A robust numerical method for the potential vorticity based control variable transform in variational data assimilation

2011 ◽  
Vol 137 (657) ◽  
pp. 1083-1094 ◽  
Author(s):  
S. Buckeridge ◽  
M.J.P. Cullen ◽  
R. Scheichl ◽  
M. Wlasak
Keyword(s):  
Data Assimilation ◽  
Numerical Method ◽  
Potential Vorticity ◽  
Control Variable ◽  
Variational Data Assimilation

scholarly journals CIRA/CSU Four-Dimensional Variational Data Assimilation System

2005 ◽  
Vol 133 (4) ◽  
pp. 829-843 ◽  
Author(s):  
Milija Zupanski ◽  
Dusanka Zupanski ◽  
Tomislava Vukicevic ◽  
Kenneth Eis ◽  
Thomas Vonder Haar
Keyword(s):  
Data Assimilation ◽  
Initial Conditions ◽  
Control Variable ◽  
Three Dimensional ◽  
Atmospheric Modeling ◽  
Variational Data Assimilation ◽  
Regional Atmospheric Modeling ◽  
The Impact ◽  
Data Assimilation System ◽  
Assimilation System

A new four-dimensional variational data assimilation (4DVAR) system is developed at the Cooperative Institute for Research in the Atmosphere (CIRA)/Colorado State University (CSU). The system is also called the Regional Atmospheric Modeling Data Assimilation System (RAMDAS). In its present form, the 4DVAR system is employing the CSU/Regional Atmospheric Modeling System (RAMS) nonhydrostatic primitive equation model. The Weather Research and Forecasting (WRF) observation operator is used to access the observations, adopted from the WRF three-dimensional variational data assimilation (3DVAR) algorithm. In addition to the initial conditions adjustment, the RAMDAS includes the adjustment of model error (bias) and lateral boundary conditions through an augmented control variable definition. Also, the control variable is defined in terms of the velocity potential and streamfunction instead of the horizontal winds. The RAMDAS is developed after the National Centers for Environmental Prediction (NCEP) Eta 4DVAR system, however with added improvements addressing its use in a research environment. Preliminary results with RAMDAS are presented, focusing on the minimization performance and the impact of vertical correlations in error covariance modeling. A three-dimensional formulation of the background error correlation is introduced and evaluated. The Hessian preconditioning is revisited, and an alternate algebraic formulation is presented. The results indicate a robust minimization performance.

scholarly journals Displacing Potential Vorticity Structures by the Assimilation of Pseudo-Observations

2011 ◽  
Vol 139 (2) ◽  
pp. 549-565 ◽  
Author(s):  
Yann Michel
Keyword(s):  
Data Assimilation ◽  
Potential Vorticity ◽  
Variational Data Assimilation ◽  
Tuning Parameter ◽  
Data Assimilation Scheme ◽  
The Difference ◽  
Upper Level ◽  
Meteorological Features ◽  
Assimilation Scheme ◽  
Dry Intrusions

Abstract Classic formulations of variational data assimilation in amplitude space are not able to directly handle observations that measure the geographical positions of meteorological features like fronts and vortices. These observations can be derived from satellite images, as is already the case for tropical cyclones. Although some advanced data assimilation algorithms have been specifically designed to tackle the problem, a widespread way of dealing with this information is to use so-called bogussing pseudo-observations: user-specified artificial observations are inserted in a traditional data assimilation scheme. At the midlatitudes, there is a relationship between dry intrusions in water vapor images and upper-level potential vorticity structures. Some prior work has also shown that it was possible to automatically identify dry intrusions with tracking algorithms. The difference of positions between model and image dry intrusions could therefore be used as observations of the misplacement of potential vorticity structures. One strategy to achieve the displacement of potential vorticity anomalies is to sample them, and assimilate the values at displaced locations. The uncertainty of these pseudo-observations is left as a tuning parameter to try to make the displacement both effective and robust. A simple one-dimensional assimilation model is used to study the displacement of curves defined by Gaussian humps. The concept is then illustrated in realistic examples from real synoptic systems, where pseudo-observations of potential vorticity are incorporated in a global variational data assimilation scheme. Overall and despite reasonable optimization, the results contain artifacts. This suggests that the use of pseudo-observations to displace identifiable structures is not an effective strategy.

scholarly journals An Overlooked Issue of Variational Data Assimilation

2015 ◽  
Vol 143 (10) ◽  
pp. 3925-3930 ◽  
Author(s):  
Benjamin Ménétrier ◽  
Thomas Auligné
Keyword(s):  
Data Assimilation ◽  
Cost Function ◽  
Control Variable ◽  
Variational Data Assimilation ◽  
Inner Product ◽  
Background Error ◽  
Error Covariance ◽  
Definition Of ◽  
Linear Unbiased Estimate ◽  
The Cost

Abstract The control variable transform (CVT) is a keystone of variational data assimilation. In publications using such a technique, the background term of the transformed cost function is defined as a canonical inner product of the transformed control variable with itself. However, it is shown in this paper that this practical definition of the cost function is not correct if the CVT uses a square root of the background error covariance matrix that is not square. Fortunately, it is then shown that there is a manifold of the control space for which this flaw has no impact, and that most minimizers used in practice precisely work in this manifold. It is also shown that both correct and practical transformed cost functions have the same minimum. This explains more rigorously why the CVT is working in practice. The case of a singular is finally detailed, showing that the practical cost function still reaches the best linear unbiased estimate (BLUE).

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.

Double-scale diffusive wave model dedicated to spatial river observation and associated covariance kernel for variational data assimilation 

2021 ◽  
Author(s):  
Thibault Malou ◽  
Jérome Monnier
Keyword(s):  
Data Assimilation ◽  
Control Variable ◽  
Variational Data Assimilation ◽  
Covariance Operator ◽  
Background Error ◽  
Green Kernel ◽  
Covariance Kernel ◽  
Covariance Operators ◽  
Physically Based ◽  
Double Scale

<p>The spatial altimetry provides an important amount of water surface height data from multi-missions satellites (especially Jason-3, Sentinel-3A/B and the forthcoming NASA-CNES SWOT mission). To exploit at best the potential of spatial altimetry, the present study proposes on the derivation of a model adapted to spatial observations scale; a diffusive-wave type model but adapted to a double scale [1].</p><p>Moreover, Green-like kernel can be employed to derived covariance operators, therefore they may provide an approximation of the covariance kernel of the background error in Variational Data Assimilation processes. Following the derivation of the aforementioned original flow model, we present the derivation of a Green kernel which provides an approximation of the covariance kernel of the background error for the bathymetry (i.e. the control variable) [2].</p><p>This approximation of the covariance kernel is used to infer the bathymetry in the classical Saint-Venant’s (Shallow-Water) equations with better accuracy and faster convergence than if not introducing an adequate covariance operator [3].</p><p>Moreover, this Green kernel helps to analyze the sensitivity of the double-scale diffusive waves (or even the Saint-Venant’s equations) with respect to the bathymetry.</p><p>Numerical results are analyzed on real like datasets (derived from measurements of the Rio Negro, Amazonia basin).</p><p>The double-scale diffusive wave provide more accurate results than the classical version. Next, in terms of inversions, the derived physically-based covariance operators enable to improve the inferences, compared to the usual exponential one.</p><p>[1] T. Malou, J. Monnier "Double-scale diffusive wave equations dedicated to spatial river observations". In prep.</p><p>[2] T. Malou, J. Monnier "Physically-based covariance kernel for variational data assimilation in spatial hydrology". In prep.</p><p>[3] K. Larnier, J. Monnier, P.-A. Garambois, J. Verley. "River discharge and bathymetry estimations from SWOT altimetry measurements". Inv. Pb. Sc. Eng (2020).</p>

Comparison of the Impacts of Momentum Control Variables on High-Resolution Variational Data Assimilation and Precipitation Forecasting

2015 ◽  
Vol 144 (1) ◽  
pp. 149-169 ◽  
Author(s):  
Juanzhen Sun ◽  
Hongli Wang ◽  
Wenxue Tong ◽  
Ying Zhang ◽  
Chung-Yi Lin ◽  
...  
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Control Variable ◽  
Wrf Model ◽  
Variational Data Assimilation ◽  
Error Modeling ◽  
Limited Area ◽  
Control Variables ◽  
Background Error ◽  
Precipitation Prediction

Abstract The momentum variables of streamfunction and velocity potential are used as control variables in a number of operational variational data assimilation systems. However, in this study it is shown that, for limited-area high-resolution data assimilation, the momentum control variables ψ and χ (ψχ) pose potential difficulties in background error modeling and, hence, may result in degraded analysis and forecast when compared with the direct use of x and y components of wind (UV). In this study, the characteristics of the modeled background error statistics, derived from an ensemble generated from Weather Research and Forecasting (WRF) Model real-time forecasts of two summer months, are first compared between the two control variable options. Assimilation and forecast experiments are then conducted with both options for seven convective events in a domain that encompasses the Rocky Mountain Front Range using the three-dimensional variational data assimilation (3DVar) system of the WRF Model. The impacts of the two control variable options are compared in terms of their skills in short-term qualitative precipitation forecasts. Further analysis is performed for one case to examine the impacts when radar observations are included in the 3DVar assimilation. The main findings are as follows: 1) the background error modeling used in WRF 3DVar with the control variables ψχ increases the length scale and decreases the variance for u and υ, which causes negative impact on the analysis of the velocity field and on precipitation prediction; 2) the UV-based 3DVar allows closer fits to radar wind observations; and 3) the use of UV control variables improves the 0–12-h precipitation prediction.

scholarly journals Some Observing System Simulation Experiments with a Hybrid 3DEnVAR System for Storm-Scale Radar Data Assimilation

2014 ◽  
Vol 142 (9) ◽  
pp. 3326-3346 ◽  
Author(s):  
Jidong Gao ◽  
David J. Stensrud
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Control Variable ◽  
Simulated Data ◽  
Variational Data Assimilation ◽  
Sampling Errors ◽  
Advanced Regional Prediction System ◽  
Sensitivity Experiments ◽  
Variable Approach ◽  
Regional Prediction

A hybrid three-dimensional ensemble–variational data assimilation (3DEnVAR) algorithm is developed based on the 3D variational data assimilation (3DVAR) and ensemble Kalman filter (EnKF) programs with the Advanced Regional Prediction System (ARPS). The method uses the extended control variable approach to combine the static and ensemble-derived flow-dependent forecast error covariances. The method is applied to the assimilation of simulated data from two radars for a supercell storm. Some sensitivity experiments are performed to answer questions about how flow-dependent covariance estimated from the forecast ensemble can be best used in the hybrid 3DEnVAR scheme. When the ensemble size is relatively small (with 5 or 10 ensemble members), it is found that experiments with a weaker weighting value for the ensemble covariance leads to better analysis results. Even when severe sampling errors exist, introducing ensemble-estimated covariances into the variational method still benefits the analysis. For reasonably large ensemble sizes (50–100 members), a stronger relative weighting (>0.8) for the ensemble covariance leads to better analyses from the hybrid 3DEnVAR. In addition, the sensitivity experiments also indicate that the best results are obtained when the number of the augmented control variables is a function of three spatial dimensions and ensemble members, and is the same for all analysis variables.

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.

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