A review of forecast error covariance statistics in atmospheric variational data assimilation. II: Modelling the forecast error covariance statistics

2008 ◽  
Vol 134 (637) ◽  
pp. 1971-1996 ◽  
Author(s):  
R. N. Bannister
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Variational Data Assimilation ◽  
Error Covariance

A New Approach for Estimating the Observation Impact in Ensemble–Variational Data Assimilation

2018 ◽  
Vol 146 (2) ◽  
pp. 447-465 ◽  
Author(s):  
Mark Buehner ◽  
Ping Du ◽  
Joël Bédard
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Forecast Model ◽  
Variational Data Assimilation ◽  
Observation Error ◽  
New Approach ◽  
Regional Prediction ◽  
Observation Impact ◽  
Adjoint Approach ◽  
The Impact

Abstract Two types of approaches are commonly used for estimating the impact of arbitrary subsets of observations on short-range forecast error. The first was developed for variational data assimilation systems and requires the adjoint of the forecast model. Comparable approaches were developed for use with the ensemble Kalman filter and rely on ensembles of forecasts. In this study, a new approach for computing observation impact is proposed for ensemble–variational data assimilation (EnVar). Like standard adjoint approaches, the adjoint of the data assimilation procedure is implemented through the iterative minimization of a modified cost function. However, like ensemble approaches, the adjoint of the forecast step is obtained by using an ensemble of forecasts. Numerical experiments were performed to compare the new approach with the standard adjoint approach in the context of operational deterministic NWP. Generally similar results are obtained with both approaches, especially when the new approach uses covariance localization that is horizontally advected between analysis and forecast times. However, large differences in estimated impacts are obtained for some surface observations. Vertical propagation of the observation impact is noticeably restricted with the new approach because of vertical covariance localization. The new approach is used to evaluate changes in observation impact as a result of the use of interchannel observation error correlations for radiance observations. The estimated observation impact in similarly configured global and regional prediction systems is also compared. Overall, the new approach should provide useful estimates of observation impact for data assimilation systems based on EnVar when an adjoint model is not available.

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 The Development of a Hybrid EnKF-3DVAR Algorithm for Storm-Scale Data Assimilation

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jidong Gao ◽  
Ming Xue ◽  
David J. Stensrud
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Control Variable ◽  
Radar Data ◽  
Ensemble Forecasts ◽  
Advanced Regional Prediction System ◽  
Error Covariance ◽  
Variable Approach ◽  
Regional Prediction ◽  
Rms Errors

A hybrid 3DVAR-EnKF data assimilation algorithm is developed based on 3DVAR and ensemble Kalman filter (EnKF) programs within the Advanced Regional Prediction System (ARPS). The hybrid algorithm uses the extended alpha control variable approach to combine the static and ensemble-derived flow-dependent forecast error covariances. The hybrid variational analysis is performed using an equal weighting of static and flow-dependent error covariance as derived from ensemble forecasts. The method is first applied to the assimilation of simulated radar data for a supercell storm. Results obtained using 3DVAR (with static covariance entirely), hybrid 3DVAR-EnKF, and the EnKF are compared. When data from a single radar are used, the EnKF method provides the best results for the model dynamic variables, while the hybrid method provides the best results for hydrometeor related variables in term of rms errors. Although storm structures can be established reasonably well using 3DVAR, the rms errors are generally worse than seen from the other two methods. With two radars, the results from 3DVAR are closer to those from EnKF. Our tests indicate that the hybrid scheme can reduce the storm spin-up time because it fits the observations, especially the reflectivity observations, better than the EnKF and the 3DVAR at the beginning of the assimilation cycles.

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 Localized Ensemble-Based Tangent Linear Models and Their Use in Propagating Hybrid Error Covariance Models

2016 ◽  
Vol 144 (4) ◽  
pp. 1383-1405 ◽  
Author(s):  
Sergey Frolov ◽  
Craig H. Bishop
Keyword(s):  
Data Assimilation ◽  
Short Duration ◽  
Linear Models ◽  
Forecast Error ◽  
Weather Forecast ◽  
Step Function ◽  
Rank Deficiency ◽  
One Dimensional ◽  
Error Covariance ◽  
Covariance Models

Abstract Hybrid error covariance models that blend climatological estimates of forecast error covariances with ensemble-based, flow-dependent forecast error covariances have led to significant reductions in forecast error when employed in 4DVAR data assimilation schemes. Tangent linear models (TLMs) designed to predict the differences between perturbed and unperturbed simulations of the weather forecast are a key component of such 4DVAR schemes. However, many forecasting centers have found that TLMs and their adjoints do not scale well computationally and are difficult to create and maintain—particularly for coupled ocean–wave–ice–atmosphere models. In this paper, the authors create ensemble-based TLMs (ETLMs) and test their ability to propagate both climatological and flow-dependent parts of hybrid error covariance models. These tests demonstrate that rank deficiency limits the utility of unlocalized ETLMs. High-rank, time-evolving, flow-adaptive localization functions are constructed and tested using recursive application of short-duration ETLMs, each of which is localized using a static localization. Since TLM operators do not need to be semipositive definite, the authors experiment with a variety of localization approaches including step function localization. The step function localization leads to a local formulation that was found to be highly effective. In tests using simple one-dimensional models with both dispersive and nondispersive dynamics, it is shown that practical ETLM configurations were effective at propagating covariances as far as four error correlation scales.

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