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46
An Ensemble Adjustment Kalman Filter for Data Assimilation
, 2001
"... A theory for estimating the probability distribution of the state of a model given a set of observations exists. This nonlinear ..."
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Cited by 120 (4 self)
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A theory for estimating the probability distribution of the state of a model given a set of observations exists. This nonlinear
Using Bayesian model averaging to calibrate forecast ensembles. Monthly Weather Review 133
, 2005
"... Ensembles used for probabilistic weather forecasting often exhibit a spreaderror correlation, but they tend to be underdispersive. This paper proposes a statistical method for postprocessing ensembles based on Bayesian model averaging (BMA), which is a standard method for combining predictive distr ..."
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Cited by 71 (28 self)
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Ensembles used for probabilistic weather forecasting often exhibit a spreaderror correlation, but they tend to be underdispersive. This paper proposes a statistical method for postprocessing ensembles based on Bayesian model averaging (BMA), which is a standard method for combining predictive distributions from different sources. The BMA predictive probability density function (PDF) of any quantity of interest is a weighted average of PDFs centered on the individual biascorrected forecasts, where the weights are equal to posterior probabilities of the models generating the forecasts and reflect the models ’ relative contributions to predictive skill over the training period. The BMA weights can be used to assess the usefulness of ensemble members, and this can be used as a basis for selecting ensemble members; this can be useful given the cost of running large ensembles. The BMA PDF can be represented as an unweighted ensemble of any desired size, by simulating from the BMA predictive distribution. The BMA predictive variance can be decomposed into two components, one corresponding to the betweenforecast variability, and the second to the withinforecast variability. Predictive PDFs or intervals based solely on the ensemble spread incorporate the first component but not the second. Thus BMA provides a theoretical explanation of the tendency of ensembles to exhibit a spreaderror correlation but yet
A Hybrid Ensemble Kalman Filter / 3DVariational Analysis Scheme
"... A hybrid 3dimensional variational (3DVar) / ensemble Kalman filter analysis scheme is demonstrated using a quasigeostrophic model under perfectmodel assumptions. Four networks with differing observational densities are tested, including one network with a data void. The hybrid scheme operates by ..."
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Cited by 60 (15 self)
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A hybrid 3dimensional variational (3DVar) / ensemble Kalman filter analysis scheme is demonstrated using a quasigeostrophic model under perfectmodel assumptions. Four networks with differing observational densities are tested, including one network with a data void. The hybrid scheme operates by computing a set of parallel data assimilation cycles, with each member of the set receiving unique perturbed observations. The perturbed observations are generated by adding random noise consistent with observation error statistics to the control set of observations. Background error statistics for the data assimilation are estimated from a linear combination of timeinvariant 3DVar covariances and flowdependent covariances developed from the ensemble of shortrange forecasts. The hybrid scheme allows the user to weight the relative contributions of the 3DVar and ensemblebased background covariances. The analysis scheme was cycled for 90 days, with new observations assimilated every 12 h...
Interpretation Of Rank Histograms For Verifying Ensemble Forecasts
, 2000
"... Rank histograms are a tool for evaluating ensemble forecasts. They are useful for determining the reliability of ensemble forecasts and for diagnosing errors in its mean and spread. Rank histograms are generated by repeatedly tallying the rank of the verification (usually, an observation) relative t ..."
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Cited by 49 (5 self)
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Rank histograms are a tool for evaluating ensemble forecasts. They are useful for determining the reliability of ensemble forecasts and for diagnosing errors in its mean and spread. Rank histograms are generated by repeatedly tallying the rank of the verification (usually, an observation) relative to values from an ensemble sorted from lowest to highest. However, an uncritical use of the rank histogram can lead to misinterpretations of the qualities of that ensemble. For example, a flat rank histogram, ususally taken as a sign of reliability, can still be generated from unreliable ensembles. Similarly, a Ushaped rank histogram, commonly understood as indicating a lack of variability in the ensemble, can also be a sign of conditional bias. It is also shown that flat rank histograms can be generated for some model variables if the variance of the ensemble is correctly specified, yet if covariances between model grid points are improperly specified, rank histograms for combinations of mo...
Probabilistic forecasts, calibration and sharpness
 Journal of the Royal Statistical Society Series B
, 2007
"... Summary. Probabilistic forecasts of continuous variables take the form of predictive densities or predictive cumulative distribution functions. We propose a diagnostic approach to the evaluation of predictive performance that is based on the paradigm of maximizing the sharpness of the predictive dis ..."
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Cited by 38 (15 self)
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Summary. Probabilistic forecasts of continuous variables take the form of predictive densities or predictive cumulative distribution functions. We propose a diagnostic approach to the evaluation of predictive performance that is based on the paradigm of maximizing the sharpness of the predictive distributions subject to calibration. Calibration refers to the statistical consistency between the distributional forecasts and the observations and is a joint property of the predictions and the events that materialize. Sharpness refers to the concentration of the predictive distributions and is a property of the forecasts only. A simple theoretical framework allows us to distinguish between probabilistic calibration, exceedance calibration and marginal calibration. We propose and study tools for checking calibration and sharpness, among them the probability integral transform histogram, marginal calibration plots, the sharpness diagram and proper scoring rules. The diagnostic approach is illustrated by an assessment and ranking of probabilistic forecasts of wind speed at the Stateline wind energy centre in the US Pacific Northwest. In combination with crossvalidation or in the time series context, our proposal provides very general, nonparametric alternatives to the use of information criteria for model diagnostics and model selection.
2000: A comparison of probabilistic forecasts from bred, singularvector, and perturbation observation ensembles
 Mon. Wea. Rev
"... The statistical properties of analysis and forecast errors from commonly used ensemble perturbation methodologies are explored. A quasigeostrophic channel model is used, coupled with a 3Dvariational data assimilation scheme. A perfect model is assumed. Three perturbation methodologies are considere ..."
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Cited by 33 (6 self)
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The statistical properties of analysis and forecast errors from commonly used ensemble perturbation methodologies are explored. A quasigeostrophic channel model is used, coupled with a 3Dvariational data assimilation scheme. A perfect model is assumed. Three perturbation methodologies are considered. The breeding and singularvector (SV) methods approximate the strategies currently used at operational centers in the United States and Europe, respectively. The perturbed observation (PO) methodology approximates a random sample from the analysis probability density function (pdf) and is similar to the method performed at the Canadian Meteorological Centre. Initial conditions for the PO ensemble are analyses from independent, parallel data assimilation cycles. Each assimilation cycle utilizes observations perturbed by random noise whose statistics are consistent with observational error covariances. Each member’s assimilation/forecast cycle is also started from a distinct initial condition. Relative to breeding and SV, the PO method here produced analyses and forecasts with desirable statistical characteristics. These include consistent rank histogram uniformity for all variables at all lead times, high spread/ skill correlations, and calibrated, reducederror probabilistic forecasts. It achieved these improvements primarily because 1) the ensemble mean of the PO initial conditions was more accurate than the mean of the bred or
Probabilistic quantitative precipitation forecasting using Bayesian model averaging. Monthly Weather Review 135
 Monthly Weather Review
, 2007
"... and useful comments, and for providing data. They are also grateful to Patrick Tewson for implementing the UW Ensemble BMA website. This research was supported by the DoD Multidisciplinary University Research Initiative (MURI) program administered by the Office of Naval Research under Grant N000140 ..."
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Cited by 32 (20 self)
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and useful comments, and for providing data. They are also grateful to Patrick Tewson for implementing the UW Ensemble BMA website. This research was supported by the DoD Multidisciplinary University Research Initiative (MURI) program administered by the Office of Naval Research under Grant N000140110745. Bayesian model averaging (BMA) is a statistical way of postprocessing forecast ensembles to create predictive probability density functions (PDFs) for weather quantities. It represents the predictive PDF as a weighted average of PDFs centered on the individual biascorrected forecasts, where the weights are posterior probabilities of the models generating the forecasts and reflect the forecasts ’ relative contributions to predictive skill over a training period. It was developed initially for quantities whose PDFs can be approximated by normal distributions, such as temperature and sealevel pressure. BMA does not apply in its original form to precipitation, because the predictive PDF of precipitation is nonnormal in two major ways: it has a positive probability of being equal to zero, and it is skewed. Here we extend BMA to probabilistic quantitative precipitation forecasting. The predictive PDF corresponding to
Calibrated probabilistic forecasting using ensemble model output statistics and minimum CRPS estimation
 Monthly Weather Review
, 2005
"... Ensemble prediction systems typically show positive spreaderror correlation, but they are subject to forecast bias and underdispersion, and therefore uncalibrated. This work proposes the use of ensemble model output statistics (EMOS), an easy to implement postprocessing technique that addresses b ..."
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Cited by 31 (9 self)
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Ensemble prediction systems typically show positive spreaderror correlation, but they are subject to forecast bias and underdispersion, and therefore uncalibrated. This work proposes the use of ensemble model output statistics (EMOS), an easy to implement postprocessing technique that addresses both forecast bias and underdispersion and takes account of the spreadskill relationship. The technique is based on multiple linear regression and akin to the superensemble approach that has traditionally been used for deterministicstyle forecasts. The EMOS technique yields probabilistic forecasts that take the form of Gaussian predictive probability density functions (PDFs) for continuous weather variables, and can be applied to gridded model output. The EMOS predictive mean is an optimal, biascorrected weighted average of the ensemble member forecasts, with coefficients that are constrained to be nonnegative and associated with the member model skill. The EMOS predictive mean provides a highly accurate deterministicstyle forecast. The EMOS predictive variance is a linear function of the ensemble spread. For fitting the EMOS coefficients, the method of minimum CRPS estimation is introduced.