scholarly journals Interpreting estimated observation error statistics of weather radar measurements using the ICON-LAM-KENDA system

2021 ◽  
Vol 14 (8) ◽  
pp. 5735-5756
Author(s):  
Yuefei Zeng ◽  
Tijana Janjic ◽  
Yuxuan Feng ◽  
Ulrich Blahak ◽  
Alberto de Lozar ◽  
...  
Keyword(s):  
Covariance Matrix ◽  
A Priori ◽  
Weather Radar ◽  
Radar Observation ◽  
Wind Data ◽  
Observation Error ◽  
Error Statistics ◽  
Error Sources ◽  
Radar Measurements ◽  
Observation Space

Abstract. Assimilation of weather radar measurements including radar reflectivity and radial wind data has been operational at the Deutscher Wetterdienst, with a diagonal observation error (OE) covariance matrix. For an implementation of a full OE covariance matrix, the statistics of the OE have to be a priori estimated, for which the Desroziers method has been often used. However, the resulted statistics consists of contributions from different error sources and are difficult to interpret. In this work, we use an approach that is based on samples for truncation error in radar observation space to approximate the representation error due to unresolved scales and processes (RE) and compare its statistics with the OE statistics estimated by the Desroziers method. It is found that the statistics of the RE help the understanding of several important features in the variances and correlation length scales of the OE for both reflectivity and radial wind data and the other error sources from the microphysical scheme, radar observation operator and the superobbing technique may also contribute, for instance, to differences among different elevations and observation types. The statistics presented here can serve as a guideline for selecting which observations are assimilated and for assignment of the OE covariance matrix that can be diagonal or full and correlated.

scholarly journals Interpreting estimated Observation Error Statistics of Weather Radar Measurements using the ICON-LAM-KENDA System

2021 ◽  
Author(s):  
Yuefei Zeng ◽  
Tijana Janjic ◽  
Yuxuan Feng ◽  
Ulrich Blahak ◽  
Alberto de Lozar ◽  
...  
Keyword(s):  
Covariance Matrix ◽  
A Priori ◽  
Weather Radar ◽  
Radar Observation ◽  
Wind Data ◽  
Observation Error ◽  
Error Statistics ◽  
Error Sources ◽  
Radar Measurements ◽  
Observation Space

Abstract. Assimilation of weather radar measurements including radar reflectivity and radial wind data has been operational at the Deutscher Wetterdienst, with a diagonal observation error (OE) covariance matrix. For an implementation of a full OE covariance matrix, the statistics of the OE have to be a priori estimated, for which the Desroziers method has been often used. However, the resulted statistics consists of contributions from different error sources and are difficult to interpret. In this work, we use an approach that is based on samples for truncation error in radar observation space to approximate the representation error due to unresolved scales and processes (RE) and compare its statistics with the OE statistics estimated by the Desroziers method. It is found that the statistics of the RE help the understanding of several important features in the variances and correlation length scales of the OE for both reflectivity and radial wind data and the other error sources from the microphysical scheme, radar observation operator and the superobbing technique may also contribute, for instance, to differences among different elevations and observation types. The statistics presented here can serve as a guideline for selecting which observations to assimilate and for assignment of the OE covariance matrix that can be diagonal or full and correlated.

scholarly journals An Efficient Way to Account for Observation Error Correlations in the Assimilation of Data from the Future SWOT High-Resolution Altimeter Mission

2016 ◽  
Vol 33 (12) ◽  
pp. 2755-2768 ◽  
Author(s):  
Giovanni Abdelnur Ruggiero ◽  
Emmanuel Cosme ◽  
Jean-Michel Brankart ◽  
Julien Le Sommer ◽  
Clement Ubelmann
Keyword(s):  
Covariance Matrix ◽  
Large Fraction ◽  
Observation Error ◽  
Error Statistics ◽  
Practical Applications ◽  
Spatially Correlated ◽  
The Future ◽  
Mean Square Errors ◽  
Observation Vector ◽  
Filter Analysis

AbstractMost data assimilation algorithms require the inverse of the covariance matrix of the observation errors. In practical applications, the cost of computing this inverse matrix with spatially correlated observation errors is prohibitive. Common practices are therefore to subsample or combine the observations so that the errors of the assimilated observations can be considered uncorrelated. As a consequence, a large fraction of the available observational information is not used in practical applications. In this study, a method is developed to account for the correlations of the errors that will be present in the wide-swath sea surface height measurements, for example, the Surface Water and Ocean Topography (SWOT) mission. It basically consists of the transformation of the observation vector so that the inverse of the corresponding covariance matrix can be replaced by a diagonal matrix, thus allowing to genuinely take into account errors that are spatially correlated in physical space. Numerical experiments of ensemble Kalman filter analysis of SWOT-like observations are conducted with three different observation error covariance matrices. Results suggest that the proposed method provides an effective way to account for error correlations in the assimilation of the future SWOT data. The transformation of the observation vector proposed herein yields both a significant reduction of the root-mean-square errors and a good consistency between the filter analysis error statistics and the true error statistics.

scholarly journals Efficient Adaptive Error Parameterizations for Square Root or Ensemble Kalman Filters: Application to the Control of Ocean Mesoscale Signals

2010 ◽  
Vol 138 (3) ◽  
pp. 932-950 ◽  
Author(s):  
Jean-Michel Brankart ◽  
Emmanuel Cosme ◽  
Charles-Emmanuel Testut ◽  
Pierre Brasseur ◽  
Jacques Verron
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Error Estimates ◽  
Forecast Error ◽  
Observation Error ◽  
Square Root ◽  
Error Statistics ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Optimal Estimates

Abstract In Kalman filter applications, an adaptive parameterization of the error statistics is often necessary to avoid filter divergence, and prevent error estimates from becoming grossly inconsistent with the real error. With the classic formulation of the Kalman filter observational update, optimal estimates of general adaptive parameters can only be obtained at a numerical cost that is several times larger than the cost of the state observational update. In this paper, it is shown that there exists a few types of important parameters for which optimal estimates can be computed at a negligible numerical cost, as soon as the computation is performed using a transformed algorithm that works in the reduced control space defined by the square root or ensemble representation of the forecast error covariance matrix. The set of parameters that can be efficiently controlled includes scaling factors for the forecast error covariance matrix, scaling factors for the observation error covariance matrix, or even a scaling factor for the observation error correlation length scale. As an application, the resulting adaptive filter is used to estimate the time evolution of ocean mesoscale signals using observations of the ocean dynamic topography. To check the behavior of the adaptive mechanism, this is done in the context of idealized experiments, in which model error and observation error statistics are known. This ideal framework is particularly appropriate to explore the ill-conditioned situations (inadequate prior assumptions or uncontrollability of the parameters) in which adaptivity can be misleading. Overall, the experiments show that, if used correctly, the efficient optimal adaptive algorithm proposed in this paper introduces useful supplementary degrees of freedom in the estimation problem, and that the direct control of these statistical parameters by the observations increases the robustness of the error estimates and thus the optimality of the resulting Kalman filter.

Enhancing the impact of IASI observations through an updated observation-error covariance matrix

2016 ◽  
Vol 142 (697) ◽  
pp. 1767-1780 ◽  
Author(s):  
Niels Bormann ◽  
Massimo Bonavita ◽  
Rossana Dragani ◽  
Reima Eresmaa ◽  
Marco Matricardi ◽  
...  
Keyword(s):  
Covariance Matrix ◽  
Observation Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
The Impact

scholarly journals Influence of Disdrometer Type on Weather Radar Algorithms from Measured DSD: Application to Italian Climatology

Atmosphere ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 360 ◽  
Author(s):  
Elisa Adirosi ◽  
Nicoletta Roberto ◽  
Mario Montopoli ◽  
Eugenio Gorgucci ◽  
Luca Baldini
Keyword(s):  
Drop Size ◽  
Weather Radar ◽  
Size Distributions ◽  
Regression Methods ◽  
Radar Meteorology ◽  
Quality Checks ◽  
Radar Measurements ◽  
Drop Size Distributions ◽  
First And Second Generation ◽  
Theoretical Considerations

Relations for retrieving precipitation and attenuation information from radar measurements play a key role in radar meteorology. The uncertainty in such relations highly affects the precipitation and attenuation estimates. Weather radar algorithms are often derived by applying regression methods to precipitation measurements and radar observables simulated from datasets of drop size distributions (DSD) using microphysical and electromagnetic assumptions. DSD datasets can be derived from theoretical considerations or obtained from experimental measurements collected throughout the years by disdrometers. Although the relations obtained from experimental disdrometer datasets can be generally considered more representative of a specific climatology, the measuring errors, which depend on the specific type of disdrometer used, introduce an element of uncertainty to the final retrieval algorithms. Eventually, data quality checks and filtering procedures applied to disdrometer measurements play an important role. In this study, we pursue two main goals: (i) evaluate two different techniques for establishing weather radar algorithms from measured DSD, and (ii) investigate to what extent dual-polarization radar algorithms derived from experimental DSD datasets are influenced by the different error structures introduced by the various disdrometer types (namely 2D video disdrometer, first and second generation of OTT Parsivel disdrometer, and Thies Clima disdrometer) used to collect the data. Furthermore, weather radar algorithms optimized for Italian climatology are presented and discussed.

scholarly journals Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Algorithms ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 228
Author(s):  
Rasoul Shafipour ◽  
Gonzalo Mateos
Keyword(s):  
Inverse Problem ◽  
Covariance Matrix ◽  
A Priori ◽  
Dynamic Network ◽  
Streaming Data ◽  
Optimal Time ◽  
Time Varying ◽  
Graph Learning ◽  
Topology Inference ◽  
Diffusion Dynamics

We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations’ covariance matrix and the so-called graph shift operator (GSO—a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations’ empirical covariance matrix. For streaming data, said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.

Weather radar calibration by means of the metallic sphere and multiparameter radar measurements

1995 ◽  
Vol 18 (1) ◽  
pp. 57-70 ◽  
Author(s):  
G. Scarchilli ◽  
E. Gorgucci ◽  
D. Giuli ◽  
L. Baldini ◽  
L. Facheris ◽  
...  
Keyword(s):  
Weather Radar ◽  
Radar Measurements ◽  
Radar Calibration ◽  
Multiparameter Radar

scholarly journals Multiscale Representation of Observation Error Statistics in Data Assimilation

Sensors ◽  
2020 ◽  
Vol 20 (5) ◽  
pp. 1460
Author(s):  
Vincent Chabot ◽  
Maëlle Nodet ◽  
Arthur Vidard
Keyword(s):  
Data Assimilation ◽  
Real Life ◽  
Covariance Matrices ◽  
Multiscale Modelling ◽  
Observation Error ◽  
Error Statistics ◽  
Life Data ◽  
Promising Tool ◽  
Error Covariance ◽  
Real Life Data

Accounting for realistic observation errors is a known bottleneck in data assimilation, because dealing with error correlations is complex. Following a previous study on this subject, we propose to use multiscale modelling, more precisely wavelet transform, to address this question. This study aims to investigate the problem further by addressing two issues arising in real-life data assimilation: how to deal with partially missing data (e.g., concealed by an obstacle between the sensor and the observed system), and how to solve convergence issues associated with complex observation error covariance matrices? Two adjustments relying on wavelets modelling are proposed to deal with those, and offer significant improvements. The first one consists of adjusting the variance coefficients in the frequency domain to account for masked information. The second one consists of a gradual assimilation of frequencies. Both of these fully rely on the multiscale properties associated with wavelet covariance modelling. Numerical results on twin experiments show that multiscale modelling is a promising tool to account for correlations in observation errors in realistic applications.

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