scholarly journals Optimized Localization and Hybridization to Filter Ensemble-Based Covariances

2015 ◽  
Vol 143 (10) ◽  
pp. 3931-3947 ◽  
Author(s):  
Benjamin Ménétrier ◽  
Thomas Auligné
Keyword(s):  
Data Assimilation ◽  
Experimental Evidence ◽  
Covariance Matrix ◽  
Experimental Results ◽  
Objective Method ◽  
Linear Filtering ◽  
Ensemble Size ◽  
Optimal Weights ◽  
Ensemble Data ◽  
Vertical Level

Abstract Localization and hybridization are two methods used in ensemble data assimilation to improve the accuracy of sample covariances. It is shown in this paper that it is beneficial to consider them jointly in the framework of linear filtering of sample covariances. Following previous work on localization, an objective method is provided to optimize both localization and hybridization coefficients simultaneously. Theoretical and experimental evidence shows that if optimal weights are used, localized-hybridized sample covariances are always more accurate than their localized-only counterparts, whatever the static covariance matrix specified for the hybridization. Experimental results obtained using a 1000-member ensemble as a reference show that the method developed in this paper can efficiently provide localization and hybridization coefficients consistent with the variable, vertical level, and ensemble size. Spatially heterogeneous optimization is shown to improve the accuracy of the filtered covariances, and consideration of both vertical and horizontal covariances is proven to have an impact on the hybridization coefficients.

scholarly journals Improving Weather Forecast Skill through Reduced-Precision Data Assimilation

2017 ◽  
Vol 146 (1) ◽  
pp. 49-62 ◽  
Author(s):  
Sam Hatfield ◽  
Aneesh Subramanian ◽  
Tim Palmer ◽  
Peter Düben
Keyword(s):  
Data Assimilation ◽  
Observation Error ◽  
Double Precision ◽  
Ensemble Size ◽  
Error Statistics ◽  
Rounding Errors ◽  
Precision Data ◽  
Ensemble Data Assimilation ◽  
Ensemble Data ◽  
Computational Resources

Abstract A new approach for improving the accuracy of data assimilation, by trading numerical precision for ensemble size, is introduced. Data assimilation is inherently uncertain because of the use of noisy observations and imperfect models. Thus, the larger rounding errors incurred from reducing precision may be within the tolerance of the system. Lower-precision arithmetic is cheaper, and so by reducing precision in ensemble data assimilation, computational resources can be redistributed toward, for example, a larger ensemble size. Because larger ensembles provide a better estimate of the underlying distribution and are less reliant on covariance inflation and localization, lowering precision could actually permit an improvement in the accuracy of weather forecasts. Here, this idea is tested on an ensemble data assimilation system comprising the Lorenz ’96 toy atmospheric model and the ensemble square root filter. The system is run at double-, single-, and half-precision (the latter using an emulation tool), and the performance of each precision is measured through mean error statistics and rank histograms. The sensitivity of these results to the observation error and the length of the observation window are addressed. Then, by reinvesting the saved computational resources from reducing precision into the ensemble size, assimilation error can be reduced for (hypothetically) no extra cost. This results in increased forecasting skill, with respect to double-precision assimilation.

scholarly journals Representing model error in ensemble data assimilation

2014 ◽  
Vol 21 (5) ◽  
pp. 971-985 ◽  
Author(s):  
C. Cardinali ◽  
N. Žagar ◽  
G. Radnoti ◽  
R. Buizza
Keyword(s):  
Data Assimilation ◽  
Covariance Matrix ◽  
Model Error ◽  
The Other ◽  
Error Statistics ◽  
Model Uncertainties ◽  
Background Error ◽  
Error Covariance ◽  
Ensemble Data ◽  
Assimilation System

Abstract. The paper investigates a method to represent model error in the ensemble data assimilation (EDA) system. The ECMWF operational EDA simulates the effect of both observations and model uncertainties. Observation errors are represented by perturbations with statistics characterized by the observation error covariance matrix whilst the model uncertainties are represented by stochastic perturbations added to the physical tendencies to simulate the effect of random errors in the physical parameterizations (ST-method). In this work an alternative method (XB-method) is proposed to simulate model uncertainties by adding perturbations to the model background field. In this way the error represented is not just restricted to model error in the usual sense but potentially extends to any form of background error. The perturbations have the same correlation as the background error covariance matrix and their magnitude is computed from comparing the high-resolution operational innovation variances with the ensemble variances when the ensemble is obtained by perturbing only the observations (OBS-method). The XB-method has been designed to represent the short range model error relevant for the data assimilation window. Spread diagnostic shows that the XB-method generates a larger spread than the ST-method that is operationally used at ECMWF, in particular in the extratropics. Three-dimensional normal-mode diagnostics indicate that XB-EDA spread projects more than the spread from the other EDAs onto the easterly inertia-gravity modes associated with equatorial Kelvin waves, tropical dynamics and, in general, model error sources. The background error statistics from the above described EDAs have been employed in the assimilation system. The assimilation system performance showed that the XB-method background error statistics increase the observation influence in the analysis process. The other EDA background error statistics, when inflated by a global factor, generate analyses with 30–50% smaller degree of freedom of signal. XB-EDA background error variances have not been inflated. The presented EDAs have been used to generate the initial perturbations of the ECMWF ensemble prediction system (EPS) of which the XB-EDA induces the largest EPS spread, also in the medium range, leading to a more reliable ensemble. Compared to ST-EDA, XB-EDA leads to a small improvement of the EPS ignorance skill score at day 3 and 7.

scholarly journals EnKF and Hybrid Gain Ensemble Data Assimilation. Part I: EnKF Implementation

2015 ◽  
Vol 143 (12) ◽  
pp. 4847-4864 ◽  
Author(s):  
Mats Hamrud ◽  
Massimo Bonavita ◽  
Lars Isaksen
Keyword(s):  
Data Assimilation ◽  
State Of The Art ◽  
Horizontal Resolution ◽  
The Novel ◽  
Model Errors ◽  
Ensemble Size ◽  
Wind Fields ◽  
Ensemble Data ◽  
Computational Properties ◽  
Novel Algorithm

Abstract The desire to do detailed comparisons between variational and more scalable ensemble-based data assimilation systems in a semioperational environment has led to the development of a state-of-the-art EnKF system at ECMWF. A broad description of the ECMWF EnKF is given in this paper, focusing on highlighting differences compared to standard EnKF practice. In particular, a discussion of the novel algorithm used to control imbalances between the mass and wind fields in the EnKF analysis is given. The scalability and computational properties of the EnKF are reviewed and the implementation choices adopted at ECMWF described. The sensitivity of the ECMWF EnKF to ensemble size, horizontal resolution, and representation of model errors is also discussed. A comparison with 4DVar will be found in Part II of this two-part study.

scholarly journals Observation-Informed Generalized Hybrid Error Covariance Models

2018 ◽  
Vol 146 (11) ◽  
pp. 3605-3622 ◽  
Author(s):  
Elizabeth A. Satterfield ◽  
Daniel Hodyss ◽  
David D. Kuhl ◽  
Craig H. Bishop
Keyword(s):  
Data Assimilation ◽  
Covariance Matrix ◽  
Sample Variance ◽  
Calibration Function ◽  
Covariance Model ◽  
True Error ◽  
Ensemble Data Assimilation ◽  
Error Covariance ◽  
Ensemble Data ◽  
Prior Variance

Abstract Because of imperfections in ensemble data assimilation schemes, one cannot assume that the ensemble-derived covariance matrix is equal to the true error covariance matrix. Here, we describe a simple and intuitively compelling method to fit calibration functions of the ensemble sample variance to the mean of the distribution of true error variances, given an ensemble estimate. We demonstrate that the use of such calibration functions is consistent with theory showing that, when sampling error in the prior variance estimate is considered, the gain that minimizes the posterior error variance uses the expected true prior variance, given an ensemble sample variance. Once the calibration function has been fitted, it can be combined with ensemble-based and climatologically based error correlation information to obtain a generalized hybrid error covariance model. When the calibration function is chosen to be a linear function of the ensemble variance, the generalized hybrid error covariance model is the widely used linear hybrid consisting of a weighted sum of a climatological and an ensemble-based forecast error covariance matrix. However, when the calibration function is chosen to be, say, a cubic function of the ensemble sample variance, the generalized hybrid error covariance model is a nonlinear function of the ensemble estimate. We consider idealized univariate data assimilation and multivariate cycling ensemble data assimilation to demonstrate that the generalized hybrid error covariance model closely approximates the optimal weights found through computationally expensive tuning in the linear case and, in the nonlinear case, outperforms any plausible linear model.

Initiation of ensemble data assimilation

2006 ◽  
Author(s):  
M. Zupanski ◽  
S. J. Fletcher ◽  
I. M. Navon ◽  
B. Uzunoglu ◽  
R. P. Heikes ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Ensemble Data Assimilation ◽  
Ensemble Data

Using a machine learning proxy for localization in ensemble data assimilation

2021 ◽  
Vol 25 (3) ◽  
pp. 931-944
Author(s):  
Johann M. Lacerda ◽  
Alexandre A. Emerick ◽  
Adolfo P. Pires
Keyword(s):  
Machine Learning ◽  
Data Assimilation ◽  
Ensemble Data Assimilation ◽  
Ensemble Data

scholarly journals Self-Governance in Generalized Exchange. A Laboratory Experiment on the Structural Embeddedness of Peer Punishment

Games ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 50
Author(s):  
Georg Kanitsar
Keyword(s):  
Laboratory Experiment ◽  
Public Good ◽  
Experimental Evidence ◽  
Experimental Results ◽  
Social Cooperation ◽  
The Public ◽  
Norm Enforcement ◽  
Structural Setting ◽  
Structural Embeddedness ◽  
Generalized Exchange

Peer punishment is widely lauded as a decentralized solution to the problem of social cooperation. However, experimental evidence of its effectiveness primarily stems from public good structures. This paper explores peer punishment in another structural setting: a system of generalized exchange. In a laboratory experiment, a repeated four-player prisoner’s dilemma is arranged either in a public good structure or in a circular network of generalized exchange. The experimental results demonstrate that the merits of peer punishment do not extend to generalized exchange. In the public good, peer punishment was primarily altruistic, was sensitive to costs, and promoted cooperation. In generalized exchange, peer punishment was also altruistic and relatively frequent, but did not increase cooperation. While the dense punishment network underlying the public good facilitates norm enforcement, generalized exchange decreases control over norm violators and reduces the capacity of peer punishment. I conclude that generalized exchange systems require stronger forms of punishment to sustain social cooperation.

scholarly journals Three doors anomaly, “should I stay, or should I go”: an artefactual field experiment

2021 ◽  
Author(s):  
Andrea Morone ◽  
Rocco Caferra ◽  
Alessia Casamassima ◽  
Alessandro Cascavilla ◽  
Paola Tiranzoni
Keyword(s):  
Field Experiment ◽  
Experimental Evidence ◽  
Bayesian Updating ◽  
Anomalous Behavior ◽  
Status Quo ◽  
Experimental Results ◽  
Illusion Of Control ◽  
Optimal Decision ◽  
Status Quo Bias ◽  
The Impact

AbstractThis work aims to identify and quantify the biases behind the anomalous behavior of people when they deal with the Three Doors dilemma, which is a really simple but counterintuitive game. Carrying out an artefactual field experiment and proposing eight different treatments to isolate the anomalies, we provide new interesting experimental evidence on the reasons why subjects fail to take the optimal decision. According to the experimental results, we are able to quantify the size and the impact of three main biases that explain the anomalous behavior of participants: Bayesian updating, illusion of control and status quo bias.

Litigation Spending and Care under the English and American Rules: Experimental Evidence

2021 ◽  
Author(s):  
Baptiste Massenot ◽  
Maria Maraki ◽  
Christian Thöni
Keyword(s):  
Experimental Evidence ◽  
Rent Seeking ◽  
Experimental Results ◽  
Settlement Rate ◽  
Levels Of Care ◽  
Personal Cost

Abstract We investigate the effects of fee-shifting in an experimental litigation game. In our setup, a defendant may cause harm to a plaintiff. The defendant can take precautions to lower the probability of harm at a personal cost. In case of harm, the parties go to court, where the winner is determined by a rent-seeking contest. We compare two fee-shifting rules: under the American rule each party bears its own litigation costs; under the English rule the loser has to reimburse the winner’s expenses. We test the hypothesis that the English rule leads to higher litigation spending but also to higher care compared to the American rule. The experimental results largely support the predictions: fee-shifting leads to higher litigation spending, which motivates higher levels of care. When the parties are offered the possibility to settle their dispute out of court, fee-shifting leads to even higher litigation spending in court, but it neither affects the settlement rate nor care.

Convective Losses From Cavity Solar Receivers—Comparisons Between Analytical Predictions and Experimental Results

1983 ◽  
Vol 105 (1) ◽  
pp. 29-33 ◽  
Author(s):  
A. M. Clausing
Keyword(s):  
Experimental Data ◽  
Experimental Evidence ◽  
Analytical Model ◽  
Excellent Agreement ◽  
Experimental Results ◽  
Simple Analytical Model ◽  
Refined Model ◽  
Wall Area

Cavity solar receivers are generally believed to have higher thermal efficiencies than external receivers due to reduced losses. A simple analytical model was presented by the author which indicated that the ability to heat the air inside the cavity often controls the convective loss from cavity receivers. Thus, if the receiver contains a large amount of inactive hot wall area, it can experience a large convective loss. Excellent experimental data from a variety of cavity configurations and orientations have recently become available. These data provided a means of testing and refining the analytical model. In this manuscript, a brief description of the refined model is presented. Emphasis is placed on using available experimental evidence to substantiate the hypothesized mechanisms and assumptions. Detailed comparisons are given between analytical predictions and experimental results. Excellent agreement is obtained, and the important mechanisms are more clearly delineated.

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