sense that the network is trained using macroscale concentrations and gradients of concentration as components of the feature space rather than incorporating them as part of a constraint in the optimization process. Network training and solutions to the macroscale transport equations were computed for two different tissues. The two tissue types (brain and liver) exhibit markedly different geometrical complexity and spatial scale (cell size and sample size). The upscaled solutions for the average concentration are compared with numerical solutions derived from the microscale concentration fields by a posteriori averaging. There are three outcomes of this work of particular note. 1) Our overall approach results in an upscaled nonlinear PDE. The PDE is closed using a neural network, and our approach results in the definition of the classical effectiveness factor for effecting closure. 2) We identify particular source terms for the closure problem that are important for representing the structure of the closure. These source terms involve macroscale concentrations and their gradients. We adopt these source terms to use as explicit features in the learning algorithm. We find the trained networks that include the macroscale source terms generate models that are able to predict the correction factor with increased fidelity over those that do not. 3) We find that the trained network exhibits good generalizability, and it is able to predict the effectiveness factor with high fidelity for realistically-structured tissues despite the significantly different scale and geometrical complexity of the two example tissue types. This latter result emphasizes our purposeful connection between conventional averaging methods with the use of machine learning for closure; this contrasts with some machine learning methods for upscaling where the exact form of the macroscale equation remains unknown.
The rigorous upscaling of advection-dominated transport in heterogeneous porous media via the Method of Finite Averages
Systems involving advection-dominated transport through heterogeneous porous and fractured media are ubiquitous in subsurface engineering applications. However, upscaling such systems continues to challenge rigorous modeling efforts, particularly when advection is stronger than diffusion at fine spatial scales (i.e., when the Péclet number is greater than one at length scales that characterize a system’s unit-cells, representative elementary volumes, or averaging regions). Here, in this work, we propose and validate a strategy for extending the Method of Finite Averages (MoFA), a rigorous upscaling methodology for heterogeneous porous media, to upscale transport systems experiencing stronger advection than diffusion at fine scales (i.e., fine-scale Péclet numbers greater than one). We detail the strategy, the physical conditions under which it can be applied while retaining a priori modeling error guarantees, and implement the strategy to obtain a MoFA model for advective-diffusive transport that accommodates advective physics at fine spatial scales. We then perform two numerical experiments considering systems with system-scale Péclet numbers of 300 and 1000 — which correspond to fine-scale Péclet numbers of 30 and 100, respectively — to verify that the error guarantees are met under the strategy. After, we conduct a numerical study to demonstrate the strategy’s advantages over the original MoFA methodology. The results suggest that rigorously-upscaled transport models for heterogeneous porous media experiencing advective physics at finer spatial scales can be derived through MoFA and resolved orders of magnitude faster than their pore-scale counterparts. The results also suggest that the presented strategy is limited to modeling shallow concentration gradients when there are large differences between the time scales related to advection and a system’s temporally-varying boundary conditions. This limitation hinders the strategy’s practicality in modeling more advective systems, and as such, opportunity exists for developing additional strategies that accommodate rapidly-varying boundary conditions — and consequentially, steeper concentration gradients — while modeling advective systems with MoFA.
Revisiting a Drag Partition Model For Canopy-Like Roughness Elements
Turbulent flows over a large surface area (S) covered by n obstacles experience an overall drag due to the presence of the ground and the protruding obstacles into the flow. The drag partition between the roughness obstacles and the ground is analyzed using an analytical model proposed by Raupach (Boundary-Layer Meteorol 60:375-395, 1992) and is hereafter referred to as R92. The R92 is based on the premise that the wake behind an isolated roughness element can be described by a shelter area A and a shelter volume V. The individual sizes of A and V without any interference from other obstacles can be determined from scaling analysis for the spread of wakes. To upscale from an individual roughness element to n/S elements where wakes may interact, R92 adopted a background stress re-normalizing instead of reducing A or V with each element addition. This work demonstrates that R92’s approach results in a linear background stress reduction in A and V only when the ratio of n/S is small, due to a low probability of wake interactions. This probabilistic nature suggests that up-scaling from individual to multiple roughness elements can be re-formulated using stochastic averaging methods proposed here. The two approaches are shown to recover R92 under plausible conditions. An alternative scaling for the shelter volume is also proposed here using thermodynamic arguments of work and dissipation though the final outcome remains similar to R92. Comparisons between R92 and available data spanning more than two decades after R92 on blocks and vegetation-like roughness elements confirm the practical utility of R92. The agreement between R92 and this updated databases of experiments and simulations confirm the potential use of R92 in large-scale models provided that the relevant parameters accommodate certain features of the roughness element type (cube versus vegetation-like) and, to a lesser extent, their configuration throughout S. Last, a comparison between R92 and models based on first-order closure principles with constant mixing length suggests that R92 can outperform such models when evaluated across a wide range of roughness densities.