Assessing Predictability with a Local Ensemble Kalman Filter

2007 ◽  
Vol 64 (4) ◽  
pp. 1116-1140 ◽  
Author(s):  
David Kuhl ◽  
Istvan Szunyogh ◽  
Eric J. Kostelich ◽  
Gyorgyi Gyarmati ◽  
D. J. Patil ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Initial Conditions ◽  
Forecast Error ◽  
Weather Prediction ◽  
Forecast Errors ◽  
Data Assimilation Scheme ◽  
Ensemble Mean ◽  
Assimilation Scheme

Abstract In this paper, the spatiotemporally changing nature of predictability is studied in a reduced-resolution version of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS), a state-of-the-art numerical weather prediction model. Atmospheric predictability is assessed in the perfect model scenario for which forecast uncertainties are entirely due to uncertainties in the estimates of the initial states. Uncertain initial conditions (analyses) are obtained by assimilating simulated noisy vertical soundings of the “true” atmospheric states with the local ensemble Kalman filter (LEKF) data assimilation scheme. This data assimilation scheme provides an ensemble of initial conditions. The ensemble mean defines the initial condition of 5-day deterministic model forecasts, while the time-evolved members of the ensemble provide an estimate of the evolving forecast uncertainties. The observations are randomly distributed in space to ensure that the geographical distribution of the analysis and forecast errors reflect predictability limits due to the model dynamics and are not affected by inhomogeneities of the observational coverage. Analysis and forecast error statistics are calculated for the deterministic forecasts. It is found that short-term forecast errors tend to grow exponentially in the extratropics and linearly in the Tropics. The behavior of the ensemble is explained by using the ensemble dimension (E dimension), a spatiotemporally evolving measure of the evenness of the distribution of the variance between the principal components of the ensemble-based forecast error covariance matrix. It is shown that in the extratropics the largest forecast errors occur for the smallest E dimensions. Since a low value of the E dimension guarantees that the ensemble can capture a large portion of the forecast error, the larger the forecast error the more certain that the ensemble can fully capture the forecast error. In particular, in regions of low E dimension, ensemble averaging is an efficient error filter and the ensemble spread provides an accurate prediction of the upper bound of the error in the ensemble-mean forecast.

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.

Intercomparison of an Ensemble Kalman Filter with Three- and Four-Dimensional Variational Data Assimilation Methods in a Limited-Area Model over the Month of June 2003

2011 ◽  
Vol 139 (2) ◽  
pp. 566-572 ◽  
Author(s):  
Meng Zhang ◽  
Fuqing Zhang ◽  
Xiang-Yu Huang ◽  
Xin Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Forecast Error ◽  
Wrf Model ◽  
Warm Season ◽  
Variational Data Assimilation ◽  
Lead Times ◽  
Limited Area ◽  
Forecast Errors

Abstract This study compares the performance of an ensemble Kalman filter (EnKF) with both the three-dimensional and four-dimensional variational data assimilation (3DVar and 4DVar) methods of the Weather Research and Forecasting (WRF) model over the contiguous United States in a warm-season month (June) of 2003. The data assimilated every 6 h include conventional sounding and surface observations as well as data from wind profilers, ships and aircraft, and the cloud-tracked winds from satellites. The performances of these methods are evaluated through verifying the 12- to 72-h forecasts initialized twice daily from the analysis of each method against the standard sounding observations. It is found that 4DVar has consistently smaller error than that of 3DVar for winds and temperature at all forecast lead times except at 60 and 72 h when their forecast errors become comparable in amplitude, while the two schemes have similar performance in moisture at all lead times. The forecast error of the EnKF is comparable to that of the 4DVar at 12–36-h lead times, both of which are substantially smaller than that of the 3DVar, despite the fact that 3DVar fits the sounding observations much more closely at the analysis time. The advantage of the EnKF becomes even more evident at 48–72-h lead times; the 72-h forecast error of the EnKF is comparable in magnitude to the 48-h error of 3DVar/4DVar.

scholarly journals Southern High-Latitude Ensemble Data Assimilation in the Antarctic Mesoscale Prediction System

2005 ◽  
Vol 133 (12) ◽  
pp. 3431-3449 ◽  
Author(s):  
D. M. Barker
Keyword(s):  
Data Assimilation ◽  
Sampling Error ◽  
Forecast Error ◽  
Weather Prediction ◽  
Forecast Errors ◽  
Prediction System ◽  
Spatial Covariance ◽  
Ensemble Data Assimilation ◽  
Ensemble Data ◽  
The Antarctic

Abstract Ensemble data assimilation systems incorporate observations into numerical models via solution of the Kalman filter update equations, and estimates of forecast error covariances derived from ensembles of model integrations. In this paper, a particular algorithm, the ensemble square root filter (EnSRF), is tested in a limited-area, polar numerical weather prediction (NWP) model: the Antarctic Mesoscale Prediction System (AMPS). For application in the real-time AMPS, the number of model integrations that can be run to provide forecast error covariances is limited, resulting in an ensemble sampling error that degrades the analysis fit to observations. In this work, multivariate, climatologically plausible forecast error covariances are specified via averaged forecast difference statistics. Ensemble representations of the “true” forecast errors, created using randomized control variables of the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) three-dimensional variational (3DVAR) data assimilation system, are then used to assess the dependence of sampling error on ensemble size, data density, and localization of covariances using simulated observation networks. Results highlight the detrimental impact of ensemble sampling error on the analysis increment structure of correlated, but unobserved fields—an issue not addressed by the spatial covariance localization techniques used to date. A 12-hourly cycling EnSRF/AMPS assimilation/forecast system is tested for a two-week period in December 2002 using real, conventional (surface, rawinsonde, satellite retrieval) observations. The dependence of forecast scores on methods used to maintain ensemble spread and the inclusion of perturbations to lateral boundary conditions are studied.

scholarly journals Assimilation of MODIS Dark Target and Deep Blue observations in the dust aerosol component of NMMB-MONARCH version 1.0

2017 ◽  
Vol 10 (3) ◽  
pp. 1107-1129 ◽  
Author(s):  
Enza Di Tomaso ◽  
Nick A. J. Schutgens ◽  
Oriol Jorba ◽  
Carlos Pérez García-Pando
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Mineral Dust ◽  
Positive Impact ◽  
Forecast Error ◽  
Weather Prediction ◽  
Prediction System ◽  
Deep Blue ◽  
Modis Aod ◽  
Sahel Region

Abstract. A data assimilation capability has been built for the NMMB-MONARCH chemical weather prediction system, with a focus on mineral dust, a prominent type of aerosol. An ensemble-based Kalman filter technique (namely the local ensemble transform Kalman filter – LETKF) has been utilized to optimally combine model background and satellite retrievals. Our implementation of the ensemble is based on known uncertainties in the physical parametrizations of the dust emission scheme. Experiments showed that MODIS AOD retrievals using the Dark Target algorithm can help NMMB-MONARCH to better characterize atmospheric dust. This is particularly true for the analysis of the dust outflow in the Sahel region and over the African Atlantic coast. The assimilation of MODIS AOD retrievals based on the Deep Blue algorithm has a further positive impact in the analysis downwind from the strongest dust sources of the Sahara and in the Arabian Peninsula. An analysis-initialized forecast performs better (lower forecast error and higher correlation with observations) than a standard forecast, with the exception of underestimating dust in the long-range Atlantic transport and degradation of the temporal evolution of dust in some regions after day 1. Particularly relevant is the improved forecast over the Sahara throughout the forecast range thanks to the assimilation of Deep Blue retrievals over areas not easily covered by other observational datasets. The present study on mineral dust is a first step towards data assimilation with a complete aerosol prediction system that includes multiple aerosol species.

Theoretical Application of Ensemble Kalman Filter to Adsorptive Solute Cr(VI) Transfer from Soil into Surface Runoff

2014 ◽  
Vol 919-921 ◽  
pp. 1257-1261
Author(s):  
Chao Qun Tan ◽  
Ju Xiu Tong ◽  
Bill X. Hu ◽  
Jin Zhong Yang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Surface Runoff ◽  
Amplification Factor ◽  
Forecast Error ◽  
Assimilation Effect ◽  
Solute Transfer ◽  
Error Covariance ◽  
Theoretical Application

This paper mainly discusses some details when applying data assimilation method via an ensemble Kalman filter (EnKF) to improve prediction of adsorptive solute Cr(VI) transfer from soil into runoff. Based on this work, we could make better use of our theoretical model to predict adsorptive solute transfer from soil into surface runoff in practice. The results show that the ensemble number of 100 is reasonable, considering assimilation effect and efficiency after selecting its number from 25 to 225 at an interval of 25. While the initial ensemble value makes little difference to data assimilation (DA) results. Besides, DA results could be improved by multiplying an amplification factor to forecast error covariance matrix due to underestimation of forecast error.

scholarly journals Scale-Dependent Representation of the Information Content of Observations in the Global Ensemble Kalman Filter Data Assimilation

2016 ◽  
Vol 144 (8) ◽  
pp. 2927-2945
Author(s):  
Nedjeljka Žagar ◽  
Jeffrey Anderson ◽  
Nancy Collins ◽  
Timothy Hoar ◽  
Kevin Raeder ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Information Content ◽  
Ensemble Kalman Filter ◽  
Large Scale ◽  
Variance Reduction ◽  
Weather Prediction ◽  
Current Data ◽  
Model Framework ◽  
The Tropics

Abstract Global data assimilation systems for numerical weather prediction (NWP) are characterized by significant uncertainties in tropical analysis fields. Furthermore, the largest spread of global ensemble forecasts in the short range on all scales is in the tropics. The presented results suggest that these properties hold even in the perfect-model framework and the ensemble Kalman filter data assimilation with a globally homogeneous network of wind and temperature profiles. The reasons for this are discussed by using the modal analysis, which provides information about the scale dependency of analysis and forecast uncertainties and information about the efficiency of data assimilation to reduce the prior uncertainties in the balanced and inertio-gravity dynamics. The scale-dependent representation of variance reduction of the prior ensemble by the data assimilation shows that the peak efficiency of data assimilation is on the synoptic scales in the midlatitudes that are associated with quasigeostrophic dynamics. In contrast, the variance associated with the inertia–gravity modes is less successfully reduced on all scales. A smaller information content of observations on planetary scales with respect to the synoptic scales is discussed in relation to the large-scale tropical uncertainties that current data assimilation methodologies do not address successfully. In addition, it is shown that a smaller reduction of the large-scale uncertainties in the prior state for NWP in the tropics than in the midlatitudes is influenced by the applied radius for the covariance localization.

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 Impact of surface data assimilation using an ensemble Kalman filter technique on the improvement of weather prediction

2019 ◽  
Vol 1127 ◽  
pp. 012041
Author(s):  
N J Trilaksono ◽  
M Taqiyya ◽  
N Dewani ◽  
I D G A Junnaedhi ◽  
E Riawan ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Filter Technique ◽  
Surface Data

E4DVar: Coupling an Ensemble Kalman Filter with Four-Dimensional Variational Data Assimilation in a Limited-Area Weather Prediction Model

2012 ◽  
Vol 140 (2) ◽  
pp. 587-600 ◽  
Author(s):  
Meng Zhang ◽  
Fuqing Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Prediction Model ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Coupled System ◽  
Limited Area ◽  
Ensemble Forecasts ◽  
Background Error ◽  
Hybrid Data Assimilation

A hybrid data assimilation approach that couples the ensemble Kalman filter (EnKF) and four-dimensional variational (4DVar) methods is implemented for the first time in a limited-area weather prediction model. In this coupled system, denoted E4DVar, the EnKF and 4DVar systems run in parallel while feeding into each other. The multivariate, flow-dependent background error covariance estimated from the EnKF ensemble is used in the 4DVar minimization and the ensemble mean in the EnKF analysis is replaced by the 4DVar analysis, while updating the analysis perturbations for the next cycle of ensemble forecasts with the EnKF. Therefore, the E4DVar can obtain flow-dependent information from both the explicit covariance matrix derived from ensemble forecasts, as well as implicitly from the 4DVar trajectory. The performance of an E4DVar system is compared with the uncoupled 4DVar and EnKF for a limited-area model by assimilating various conventional observations over the contiguous United States for June 2003. After verifying the forecasts from each analysis against standard sounding observations, it is found that the E4DVar substantially outperforms both the EnKF and 4DVar during this active summer month, which featured several episodes of severe convective weather. On average, the forecasts produced from E4DVar analyses have considerably smaller errors than both of the stand-alone EnKF and 4DVar systems for forecast lead times up to 60 h.

scholarly journals Convective-Scale Data Assimilation for the Weather Research and Forecasting Model Using the Local Particle Filter

2017 ◽  
Vol 145 (5) ◽  
pp. 1897-1918 ◽  
Author(s):  
Jonathan Poterjoy ◽  
Ryan A. Sobash ◽  
Jeffrey L. Anderson
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Squall Line ◽  
Monte Carlo Data ◽  
Mixing Ratios ◽  
Convective Scale ◽  
Non Gaussian ◽  
Mean Square Errors

Abstract Particle filters (PFs) are Monte Carlo data assimilation techniques that operate with no parametric assumptions for prior and posterior errors. A data assimilation method introduced recently, called the local PF, approximates the PF solution within neighborhoods of observations, thus allowing for its use in high-dimensional systems. The current study explores the potential of the local PF for atmospheric data assimilation through cloud-permitting numerical experiments performed for an idealized squall line. Using only 100 ensemble members, experiments using the local PF to assimilate simulated radar measurements demonstrate that the method provides accurate analyses at a cost comparable to ensemble filters currently used in weather models. Comparisons between the local PF and an ensemble Kalman filter demonstrate benefits of the local PF for producing probabilistic analyses of non-Gaussian variables, such as hydrometeor mixing ratios. The local PF also provides more accurate forecasts than the ensemble Kalman filter, despite yielding higher posterior root-mean-square errors. A major advantage of the local PF comes from its ability to produce more physically consistent posterior members than the ensemble Kalman filter, which leads to fewer spurious model adjustments during forecasts. This manuscript presents the first successful application of the local PF in a weather prediction model and discusses implications for real applications where nonlinear measurement operators and nonlinear model processes limit the effectiveness of current Gaussian data assimilation techniques.

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