scholarly journals A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation

2011 ◽  
Vol 46 (1) ◽  
pp. 387-391 ◽  
Author(s):  
R.E. Petrie ◽  
R.N. Bannister
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Forecast Error ◽  
Variational Data Assimilation ◽  
Error Statistics

Inhomogeneous Background Error Modeling for WRF-Var Using the NMC Method

2014 ◽  
Vol 53 (10) ◽  
pp. 2287-2309 ◽  
Author(s):  
Hongli Wang ◽  
Xiang-Yu Huang ◽  
Juanzhen Sun ◽  
Dongmei Xu ◽  
Man Zhang ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Control Variable ◽  
Variational Data Assimilation ◽  
Error Modeling ◽  
Error Statistics ◽  
Background Error ◽  
New Approach ◽  
Data Assimilation System ◽  
Assimilation System

AbstractBackground error modeling plays a key role in a variational data assimilation system. The National Meteorological Center (NMC) method has been widely used in variational data assimilation systems to generate a forecast error ensemble from which the climatological background error covariance can be modeled. In this paper, the characteristics of the background error modeling via the NMC method are investigated for the variational data assimilation system of the Weather Research and Forecasting (WRF-Var) Model. The background error statistics are extracted from short-term 3-km-resolution forecasts in June, July, and August 2012 over a limited-area domain. It is found 1) that background error variances vary from month to month and also have a feature of diurnal variations in the low-level atmosphere and 2) that u- and υ-wind variances are underestimated and their autocorrelation length scales are overestimated when the default control variable option in WRF-Var is used. A new approach of control variable transform (CVT) is proposed to model the background error statistics based on the NMC method. The new approach is capable of extracting inhomogeneous and anisotropic climatological information from the forecast error ensemble obtained via the NMC method. Single observation assimilation experiments show that the proposed method not only has the merit of incorporating geographically dependent covariance information, but also is able to produce a multivariate analysis. The results from the data assimilaton and forecast study of a real convective case show that the use of the new CVT improves synoptic weather system and precipitation forecasts for up to 12 h.

scholarly journals Can Wavelets Improve the Representation of Forecast Error Covariances in Variational Data Assimilation?

2007 ◽  
Vol 135 (2) ◽  
pp. 387-408 ◽  
Author(s):  
Ross N. Bannister
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Control Variable ◽  
Variational Data Assimilation ◽  
Covariance Structures ◽  
Spectral Space ◽  
Error Statistics ◽  
Length Scales ◽  
Spectral Bands ◽  
The Right

Abstract Two wavelet-based control variable transform schemes are described and are used to model some important features of forecast error statistics for use in variational data assimilation. The first is a conventional wavelet scheme and the other is an approximation of it. Their ability to capture the position and scale-dependent aspects of covariance structures is tested in a two-dimensional latitude–height context. This is done by comparing the covariance structures implied by the wavelet schemes with those found from the explicit forecast error covariance matrix, and with a non-wavelet-based covariance scheme used currently in an operational assimilation scheme. Qualitatively, the wavelet-based schemes show potential at modeling forecast error statistics well without giving preference to either position or scale-dependent aspects. The degree of spectral representation can be controlled by changing the number of spectral bands in the schemes, and the least number of bands that achieves adequate results is found for the model domain used. Evidence is found of a trade-off between the localization of features in positional and spectral spaces when the number of bands is changed. By examining implied covariance diagnostics, the wavelet-based schemes are found, on the whole, to give results that are closer to diagnostics found from the explicit matrix than from the nonwavelet scheme. Even though the nature of the covariances has the right qualities in spectral space, variances are found to be too low at some wavenumbers and vertical correlation length scales are found to be too long at most scales. The wavelet schemes are found to be good at resolving variations in position and scale-dependent horizontal length scales, although the length scales reproduced are usually too short. The second of the wavelet-based schemes is often found to be better than the first in some important respects, but, unlike the first, it has no exact inverse transform.

scholarly journals Multivariate Error Covariance Estimates by Monte Carlo Simulation for Assimilation Studies in the Pacific Ocean

2005 ◽  
Vol 133 (8) ◽  
pp. 2310-2334 ◽  
Author(s):  
Anna Borovikov ◽  
Michele M. Rienecker ◽  
Christian L. Keppenne ◽  
Gregory C. Johnson
Keyword(s):  
Monte Carlo ◽  
Data Assimilation ◽  
Forecast Error ◽  
Independent Set ◽  
Velocity Fields ◽  
Optimal Interpolation ◽  
Model Errors ◽  
Error Statistics ◽  
Practical Applications ◽  
Monte Carlo Techniques

Abstract One of the most difficult aspects of ocean-state estimation is the prescription of the model forecast error covariances. The paucity of ocean observations limits our ability to estimate the covariance structures from model–observation differences. In most practical applications, simple covariances are usually prescribed. Rarely are cross covariances between different model variables used. Here a comparison is made between a univariate optimal interpolation (UOI) scheme and a multivariate OI algorithm (MvOI) in the assimilation of ocean temperature profiles. In the UOI case only temperature is updated using a Gaussian covariance function. In the MvOI, salinity, zonal, and meridional velocities as well as temperature are updated using an empirically estimated multivariate covariance matrix. Earlier studies have shown that a univariate OI has a detrimental effect on the salinity and velocity fields of the model. Apparently, in a sequential framework it is important to analyze temperature and salinity together. For the MvOI an estimate of the forecast error statistics is made by Monte Carlo techniques from an ensemble of model forecasts. An important advantage of using an ensemble of ocean states is that it provides a natural way to estimate cross covariances between the fields of different physical variables constituting the model-state vector, at the same time incorporating the model’s dynamical and thermodynamical constraints as well as the effects of physical boundaries. Only temperature observations from the Tropical Atmosphere–Ocean array have been assimilated in this study. To investigate the efficacy of the multivariate scheme, two data assimilation experiments are validated with a large independent set of recently published subsurface observations of salinity, zonal velocity, and temperature. For reference, a control run with no data assimilation is used to check how the data assimilation affects systematic model errors. While the performance of the UOI and MvOI is similar with respect to the temperature field, the salinity and velocity fields are greatly improved when the multivariate correction is used, as is evident from the analyses of the rms differences between these fields and independent observations. The MvOI assimilation is found to improve upon the control run in generating water masses with properties close to the observed, while the UOI fails to maintain the temperature and salinity structure.

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.

scholarly journals Simulation of Monsoon Depressions Using WRF-VAR: Impact of Different Background Error Statistics and Lateral Boundary Conditions

2014 ◽  
Vol 142 (10) ◽  
pp. 3586-3613 ◽  
Author(s):  
A. Routray ◽  
S. C. Kar ◽  
P. Mali ◽  
K. Sowjanya
Keyword(s):  
Data Assimilation ◽  
Boundary Conditions ◽  
Initial Conditions ◽  
Variational Data Assimilation ◽  
Error Statistics ◽  
Background Error ◽  
Single Observation ◽  
Monsoon Depressions ◽  
Data Assimilation System ◽  
Assimilation System

Abstract In a variational data assimilation system, background error statistics (BES) spread the influence of the observations in space and filter analysis increments through dynamic balance or statistical relationships. In a data-sparse region such as the Bay of Bengal, BES play an important role in defining the location and structure of monsoon depressions (MDs). In this study, the Indian-region-specific BES have been computed for the Weather Research and Forecasting (WRF) three-dimensional variational data assimilation system. A comparative study using single observation tests is carried out using the computed BES and global BES within the WRF system. Both sets of BES are used in the assimilation cycles and forecast runs for simulating the meteorological features associated with the MDs. Numerical experiments have been conducted to assess the relative impact of various BES in the analysis and simulations of the MDs. The results show that use of regional BES in the assimilation cycle has a positive impact on the prediction of the location, propagation, and development of rainbands associated with the MDs. The track errors of MDs are smaller when domain-specific BES are used in the assimilation cycle. Additional experiments have been conducted using data from the Interim European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-Interim) as initial and boundary conditions (IBCs) in the assimilation cycle. The results indicate that the use of domain-dependent BES and high-resolution ERA-I data as IBCs further improved the initial conditions for the model leading to better forecasts of the MDs.

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.

Four-dimensional variational data assimilation for high resolution nested models

2011 ◽  
Vol 46 (1) ◽  
pp. 137-141 ◽  
Author(s):  
G.M. Baxter ◽  
S.L. Dance ◽  
A.S. Lawless ◽  
N.K. Nichols
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Variational Data Assimilation ◽  
Nested Models

scholarly journals Development and evaluation of a high-resolution reanalysis of the East Australian Current region using the Regional Ocean Modelling System (ROMS 3.4) and Incremental Strong-Constraint 4-Dimensional Variational data assimilation (IS4D-Var)

2016 ◽  
Author(s):  
Colette Kerry ◽  
Brian Powell ◽  
Moninya Roughan ◽  
Peter Oke
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Water Column ◽  
Marked Improvement ◽  
Variational Data Assimilation ◽  
Surface Velocity ◽  
East Australian Current ◽  
Strong Constraint ◽  
Ocean Modelling ◽  
Modelling System

Abstract. As with other western boundary currents globally, the East Australian Current (EAC) is inherently dynamic making it a challenge to model and predict. For the EAC region, we combine a high-resolution state-of-the-art numerical ocean model with a variety of traditional and newly available observations using an advanced variational data assimilation scheme. The numerical model is configured using the Regional Ocean Modelling System (ROMS 3.4) and takes boundary forcing from the BlueLink ReANalysis (BRAN3). For the data assimilation we use an Incremental Strong-Constraint 4-Dimensional Variational (IS4D-Var) scheme. This paper describes the data assimilative model configuration that achieves an optimised minimisation of the difference between the modelled solution and the observations to give a dynamically-consistent `best-estimate' of the ocean state over a 2-year period. The reanalysis is shown to represent both assimilated and non-assimilated observations well. It achieves mean spatially-averaged RMS residuals with the observations of 7 cm for SSH and 0.4 °C for SST over the assimilation period. The time-mean RMS residual for subsurface temperature measured by Argo floats is a maximum of 1 °C between water depths of 100–300 m and smaller throughout the rest of the water column. Velocities at several offshore and continental shelf moorings are well represented in the reanalysis with complex correlations between 0.8–1 for all observations in the upper 500 m. Surface radial velocities from a high-frequency radar array are assimilated and the reanalysis provides surface velocity estimates with complex correlations with observed velocities of 0.8–1 across the radar footprint. Comparison with independent (non-assimilated) shipboard CTD cast observations shows a marked improvement in the representation of the subsurface ocean in the reanalysis, with the RMS residual in potential density reduced to about half of the residual with the free-running model in the upper eddy-influenced part of the water column. This shows that information is successfully propagated from observed variables to unobserved regions as the assimilation system uses the model dynamics to determine covariance, such that the ocean state better fits and is in balance with the observations. This is the first study to generate a reanalysis of the region at such a high resolution, making use of an unprecedented observational data set and using an assimilation method that uses the time-evolving model physics to adjust the model in a dynamically consistent way. As such, the reanalysis potentially represents a marked improvement in our ability to capture important circulation dynamics in the EAC. The reanalysis is being used to study EAC dynamics, observation impact in state-estimation and as forcing for a variety of downscaling studies.

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