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Results for “Ensemble-based methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

The Kalman filter is the optimal filter in the presence of known gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions. Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz model as well as more realistic models of the means and atmosphere. A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter situations to allow for correct update of the ensemble members. The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to be quite puzzling in that results state estimates are worse than for their filter analogue. In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use the Lorenz model to test and compare the behavior of a variety of implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Zhu, Yanqui↗
NASA NTRS1999

The Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

The Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Zhu, Yanqiu↗
NASA NTRS2014

Development of Super Ensemble-Based Aviation Turbulence Guidance (SEATG) for Air Traffic Management

A new method for forecasting turbulence is developed and evaluated using the high resolution weather model and in situ turbulence observations from commercial aircraft. The new method is an ensemble of various turbulence metrics from multiple time-lagged ensemble forecasts created using a sequence of four procedures. These include weather modeling, calculation of turbulence metrics, mapping the metrics into a common turbulence-scale, and production of final forecast. The new method uses similar methodology as current operational turbulence forecast with three improvements. First, it uses a higher resolution ((delta)x = 3 km) weather model to capture cloud resolving scale phenomena. Second, it computes the metrics for multiple forecasts that are combined at the same valid time resulting in a time-lagged ensemble of multiple turbulence metrics. Finally, it provides both deterministic and probabilistic turbulence forecasts. Results show the new forecasts match well with observed radar reflectivity along a surface front as well as convectively induced turbulence outside the clouds on research period. Overall performance skill of the new turbulence forecast compared with the observed EDR data during the research period is superior to any single turbulence metric. The probabilistic turbulence forecast is used in an example air traffic management application for creating a wind-optimal route considering turbulence information. The wind-optimal route passing through areas of 50% potential for moderate-or-greater turbulence and the lateral turbulence avoidance routes starting from three different waypoints along the wind-optimal route from Los Angeles international airport to John F. Kennedy international airport are calculated using different turbulence forecasts. This example shows additional flight time is required to avoid potential turbulence encounters.

modeling↗
NASA NTRS2006

An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems

Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

Monte Carlo↗
NASA NTRSDate not supplied

A Generalized, Compactly-Supported Correlation Function for Data Assimilation Applications

Correlation functions play an essential role in modern data assimilation, where they are used to model covariances given a set of tunable parameters or applied as tapering functions to localize covariances in ensemble-based schemes. One of the most widely-used correlation functions in data assimilation is the Gaspari and Cohn (1999) piecewise-rational, compactly-supported parametric correlation function (hereafter referred to as GC99). The GC99 correlation function is useful due to its tunable cut-off parameter c and Gaussian-like shape achieved when the parameter a is set to one-half. These properties are attractive for tapering functions in data assimilation applications. However, the GC99 correlation function is homogeneous over Euclidean 3-space and isotropic when restricted to the sphere, properties that may be less than ideal for some geophysical applications. GC99 is also compactly-supported on a sphere of fixed radius, which requires tuning of the cut-off parameter c that can depend on the specific application. This work presents a generalization of the GC99 correlation function that allows the cut-off parameter c and shape parameter a to vary over space to gain more flexibility in shape while maintaining its compact support property. The function, which we call the Generalized Gaspari Cohn (GenGC) correlation function, introduces inhomogeneity in Euclidean 3-space and anisotropy when restricted to the sphere by allowing both parameters c and a to vary, as functions, over the spatial domain. The GC99 correlation function is a special case of GenGC where the functions c and a are held constant, as fixed parameters rather than functions. The GenGC correlation function also generalizes the follow-on to the work of Gaspari and Cohn (1999) presented in Gaspari et al. (2006), which allowed a to vary while keeping c fixed. We illustrate through simple one- and two-dimensional examples the variety of inhomogeneous and anisotropic correlation functions GenGC can produce by varying c and a over space, and suggest applications where they may be useful in data assimilation, such as covariance modeling or localization. In particular, we describe how the GenGC correlation function can be used to construct covariances using correlation length and variance fields derived from dynamics. For example, the correlation length field for advective dynamics is governed by a partial differential equation (PDE) in N spatial dimensions, where N is the number of space dimensions of the state. Correlation length fields can be determined from this PDE and used with GenGC to construct the corresponding correlations. We can then approximate the full covariance by rescaling by the variance, which also satisfies a PDE in N spatial dimensions for advective dynamics. Thus we can approximate the full covariance without solving the covariance PDE, which is in 2N spatial dimensions, by solving just two PDEs each in only N spatial dimensions. This approach to evolving the correlation length and variance fields, then reconstructing the correlations using GenGC, is suggested as an alternative to current methods of covariance modeling in data assimilation algorithms.

GC99↗
NASA NTRSDate not supplied

Spaceborne Lidar Retrievals of PM2.5 for Air Quality Studies and Applications

Fine particulate matter (PM2.5) substantially contributes to air pollution and negatively affects human health. While many studies have investigated the use of passive column-integrated aerosol optical depth to infer surface PM2.5, the use of lidar observations for air quality characterization is not nearly as extensive. Lidar measurements are critical, however, due to the vertical aerosol information they provide, including near the surface. In this presentation, we first provide an overview of various lidar-based approaches for estimating PM2.5 concentrations and then discuss how lidar measurements can assist other air quality applications. For example, estimates of PM2.5 have been obtained in a physics-based approach through CALIOP near-surface aerosol extinction retrievals, assumptions on the mass extinction efficiency, and incorporating other parameters (an aerosol hygroscopic growth factor and PM2.5/PM10 ratio). Application of this algorithm over the contiguous United States (CONUS) from 2006 to 2018 yielded larger PM2.5 values over the eastern and western CONUS (~10-15 μg/m³) and lower PM2.5 levels in the central CONUS (~5 μg/m³). These spatial patterns were similar to those from gridded PM2.5 concentrations obtained through in situ measurements at ground stations operated by the US Environmental Protection Agency. In another approach, the Cloud Aerosol Transport System (CATS) lidar was used with the Goddard Earth Observing System (GEOS) model in a 1D ensemble-based variational technique to obtain PM2.5 over the US and Europe, and the spatial patterns of the CATS/GEOS based PM2.5 concentrations generally captured those from surface stations (with corresponding hourly EPA PM2.5 vs CATS PM2.5 statistics of R=0.4 and bias=1.5 μg/m³). In our recent work, as part of the Models, In situ, and Remote sensing of Aerosols (MIRA) Working Group, we have applied both the CALIOP and CATS/GEOS based approaches over the highly polluted country of India during the post-monsoon season (September-October 2016). We derived elevated levels of two-month mean PM2.5 (~100 μg/m³) in northern India, especially near New Delhi. These high PM2.5 concentrations in the Indo-Gangetic plain are driven in large part from the seasonal burning of crop residue and meteorological conditions typical at this time of the year, such as low wind speeds and a shallow boundary layer. While the satellite-derived PM2.5 moderately replicates (R = ~0.7-0.9) the spatial variability in the two-month mean of surface in situ PM2.5 from monitoring sites operated by the Central and State Pollution Control Boards, we show results from specific scenes for which there are large deviations between the satellite-derived PM2.5 and in situ measurements. Other current work on this topic focuses on developing PM2.5 estimates using airborne high spectral resolution lidar measurements through machine learning regression algorithms and involves several parameters (e.g., aerosol extinction, color ratio, lidar ratio). Application of this method over major metropolitan areas in the US and Asia have resulted in high correlations (R = 0.93) with surface measurements. This airborne lidar approach can be adapted to spaceborne lidar measurements, and all three of these approaches can be applied to ESA’s EarthCARE Atmospheric Lidar instrument, setting the stage for the future Cloud Aerosol Lidar for Global Scale Observations of the Ocean-Land Atmosphere System (CALIGOLA) mission. Ultimately, beyond estimates of PM2.5, the aerosol vertical distribution from lidars can benefit studies involving passive sensor approaches for PM2.5 proxies (including from geostationary satellites), wildfire smoke plume injection heights, volcanic emissions (e.g., ash height retrievals), and aerosol/air quality model assimilation, evaluation, and forecasts.

Travis D Toth↗