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

Covariance Operator ◽

Background Error ◽

Green Kernel ◽

Covariance Kernel ◽

Covariance Operators ◽

Physically Based ◽

Double Scale

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].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].This approximation of the covariance kernel is used to infer the bathymetry in the classical Saint-Venant&#8217;s (Shallow-Water) equations with better accuracy and faster convergence than if not introducing an adequate covariance operator [3].Moreover, this Green kernel helps to analyze the sensitivity of the double-scale diffusive waves (or even the Saint-Venant&#8217;s equations) with respect to the bathymetry.Numerical results are analyzed on real like datasets (derived from measurements of the Rio Negro, Amazonia basin).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.[1] T. Malou, J. Monnier "Double-scale diffusive wave equations dedicated to spatial river observations". In prep.[2] T. Malou, J. Monnier "Physically-based covariance kernel for variational data assimilation in spatial hydrology". In prep.[3] K. Larnier, J. Monnier, P.-A. Garambois, J. Verley. "River discharge and bathymetry estimations from SWOT altimetry measurements". Inv. Pb. Sc. Eng (2020).

An Overlooked Issue of Variational Data Assimilation

10.1175/mwr-d-14-00404.1 ◽

2015 ◽

Vol 143 (10) ◽

pp. 3925-3930 ◽

Cited By ~ 7

Author(s):

Benjamin Ménétrier ◽

Thomas Auligné

Keyword(s):

Data Assimilation ◽

Cost Function ◽

Control Variable ◽

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

Journal of Applied Meteorology and Climatology ◽

10.1175/jamc-d-13-0281.1 ◽

2014 ◽

Vol 53 (10) ◽

pp. 2287-2309 ◽

Cited By ~ 26

Author(s):

Hongli Wang ◽

Xiang-Yu Huang ◽

Juanzhen Sun ◽

Dongmei Xu ◽

Man Zhang ◽

...

Keyword(s):

Data Assimilation ◽

Forecast Error ◽

Control Variable ◽

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.

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

10.1175/mwr-d-14-00205.1 ◽

2015 ◽

Vol 144 (1) ◽

pp. 149-169 ◽

Cited By ~ 42

Author(s):

Juanzhen Sun ◽

Hongli Wang ◽

Wenxue Tong ◽

Ying Zhang ◽

Chung-Yi Lin ◽

...

Keyword(s):

High Resolution ◽

Data Assimilation ◽

Control Variable ◽

Wrf Model ◽

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.

A hybrid variational ensemble data assimilation for the HIgh Resolution Limited Area Model (HIRLAM)

Nonlinear Processes in Geophysics ◽

10.5194/npg-21-303-2014 ◽

2014 ◽

Vol 21 (1) ◽

pp. 303-323 ◽

Cited By ~ 18

Author(s):

N. Gustafsson ◽

J. Bojarova ◽

O. Vignes

Keyword(s):

Data Assimilation ◽

Control Variable ◽

Full Rank ◽

Ensemble Member ◽

Limited Area ◽

Background Error ◽

Ensemble Data Assimilation ◽

Ensemble Data ◽

Improved Performance

Abstract. A hybrid variational ensemble data assimilation has been developed on top of the HIRLAM variational data assimilation. It provides the possibility of applying a flow-dependent background error covariance model during the data assimilation at the same time as full rank characteristics of the variational data assimilation are preserved. The hybrid formulation is based on an augmentation of the assimilation control variable with localised weights to be assigned to a set of ensemble member perturbations (deviations from the ensemble mean). The flow-dependency of the hybrid assimilation is demonstrated in single simulated observation impact studies and the improved performance of the hybrid assimilation in comparison with pure 3-dimensional variational as well as pure ensemble assimilation is also proven in real observation assimilation experiments. The performance of the hybrid assimilation is comparable to the performance of the 4-dimensional variational data assimilation. The sensitivity to various parameters of the hybrid assimilation scheme and the sensitivity to the applied ensemble generation techniques are also examined. In particular, the inclusion of ensemble perturbations with a lagged validity time has been examined with encouraging results.

A GSI-Based Coupled EnSRF–En3DVar Hybrid Data Assimilation System for the Operational Rapid Refresh Model: Tests at a Reduced Resolution

10.1175/mwr-d-13-00242.1 ◽

2014 ◽

Vol 142 (10) ◽

pp. 3756-3780 ◽

Cited By ~ 40

Author(s):

Yujie Pan ◽

Kefeng Zhu ◽

Ming Xue ◽

Xuguang Wang ◽

Ming Hu ◽

...

Keyword(s):

Data Assimilation ◽

Hybrid System ◽

Control Variable ◽

Three Dimensional ◽

Horizontal Resolution ◽

Precipitation Forecast ◽

Background Error ◽

Hybrid Data Assimilation ◽

Noticeable Improvement ◽

Forecasting System

Abstract A coupled ensemble square root filter–three-dimensional ensemble-variational hybrid (EnSRF–En3DVar) data assimilation (DA) system is developed for the operational Rapid Refresh (RAP) forecasting system. The En3DVar hybrid system employs the extended control variable method, and is built on the NCEP operational gridpoint statistical interpolation (GSI) three-dimensional variational data assimilation (3DVar) framework. It is coupled with an EnSRF system for RAP, which provides ensemble perturbations. Recursive filters (RF) are used to localize ensemble covariance in both horizontal and vertical within the En3DVar. The coupled En3DVar hybrid system is evaluated with 3-h cycles over a 9-day period with active convection. All conventional observations used by operational RAP are included. The En3DVar hybrid system is run at ⅓ of the operational RAP horizontal resolution or about 40-km grid spacing, and its performance is compared to parallel GSI 3DVar and EnSRF runs using the same datasets and resolution. Short-term forecasts initialized from the 3-hourly analyses are verified against sounding and surface observations. When using equally weighted static and ensemble background error covariances and 40 ensemble members, the En3DVar hybrid system outperforms the corresponding GSI 3DVar and EnSRF. When the recursive filter coefficients are tuned to achieve a similar height-dependent localization as in the EnSRF, the En3DVar results using pure ensemble covariance are close to EnSRF. Two-way coupling between EnSRF and En3DVar did not produce noticeable improvement over one-way coupling. Downscaled precipitation forecast skill on the 13-km RAP grid from the En3DVar hybrid is better than those from GSI 3DVar analyses.

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

10.1175/mwr-d-13-00285.1 ◽

2014 ◽

Vol 142 (10) ◽

pp. 3586-3613 ◽

Cited By ~ 20

Author(s):

A. Routray ◽

S. C. Kar ◽

P. Mali ◽

K. Sowjanya

Keyword(s):

Data Assimilation ◽

Boundary Conditions ◽

Initial Conditions ◽

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.

A radar reflectivity operator with ice-phase hydrometeors for variational data assimilation (version 1.0) and its evaluation with real radar data

Geoscientific Model Development ◽

10.5194/gmd-12-4031-2019 ◽

2019 ◽

Vol 12 (9) ◽

pp. 4031-4051 ◽

Cited By ~ 1

Author(s):

Shizhang Wang ◽

Zhiquan Liu

Keyword(s):

Data Assimilation ◽

Three Dimensional ◽

Wrf Model ◽

Radar Data ◽

Poor Quality ◽

Radar Reflectivity ◽

Background Error ◽

Background Fields ◽

Ice Phase

Abstract. A reflectivity forward operator and its associated tangent linear and adjoint operators (together named RadarVar) were developed for variational data assimilation (DA). RadarVar can analyze both rainwater and ice-phase species (snow and graupel) by directly assimilating radar reflectivity observations. The results of three-dimensional variational (3D-Var) DA experiments with a 3 km grid mesh setting of the Weather Research and Forecasting (WRF) model showed that RadarVar was effective at producing an analysis of reflectivity pattern and intensity similar to the observed data. Two to three outer loops with 50–100 iterations in each loop were needed to obtain a converged 3-D analysis of reflectivity, rainwater, snow, and graupel, including the melting layers with mixed-phase hydrometeors. It is shown that the deficiencies in the analysis using this operator, caused by the poor quality of the background fields and the use of the static background error covariance, can be partially resolved by using radar-retrieved hydrometeors in a preprocessing step and tuning the spatial correlation length scales of the background errors. The direct radar reflectivity assimilation using RadarVar also improved the short-term (2–5 h) precipitation forecasts compared to those of the experiment without DA.