scholarly journals Analytic characterization of random errors in spectral dual-polarized cloud radar observations

2021 ◽  
Author(s):  
Alexander Myagkov ◽  
Davide Ori
Keyword(s):  
Covariance Matrix ◽  
Joint Probability ◽  
Complete Characterization ◽  
Linear Functions ◽  
Random Errors ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Mathematical Equations ◽  
Differential Reflectivity

Abstract. This study presents the first-ever complete characterization of random errors in dual-polarimetric spectral observations of meteorological targets by cloud radars. The characterization is given by means of mathematical equations for joint probability density functions (PDF) and error covariance matrices. The derived equations are checked for consistency using real radar measurements. One of the main conclusions of the study is that the convenient representation of spectral polarimetric measurements including differential reflectivity ZDR, correlation coefficient pHV, and differential phase ΦDP is not suited for the proper characterization of the error covariance matrix. This is because the aforementioned quantities are complex, non-linear functions of the radar raw data and thus their error covariance matrix is commonly derived using simplified linear relations and by neglecting the correlation of errors. This study formulates the spectral polarimetric measurements in terms of a different set of quantities that allows for a proper analytic treatment of their error covariance matrix. The results given in this study allow for utilization of spectral polarimetric measurements for advanced meteorological applications, among which are variational retrieval techniques, data assimilation, and sensitivity analysis.

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

Impact of AMSU-A Radiances in a Column Ensemble Kalman Filter

2018 ◽  
Vol 146 (12) ◽  
pp. 3949-3976 ◽  
Author(s):  
Herschel L. Mitchell ◽  
P. L. Houtekamer ◽  
Sylvain Heilliette
Keyword(s):  
Covariance Matrix ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Microwave Sounding Unit ◽  
The Matrix ◽  
Microwave Sounding ◽  
Background Temperature ◽  
The Difference

Abstract A column EnKF, based on the Canadian global EnKF and using the RTTOV radiative transfer (RT) model, is employed to investigate issues relating to the EnKF assimilation of Advanced Microwave Sounding Unit-A (AMSU-A) radiance measurements. Experiments are performed with large and small ensembles, with and without localization. Three different descriptions of background temperature error are considered: 1) using analytical vertical modes and hypothetical spectra, 2) using the vertical modes and spectrum of a covariance matrix obtained from the global EnKF after 2 weeks of cycling, and 3) using the vertical modes and spectrum of the static background error covariance matrix employed to initiate a global data assimilation cycle. It is found that the EnKF performs well in some of the experiments with background error description 1, and yields modest error reductions with background error description 3. However, the EnKF is virtually unable to reduce the background error (even when using a large ensemble) with background error description 2. To analyze these results, the different background error descriptions are viewed through the prism of the RT model by comparing the trace of the matrix , where is the RT model and is the background error covariance matrix. Indeed, this comparison is found to explain the difference in the results obtained, which relates to the degree to which deep modes are, or are not, present in the different background error covariances. The results suggest that, after 2 weeks of cycling, the global EnKF has virtually eliminated all background error structures that can be “seen” by the AMSU-A radiances.

RECURSIVE UPDATING OF ERROR COVARIANCE MATRIX IN SUBSPACE METHODS

2006 ◽  
Vol 39 (1) ◽  
pp. 285-290 ◽  
Author(s):  
Yoshinori Takei ◽  
Hidehito Nanto ◽  
Shunshoku Kanae ◽  
Zi-Jiang Yang ◽  
Kiyoshi Wada
Keyword(s):  
Covariance Matrix ◽  
Subspace Methods ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Recursive Updating

Intelligent Error Covariance Matrix Resetting for Maneuver Target Tracking

2008 ◽  
Vol 8 (12) ◽  
pp. 2279-2285 ◽  
Author(s):  
M.H. Bahari ◽  
A. Karsaz ◽  
M.B. Naghibi-S
Keyword(s):  
Target Tracking ◽  
Covariance Matrix ◽  
Error Covariance Matrix ◽  
Error Covariance

scholarly journals Best linear unbiased estimation for varying probability with and without replacement sampling

2019 ◽  
Vol 7 (1) ◽  
pp. 78-91
Author(s):  
Stephen Haslett
Keyword(s):  
Parameter Estimation ◽  
Covariance Matrix ◽  
Linear Models ◽  
Unbiased Estimation ◽  
Error Covariance Matrix ◽  
Best Linear Unbiased Estimation ◽  
Error Covariance ◽  
Inclusion Probabilities ◽  
Best Linear Unbiased ◽  
Linear Unbiased Estimation

Abstract When sample survey data with complex design (stratification, clustering, unequal selection or inclusion probabilities, and weighting) are used for linear models, estimation of model parameters and their covariance matrices becomes complicated. Standard fitting techniques for sample surveys either model conditional on survey design variables, or use only design weights based on inclusion probabilities essentially assuming zero error covariance between all pairs of population elements. Design properties that link two units are not used. However, if population error structure is correlated, an unbiased estimate of the linear model error covariance matrix for the sample is needed for efficient parameter estimation. By making simultaneous use of sampling structure and design-unbiased estimates of the population error covariance matrix, the paper develops best linear unbiased estimation (BLUE) type extensions to standard design-based and joint design and model based estimation methods for linear models. The analysis covers both with and without replacement sample designs. It recognises that estimation for with replacement designs requires generalized inverses when any unit is selected more than once. This and the use of Hadamard products to link sampling and population error covariance matrix properties are central topics of the paper. Model-based linear model parameter estimation is also discussed.

scholarly journals Estimating model error covariance matrix parameters in extended Kalman filtering

2014 ◽  
Vol 21 (5) ◽  
pp. 919-927 ◽  
Author(s):  
A. Solonen ◽  
J. Hakkarainen ◽  
A. Ilin ◽  
M. Abbas ◽  
A. Bibov
Keyword(s):  
Covariance Matrix ◽  
Weather Prediction ◽  
Estimation Method ◽  
Model Error ◽  
Tuning Parameter ◽  
Extended Kalman Filtering ◽  
Error Covariance Matrix ◽  
Nonlinear Dynamical ◽  
Error Covariance

Abstract. The extended Kalman filter (EKF) is a popular state estimation method for nonlinear dynamical models. The model error covariance matrix is often seen as a tuning parameter in EKF, which is often simply postulated by the user. In this paper, we study the filter likelihood technique for estimating the parameters of the model error covariance matrix. The approach is based on computing the likelihood of the covariance matrix parameters using the filtering output. We show that (a) the importance of the model error covariance matrix calibration depends on the quality of the observations, and that (b) the estimation approach yields a well-tuned EKF in terms of the accuracy of the state estimates and model predictions. For our numerical experiments, we use the two-layer quasi-geostrophic model that is often used as a benchmark model for numerical weather prediction.

scholarly journals A Combinatorial Approach for Small and Strong Formulations of Disjunctive Constraints

2019 ◽  
Vol 44 (3) ◽  
pp. 793-820 ◽  
Author(s):  
Joey Huchette ◽  
Juan Pablo Vielma
Keyword(s):  
Piecewise Linear ◽  
Expressive Power ◽  
Complete Characterization ◽  
Linear Functions ◽  
Mixed Integer ◽  
Ordered Sets ◽  
Special Ordered Sets ◽  
Disjunctive Constraints

A framework is presented for constructing strong mixed-integer programming formulations for logical disjunctive constraints. This approach is a generalization of the logarithmically sized formulations of Vielma and Nemhauser for special ordered sets of type 2 (SOS2) constraints, and a complete characterization of its expressive power is offered. The framework is applied to a variety of disjunctive constraints, producing novel small and strong formulations for outer approximations of multilinear terms, generalizations of special ordered sets, piecewise linear functions over a variety of domains, and obstacle avoidance constraints.

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