Application of the Sequential Three-Dimensional Variational Method to Assimilating SST in a Global Ocean Model

2008 ◽  
Vol 25 (6) ◽  
pp. 1018-1033 ◽  
Author(s):  
Zhongjie He ◽  
Yuanfu Xie ◽  
Wei Li ◽  
Dong Li ◽  
Guijun Han ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Three Dimensional ◽  
Ocean Model ◽  
Global Ocean ◽  
Background Error ◽  
Recursive Filters ◽  
Error Covariance ◽  
Observation Network ◽  
Isotropic Functions ◽  
Dependent Error

Abstract A recursive filter or parameterized curve fitting technique is usually used in a three-dimensional variational data assimilation (3DVAR) scheme to approximate the background error covariance, which can only represent the errors of an ocean field over a predetermined scale. Without an accurate flow-dependent error covariance that is also local and time dependent, a 3DVAR system may not provide good analyses because it is optimal only under the assumption of an accurate covariance. In this study, a sequential 3DVAR (S3DVAR) is formulated in model grid space to examine if there is useful information that can be extracted from the observation. This formulation is composed of a series of 3DVARs, each of which uses recursive filters with different length scales. It can provide an inhomogeneous and anisotropic analysis for the wavelengths that can be resolved by the observation network, just as with the conventional Barnes analysis or successive corrections. Being a variational formulation, S3DVAR can deal with data globally with an explicit specification of the observation errors; explicit physical balances or constraints; and advanced datasets, such as satellite and radar. Even though the S3DVAR analysis can be viewed as a set of isotropic functions superpositioned together, this superposition is not prespecified as in a single 3DVAR approach but is determined by the information that can be resolved by observation. The S3DVAR is adopted in a global sea surface temperature (SST) data assimilation system, into which the shipboard SSTs and the 4-km Advanced Very High Resolution Radiometer (AVHRR) Pathfinder daily SSTs are assimilated, respectively. The results demonstrate that the proposed S3DVAR works better in practice than a single 3DVAR.

scholarly journals A Comparison of Multiscale GSI-Based EnKF and 3DVar Data Assimilation Using Radar and Conventional Observations for Midlatitude Convective-Scale Precipitation Forecasts

2015 ◽  
Vol 143 (8) ◽  
pp. 3087-3108 ◽  
Author(s):  
Aaron Johnson ◽  
Xuguang Wang ◽  
Jacob R. Carley ◽  
Louis J. Wicker ◽  
Christopher Karstens
Keyword(s):  
Data Assimilation ◽  
Multiscale Analysis ◽  
Multiple Scales ◽  
Three Dimensional ◽  
Forecast Period ◽  
Background Error ◽  
Cold Pools ◽  
Error Covariance ◽  
Convective Scale

Abstract A GSI-based data assimilation (DA) system, including three-dimensional variational assimilation (3DVar) and ensemble Kalman filter (EnKF), is extended to the multiscale assimilation of both meso- and synoptic-scale observation networks and convective-scale radar reflectivity and velocity observations. EnKF and 3DVar are systematically compared in this multiscale context to better understand the impacts of differences between the DA techniques on the analyses at multiple scales and the subsequent convective-scale precipitation forecasts. Averaged over 10 diverse cases, 8-h precipitation forecasts initialized using GSI-based EnKF are more skillful than those using GSI-based 3DVar, both with and without storm-scale radar DA. The advantage from radar DA persists for ~5 h using EnKF, but only ~1 h using 3DVar. A case study of an upscale growing MCS is also examined. The better EnKF-initialized forecast is attributed to more accurate analyses of both the mesoscale environment and the storm-scale features. The mesoscale location and structure of a warm front is more accurately analyzed using EnKF than 3DVar. Furthermore, storms in the EnKF multiscale analysis are maintained during the subsequent forecast period. However, storms in the 3DVar multiscale analysis are not maintained and generate excessive cold pools. Therefore, while the EnKF forecast with radar DA remains better than the forecast without radar DA throughout the forecast period, the 3DVar forecast quality is degraded by radar DA after the first hour. Diagnostics revealed that the inferior analysis at mesoscales and storm scales for the 3DVar is primarily attributed to the lack of flow dependence and cross-variable correlation, respectively, in the 3DVar static background error covariance.

scholarly journals The impacts of uncertainties in emissions on aerosol data assimilation and short-term PM<sub>2.5</sub> predictions in CMAQ v5.2.1 over East Asia

2020 ◽  
Author(s):  
Sojin Lee ◽  
Chul Han Song ◽  
Kyung Man Han ◽  
Daven K. Henze ◽  
Kyunghwa Lee ◽  
...  
Keyword(s):  
Air Quality ◽  
Data Assimilation ◽  
East Asia ◽  
Conventional Method ◽  
Meteorological Data ◽  
Three Dimensional ◽  
Short Term ◽  
Background Error ◽  
Multi Scale ◽  
Error Covariance

Abstract. For the purpose of improving PM prediction skills in East Asia, we estimated a new background error covariance matrix (BEC) for aerosol data assimilation using surface PM2.5 observations that accounts for the uncertainties in anthropogenic emissions. In contrast to the conventional method to estimate the BEC that uses perturbations in meteorological data, this method additionally considered the perturbations using two different emission inventories. The impacts of the new BEC were then tested for the prediction of surface PM2.5 over East Asia using Community Multi-scale Air Quality (CMAQ) initialized by three-dimensional variational method (3D-VAR). The surface PM2.5 data measured at 154 sites in South Korea and 1,535 sites in China were assimilated every six hours during the Korea-United States Air Quality Study (KORUS-AQ) campaign period (1 May–14 June 2016). Data assimilation with our new BEC showed better agreement with the surface PM2.5 observations than that with the conventional method. Our method also showed closer agreement with the observations in 24-hour PM2.5 predictions with ~ 44 % fewer negative biases than the conventional method. We conclude that increased standard deviations, together with horizontal and vertical length scales in the new BEC, tend to improve the data assimilation and short-term predictions for the surface PM2.5. This paper also suggests further research efforts devoted to estimating the BEC to improve PM2.5 predictions.

scholarly journals A New Data Assimilation Scheme: The Space-Expanded Ensemble Localization Kalman Filter

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Hongze Leng ◽  
Junqiang Song ◽  
Fengshun Lu ◽  
Xiaoqun Cao
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Forecast Error ◽  
Three Dimensional ◽  
Full Rank ◽  
Observation Error ◽  
Model Framework ◽  
Background Error ◽  
Error Covariance ◽  
Expanded Ensemble

This study considers a new hybrid three-dimensional variational (3D-Var) and ensemble Kalman filter (EnKF) data assimilation (DA) method in a non-perfect-model framework, named space-expanded ensemble localization Kalman filter (SELKF). In this method, the localization operation is directly applied to the ensemble anomalies with a Schur Product, rather than to the full error covariance of the state in the EnKF. Meanwhile, the correction space of analysis increment is expanded to a space with larger dimension, and the rank of the forecast error covariance is significantly increased. This scheme can reduce the spurious correlations in the covariance and approximate the full-rank background error covariance well. Furthermore, a deterministic scheme is used to generate the analysis anomalies. The results show that the SELKF outperforms the perturbed EnKF given a relatively small ensemble size, especially when the length scale is relatively long or the observation error covariance is relatively small.

scholarly journals An Ensemble-Based Four-Dimensional Variational Data Assimilation Scheme. Part III: Antarctic Applications with Advanced Research WRF Using Real Data

2013 ◽  
Vol 141 (8) ◽  
pp. 2721-2739 ◽  
Author(s):  
Chengsi Liu ◽  
Qingnong Xiao
Keyword(s):  
Data Assimilation ◽  
Three Dimensional ◽  
Real Data ◽  
Variational Data Assimilation ◽  
Ensemble Forecasts ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Short Period ◽  
Inflation Factor

Abstract A four-dimensional ensemble-based variational data assimilation (4DEnVar) algorithm proposed in Part I of the 4DEnVar series (denoted En4DVar in Part I, but here we refer to it as 4DEnVar according to WMO conference recommendation to differentiate it from En4DVar algorithm using adjoint model) uses a flow-dependent background error covariance calculated from ensemble forecasts and performs 4DVar optimization based on an incremental approach and a preconditioning algorithm. In Part II, the authors evaluated 4DEnVar with observing system simulation experiments (OSSEs) using the Advanced Research Weather Research and Forecasting Model (ARW-WRF, hereafter WRF). The current study extends the 4DEnVar to assimilate real observations for a cyclone in the Antarctic and the Southern Ocean in October 2007. The authors performed an intercomparison of four different WRF variational approaches for the case, including three-dimensional variational data assimilation (3DVar), first guess at the appropriate time (FGAT), and ensemble-based three-dimensional (En3DVar) and four-dimensional (4DEnVar) variational data assimilations. It is found that all data assimilation approaches produce positive impacts in this case. Applying the flow-dependent background error covariance in En3DVar and 4DEnVar yields forecast skills superior to those with the homogeneous and isotropic background error covariance in 3DVar and FGAT. In addition, the authors carried out FGAT and 4DEnVar 3-day cycling and 72-h forecasts. The results show that 4DEnVar produces a better performance in the cyclone prediction. The inflation factor on 4DEnVar can effectively improve the 4DEnVar analysis. The authors also conducted a short period (10-day lifetime of the cyclone in the domain) of analysis/forecast intercomparison experiments using 4DEnVar, FGAT, and 3DVar. The 4DEnVar scheme demonstrates overall superior and robust performance.

scholarly journals Using Temperature–Salinity Relations in a Global Ocean Implementation of a Multivariate Data Assimilation Scheme

2007 ◽  
Vol 135 (11) ◽  
pp. 3785-3807 ◽  
Author(s):  
A. Bellucci ◽  
S. Masina ◽  
P. DiPietro ◽  
A. Navarra
Keyword(s):  
Data Assimilation ◽  
General Circulation ◽  
Circulation Model ◽  
Ocean General Circulation Model ◽  
Global Ocean ◽  
Special Focus ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
The Impact

Abstract In this paper results from the application of an ocean data assimilation (ODA) system, combining a multivariate reduced-order optimal interpolator (OI) scheme with a global ocean general circulation model (OGCM), are described. The present ODA system, designed to assimilate in situ temperature and salinity observations, has been used to produce ocean reanalyses for the 1962–2001 period. The impact of assimilating observed hydrographic data on the ocean mean state and temporal variability is evaluated. A special focus of this work is on the ODA system skill in reproducing a realistic ocean salinity state. Results from a hierarchy of different salinity reanalyses, using varying combinations of assimilated data and background error covariance structures, are described. The impact of the space and time resolution of the background error covariance parameterization on salinity is addressed.

Retrieval of Moisture from Simulated GPS Slant-Path Water Vapor Observations Using 3DVAR with Anisotropic Recursive Filters

2007 ◽  
Vol 135 (4) ◽  
pp. 1506-1521 ◽  
Author(s):  
Haixia Liu ◽  
Ming Xue ◽  
R. James Purser ◽  
David F. Parrish
Keyword(s):  
Water Vapor ◽  
Weather Prediction ◽  
Three Dimensional ◽  
Background Error ◽  
Special Configuration ◽  
Background Error Covariance ◽  
Recursive Filters ◽  
Error Covariance ◽  
Slant Path ◽  
The Impact

Abstract Anisotropic recursive filters are implemented within a three-dimensional variational data assimilation (3DVAR) framework to efficiently model the effect of flow-dependent background error covariance. The background error covariance is based on an estimated error field and on the idea of Riishøjgaard. In the anisotropic case, the background error pattern can be stretched or flattened in directions oblique to the alignment of the grid coordinates and is constructed by applying, at each point, six recursive filters along six directions corresponding, in general, to a special configuration of oblique lines of the grid. The recursive filters are much more efficient than corresponding explicit filters used in an earlier study and are therefore more suitable for real-time numerical weather prediction. A set of analysis experiments are conducted at a mesoscale resolution to examine the effectiveness of the 3DVAR system in analyzing simulated global positioning system (GPS) slant-path water vapor observations from ground-based GPS receivers and observations from collocated surface stations. It is shown that the analyses produced with recursive filters are at least as good as those with corresponding explicit filters. In some cases, the recursive filters actually perform better. The impact of flow-dependent background errors modeled using the anisotropic recursive filters is also examined. The use of anisotropic filters improves the analysis, especially in terms of finescale structures. The analysis system is found to be effective in the presence of typical observational errors. The sensitivity of isotropic and anisotropic recursive-filter analyses to the decorrelation scales is also examined systematically.

scholarly journals Data assimilation of Argo profiles in a northwestern Pacific model

2017 ◽  
Vol 17 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Zhaoyi Wang ◽  
Andrea Storto ◽  
Nadia Pinardi ◽  
Guimei Liu ◽  
Hui Wang
Keyword(s):  
Data Assimilation ◽  
Positive Impact ◽  
Three Dimensional ◽  
Predictive Performance ◽  
Ocean Model ◽  
Northwestern Pacific ◽  
Background Error ◽  
Salinity Data ◽  
Argo Profiles ◽  
Assimilation Scheme

Abstract. Based on a novel estimation of background-error covariances for assimilating Argo profiles, an oceanographic three-dimensional variational (3DVAR) data assimilation scheme was developed for the northwestern Pacific Ocean model (NwPM) for potential use in operational predictions and maritime safety applications. Temperature and salinity data extracted from Argo profiles from January to December 2010 were assimilated into the NwPM. The results show that the average daily temperature (salinity) root mean square error (RMSE) decreased from 0.99 °C (0.10 psu) to 0.62 °C (0.07 psu) in assimilation experiments throughout the northwestern Pacific, which represents a 37.2 % (27.6 %) reduction in the error. The temperature (salinity) RMSE decreased by  ∼  0.60 °C ( ∼  0.05 psu) for the upper 900 m (1000 m). Sea level, temperature and salinity were in better agreement with in situ and satellite datasets after data assimilation than before. In addition, a 1-month experiment with daily analysis cycles and 5-day forecasts explored the performance of the system in an operational configuration. The results highlighted the positive impact of the 3DVAR initialization at all forecast ranges compared to the non-assimilative experiment. Therefore, the 3DVAR scheme proposed here, coupled to ROMS, shows a good predictive performance and can be used as an assimilation scheme for operational forecasting.

scholarly journals THE INFLUENCE OF BACKGROUND ERROR COVARIANCE OF GSI THREE-DIMENSIONAL VARIATIONAL DATA ASSIMILATION ON METEOROLOGY AND AEROSOL PREDICTION

2018 ◽  
Vol XLII-3/W5 ◽  
pp. 17-23
Author(s):  
Y. Hu ◽  
M. Zhang ◽  
Y. Liang ◽  
L. Ye ◽  
D. Zhao ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Three Dimensional ◽  
Variational Data Assimilation ◽  
Small Scale ◽  
Length Scale ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Horizontal Length ◽  
Mean Square Errors

<p><strong>Abstract.</strong> Background error covariance (BEC) plays a key role in a variational data assimilation system. It determines variable analysis increments by spreading information from observation points. In order to test the influence of BEC on the GSI data assimilation and prediction of aerosol in Beijing-Tianjin-Hebei, a regional BEC is calculated using one month series of numerical forecast fields of November 2017 based on the National Meteorological Center (NMC) method, and compared with the global BEC.The results show that the standard deviation of stream function of the regional BEC is larger than that of the global BEC. And the horizontal length-scale of the regional BEC is smaller than that of the global BEC, white the vertical length-scale of the regional BEC is similar with that of the global BEC. The increments of the assimilation experiment with the regional BEC present more small scale information than that with the global BEC. The forecast skill of the experiment with the regional BEC is higher than that with the global BEC in the stations of Beijing, Tianjin, Chengde and Taiyuan, and the average root-mean-square errors (RMSE) reduces by over 13.4%.</p>

scholarly journals Background error covariance with balance constraints for aerosol species and applications in variational data assimilation

2016 ◽  
Vol 9 (8) ◽  
pp. 2623-2638 ◽  
Author(s):  
Zengliang Zang ◽  
Zilong Hao ◽  
Yi Li ◽  
Xiaobin Pan ◽  
Wei You ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Three Dimensional ◽  
Variational Data Assimilation ◽  
Statistical Regression ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Balance Analysis ◽  
Cross Correlations ◽  
Data Assimilation System

Abstract. Balance constraints are important for background error covariance (BEC) in data assimilation to spread information between different variables and produce balance analysis fields. Using statistical regression, we develop a balance constraint for the BEC of aerosol variables and apply it to a three-dimensional variational data assimilation system in the WRF/Chem model; 1-month forecasts from the WRF/Chem model are employed for BEC statistics. The cross-correlations between the different species are generally high. The largest correlation occurs between elemental carbon and organic carbon with as large as 0.9. After using the balance constraints, the correlations between the unbalanced variables reduce to less than 0.2. A set of data assimilation and forecasting experiments is performed. In these experiments, surface PM2.5 concentrations and speciated concentrations along aircraft flight tracks are assimilated. The analysis increments with the balance constraints show spatial distributions more complex than those without the balance constraints, which is a consequence of the spreading of observation information across variables due to the balance constraints. The forecast skills with the balance constraints show substantial and durable improvements from the 2nd hour to the 16th hour compared with the forecast skills without the balance constraints. The results suggest that the developed balance constraints are important for the aerosol assimilation and forecasting.

scholarly journals Analysis and Forecasting of Sea Ice Conditions with Three-Dimensional Variational Data Assimilation and a Coupled Ice–Ocean Model

2010 ◽  
Vol 27 (2) ◽  
pp. 353-369 ◽  
Author(s):  
Alain Caya ◽  
Mark Buehner ◽  
Tom Carrieres
Keyword(s):  
Data Assimilation ◽  
Sea Ice ◽  
Three Dimensional ◽  
Ocean Model ◽  
Variational Data Assimilation ◽  
Error Statistics ◽  
Background Error ◽  
Gaussian Shape ◽  
Ice Conditions ◽  
Image Analyses

Abstract A three-dimensional variational data assimilation (3DVAR) system has been developed to provide analyses of the ice–ocean state and to initialize a coupled ice–ocean numerical model for forecasting sea ice conditions. This study focuses on the estimation of the background-error statistics, including the spatial and multivariate covariances, and their impact on the quality of the resulting sea ice analyses and forecasts. The covariances are assumed to be horizontally homogeneous and fixed in time. The horizontal correlations are assumed to have a Gaussian shape and are modeled by integrating a diffusion equation. A relatively simple implementation of the ensemble Kalman filter is used to produce ensembles of the ice–ocean model state that are representative of background error and from which the 3DVAR covariance parameters are estimated. Data assimilation experiments, using various configurations of 3DVAR and simpler assimilation approaches, are conducted over a 7-month period during the winter of 2006/07 for the Canadian east coast region. The only data assimilated are the gridded daily ice charts and RADARSAT image analyses produced by the Canadian Ice Service. All of the data assimilation experiments produce significantly improved short-term forecasts as compared with persistence. When assimilating the same data, the forecast quality from the experiments employing either the 3DVAR, direct insertion, or nudging is quite similar. However, assimilation of both the daily ice charts and RADARSAT image analyses in 3DVAR results in significant improvements to the sea ice concentration forecasts. This result supports the use of a data assimilation approach, such as 3DVAR, for combining multiple sources of observational data together with a sophisticated forecast model to provide analyses and forecasts of sea ice conditions.

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