scholarly journals Model Error Representation in an Operational Ensemble Kalman Filter

2009 ◽  
Vol 137 (7) ◽  
pp. 2126-2143 ◽  
Author(s):  
P. L. Houtekamer ◽  
Herschel L. Mitchell ◽  
Xingxiu Deng
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Model Error ◽  
Ensemble Prediction ◽  
Isotropic Model ◽  
Error Sources ◽  
Ensemble Prediction System ◽  
Stochastic Perturbations ◽  
Ensemble Mean ◽  
The Impact

Since 12 January 2005, an ensemble Kalman filter (EnKF) has been used operationally at the Meteorological Service of Canada to provide the initial conditions for the medium-range forecasts of the ensemble prediction system. One issue in EnKF development is how to best account for model error. It is shown that in a perfect-model environment, without any model error or model error simulation, the EnKF spread remains representative of the ensemble mean error with respect to a truth integration. Consequently, the EnKF can be used to quantify the impact of the various error sources in a data-assimilation cycle on the quality of the ensemble mean. Using real rather than simulated observations, but still not simulating model error in any manner, the rms ensemble spread is found to be too small by approximately a factor of 2. It is then attempted to account for model error by using various combinations of the following four different approaches: (i) additive isotropic model error perturbations; (ii) different versions of the model for different ensemble members; (iii) stochastic perturbations to physical tendencies; and (iv) stochastic kinetic energy backscatter. The addition of isotropic model error perturbations is found to have the biggest impact. The identification of model error sources could lead to a more realistic, likely anisotropic, parameterization. Using different versions of the model has a small but clearly positive impact and consequently both (i) and (ii) are used in the operational EnKF. The use of approaches (iii) and (iv) did not lead to further improvements.

scholarly journals Higher Resolution in an Operational Ensemble Kalman Filter

2014 ◽  
Vol 142 (3) ◽  
pp. 1143-1162 ◽  
Author(s):  
P. L. Houtekamer ◽  
Xingxiu Deng ◽  
Herschel L. Mitchell ◽  
Seung-Jong Baek ◽  
Normand Gagnon
Keyword(s):  
Kalman Filter ◽  
Temporal Resolution ◽  
Ensemble Kalman Filter ◽  
Forecast Model ◽  
Horizontal Resolution ◽  
Ensemble Prediction ◽  
Time Step ◽  
Ensemble Prediction System ◽  
Medium Range ◽  
The Impact

Abstract Recently, the computing facilities available to the Meteorological Service of Canada were significantly upgraded. This provided an opportunity to improve the resolution of the global ensemble Kalman filter (EnKF) and the medium-range Global Ensemble Prediction System (GEPS). In the EnKF, the main upgrades include improved horizontal, vertical, and temporal resolution. With the introduction of the higher horizontal resolution, it was decided to use a filtered topography in order to address an occasional instability problem. At the same time, the number of assimilated radiance observations was increased via a relaxation of the data-thinning procedures. In the medium-range GEPS, which already used the higher horizontal resolution, the filtered topography was also adopted. Likewise, the temporal resolution was increased to be the same as in the short-range integrations of the EnKF. With these changes, the grid used by the Canadian EnKF has 600 × 300 points in the horizontal and 74 vertical levels. The forecast model uses a 20-min time step and, for time interpolation of the model trajectories, model states are stored every hour. The EnKF uses an ensemble having 192 members. This paper sequentially examines the impact of these implemented changes. The upgraded EnKF became operational at the Canadian Meteorological Centre in mid-February 2013.

scholarly journals Verification of 24-h Quantitative Precipitation Forecasts over the Pacific Northwest from a High-Resolution Ensemble Kalman Filter System

2017 ◽  
Vol 32 (3) ◽  
pp. 1185-1208 ◽  
Author(s):  
Phillipa Cookson-Hills ◽  
Daniel J. Kirshbaum ◽  
Madalina Surcel ◽  
Jonathan G. Doyle ◽  
Luc Fillion ◽  
...  
Keyword(s):  
Kalman Filter ◽  
High Resolution ◽  
Data Assimilation ◽  
Pacific Northwest ◽  
Ensemble Kalman Filter ◽  
Ensemble Prediction ◽  
Forecast Errors ◽  
Ensemble Prediction System ◽  
The Pacific ◽  
Quantitative Precipitation Forecasts

Abstract Environment and Climate Change Canada (ECCC) has recently developed an experimental high-resolution EnKF (HREnKF) regional ensemble prediction system, which it tested over the Pacific Northwest of North America for the first half of February 2011. The HREnKF has 2.5-km horizontal grid spacing and assimilates surface and upper-air observations every hour. To determine the benefits of the HREnKF over less expensive alternatives, its 24-h quantitative precipitation forecasts are compared with those from a lower-resolution (15 km) regional ensemble Kalman filter (REnKF) system and to ensembles directly downscaled from the REnKF using the same grid as the HREnKF but with no additional data assimilation (DS). The forecasts are verified against rain gauge observations and gridded precipitation analyses, the latter of which are characterized by uncertainties of comparable magnitude to the model forecast errors. Nonetheless, both deterministic and probabilistic verification indicates robust improvements in forecast skill owing to the finer grids of the HREnKF and DS. The HREnKF exhibits a further improvement in performance over the DS in the first few forecast hours, suggesting a modest positive impact of data assimilation. However, this improvement is not statistically significant and may be attributable to other factors.

scholarly journals Sensitivity of Global Ensemble Forecasts to the Initial Ensemble Mean and Perturbations: Comparison of EnKF, Singular Vector, and 4D-Var Approaches

2010 ◽  
Vol 138 (10) ◽  
pp. 3886-3904 ◽  
Author(s):  
Mark Buehner ◽  
Ahmed Mahidjiba
Keyword(s):  
Ensemble Prediction ◽  
Boreal Summer ◽  
Prediction System ◽  
Ensemble Forecasts ◽  
Ensemble Prediction System ◽  
Var Analysis ◽  
Initial Ensemble ◽  
Ensemble Mean ◽  
The Tropics ◽  
The Impact

Abstract This study examines the sensitivity of global ensemble forecasts to the use of different approaches for specifying both the initial ensemble mean and perturbations. The current operational ensemble prediction system of the Meteorological Service of Canada uses the ensemble Kalman filter (EnKF) to define both the ensemble mean and perturbations. To evaluate the impact of different approaches for obtaining the initial ensemble perturbations, the operational EnKF approach is compared with using either no initial perturbations or perturbations obtained using singular vectors (SVs). The SVs are computed using the (dry) total-energy norm with a 48-h optimization time interval. Random linear combinations of 60 SVs are computed for each of three regions. Next, the impact of replacing the initial ensemble mean, currently the EnKF ensemble mean analysis, with the higher-resolution operational four-dimensional variational data assimilation (4D-Var) analysis is evaluated. For this comparison, perturbations are provided by the EnKF. All experiments are performed over two-month periods during both the boreal summer and winter using a system very similar to the global ensemble prediction system that became operational on 10 July 2007. Relative to the operational configuration that relies on the EnKF, the use of SVs to compute initial perturbations produces small, but statistically significant differences in probabilistic forecast scores in favor of the EnKF both in the tropics and, for a limited set of forecast lead times, in the summer hemisphere extratropics, whereas the results are very similar in the winter hemisphere extratropics. Both approaches lead to significantly better ensemble forecasts than with no initial perturbations, though results are quite similar in the tropics when using SVs and no perturbations. The use of an initial-time norm that does not include information on analysis uncertainty and the lack of linearized moist processes in the calculation of the SVs are two factors that limit the quality of the resulting SV-based ensemble forecasts. Relative to the operational configuration, use of the 4D-Var analysis to specify the initial ensemble mean results in improved probabilistic forecast scores during the boreal summer period in the southern extratropics and tropics, but a near-neutral impact otherwise.

scholarly journals Representation of model error in a convective-scale ensemble prediction system

2014 ◽  
Vol 21 (1) ◽  
pp. 19-39 ◽  
Author(s):  
L. H. Baker ◽  
A. C. Rudd ◽  
S. Migliorini ◽  
R. N. Bannister
Keyword(s):  
Model Error ◽  
Ensemble Prediction ◽  
Initial Condition ◽  
Prediction System ◽  
Ensemble Prediction System ◽  
Near Surface ◽  
Skill Scores ◽  
The Uk ◽  
Parameter Values ◽  
The Impact

Abstract. In this paper ensembles of forecasts (of up to six hours) are studied from a convection-permitting model with a representation of model error due to unresolved processes. The ensemble prediction system (EPS) used is an experimental convection-permitting version of the UK Met Office's 24-member Global and Regional Ensemble Prediction System (MOGREPS). The method of representing model error variability, which perturbs parameters within the model's parameterisation schemes, has been modified and we investigate the impact of applying this scheme in different ways. These are: a control ensemble where all ensemble members have the same parameter values; an ensemble where the parameters are different between members, but fixed in time; and ensembles where the parameters are updated randomly every 30 or 60 min. The choice of parameters and their ranges of variability have been determined from expert opinion and parameter sensitivity tests. A case of frontal rain over the southern UK has been chosen, which has a multi-banded rainfall structure. The consequences of including model error variability in the case studied are mixed and are summarised as follows. The multiple banding, evident in the radar, is not captured for any single member. However, the single band is positioned in some members where a secondary band is present in the radar. This is found for all ensembles studied. Adding model error variability with fixed parameters in time does increase the ensemble spread for near-surface variables like wind and temperature, but can actually decrease the spread of the rainfall. Perturbing the parameters periodically throughout the forecast does not further increase the spread and exhibits "jumpiness" in the spread at times when the parameters are perturbed. Adding model error variability gives an improvement in forecast skill after the first 2–3 h of the forecast for near-surface temperature and relative humidity. For precipitation skill scores, adding model error variability has the effect of improving the skill in the first 1–2 h of the forecast, but then of reducing the skill after that. Complementary experiments were performed where the only difference between members was the set of parameter values (i.e. no initial condition variability). The resulting spread was found to be significantly less than the spread from initial condition variability alone.

scholarly journals Toward Random Sampling of Model Error in the Canadian Ensemble Prediction System

2010 ◽  
Vol 138 (5) ◽  
pp. 1877-1901 ◽  
Author(s):  
Martin Charron ◽  
Gérard Pellerin ◽  
Lubos Spacek ◽  
P. L. Houtekamer ◽  
Normand Gagnon ◽  
...  
Keyword(s):  
Ensemble Kalman Filter ◽  
Ensemble Prediction ◽  
Prediction System ◽  
Ensemble Prediction System ◽  
Predictive Skill ◽  
Global Environmental ◽  
The Impact ◽  
Horizontal Grid ◽  
Probabilistic Measures ◽  
Global Environmental Multiscale

Abstract An updated global ensemble prediction system became operational at the Meteorological Service of Canada in July 2007. The new elements of the system include the use of 20 members instead of 16, a single dynamical core [the Global Environmental Multiscale (GEM) model], stochastic physical tendency perturbations and a kinetic energy backscatter algorithm, an ensemble Kalman filter with four-dimensional data handling, and a decrease from 1.2° to 0.9° in horizontal grid spacing. This system is compared with the former operational one using a variety of probabilistic measures. For global upper-air dynamical fields, the improvement in predictive skill for equivalent forecast quality is from 9 to 16 h around day 6. Precipitation forecasts, verified over Canada, are also significantly improved. The impact of each of the abovementioned new elements of the ensemble prediction system is also evaluated separately in a series of sensitivity experiments for which one given element is removed from the system.

scholarly journals Comparison of Single-Parameter and Multiparameter Ensembles for Assimilation of Radar Observations Using the Ensemble Kalman Filter

2012 ◽  
Vol 140 (2) ◽  
pp. 562-586 ◽  
Author(s):  
Nusrat Yussouf ◽  
David J. Stensrud
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Extreme Values ◽  
Model Error ◽  
Single Parameter ◽  
Cold Pool ◽  
Microphysics Scheme ◽  
Radar Observations ◽  
Microphysical Parameters ◽  
The Impact

Observational studies indicate that the densities and intercept parameters of hydrometeor distributions can vary widely among storms and even within a single storm. Therefore, assuming a fixed set of microphysical parameters within a given microphysics scheme can lead to significant errors in the forecasts of storms. To explore the impact of variations in microphysical parameters, Observing System Simulation Experiments are conducted based on both perfect- and imperfect-model assumptions. Two sets of ensembles are designed using either fixed or variable parameters within the same single-moment microphysics scheme. The synthetic radar observations of a splitting supercell thunderstorm are assimilated into the ensembles over a 30-min period using an ensemble Kalman filter data assimilation technique followed by 1-h ensemble forecasts. Results indicate that in the presence of a model error, a multiparameter ensemble with a combination of different hydrometeor density and intercept parameters leads to improved analyses and forecasts and better captures the truth within the forecast envelope compared to single-parameter ensemble experiments with a single, constant, inaccurate hydrometeor intercept and density parameters. This conclusion holds when examining the general storm structure, the intensity of midlevel rotation, surface cold pool strength, and the extreme values of the model fields that are most helpful in determining and identifying potential hazards. Under a perfect-model assumption, the single- and multiparameter ensembles perform similarly as model error does not play a role in these experiments. This study highlights the potential for using a variety of realistic microphysical parameters across the ensemble members in improving the analyses and very short-range forecasts of severe weather events.

scholarly journals A Real-Time Convection-Allowing Ensemble Prediction System Initialized by Mesoscale Ensemble Kalman Filter Analyses

2015 ◽  
Vol 30 (5) ◽  
pp. 1158-1181 ◽  
Author(s):  
Craig S. Schwartz ◽  
Glen S. Romine ◽  
Morris L. Weisman ◽  
Ryan A. Sobash ◽  
Kathryn R. Fossell ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Real Time ◽  
Ensemble Kalman Filter ◽  
Wrf Model ◽  
Severe Weather ◽  
Ensemble Prediction ◽  
Limited Area ◽  
Ensemble Forecasts ◽  
Ensemble Prediction System ◽  
Weather Events

Abstract In May and June 2013, the National Center for Atmospheric Research produced real-time 48-h convection-allowing ensemble forecasts at 3-km horizontal grid spacing using the Weather Research and Forecasting (WRF) Model in support of the Mesoscale Predictability Experiment field program. The ensemble forecasts were initialized twice daily at 0000 and 1200 UTC from analysis members of a continuously cycling, limited-area, mesoscale (15 km) ensemble Kalman filter (EnKF) data assimilation system and evaluated with a focus on precipitation and severe weather guidance. Deterministic WRF Model forecasts initialized from GFS analyses were also examined. Subjectively, the ensemble forecasts often produced areas of intense convection over regions where severe weather was observed. Objective statistics confirmed these subjective impressions and indicated that the ensemble was skillful at predicting precipitation and severe weather events. Forecasts initialized at 1200 UTC were more skillful regarding precipitation and severe weather placement than forecasts initialized 12 h earlier at 0000 UTC, and the ensemble forecasts were typically more skillful than GFS-initialized forecasts. At times, 0000 UTC GFS-initialized forecasts had temporal distributions of domain-average rainfall closer to observations than EnKF-initialized forecasts. However, particularly when GFS analyses initialized WRF Model forecasts, 1200 UTC forecasts produced more rainfall during the first diurnal maximum than 0000 UTC forecasts. This behavior was mostly attributed to WRF Model initialization of clouds and moist physical processes. The success of these real-time ensemble forecasts demonstrates the feasibility of using limited-area continuously cycling EnKFs as a method to initialize convection-allowing ensemble forecasts, and future real-time high-resolution ensemble development leveraging EnKFs seems justified.

scholarly journals Why Should Ensemble Spread Match the RMSE of the Ensemble Mean?

2014 ◽  
Vol 15 (4) ◽  
pp. 1708-1713 ◽  
Author(s):  
V. Fortin ◽  
M. Abaza ◽  
F. Anctil ◽  
R. Turcotte
Keyword(s):  
Good Practice ◽  
Ensemble Prediction ◽  
Square Root ◽  
Prediction System ◽  
Mean Square ◽  
Ensemble Spread ◽  
Ensemble Prediction System ◽  
Correct Equation ◽  
Ensemble Mean ◽  
The Impact

Abstract When evaluating the reliability of an ensemble prediction system, it is common to compare the root-mean-square error of the ensemble mean to the average ensemble spread. While this is indeed good practice, two different and inconsistent methodologies have been used over the last few years in the meteorology and hydrology literature to compute the average ensemble spread. In some cases, the square root of average ensemble variance is used, and in other cases, the average of ensemble standard deviation is computed instead. The second option is incorrect. To avoid the perpetuation of practices that are not supported by probability theory, the correct equation for computing the average ensemble spread is obtained and the impact of using the wrong equation is illustrated.

scholarly journals An Ensemble Kalman Filter for Numerical Weather Prediction Based on Variational Data Assimilation: VarEnKF

2017 ◽  
Vol 145 (2) ◽  
pp. 617-635 ◽  
Author(s):  
Mark Buehner ◽  
Ron McTaggart-Cowan ◽  
Sylvain Heilliette
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Variational Approach ◽  
Variational Data Assimilation ◽  
Ensemble Prediction ◽  
Deterministic System ◽  
Ensemble Forecasts ◽  
Background Error ◽  
Ensemble Mean

Several NWP centers currently employ a variational data assimilation approach for initializing deterministic forecasts and a separate ensemble Kalman filter (EnKF) system both for initializing ensemble forecasts and for providing ensemble background error covariances for the deterministic system. This study describes a new approach for performing the data assimilation step within a perturbed-observation EnKF. In this approach, called VarEnKF, the analysis increment is computed with a variational data assimilation approach both for the ensemble mean and for all of the ensemble perturbations. To obtain a computationally efficient algorithm, a much simpler configuration is used for the ensemble perturbations, whereas the configuration used for the ensemble mean is similar to that used for the deterministic system. Numerous practical benefits may be realized by using a variational approach for both deterministic and ensemble prediction, including improved efficiency for the development and maintenance of the computer code. Also, the use of essentially the same data assimilation algorithm would likely reduce the amount of numerical experimentation required when making system changes, since their impacts in the two systems would be very similar. The variational approach enables the use of hybrid background error covariances and may also allow the assimilation of a larger volume of observations. Preliminary tests with the Canadian global 256-member system produced significantly improved ensemble forecasts with VarEnKF as compared with the current EnKF and at a comparable computational cost. These improvements resulted entirely from changes to the ensemble mean analysis increment calculation. Moreover, because each ensemble perturbation is updated independently, VarEnKF scales perfectly up to a very large number of processors.

Atmospheric Data Assimilation with an Ensemble Kalman Filter: Results with Real Observations

2005 ◽  
Vol 133 (3) ◽  
pp. 604-620 ◽  
Author(s):  
P. L. Houtekamer ◽  
Herschel L. Mitchell ◽  
Gérard Pellerin ◽  
Mark Buehner ◽  
Martin Charron ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Initial Conditions ◽  
Forecast Error ◽  
Lower Troposphere ◽  
Model Error ◽  
Atmospheric Data ◽  
Ensemble Mean ◽  
Parameterized Model

Abstract An ensemble Kalman filter (EnKF) has been implemented for atmospheric data assimilation. It assimilates observations from a fairly complete observational network with a forecast model that includes a standard operational set of physical parameterizations. To obtain reasonable results with a limited number of ensemble members, severe horizontal and vertical covariance localizations have been used. It is observed that the error growth in the data assimilation cycle is mainly due to model error. An isotropic parameterization, similar to the forecast-error parameterization in variational algorithms, is used to represent model error. After some adjustment, it is possible to obtain innovation statistics that agree with the ensemble-based estimate of the innovation amplitudes for winds and temperature. Currently, no model error is added for the humidity variable, and, consequently, the ensemble spread for humidity is too small. After about 5 days of cycling, fairly stable global filter statistics are obtained with no sign of filter divergence. The quality of the ensemble mean background field, as verified using radiosonde observations, is similar to that obtained using a 3D variational procedure. In part, this is likely due to the form chosen for the parameterized model error. Nevertheless, the degree of similarity is surprising given that the background-error statistics used by the two procedures are rather different, with generally larger background errors being used by the variational scheme. A set of 5-day integrations has been started from the ensemble of initial conditions provided by the EnKF. For the middle and lower troposphere, the growth rates of the perturbations are somewhat smaller than the growth rate of the actual ensemble mean error. For the upper levels, the perturbation patterns decay for about 3 days as a consequence of diffusive model dynamics. These decaying perturbations tend to severely underestimate the actual error that grows rapidly near the model top.

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