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At least 1,423 records · Page 79

Modelling Temporal Variability in the Carbon Balance of a Spruce/Moss Boreal Forest

A model of the daily carbon balance of a black spruce/feathermoss boreal forest ecosystem was developed and results compared to preliminary data from the 1994 BOREAS field campaign in northern Manitoba, Canada. The model, driven by daily weather conditions, simulated daily soil climate status (temperature and moisture profiles), spruce photosynthesis and respiration, moss photosynthesis and respiration, and litter decomposition. Model agreement with preliminary field data was good for net ecosystem exchange (NEE), capturing both the asymmetrical seasonality and short-term variability. During the growing season simulated daily NEE ranged from -4 g C m(exp -2) d(exp -1) (carbon uptake by ecosystem) to + 2 g C m(exp -2) d(exp -1) (carbon flux to atmosphere), with fluctuations from day to day. In the early winter simulated NEE values were + 0.5 g C m(exp -2) d(exp -1), dropping to + 0.2 g C m(exp -2) d(exp -1) in mid-winter. Simulated soil respiration during the growing season (+ 1 to + 5 g C m(exp -2) d(exp -1)) was dominated by metabolic respiration of the live moss, with litter decomposition usually contributing less than 30% and live spruce root respiration less than 10% of the total. Both spruce and moss net primary productivity (NPP) rates were higher in early summer than late summer. Simulated annual NEE for 1994 was -51 g C m(exp -2) y(exp -1), with 83% going into tree growth and 17% into the soil carbon accumulation. Moss NPP (58 g C m(exp -2) d(exp -1)) was considered to be litter (i.e. soil carbon input; no net increase in live moss biomass). Ecosystem respiration during the snow-covered season (84 g Cm(exp -2)) was 58% of the growing season net carbon uptake. A simulation of the same site for 1968-1989 showed about 10-20% year-to-year variability in heterotrophic respiration (mean of + 113 g C m-2 y@1). Moss NPP ranged from 19 to 114 g C m(exp -2) y(exp -1); spruce NPP from 81 to 150 g C nt-2 y,@l; spruce growth (NPP minus litterfall) from 34 to 103 g C m(exp -2) y(exp -1); NEE ranged from +37 to -142 g C m(exp -2) y(exp -1). Values for these carbon balance terms in 1994 were slightly smaller than the 1969 - 89 means. Higher ecosystem productivity years (more negative NEE) generally had early springs and relatively wet summers; lower productivity years had late springs and relatively dry summers.

Frolking, S.↗

General Purpose Data-Driven Online System Health Monitoring with Applications to Space Operations

Modern space transportation and ground support system designs are becoming increasingly sophisticated and complex. Determining the health state of these systems using traditional parameter limit checking, or model-based or rule-based methods is becoming more difficult as the number of sensors and component interactions grows. Data-driven monitoring techniques have been developed to address these issues by analyzing system operations data to automatically characterize normal system behavior. System health can be monitored by comparing real-time operating data with these nominal characterizations, providing detection of anomalous data signatures indicative of system faults, failures, or precursors of significant failures. The Inductive Monitoring System (IMS) is a general purpose, data-driven system health monitoring software tool that has been successfully applied to several aerospace applications and is under evaluation for anomaly detection in vehicle and ground equipment for next generation launch systems. After an introduction to IMS application development, we discuss these NASA online monitoring applications, including the integration of IMS with complementary model-based and rule-based methods. Although the examples presented in this paper are from space operations applications, IMS is a general-purpose health-monitoring tool that is also applicable to power generation and transmission system monitoring.

Iverson, David L.↗

Probing interfacial momentum closures in two-phase bubbly flow with machine learning-aided methods

Computational fluid dynamics (CFD) approach has already reached a high level of maturity for single-phase flows, however the development of closure models for two-phase flow requires additional attention. Multiphase CFD (M-CFD) methods resolve the conservation equations for mass, momentum and energy while differing in the approaches and strategies adopted in the physical closure models. The most widely adopted framework for M-CFD is the Eulerian-Eulerian two-fluid approach which assumes that all phases are co-existing inside each computational cell. For each fluid, the full set of conservation equations is solved; therefore, each fluid has a different velocity field. For adiabatic two-phase flow, the mechanisms of the interfacial momentum transfer are modeled by the interfacial forces representing different physical mechanisms. One of the crucial issues in the development and application of two-fluid model is the understanding of the interfacial momentum closures which determines the bubble distribution and migration behaviors. Dedicated experiments are performed to support the physical understanding and drive the closures’ development. However, limitations exist due to the uncertainties in the experimental measurement and the simplified analytical assumptions which have difficulties on representing the complex non-linear flow fields. In this paper, a data-driven approach, Feature Similarity Measurement (FSM), is developed and proposed to resolve the challenges of modeling the interfacial forces closures. Case study is performed with two-phase flow scenarios where the high-fidelity experimental data is available. Within the Eulerian-Eulerian two-fluid framework, only momentum equations for gas and liquid phases are solved and reduced-order interfacial momentum closures are aided with FSM. Predictions of void fraction and velocity fields are analyzed and demonstrate the potential of machine learning-driven interfacial forces closures.

97 MATHEMATICS AND COMPUTING↗

Image Collection Simulation Using High-Resolution Atmospheric Modeling

A new method is described for simulating the passive remote sensing image collection of ground targets that includes effects from atmospheric physics and dynamics at fine spatial and temporal scales. The innovation in this research is the process of combining a high-resolution weather model with image collection simulation to attempt to account for heterogeneous and high-resolution atmospheric effects on image products. The atmosphere was modeled on a 3D voxel grid by a Large-Eddy Simulation (LES) driven by forcing data constrained by local ground-based and air-based observations. The spatial scale of the atmospheric model (10–100 m) came closer than conventional weather forecast scales (10–100 km) to approaching the scale of typical commercial multispectral imagery (2 m). This approach was demonstrated through a ground truth experiment conducted at the Department of Energy Atmospheric Radiation Measurement Southern Great Plains site. In this experiment, calibrated targets (colored spectral tarps) were placed on the ground, and the scene was imaged with WorldView-3 multispectral imagery at a resolution enabling the tarps to be visible in at least 9–12 image pixels. The image collection was simulated with Digital Imaging and Remote Sensing Image Generation (DIRSIG) software, using the 3D atmosphere from the LES model to generate a high-resolution cloud mask. The high-resolution atmospheric model-predicted cloud coverage was usually within 23% of the measured cloud cover. The simulated image products were comparable to the WorldView-3 satellite imagery in terms of the variations of cloud distributions and spectral properties of the ground targets in clear-sky regions, suggesting the potential utility of the proposed modeling framework in improving simulation capabilities, as well as testing and improving the operation of image collection processes.

54 ENVIRONMENTAL SCIENCES↗

Data-driven Detection and Early Prediction of Thermoacoustic Instability in a Multi-nozzle Combustor

Thermoacoustic instability (TAI) is a critical issue in modern lean-burn gas-turbine combustors, which is induced by a strong coupling between the resonant combustor acoustics and fluctuations in the heat release rate. This instability may lead to high-amplitude pressure waves that generate undesirable noise levels as well as fatigue stresses in mechanical structures of the combustor. The intense pressure fluctuations due to TAI may also cause large flow perturbations and possibly flow reversal that may lead to flame oscillations, flame liftoff, and even flame blow-out. Hence, there is a strong need for exercising control actions in a timely fashion to mitigate the TAI phenomena. Anomaly detection is an essential prerequisite to the design of a good controller and such a detector must be able to reliably predict a forthcoming TAI. To detect and predict the onset of a TAI from an ensemble of pressure time series, this paper investigates three data-driven methods: Fast Fourier transform (FFT), symbolic time series analysis (STSA), and hidden Markov modeling (HMM). The main focus of the paper is to make a comparative evaluation of these three anomaly detection methods for classification of the current regime of operation into stable and unstable categories as well as for real-time identification of precursors to impending instabilities with short-length time series of measured variables (e.g., pressure oscillations). Finally, the results, generated on experimental data from a multi-nozzle combustor apparatus, have been compared to evaluate the performance of FFT, STSA, and HMM methods for TAI analysis.

42 ENGINEERING↗

Evaluation of the Event Driven Phenology Model Coupled with the VegET Evapotranspiration Model Through Comparisons with Reference Datasets in a Spatially Explicit Manner

A new model coupling scheme with remote sensing data assimilation was developed for estimation of daily actual evapotranspiration (ET). The scheme represents a mix of the VegET, a physically based model to estimate ET from a water balance, and an event driven phenology model (EDPM), where the EDPM is an empirically derived crop specific model capable of producing seasonal trajectories of canopy attributes. In this experiment, the scheme was deployed in a spatially explicit manner within the croplands of the Northern Great Plains. The evaluation was carried out using 2007-2009 land surface forcing data from the North American Land Data Assimilation System (NLDAS) and crop maps derived from remotely sensed data of NASA's Moderate Resolution Imaging Spectroradiometer (MODIS). We compared the canopy parameters produced by the phenology model with normalized difference vegetation index (NDVI) data derived from the MODIS nadir bi-directional reflectance distribution function (BRDF) adjusted reflectance (NBAR) product. The expectations of the EDPM performance in prognostic mode were met, producing determination coefficient (r2) of 0.8 +/-.0.15. Model estimates of NDVI yielded root mean square error (RMSE) of 0.1 +/-.0.035 for the entire study area. Retrospective correction of canopy dynamics with MODIS NDVI brought the errors down to just below 10% of observed data range. The ET estimates produced by the coupled scheme were compared with ones from the MODIS land product suite. The expected r2=0.7 +/-.15 and RMSE = 11.2 +/-.4 mm per 8 days were met and even exceeded by the coupling scheme0 functioning in both prognostic and retrospective modes. Minor setbacks of the EDPM and VegET performance (r2 about 0.5 and additional 30 % of RMSR) were found on the peripheries of the study area and attributed to the insufficient EDPM training and to spatially varying accuracy of crop maps. Overall the experiment provided sufficient evidence of soundness and robustness of the EDPM and VegET coupling scheme, assuring its potential for spatially explicit applications.

Kovalskyy, V.↗

Expanded analysis of machine learning models for nuclear transient identification using TPOT

Industries around the world are becoming more and more data driven. The nuclear field is no exception with several different applications being proposed. One popular area of research is the use of machine learning in transient detection. This paper seeks to build upon a previous study which made use of the AutoML package TPOT to train traditional machine learning models to classify transient events occurring with a reactor. Synthetic data was once again collected using a GPWR reactor simulator. Data on 12 different events was collected using 15 different initial conditions. Here, a dataset consisting of over 100,000 data points was compiled and used to train 7 different machine learning models using a pre-defined TPOT dictionary with 12 different preprocessing techniques. Three of the trained models were able to produce validation results in the 90s with the expanded dataset. Once the models were trained, it was possible to look into where during the simulation, misclassifications occurred. Using these three models, analysis was done to determine if TPOT could be used to train models that were effective if important features were missing. The results from this were positive with the newly trained models scoring close to the original models. Finally, to conclude this study, the three high performing models were retrained using different random states to see if there was any major variation when different states were used.

42 ENGINEERING↗

Data-driven predictions of the time remaining until critical global warming thresholds are reached

Leveraging artificial neural networks (ANNs) trained on climate model output, we use the spatial pattern of historical temperature observations to predict the time until critical global warming thresholds are reached. Although no observations are used during the training, validation, or testing, the ANNs accurately predict the timing of historical global warming from maps of historical annual temperature. The central estimate for the 1.5 °C global warming threshold is between 2033 and 2035, including a ±1σ range of 2028 to 2039 in the Intermediate (SSP2-4.5) climate forcing scenario, consistent with previous assessments. However, our data-driven approach also suggests a substantial probability of exceeding the 2 °C threshold even in the Low (SSP1-2.6) climate forcing scenario. While there are limitations to our approach, our results suggest a higher likelihood of reaching 2 °C in the Low scenario than indicated in some previous assessments—though the possibility that 2 °C could be avoided is not ruled out. Explainable AI methods reveal that the ANNs focus on particular geographic regions to predict the time until the global threshold is reached. Our framework provides a unique, data-driven approach for quantifying the signal of climate change in historical observations and for constraining the uncertainty in climate model projections. Given the substantial existing evidence of accelerating risks to natural and human systems at 1.5 °C and 2 °C, our results provide further evidence for high-impact climate change over the next three decades.

54 ENVIRONMENTAL SCIENCES↗

Search for light neutral particles decaying promptly into collimated pairs of electrons or muons in pp collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

A search for a dark photon, a new light neutral particle, which decays promptly into collimated pairs of electrons or muons is presented. The search targets dark photons resulting from the exotic decay of the Standard Model Higgs boson, assuming its production via the dominant gluon-gluon fusion mode. The analysis is based on 140 fb -1 of data collected with the ATLAS detector at the Large Hadron Collider from proton-proton collisions at a center-of-mass energy of 13 TeV. Events with collimated pairs of electrons or muons are analysed and background contributions are estimated using data-driven techniques. No significant excess in the data above the Standard Model background is observed. Upper limits are set at 95% confidence level on the branching ratio of the Higgs boson decay into dark photons between 0.001% and 5%, depending on the assumed dark photon mass and signal model.

Aad, G. [Aix-Marseille Université] (ORCID:00000002↗

Reconstructing gravity on cosmological scales

We present the data-driven late-time reconstruction of gravitational theories and dark energy models on cosmological scales. We showcase the power of present cosmological probes at constraining these models and quantify the knowledge of their properties that can be acquired through state of the art data. This reconstruction exploits the power of the effective field theory approach to dark energy and modified gravity phenomenology, which compresses the freedom in defining such models into a finite set of functions that can be reconstructed across cosmic times using cosmological data. We consider several model classes described within this framework and thoroughly discuss their phenomenology and data implications. In this work, we find that some models can alleviate the present discrepancy in the determination of the Hubble constant as inferred from the cosmic microwave background and as directly measured. This results in a statistically significant preference for the reconstructed theories over the standard cosmological model.

79 ASTRONOMY AND ASTROPHYSICS↗

Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

Here we analyze a plurality of epidemiological models through the lens of physics-informed neural networks (PINNs) that enable us to identify time-dependent parameters and data-driven fractional differential operators. In particular, we consider several variations of the classical susceptible-infectious-removed (SIR) model by introducing more compartments and fractional-order and time-delay models. We report the results for the spread of COVID-19 in New York City, Rhode Island and Michigan states and Italy, by simultaneously inferring the unknown parameters and the unobserved dynamics. For integer-order and time-delay models, we fit the available data by identifying time-dependent parameters, which are represented by neural networks. In contrast, for fractional differential models, we fit the data by determining different time-dependent derivative orders for each compartment, which we represent by neural networks. We investigate the structural and practical identifiability of these unknown functions for different datasets, and quantify the uncertainty associated with neural networks and with control measures in forecasting the pandemic.

60 APPLIED LIFE SCIENCES↗

GCAM-Demeter LU dataset

The dataset includes the projected global gridded land cover (excluding the Antarctic) for the period of 2015-2100 at 0.05-degree resolution and 5-year time step under fifteen SSP-RCP scenarios driven by five GCMs (i.e., gfdl, hadgem, ipsl, miroc, and noresm), using the Global Change Analysis Model (GCAM) and a geospatial downscaling model (Demeter). The data has been stored in self-describing NetCDF format. The dataset also includes the mean and standard deviation of the results driven by the five GCMs. More specifically, the data in each year includes grid-explicit fraction (in percent) of each of the 32 plant functional types that are widely used in current Earth system models. The NetCDF files are named as “GCAM_Demeter_LU_SSP_RCP_Model_Year.nc”, where “SSP” and “RCP” denote the SSP and RCP scenarios, including 'ssp1_rcp26', 'ssp1_rcp45', 'ssp1_rcp60', 'ssp2_rcp26', 'ssp2_rcp45', 'ssp2_rcp60', 'ssp3_rcp45', 'ssp3_rcp60', 'ssp4_rcp26', 'ssp4_rcp45', 'ssp4_rcp60', 'ssp5_rcp26', 'ssp5_rcp45', 'ssp5_rcp60', and 'ssp5_rcp85'. “Year” denotes the year of the land use data, and “GCM” denotes the source driving forcing data from five global climate models (gfdl, hadgem, ipsl, miroc, and noresm), or the mean (“modelmean”) and the standard deviation (“modelstd”) of the results from the five GCMs.

54 ENVIRONMENTAL SCIENCES↗

Data Science for Weather Impacts on Crop Yield

Private businesses in sectors, such as food, energy, and retail, as well as public sector and federal agencies are interested in the predictive understanding of weather impacts on crop yield, which is an important aspect of food security. Scientific literature has mainly examined how crop yield is impacted by growing season-averaged weather indices. Although a few studies did consider weather extremes in their analysis, their scope was either restricted to measuring their conditional relationship with yield or the extreme event types considered were limited. Selection of regression models, whether the more commonly used linear approaches or nonlinear methods, have not been appropriately justified in this context. Here, we develop data-driven methods to examine two inter-related hypotheses for improved scientific understanding and enhanced predictive modeling. The first hypothesis, that extreme weather indices have a statistically significant information content in them is found to be valid based on linear and nonlinear methods for pairwise dependence. The second hypothesis, examines the value addition of nonlinear regression methods, and suggests that linear approaches may not alone be adequate. The results of this study can inform scientific understanding, generation and relevance of indices and end-to-end risk assessment systems in the context of climate impacts on crop yield. An immediate application may be in the context of NASA Earth Exchange (NEX) which facilitates the generation and dissemination of impacts relevant weather data and indices using a multitude of satellite-derived data sets and model outputs.

Data mining, food security, weather impacts↗

Data-driven Optimal Control Strategy for Virtual Synchronous Generator via Deep Reinforcement Learning Approach

This paper aims at developing a data-driven optimal control strategy for virtual synchronous generator (VSG) in the scenario where no expert knowledge or requirement for system model is available. Firstly, the optimal and adaptive control problem for VSG is transformed into a reinforcement learning task. Specifically, the control variables, i.e., virtual inertia and damping factor, are defined as the actions. Meanwhile, the active power output, angular frequency and its derivative are considered as the observations. Moreover, the reward mechanism is designed based on three preset characteristic functions to quantify the control targets: (1) maintaining the deviation of angular frequency within special limits; (2) preserving well-damped oscillations for both the angular frequency and active power output; (3) obtaining slow frequency drop in the transient process. Next, to maximize the cumulative rewards, a decentralized deep policy gradient algorithm, which features model-free and faster convergence, is developed and employed to find the optimal control policy. With this effort, a data-driven adaptive VSG controller can be obtained. By using the proposed controller, the inverter-based distributed generator can adaptively adjust its control variables based on current observations to fulfill the expected targets in model-free fashion. Finally, simulation results validate the feasibility and effectiveness of the proposed approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Computation of three dimensional turbulent boundary layers in internal flows, including turbomachinery rotor blades

A method is developed for predicting three-dimensional turbulent boundary layers occurring in internal flows, including rotor blades of turbomachinery. These boundary layers are complex, turbulent, and are subject to Coriolis and centrifugal forces. The algebraic Reynolds stress model (ARSM) developed in this paper satisfies the realizability conditions exactly and captures the changes in turbulenet structure arising from curvature and rotation. The prediction of pressure driven secondary flow agrees well with the data and all the three turbulent models (k-e, algebraic eddy viscosity, and ARSM) show the same level of agreement. The prediction of boundary layer on rotor blades shows much better agreement with the ARSM. It is essential to employ the higher order models to capture the effects of rotation and curvature and three-dimensional boundary layers in turbomachinery.

Zhang, J.↗

General Purpose Data-Driven Monitoring for Space Operations

As modern space propulsion and exploration systems improve in capability and efficiency, their designs are becoming increasingly sophisticated and complex. Determining the health state of these systems, using traditional parameter limit checking, model-based, or rule-based methods, is becoming more difficult as the number of sensors and component interactions grow. Data-driven monitoring techniques have been developed to address these issues by analyzing system operations data to automatically characterize normal system behavior. System health can be monitored by comparing real-time operating data with these nominal characterizations, providing detection of anomalous data signatures indicative of system faults or failures. The Inductive Monitoring System (IMS) is a data-driven system health monitoring software tool that has been successfully applied to several aerospace applications. IMS uses a data mining technique called clustering to analyze archived system data and characterize normal interactions between parameters. The scope of IMS based data-driven monitoring applications continues to expand with current development activities. Successful IMS deployment in the International Space Station (ISS) flight control room to monitor ISS attitude control systems has led to applications in other ISS flight control disciplines, such as thermal control. It has also generated interest in data-driven monitoring capability for Constellation, NASA's program to replace the Space Shuttle with new launch vehicles and spacecraft capable of returning astronauts to the moon, and then on to Mars. Several projects are currently underway to evaluate and mature the IMS technology and complementary tools for use in the Constellation program. These include an experiment on board the Air Force TacSat-3 satellite, and ground systems monitoring for NASA's Ares I-X and Ares I launch vehicles. The TacSat-3 Vehicle System Management (TVSM) project is a software experiment to integrate fault and anomaly detection algorithms and diagnosis tools with executive and adaptive planning functions contained in the flight software on-board the Air Force Research Laboratory TacSat-3 satellite. The TVSM software package will be uploaded after launch to monitor spacecraft subsystems such as power and guidance, navigation, and control (GN&C). It will analyze data in real-time to demonstrate detection of faults and unusual conditions, diagnose problems, and react to threats to spacecraft health and mission goals. The experiment will demonstrate the feasibility and effectiveness of integrated system health management (ISHM) technologies with both ground and on-board experiments.

Iverson, David L.↗

Evaluation and Intercomparison of Wildfire Smoke Forecasts from Multiple Modeling Systems for the 2019 Williams Flats Fire

Wildfire smoke is one of the most significant concerns of human and environmental health, associated with its substantial impacts on air quality, weather, and climate. However, biomass burning emissions and smoke remain among the largest sources of uncertainties in air quality forecasts. In this study, we evaluate the smoke emissions and plume forecasts from 12 state-of-the-art air quality forecasting systems during the Williams Flats fire in Washington State, US, August 2019, which was intensively observed during the Fire Influence on Regional to Global Environments and Air Quality (FIREX-AQ) field campaign. Model forecasts with lead times within 1 d are intercompared under the same framework based on observations from multiple platforms to reveal their performance regarding fire emissions, aerosol optical depth (AOD), surface PM2.5, plume injection, and surface PM2.5 to AOD ratio. The comparison of smoke organic carbon (OC) emissions suggests a large range of daily totals among the models, with a factor of 20 to 50. Limited representations of the diurnal patterns and day-to-day variations of emissions highlight the need to incorporate new methodologies to predict the temporal evolution and reduce uncertainty of smoke emission estimates. The evaluation of smoke AOD (sAOD) forecasts suggests overall underpredictions in both the magnitude and smoke plume area for nearly all models, although the high-resolution models have a better representation of the fine-scale structures of smoke plumes. The models driven by fire radiative power (FRP)-based fire emissions or assimilating satellite AOD data generally outperform the others. Additionally, limitations of the persistence assumption used when predicting smoke emissions are revealed by substantial underpredictions of sAOD on 8 August 2019, mainly over the transported smoke plumes, owing to the underestimated emissions on 7 August. In contrast, the surface smoke PM2.5 (sPM2.5) forecasts show both positive and negative overall biases for these models, with most members presenting more considerable diurnal variations of sPM2.5. Overpredictions of sPM2.5 are found for the models driven by FRP-based emissions during nighttime, suggesting the necessity to improve vertical emission allocation within and above the planetary boundary layer (PBL). Smoke injection heights are further evaluated using the NASA Langley Research Center's Differential Absorption High Spectral Resolution Lidar (DIAL-HSRL) data collected during the flight observations. As the fire became stronger over 3–8 August, the plume height became deeper, with a day-to-day range of about 2–9 km a.g.l. However, narrower ranges are found for all models, with a tendency of overpredicting the plume heights for the shallower injection transects and underpredicting for the days showing deeper injections. The misrepresented plume injection heights lead to inaccurate vertical plume allocations along the transects corresponding to transported smoke that is 1 d old. Discrepancies in model performance for surface PM2.5 and AOD are further suggested by the evaluation of their ratio, which cannot be compensated for by solely adjusting the smoke emissions but are more attributable to model representations of plume injections, besides other possible factors including the evolution of PBL depths and aerosol optical property assumptions. By consolidating multiple forecast systems, these results provide strategic insight on pathways to improve smoke forecasts.

AOD↗

EMPDF : inferring the Milky Way mass with data-driven distribution function in phase space

We introduce the emPDF (empirical distribution function), a novel dynamical modelling method that infers the gravitational potential from kinematic tracers with optimal statistical efficiency under the minimal assumption of steady state. emPDF determines the best-fitting potential by maximizing the similarity between instantaneous kinematics and the time-averaged phase-space distribution function (DF), which is empirically constructed from observation upon the theoretical foundation of oPDF (Han et al. 2016). This approach eliminates the need for presumed functional forms of DFs or orbit libraries required by conventional DF- or orbit-based methods. emPDF stands out for its flexibility, efficiency, and capability in handling observational effects, making it preferable to the popular Jeans equation or other minimal assumption methods, especially for the Milky Way (MW) outer halo where tracers often have limited sample size and poor data quality. We apply emPDF to infer the MW mass profile using Gaia DR3 data of satellite galaxies and globular clusters, obtaining enclosed masses of M (,r) = 26±8, 46±8, 90±13⁠, and 149±40 x 10 10 M ⊙ at r = 30, 50, 100⁠, and 200 kpc, respectively. These are consistent with the updated constraints from simulation-informed DF fitting (Li et al. 2020). While the simulation-informed DF offers superior precision owing to the additional information extracted from simulations, emPDF is independent of such supplementary knowledge and applicable to general tracer populations. emPDF is currently implemented for tracers with complete 6D kinematics within spherical potentials, but it can potentially be extended to address more general problems.

Astrophysics of Galaxies (astro-ph.GA)↗