scholarly journals Effect of Adding Hydrometeor Mixing Ratios Control Variables on Assimilating Radar Observations for the Analysis and Forecast of a Typhoon

Atmosphere ◽  
2019 ◽  
Vol 10 (7) ◽  
pp. 415 ◽  
Author(s):  
Dongmei Xu ◽  
Feifei Shen ◽  
Jinzhong Min
Keyword(s):  
Cost Function ◽  
Positive Impact ◽  
Precipitation Forecast ◽  
Track Forecast ◽  
Error Statistics ◽  
Control Variables ◽  
Background Error ◽  
Mixing Ratios ◽  
The Cost ◽  
Assimilation Scheme

The variational data assimilation (DA) method seeks the optimal analyses by minimizing a cost function with respect to control variables (CVs). CVs are extended in this study to include hydrometeor mixing ratios related variables besides the widely used sets of CVs (momentum fields, surface pressure, temperature, and pseudo-relative humidity). The impacts of the extra CVs are investigated in terms of hydrometeor mixing ratios to the assimilation of radar radial velocity (Vr) and reflectivity (RF) for the analysis and prediction of Typhoon Chanthu (2010). It is found that the background error statistics of the extended CVs from the National Meteorological Center (NMC) method is reliable. The track forecast is improved significantly by including hydrometeor mixing ratios as CVs to assimilate radar Vr and RF. The DA experiments using the hydrometer CVs show much improved intensity analysis and forecast. It also improves the precipitation forecast skills to some extent. The positive impact is significant using a direct RF assimilation scheme, when Vr and RF data are applied together. It suggests that when we applying an indirect RF assimilation scheme, the fitting of more hydrometers in the cost function will tend to cause a slight degradation for other variables such as the wind and temperature.

scholarly journals Direct Variational Assimilation of Radar Reflectivity and Radial Velocity Data: Issues with Nonlinear Reflectivity Operator and Solutions

2020 ◽  
Vol 148 (4) ◽  
pp. 1483-1502 ◽  
Author(s):  
Chengsi Liu ◽  
Ming Xue ◽  
Rong Kong
Keyword(s):  
Radial Velocity ◽  
Cost Function ◽  
Radar Data ◽  
Radar Reflectivity ◽  
Control Variables ◽  
Mixing Ratios ◽  
Highly Nonlinear ◽  
The Cost ◽  
Lower Limits ◽  
Radial Velocity Data

Abstract Radar reflectivity (Z) data are either directly assimilated using 3DVar, 4DVar, or ensemble Kalman filter, or indirectly assimilated using, for example, cloud analysis that preretrieves hydrometeors from Z. When directly assimilating radar data variationally, issues related to the highly nonlinear Z operator arise that can cause nonconvergence and bad analyses. To alleviate the issues, treatments are proposed in this study and their performances are examined via observing system simulation experiments. They include the following: 1) When using hydrometeor mixing ratios as control variables (CVq), small background Z can cause extremely large cost function gradient. Lower limits are imposed on the mixing ratios (qLim treatment) or the equivalent reflectivity (ZeLim treatment) in Z observation operator. ZeLim is found to work better than qLim in terms of analysis accuracy and convergence speed. 2) With CVq, the assimilation of radial velocity (Vr) is ineffective when assimilated together with Z data due to the much smaller cost function gradient associated with Vr. A procedure (VrPass) that assimilates Vr data in a separate pass is found very helpful. 3) Using logarithmic hydrometeor mixing ratios as control variables (CVlogq) can also avoid extremely large cost function gradient, and has much faster convergence. However, spurious analysis increments can be created when transforming the analysis increments back to mixing ratios. A background smoothing and a lower limit are applied to the background mixing ratios, and are shown to be effective. Using CVlogq with associated treatments produces better reflectivity analysis that is much closer to the observation without resorting to multiple analysis passes, and the cost function minimization also converges faster. CVlogq is therefore recommended for variational radar data assimilation.

Use of Power Transform Mixing Ratios as Hydrometeor Control Variables for Direct Assimilation of Radar Reflectivity in GSI En3DVar and Tests with Five Convective Storms Cases

2020 ◽  
Author(s):  
Lianglyu Chen ◽  
Chengsi Liu ◽  
Ming Xue ◽  
Gang Zhao ◽  
Rong Kong ◽  
...  
Keyword(s):  
Cost Function ◽  
Radar Data ◽  
Power Parameter ◽  
Control Variables ◽  
Convective Storms ◽  
Mixing Ratios ◽  
Variational Framework ◽  
Study Power ◽  
The Cost ◽  
Outbreak Case

AbstractWhen directly assimilating radar data within a variational framework using hydrometeor mixing ratios (q) as control variables (CVq), the gradient of the cost function becomes extremely large when background mixing ratio is close to zero. This significantly slows down minimization convergence and makes the assimilation of radial velocity and other observations ineffective because of the dominance of reflectivity observation term in the cost function gradient. Using logarithmic hydrometeor mixing ratios as control variables (CVlogq) can alleviate the problem but the high nonlinearity of logarithmic transformation can introduce spurious analysis increments into mixing ratios.In this study, power transform of hydrometeors is proposed to form new control variables (CVpq) where the nonlinearity of transformation can be adjusted by tuning exponent or power parameter p. The performance of assimilating radar data using CVpq is compared with those using CVq and CVlogq for the analyses and forecasts of five convective storm cases from spring of 2017. Results show that CVpq with p = 0.4 (CVpq0.4) gives the best reflectivity forecasts in terms of root mean square error and equitable threat score. Furthermore, CVpq0.4 has faster convergence of cost function minimization than CVq and produces less spurious analysis increment than CVlogq. Compared to CVq and CVlogq, CVpq0.4 have better skills of 0-3h composite reflectivity forecasts, and the updraft helicity tracks for the 16 May 2017 Texas and Oklahoma tornado outbreak case are more consistent with observations when using CVpq0.4.

scholarly journals Assimilation of Infrared Radiance Observations with Sensitivity to Land Surfaces in the Canadian Ensemble–Variational System

2016 ◽  
Vol 55 (3) ◽  
pp. 561-578 ◽  
Author(s):  
S. K. Dutta ◽  
L. Garand ◽  
S. Heilliette
Keyword(s):  
Positive Impact ◽  
Surface Emissivity ◽  
Error Statistics ◽  
Variational System ◽  
Background Error ◽  
Infrared Radiance ◽  
Forecast Lead Time ◽  
Surface Skin Temperature ◽  
Land Surfaces ◽  
The Impact

AbstractThis study highlights recent progress at the Canadian Meteorological Centre in the assimilation of Atmospheric Infrared Sounder (AIRS) and Infrared Atmospheric Sounding Interferometer (IASI) radiance observations that are sensitive to land surfaces. The assimilation is carried out using the Canadian global ensemble–variational system. That system benefits from flow-dependent background-error statistics that include covariances between surface skin temperature and atmospheric variables. Up to 142 channels from both AIRS and IASI are assimilated. A detailed database of spectral surface emissivity is used. Forecasts are evaluated against ERA-Interim analyses, own-cycle analyses, and radiosonde observations. A conservative approach is taken, with restrictive conditions on topography and surface emissivity. From 2-month assimilation experiments, a significant positive impact is obtained in the Northern Hemisphere extratropics beyond day 2 from the surface to the upper troposphere. The impact is mixed in other regions, depending on level or forecast lead time. Causes for these mixed results are examined in view of future experiments and eventual operational implementation.

Inhomogeneous Background Error Modeling and Estimation over Antarctica

2010 ◽  
Vol 138 (6) ◽  
pp. 2229-2252 ◽  
Author(s):  
Yann Michel ◽  
Thomas Auligné
Keyword(s):  
Wrf Model ◽  
Error Modeling ◽  
Limited Area ◽  
Error Statistics ◽  
Background Error ◽  
Recursive Filters ◽  
Error Covariance ◽  
Function Decomposition ◽  
The Antarctic ◽  
Assimilation Scheme

Abstract The structure of the analysis increments in a variational data assimilation scheme is strongly driven by the formulation of the background error covariance matrix, especially in data-sparse areas such as the Antarctic region. The gridpoint background error modeling in this study makes use of regression-based balance operators between variables, empirical orthogonal function decomposition to define the vertical correlations, gridpoint variances, and high-order efficient recursive filters to impose horizontal correlations. A particularity is that the regression operators and the recursive filters have been made spatially inhomogeneous. The computation of the background error statistics is performed with the Weather Research and Forecast (WRF) model from a set of forecast differences. The mesoscale limited-area domains of interest cover Antarctica. Inhomogeneities of background errors are shown to be related to the particular orography and physics of the area. Differences seem particularly pronounced between ocean and land boundary layers.

scholarly journals Daily oceanographic analyses by the Mediterranean basin scale assimilation system

2006 ◽  
Vol 3 (6) ◽  
pp. 1977-1998 ◽  
Author(s):  
S. Dobricic ◽  
N. Pinardi ◽  
M. Adani ◽  
M. Tonani ◽  
C. Fratianni ◽  
...  
Keyword(s):  
Positive Impact ◽  
Optimal Interpolation ◽  
Background Error ◽  
Geostrophic Balance ◽  
Error Covariance ◽  
Basin Scale ◽  
Forecasting System ◽  
The Mediterranean ◽  
First Time ◽  
Assimilation Scheme

Abstract. This study presents the upgrade of the Optimal Interpolation scheme used in the basin scale assimilation scheme of the Mediterranean Forecasting System. The modifications include a daily analysis cycle, the assimilation of ARGO float profiles, the implementation of the geostrophic balance in the background error covariance matrix and the initialisation of the analyses. A series of numerical experiments showed that each modification had a positive impact on the accuracy of the analyses: The daily cycle improved the representation of the processes with a relatively high temporal variability, the assimilation of ARGO floats profiles significantly improved the salinity analyses quality, the geostrophically balanced background error covariances improved the accuracy of the surface elevation analyses, and the initialisation removed the barotropic adjustment in the forecast first time steps starting from the analysis.

scholarly journals The Use of an Ensemble Approach to Study the Background Error Covariances in a Global NWP Model

2006 ◽  
Vol 134 (9) ◽  
pp. 2466-2489 ◽  
Author(s):  
Margarida Belo Pereira ◽  
Loïk Berre
Keyword(s):  
Positive Impact ◽  
Ensemble Method ◽  
Atmospheric Variability ◽  
Error Statistics ◽  
Background Error ◽  
Perfect Model ◽  
Data Density ◽  
The Ensemble Method ◽  
Nwp Model ◽  
Spatially Varying

Abstract The estimation of the background error statistics is a key issue for data assimilation. Their time average is estimated here using an analysis ensemble method. The experiments are performed with the nonstretched version of the Action de Recherche Petite Echelle Grande Echelle global model, in a perfect-model context. The global (spatially averaged) correlation functions are sharper in the ensemble method than in the so-called National Meteorological Center (NMC) method. This is shown to be closely related to the differences in the analysis step representation. The local (spatially varying) variances appear to reflect some effects of the data density and of the atmospheric variability. The resulting geographical contrasts are found to be partly different from those that are visible in the operational variances and in the NMC method. An economical estimate is also introduced to calculate and compare the local correlation length scales. This allows for the diagnosis of some existing heterogeneities and anisotropies. This information can also be useful for the modeling of heterogeneous covariances based, for example, on wavelets. The implementation of the global covariances and of the local variances, which are provided by the ensemble method, appears moreover to have a positive impact on the forecast quality.

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).

scholarly journals A Multiscale Variational Data Assimilation Scheme: Formulation and Illustration

2015 ◽  
Vol 143 (9) ◽  
pp. 3804-3822 ◽  
Author(s):  
Zhijin Li ◽  
James C. McWilliams ◽  
Kayo Ide ◽  
John D. Farrara
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Cost Function ◽  
Spatial Scales ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
The Cost ◽  
Fine Resolution

Abstract A multiscale data assimilation (MS-DA) scheme is formulated for fine-resolution models. A decomposition of the cost function is derived for a set of distinct spatial scales. The decomposed cost function allows for the background error covariance to be estimated separately for the distinct spatial scales, and multi-decorrelation scales to be explicitly incorporated in the background error covariance. MS-DA minimizes the partitioned cost functions sequentially from large to small scales. The multi-decorrelation length scale background error covariance enhances the spreading of sparse observations and prevents fine structures in high-resolution observations from being overly smoothed. The decomposition of the cost function also provides an avenue for mitigating the effects of scale aliasing and representativeness errors that inherently exist in a multiscale system, thus further improving the effectiveness of the assimilation of high-resolution observations. A set of one-dimensional experiments is performed to examine the properties of the MS-DA scheme. Emphasis is placed on the assimilation of patchy high-resolution observations representing radar and satellite measurements, alongside sparse observations representing those from conventional in situ platforms. The results illustrate how MS-DA improves the effectiveness of the assimilation of both these types of observations simultaneously.

scholarly journals Impact of ozone observations on the structure of a tropical cyclone using coupled atmosphere–chemistry data assimilation

2015 ◽  
Vol 15 (8) ◽  
pp. 11573-11597
Author(s):  
S. Lim ◽  
S. K. Park ◽  
M. Zupanski
Keyword(s):  
Air Quality ◽  
Data Assimilation ◽  
Cost Function ◽  
Positive Impact ◽  
Eastern China ◽  
Chemical Information ◽  
Chemistry Data ◽  
Air Quality Forecast ◽  
The Cost ◽  
The Impact

Abstract. Since the air quality forecast is related to both chemistry and meteorology, the coupled atmosphere–chemistry data assimilation (DA) system is essential to air quality forecasting. Ozone (O3) plays an important role in chemical reactions and is usually assimilated in chemical DA. In tropical cyclones (TCs), O3 usually shows a lower concentration inside the eyewall and an elevated concentration around the eye, impacting atmospheric as well as chemical variables. To identify the impact of O3 observations on TC structure, including atmospheric and chemical information, we employed the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem) with an ensemble-based DA algorithm – the maximum likelihood ensemble filter (MLEF). For a TC case that occurred over the East Asia, our results indicate that the ensemble forecast is reasonable, accompanied with larger background state uncertainty over the TC, and also over eastern China. Similarly, the assimilation of O3 observations impacts atmospheric and chemical variables near the TC and over eastern China. The strongest impact on air quality in the lower troposphere was over China, likely due to the pollution advection. In the vicinity of the TC, however, the strongest impact on chemical variables adjustment was at higher levels. The impact on atmospheric variables was similar in both over China and near the TC. The analysis results are validated using several measures that include the cost function, root-mean-squared error with respect to observations, and degrees of freedom for signal (DFS). All measures indicate a positive impact of DA on the analysis – the cost function and root mean square error have decreased by 16.9 and 8.87%, respectively. In particular, the DFS indicates a strong positive impact of observations in the TC area, with a weaker maximum over northeast China.

scholarly journals Daily oceanographic analyses by Mediterranean Forecasting System at the basin scale

Ocean Science ◽  
2007 ◽  
Vol 3 (1) ◽  
pp. 149-157 ◽  
Author(s):  
S. Dobricic ◽  
N. Pinardi ◽  
M. Adani ◽  
M. Tonani ◽  
C. Fratianni ◽  
...  
Keyword(s):  
Positive Impact ◽  
Optimal Interpolation ◽  
Daily Cycle ◽  
Background Error ◽  
Geostrophic Balance ◽  
Error Covariance ◽  
Basin Scale ◽  
Forecasting System ◽  
First Time ◽  
Assimilation Scheme

Abstract. This study presents the upgrade of the Optimal Interpolation scheme used in the basin scale assimilation scheme of the Mediterranean Forecasting System. The modifications include a daily analysis cycle, the assimilation of ARGO float profiles, the implementation of the geostrophic balance in the background error covariance matrix and the initialisation of the analyses. A series of numerical experiments showed that each modification had a positive impact on the accuracy of the analyses: The daily cycle improved the representation of the processes with the temporal variability shorter than a week, the assimilation of ARGO floats profiles significantly improved the salinity analyses quality, the geostrophically balanced background error covariances improved the accuracy of the surface elevation analyses, and the initialisation removed the barotropic adjustment in the forecast first time steps starting from the analysis.

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