skip to main content

Title: Adaptive Localization for Satellite Radiance Observations in an Ensemble Kalman Filter

Localization is essential to effectively assimilate satellite radiances in ensemble Kalman filters. However, the vertical location and separation from a model grid point variable for a radiance observation are not well defined, which results in complexities when localizing the impact of radiance observations. An adaptive method is proposed to estimate an effective vertical localization independently for each assimilated channel of every satellite platform. It uses sample correlations between ensemble priors of observations and state variables from a cycling data assimilation to estimate the localization function that minimizes the sampling error. The estimated localization functions are approximated by three localization parameters: the localization width, maximum value, and vertical location of the radiance observations. Adaptively estimated localization parameters are used in assimilation experiments with the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) model and the National Oceanic and Atmospheric Administration (NOAA) operational ensemble Kalman filter (EnKF). Results show that using the adaptive localization width and vertical location for radiance observations is more beneficial than also including the maximum localization value. The experiment using the adaptively estimated localization width and vertical location performs better than the default Gaspari and Cohn (GC) experiment, and produces similar errors to the optimal GC experiment. The adaptive localization parameters can be computed during the assimilation procedure, so the computational cost needed to tune the optimal GC localization width is saved.

more » « less
Author(s) / Creator(s):
 ;  ;  ;  
Publisher / Repository:
DOI PREFIX: 10.1029
Date Published:
Journal Name:
Journal of Advances in Modeling Earth Systems
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract Particle filters avoid parametric estimates for Bayesian posterior densities, which alleviates Gaussian assumptions in nonlinear regimes. These methods, however, are more sensitive to sampling errors than Gaussian-based techniques such as ensemble Kalman filters. A recent study by the authors introduced an iterative strategy for particle filters that match posterior moments—where iterations improve the filter’s ability to draw samples from non-Gaussian posterior densities. The iterations follow from a factorization of particle weights, providing a natural framework for combining particle filters with alternative filters to mitigate the impact of sampling errors. The current study introduces a novel approach to forming an adaptive hybrid data assimilation methodology, exploiting the theoretical strengths of nonparametric and parametric filters. At each data assimilation cycle, the iterative particle filter performs a sequence of updates while the prior sample distribution is non-Gaussian, then an ensemble Kalman filter provides the final adjustment when Gaussian distributions for marginal quantities are detected. The method employs the Shapiro–Wilk test to determine when to make the transition between filter algorithms, which has outstanding power for detecting departures from normality. Experiments using low-dimensional models demonstrate that the approach has a significant value, especially for nonhomogeneous observation networks and unknown model process errors. Moreover, hybrid factors are extended to consider marginals of more than one collocated variables using a test for multivariate normality. Findings from this study motivate the use of the proposed method for geophysical problems characterized by diverse observation networks and various dynamic instabilities, such as numerical weather prediction models. Significance Statement Data assimilation statistically processes observation errors and model forecast errors to provide optimal initial conditions for the forecast, playing a critical role in numerical weather forecasting. The ensemble Kalman filter, which has been widely adopted and developed in many operational centers, assumes Gaussianity of the prior distribution and solves a linear system of equations, leading to bias in strong nonlinear regimes. On the other hand, particle filters avoid many of those assumptions but are sensitive to sampling errors and are computationally expensive. We propose an adaptive hybrid strategy that combines their advantages and minimizes the disadvantages of the two methods. The hybrid particle filter–ensemble Kalman filter is achieved with the Shapiro–Wilk test to detect the Gaussianity of the ensemble members and determine the timing of the transition between these filter updates. Demonstrations in this study show that the proposed method is advantageous when observations are heterogeneous and when the model has an unknown bias. Furthermore, by extending the statistical hypothesis test to the test for multivariate normality, we consider marginals of more than one collocated variable. These results encourage further testing for real geophysical problems characterized by various dynamic instabilities, such as real numerical weather prediction models. 
    more » « less
  2. Abstract

    Traditional ensemble Kalman filter data assimilation methods make implicit assumptions of Gaussianity and linearity that are strongly violated by many important Earth system applications. For instance, bounded quantities like the amount of a tracer and sea ice fractional coverage cannot be accurately represented by a Gaussian that is unbounded by definition. Nonlinear relations between observations and model state variables abound. Examples include the relation between a remotely sensed radiance and the column of atmospheric temperatures, or the relation between cloud amount and water vapor quantity. Part I of this paper described a very general data assimilation framework for computing observation increments for non-Gaussian prior distributions and likelihoods. These methods can respect bounds and other non-Gaussian aspects of observed variables. However, these benefits can be lost when observation increments are used to update state variables using the linear regression that is part of standard ensemble Kalman filter algorithms. Here, regression of observation increments is performed in a space where variables are transformed by the probit and probability integral transforms, a specific type of Gaussian anamorphosis. This method can enforce appropriate bounds for all quantities and deal much more effectively with nonlinear relations between observations and state variables. Important enhancements like localization and inflation can be performed in the transformed space. Results are provided for idealized bivariate distributions and for cycling assimilation in a low-order dynamical system. Implications for improved data assimilation across Earth system applications are discussed.

    more » « less
  3. Abstract

    For data assimilation to provide faithful state estimates for dynamical models, specifications of observation uncertainty need to be as accurate as possible. Innovation-based methods based on Desroziers diagnostics, are commonly used to estimate observation uncertainty, but such methods can depend greatly on the prescribed background uncertainty. For ensemble data assimilation, this uncertainty comes from statistics calculated from ensemble forecasts, which require inflation and localization to address under sampling. In this work, we use an ensemble Kalman filter (EnKF) with a low-dimensional Lorenz model to investigate the interplay between the Desroziers method and inflation. Two inflation techniques are used for this purpose: 1) a rigorously tuned fixed multiplicative scheme and 2) an adaptive state-space scheme. We document how inaccuracies in observation uncertainty affect errors in EnKF posteriors and study the combined impacts of misspecified initial observation uncertainty, sampling error, and model error on Desroziers estimates. We find that whether observation uncertainty is over- or underestimated greatly affects the stability of data assimilation and the accuracy of Desroziers estimates and that preference should be given to initial overestimates. Inline estimates of Desroziers tend to remove the dependence between ensemble spread–skill and the initially prescribed observation error. In addition, we find that the inclusion of model error introduces spurious correlations in observation uncertainty estimates. Further, we note that the adaptive inflation scheme is less robust than fixed inflation at mitigating multiple sources of error. Last, sampling error strongly exacerbates existing sources of error and greatly degrades EnKF estimates, which translates into biased Desroziers estimates of observation error covariance.

    Significance Statement

    To generate accurate predictions of various components of the Earth system, numerical models require an accurate specification of state variables at our current time. This step adopts a probabilistic consideration of our current state estimate versus information provided from environmental measurements of the true state. Various strategies exist for estimating uncertainty in observations within this framework, but are sensitive to a host of assumptions, which are investigated in this study.

    more » « less
  4. Abstract Data assimilation (DA) aims to combine observations/data with a model to maximize the utility of information for obtaining the optimal estimate. The maximum likelihood ensemble filter (MLEF) is a sequential DA method or a filter-type method. Weaknesses of the filter method are assimilating time-integrated observations and estimating empirical parameter estimation. The reason is that the forward model is employed outside of the analysis procedure in this type of DA method. To overcome these weaknesses, the MLEF is now extended as a smoother and the novel maximum likelihood ensemble smoother (MLES) is proposed. The MLES is a smoothing method with variational-like qualities, specifically in the cost function. Rather than using the error information from a single temporal location to solve for the optimal analysis update as done by the MLEF, the MLES can include observations and the forward model within a chosen time window. The newly proposed DA method is first validated by a series of rigorous and thorough performance tests using the Lorenz 96 model. Then, as DA is known to be used extensively to increase the predictability of the commonly chaotic dynamical systems seen in meteorological applications, this study demonstrates the MLES with a model chaotic problem governed by the 1D Kuramoto–Sivashinky (KS) equation. Additionally, the MLES is shown to be an effective method in improving the estimate of uncertain empirical model parameters. The MLES and MLEF are then directly compared and it is shown that the performance of the MLES is adequate and that it is a good candidate for increasing the predictability of a chaotic dynamical system. Future work will focus on an extensive application of the MLES to highly turbulent flows. 
    more » « less
  5. Abstract

    The present study investigates the impact of assimilating electron density profiles from the Constellation Observing System for Meteorology, Ionosphere, and Climate‐2 (COSMIC‐2) mission in a whole atmosphere data assimilation system. The observations are assimilated into the Whole Atmosphere Community Climate Model with thermosphere‐ionosphere eXtension (WACCMX) using the Data Assimilation Research Testbed (DART) ensemble adjustment Kalman filter. Assimilation of the COSMIC‐2 electron density profiles during the evaluation time period of 25–30 April 2020 leads to improvement in both the 1 hr forecast and analysis electron densities in WACCMX + DART. Compared to a control experiment that does not assimilate COSMIC‐2 observations, the assimilation of the COSMIC‐2 electron density profiles reduces the 1 hr forecast root mean square error (RMSE) and bias with respect to COSMIC‐2 observations at 300 km by 6.76% and 24.91%, respectively. Assimilation of the COSMIC‐2 electron density profiles does not significantly influence the RMSE and bias with respect to ground‐based Global Navigation Satellite System vertical total electron content observations. The equatorial vertical plasma drift velocity in WACCMX + DART is changed by ±5–10 ms−1due to the assimilation of the COSMIC‐2 electron density profiles, indicating that the model representation of the electrodynamics of the low latitude ionosphere are significantly impacted by the assimilation of COSMIC‐2 observations.

    more » « less