Improving Ensemble Volcanic Ash Forecasts by Direct Insertion of Satellite Data and Ensemble Filtering

Improved quantitative forecasts of volcanic ash are in great demand by the aviation industry to enable better risk management during disruptive volcanic eruption events. However, poor knowledge of volcanic source parameters and other dispersion and transport modelling uncertainties, such as those due to errors in numerical weather prediction fields, make this problem very challenging. Nonetheless, satellite-based algorithms that retrieve ash properties, such as mass load, effective radius, and cloud top height, combined with inverse modelling techniques, such as ensemble filtering, can significantly ameliorate these problems. The satellite-retrieved data can be used to better constrain the volcanic source parameters, but they can also be used to avoid the description of the volcanic source altogether by direct insertion into the forecasting model. In this study we investigate the utility of the direct insertion approach when employed within an ensemble filtering framework. Ensemble members are formed by initializing dispersion models with data from different timesteps, different values of cloud top height, thickness, and NWP ensemble members. This large ensemble is then filtered with respect to observations to produce a refined forecast. We apply this approach to 14 different eruption case studies in the tropical atmosphere. We demonstrate that the direct insertion of data improves model forecast skill, particularly when it is used in a hybrid ensemble in which some ensemble members are initialized from the volcanic source. Moreover, good forecast skill can be obtained even when detailed satellite retrievals are not available, which is frequently the case for volcanic eruptions in the tropics.

Score matching filters

<p>A widely popular group of data assimilation methods in meteorological and geophysical sciences is formed by filters based on Monte-Carlo approximation of the traditional Kalman filter, e.g. <span>E</span><span>nsemble Kalman filter </span><span>(EnKF)</span><span>, </span><span>E</span><span>nsemble </span><span>s</span><span>quare-root filter and others. Due to the computational cost, ensemble </span><span>size </span><span>is </span><span>usually </span><span>small </span><span>compar</span><span>ed</span><span> to the dimension of the </span><span>s</span><span>tate </span><span>vector. </span><span>Traditional </span> <span>EnKF implicitly uses the sample covariance which is</span><span> a poor estimate of the </span><span>background covariance matrix - singular and </span><span>contaminated by </span><span>spurious correlations. </span></p><p><span>W</span><span>e focus on modelling the </span><span>background </span><span>covariance matrix by means of </span><span>a linear model for its inverse. This is </span><span>particularly </span><span>useful</span> <span>in</span><span> Gauss-Markov random fields (GMRF), </span><span>where</span> <span>the inverse covariance matrix has </span><span>a banded </span><span>structure</span><span>. </span><span>The parameters of the model are estimated by the</span><span> score matching </span><span>method which </span><span>provides</span><span> estimators in a closed form</span><span>, cheap to compute</span><span>. The resulting estimate</span><span> is a key component of the </span><span>proposed </span><span>ensemble filtering algorithms. </span><span>Under the assumption that the state vector is a GMRF in every time-step, t</span><span>he Score matching filter with Gaussian resamplin</span><span>g (SMF-GR) </span><span>gives</span><span> in every time-step a consistent (in the large ensemble limit) estimator of mean and covariance matrix </span><span>of the forecast and analysis distribution</span><span>. Further, we propose a filtering method called Score matching ensemble filter (SMEF), based on regularization of the EnK</span><span>F</span><span>. Th</span><span>is</span><span> filter performs well even for non-Gaussian systems with non-linear dynamic</span><span>s</span><span>. </span><span>The performance of both filters is illustrated on a simple linear convection model and Lorenz-96.</span></p>

Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix

<p style='text-indent:20px;'>We present an ensemble filtering method based on a linear model for the precision matrix (the inverse of the covariance) with the parameters determined by Score Matching Estimation. The method provides a rigorous covariance regularization when the underlying random field is Gaussian Markov. The parameters are found by solving a system of linear equations. The analysis step uses the inverse formulation of the Kalman update. Several filter versions, differing in the construction of the analysis ensemble, are proposed, as well as a Score matching version of the Extended Kalman Filter.</p>

The synergistic combination of fuzzy C-means and ensemble filtering for class noise detection

Purpose The purpose of this study is to enhance data quality and overall accuracy and improve certainty by reducing the negative impacts of the FCM algorithm while clustering real-world data and also decreasing the inherent noise in data sets. Design/methodology/approach The present study proposed a new effective model based on fuzzy C-means (FCM), ensemble filtering (ENS) and machine learning algorithms, called an FCM-ENS model. This model is mainly composed of three parts: noise detection, noise filtering and noise classification. Findings The performance of the proposed model was tested by conducting experiments on six data sets from the UCI repository. As shown by the obtained results, the proposed noise detection model very effectively detected the class noise and enhanced performance in case the identified class noisy instances were removed. Originality/value To the best of the authors’ knowledge, no effort has been made to improve the FCM algorithm in relation to class noise detection issues. Thus, the novelty of existing research is combining the FCM algorithm as a noise detection technique with ENS to reduce the negative effect of inherent noise and increase data quality and accuracy.

Towards an Effective and Scalable Hybrid Data Assimilation for Hydrogeophysical Applications

&lt;p&gt;A number of studies have shown that multivariate data assimilation into the land surface models would improve model predictive skills. Soil moisture, streamflow and Evapotranspiration are among those environmental variables that greatly affect flood forecasting, drought monitoring/prediction, and agricultural production that collectively control the land and atmospheric system. However, land surface models most often do not provide accurate and reliable estimates of fluxes and storages and are subject to large uncertainties stemming from hydrometeorological forcing, model parameters, boundary or initial condition and model structure. Here, we present the state-of-the art data assimilation methods, covering the evolution of methods, discussing their pros and cons and introduce a novel approach that couples a deterministic four&amp;#8208;dimensional variational (4DVAR) assimilation method with an evolutionary ensemble filtering that together&amp;#160; significantly improve the estimation of storages and fluxes, hence better forecasting skill. The Evolutionalry Particle Filter with MCMC (EPFM) uses the Genetic Algorithm (GA) to effectively sample the particles to better represent the posterior distribution of model prognostic variables and parameters. This is followed by coupling EPFM and 4DVAR which results in a superior DA approach, the so-called Hybrid Ensemble and Variational Data Assimilation framework for Environmental systems (HEAVEN). The method explicitly accounts for model structural error during the assimilation process. The application of methods is presented for both flood and drought forecasting while utilizing the remotely sensed observations.&lt;/p&gt;

A Nested Ensemble Filtering Approach for Parameter Estimation and Uncertainty Quantification of Traffic Noise Models

In this study, a nested ensemble filtering (NEF) approach is advanced for uncertainty parameter estimation and uncertainty quantification of a traffic noise model. As an extension of the ensemble Kalman filter (EnKF) and particle filter methods, the proposed NEF method improves upon the ensemble Kalman filter (EnKF) method by incorporating the sample importance resampling (SIR) procedures into the EnKF update process. The NEF method can avoid the overshooting problem (abnormal value (e.g., outside the predefined ranges, complex values) in parameter or state samples) existing in the EnKF update process. The proposed NEF method is applied to the traffic noise prediction on the Trans-Canada Highway in the City of Regina to demonstrate its applicability. The results indicate that: (a) when determining parameters in the traffic noise prediction model, the NEF method provides accurate estimation; (b) the model parameters can be recursively corrected with the NEF method whenever a new measurement becomes available; (c) the uncertainty in the traffic noise model (should be the noise itself) can be well reduced and quantified through the proposed NEF approach.

A Multiscale Alignment Method for Ensemble Filtering with Displacement Errors

High-resolution models nowadays simulate phenomena across many scales and pose challenges to the design of efficient data assimilation methods that reduce errors at all scales. Smaller-scale features experience rapid nonlinear error growth that gives rise to displacement errors, which cause suboptimal ensemble filter performance. Previous studies have started exploring methods that can reduce displacement errors. In this study, a multiscale alignment (MSA) method is proposed for ensemble filtering. The MSA method iteratively processes the model state from the largest to the smallest scales. At each scale, an ensemble filter is applied to update the state with observations, and the analysis increments are utilized to derive displacement vectors for each member that align the ensemble at smaller scales before the next iteration. The nonlinearity in smaller-scale priors is reduced by removing larger-scale displacement errors. Because the displacement vectors are derived from analysis increments in the state space rather than the nonlinear observation-space cost function formulated in previous studies, this method provides a less costly and more robust way to solve for the displacement vectors. Observing system simulation experiments using a two-layer quasigeostrophic model were conducted to provide a proof of concept of the MSA method. Results show that the MSA method significantly improves the accuracy of posteriors compared to the existing ensemble filter methods with or without multiscale localization. Advantage of the MSA method are more evident when the ensemble size is relatively small and the cycling period is comparable to the average eddy turnover time of the dynamical system.