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Xuguang Wang

Abstract

Gridpoint statistical interpolation (GSI), a three-dimensional variational data assimilation method (3DVAR) has been widely used in operations and research in numerical weather prediction. The operational GSI uses a static background error covariance, which does not reflect the flow-dependent error statistics. Incorporating ensemble covariance in GSI provides a natural way to estimate the background error covariance in a flow-dependent manner. Different from other 3DVAR-based hybrid data assimilation systems that are preconditioned on the square root of the background error covariance, commonly used GSI minimization is preconditioned upon the full background error covariance matrix. A mathematical derivation is therefore provided to demonstrate how to incorporate the flow-dependent ensemble covariance in the GSI variational minimization.

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Xuguang Wang

Abstract

A hybrid ensemble transform Kalman filter (ETKF)–three-dimensional variational data assimilation (3DVAR) system developed for the Weather Research and Forecasting Model (WRF) was studied for the forecasts of the tracks of two major hurricanes, Ike and Gustav, in 2008 over the Gulf of Mexico. The impacts of the flow-dependent ensemble covariance generated by the ETKF were revealed by comparing the forecasts, analyses, and analysis increments generated by the hybrid data assimilation method with those generated by the 3DVAR that used the static background covariance. The root-mean-square errors of the track forecasts by the hybrid data assimilation (DA) method were smaller than those by the 3DVAR for both Ike and Gustav. Experiments showed that such improvements were due to the use of the flow-dependent covariance provided by the ETKF ensemble in the hybrid DA system. Detailed diagnostics further revealed that the increments produced by the hybrid and the 3DVAR were different for both the analyses of the hurricane itself and its environment. In particular, it was found that the hybrid, using the flow-dependent covariance that gave the hurricane-specific error covariance estimates, was able to systematically adjust the position of the hurricane during the assimilation whereas the 3DVAR was not. The study served as a pilot study to explore and understand the potential of the hybrid method for hurricane data assimilation and forecasts. Caution needs to be taken to extrapolate the results to operational forecast settings.

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Yongming Wang
and
Xuguang Wang

Abstract

A convective-scale static background-error covariance (BEC) matrix is further developed to include the capability of direct reflectivity assimilation and evaluated within the GSI-based three-dimensional variational (3DVar) and hybrid ensemble–variational (EnVar) methods. Specific developments are summarized as follows: 1) Control variables (CVs) are extended to include reflectivity, vertical velocity, and all hydrometeor types. Various horizontal momentum and moisture CV options are included. 2) Cross correlations between all CVs are established. 3) A storm intensity-dependent binning method is adopted to separately calculate static error matrices for clear-air and storms with varying intensities. The resultant static BEC matrices are simultaneously applied at proper locations guided by the observed reflectivity. 4) The EnVar is extended to adaptively incorporate static BECs based on the quality of ensemble covariances. Evaluation and examination of the new static BECs are first performed on the 8 May 2003 Oklahoma City supercell. Detailed diagnostics and 3DVar examinations suggest zonal/meridional winds and pseudo–relative humidity are selected as horizontal momentum and moisture CVs for direct reflectivity assimilation, respectively; inclusion of cross correlations favors spin up and maintains the analyzed storms; application of binning improves characteristics and persistence of the simulated storm. Relative to an experiment using the full ensemble BECs (Exp-PureEnVar), incorporating static BECs in hybrid EnVar reduces spinup time and better analyzes reflectivity distributions while the background ensemble is deficient in sampling errors. Compared to both pure 3DVar and Exp-PureEnVar, hybrid EnVar better predicts reflectivity distributions and better maintains a strong mesocyclone. Further examination through the 20 May 2013 Oklahoma supercells confirms these results and additionally demonstrates the effectiveness of adaptive hybridization.

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Yongming Wang
and
Xuguang Wang

Abstract

A GSI-based EnVar data assimilation system is extended to directly assimilate radar reflectivity to initialize convective-scale forecasts. When hydrometeor mixing ratios are used as state variables (method mixing ratio), large differences of the cost function gradients with respect to the small hydrometeor mixing ratios and wind prevent efficient convergence. Using logarithmic mixing ratios as state variables (method logarithm) fixes this problem, but generates spuriously large hydrometeor increments partly due to the transform to and from the logarithmic space. The tangent linear of the reflectivity operators further contributes to spuriously small and large hydrometeor increments in method mixing ratio and method logarithm, respectively. A new method is proposed by directly adding the reflectivity as a state variable (method dBZ). Without the tangent linear and adjoint of the nonlinear operator, the new method therefore avoids the aforementioned problems.

The newly proposed method is examined on the analysis and prediction of the 8 May 2003 Oklahoma City tornadic supercell storm. Both the probabilistic forecast of strong low-level vorticity and maintenance of strong updraft and vorticity in method dBZ are more consistent with reality than in method logarithm and method mixing ratio. Detailed diagnostics suggest that a more realistic cold pool due to the better analyzed hydrometeors in method dBZ than in other methods leads to constructive interaction between the surface gust front and the updraft aloft associated with the midlevel mesocyclone. Similar low-level vorticity forecast and maintenance of the storm are produced by the WSM6 and Thompson microphysics schemes in method dBZ. The Thompson scheme matches the reflectivity distribution with the observations better for all lead times, but shows more southeastward track bias compared to the WSM6 scheme.

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Yongming Wang
and
Xuguang Wang

Abstract

Explicit forecasts of a tornado-like vortex (TLV) require subkilometer grid spacing because of their small size. Most previous TLV prediction studies started from interpolated kilometer grid spacing initial conditions (ICs) rather than subkilometer grid spacing ICs. The tornadoes embedded in the 8 May 2003 Oklahoma City tornadic supercell are used to understand the impact of IC resolution on TLV predictions. Two ICs at 500-m and 2-km grid spacings are, respectively, produced through an efficient dual-resolution (DR) and a single-coarse-resolution (SCR) EnVar ingesting a 2-km ensemble. Both experiments launch 1-h forecasts at 500-m grid spacing. Diagnostics of data assimilation (DA) cycling reveal DR produces stronger and broader rear-flank cold pools, more intense downdrafts and updrafts with finer scales, and more hydrometeors at high altitudes through accumulated differences between two DA algorithms. Relative differences in DR, compared to SCR, include the integration from higher-resolution analyses, the update for higher-resolution backgrounds, and the propagation of ensemble perturbations along higher-resolution model trajectory. Predictions for storm morphology and cold pools are more realistic in DR than in SCR. The DR-TLV tracks match better with the observed tornado tracks than SCR-TLV in timing of intensity variation, and in duration. Additional experiments suggest 1) the analyzed kinematic variables strongly influence timing of intensity variation through affecting both low-level rear-flank outflow and midlevel updraft; 2) potential temperature analysis by DR extends the second track’s duration consistent with enhanced low-level stretching, delayed broadening large-scale downdraft, and (or) increased near-surface baroclinic vorticity supply; and 3) hydrometeor analyses have little impact on TLV predictions.

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Yue Yang
and
Xuguang Wang

Abstract

The sensitivity of convection-allowing forecasts over the continental United States to radar reflectivity data assimilation (DA) frequency is explored within the Gridpoint Statistical Interpolation (GSI)-based ensemble–variational (EnVar) system. Experiments with reflectivity DA intervals of 60, 20, and 5 min (RAIN60, RAIN20, and RAIN5, respectively) are conducted using 10 diverse cases. Quantitative verification indicates that the degree of sensitivity depends on storm features during the radar DA period. Five developing storms show high sensitivity, whereas five mature or decaying storms do not. The 20-min interval is the most reliable given its best overall performance compared to the 5- and 60-min intervals. Diagnostics suggest that the differences in analyzed cold pools (ACPs) among RAIN60, RAIN20, and RAIN5 vary by storm features during the radar DA period. Such ACP differences result in different forecast skills. In the case where RAIN20 outperforms RAIN60 and the case where RAIN5 outperforms RAIN20, assimilation of reflectivity with a higher frequency commonly produces enhanced and widespread ACPs, promoting broader storms that match better with reality than a lower frequency. In the case where RAIN5 performs worse than RAIN20, the model imbalance of RAIN5 overwhelms information gain associated with frequent assimilation, producing overestimated and spuriously fast-moving ACPs. In the cases where little sensitivity to the reflectivity DA frequency is found, similar ACPs are produced.

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Xuguang Wang
and
Ting Lei

Abstract

A four-dimensional (4D) ensemble–variational data assimilation (DA) system (4DEnsVar) was developed, building upon the infrastructure of the gridpoint statistical interpolation (GSI)-based hybrid DA system. 4DEnsVar used ensemble perturbations valid at multiple time periods throughout the DA window to estimate 4D error covariances during the variational minimization, avoiding the tangent linear and adjoint of the forecast model. The formulation of its implementation in GSI was described. The performance of the system was investigated by evaluating the global forecasts and hurricane track forecasts produced by the NCEP Global Forecast System (GFS) during the 5-week summer period assimilating operational conventional and satellite data. The newly developed system was used to address a few questions regarding 4DEnsVar. 4DEnsVar in general improved upon its 3D counterpart, 3DEnsVar. At short lead times, the improvement over the Northern Hemisphere extratropics was similar to that over the Southern Hemisphere extratropics. At longer lead times, 4DEnsVar showed more improvement in the Southern Hemisphere than in the Northern Hemisphere. The 4DEnsVar showed less impact over the tropics. The track forecasts of 16 tropical cyclones initialized by 4DEnsVar were more accurate than 3DEnsVar after 1-day forecast lead times. The analysis generated by 4DEnsVar was more balanced than 3DEnsVar. Case studies showed that increments from 4DEnsVar using more frequent ensemble perturbations approximated the increments from direct, nonlinear model propagation better than using less frequent ensemble perturbations. Consistently, the performance of 4DEnsVar including both the forecast accuracy and the balances of analyses was in general degraded when less frequent ensemble perturbations were used. The tangent linear normal mode constraint had positive impact for global forecast but negative impact for TC track forecasts.

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Aaron Johnson
and
Xuguang Wang

Abstract

Neighborhood and object-based probabilistic precipitation forecasts from a convection-allowing ensemble are verified and calibrated. Calibration methods include logistic regression, one- and two-parameter reliability-based calibration, and cumulative distribution function (CDF)-based bias adjustment. Newly proposed object-based probabilistic forecasts for the occurrence of a forecast object are derived from the percentage of ensemble members with a matching object. Verification and calibration of single- and multimodel subensembles are performed to explore the effect of using multiple models.

The uncalibrated neighborhood-based probabilistic forecasts have skill minima during the afternoon convective maximum. Calibration generally improves the skill, especially during the skill minima, resulting in positive skill. In general all calibration methods perform similarly, with a slight advantage of logistic regression (one-parameter reliability based) calibration for 1-h (6 h) accumulations.

The uncalibrated object-based probabilistic forecasts are, in general, less skillful than the uncalibrated neighborhood-based probabilistic forecasts. Object-based calibration also results in positive skill at all lead times. For object-based calibration the skill is significantly different among the calibration methods, with the logistic regression performing the best and CDF-based bias adjustment performing the worst.

For both the neighborhood and object-based probabilistic forecasts, the impact of using 10 or 25 days of training data for calibration is generally small and is most significant for the two-parameter reliability-based method. An uncalibrated Advanced Research Weather Research and Forecasting Model (ARW-WRF) subensemble is significantly more skillful than an uncalibrated WRF Nonhydrostatic Mesoscale Model (NMM) subensemble. The difference is reduced by calibration. The multimodel subensemble only shows an advantage for the neighborhood-based forecasts beyond 1-day lead time and shows no advantage for the object-based forecasts.

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Aaron Johnson
and
Xuguang Wang

Abstract

Object-based verification of deterministic forecasts from a convection-allowing ensemble for the 2009 NOAA Hazardous Weather Testbed Spring Experiment is conducted. The average of object attributes is compared between forecasts and observations and between forecasts from subensembles with different model dynamics. Forecast accuracy for the full ensemble and the subensembles with different model dynamics is also evaluated using two object-based measures: the object-based threat score (OTS) and the median of maximum interest (MMI).

Forecast objects aggregated from the full ensemble are generally more numerous, have a smaller average area, more circular average aspect ratio, and more eastward average centroid location than observed objects after the 1-h lead time. At the 1-h lead time, forecast objects are less numerous than observed objects. Members using the Advanced Research Weather Research and Forecasting Model (ARW) have fewer objects, more linear average aspect ratio, and smaller average area than members using the Nonhydrostatic Mesoscale Model (NMM). The OTS aggregated from the full ensemble is more consistent with the diurnal cycles of the traditional equitable threat score (ETS) than the MMI because the OTS places more weight on large objects, while the MMI weights all objects equally. The group of ARW members has higher OTS than the group of NMM members except at the 1-h lead time when the group of NMM members has more accurate maintenance and evolution of initially present precipitation systems provided by radar data assimilation. The differences between the ARW and NMM accuracy are more pronounced with the OTS than the MMI and the ETS.

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Bo Huang
and
Xuguang Wang

Abstract

Valid-time-shifting (VTS) ensembles, either in the form of full ensemble members (VTSM) or ensemble perturbations (VTSP), were investigated as inexpensive means to increase ensemble size in the NCEP Global Forecast System (GFS) hybrid four-dimensional ensemble–variational (4DEnVar) data assimilation system. VTSM is designed to sample timing and/or phase errors, while VTSP can eliminate spurious covariances through temporal smoothing. When applying a shifting time interval (τ = 1, 2, or 3 h), VTSM and VTSP triple the baseline background ensemble size from 80 (ENS80) to 240 (ENS240) in the EnVar variational update, where the overall cost is only increased by 23%–27%, depending on the selected τ. Experiments during a 10-week summer period show the best-performing VTSP with τ = 2 h improves global temperature and wind forecasts out to 5 days over ENS80. This could be attributed to the improved background ensemble distribution, ensemble correlation accuracy, and increased effective rank in the populated background ensemble. VTSM generally degrades global forecasts in the troposphere. Improved global forecasts above 100 hPa by VTSM may benefit from the increased spread that alleviates the underdispersiveness of the original background ensemble at such levels. Both VTSM and VTSP improve tropical cyclone track forecasts over ENS80. Although VTSM and VTSP are much less expensive than directly running a 240-member background ensemble, owing to the improved ensemble covariances, the best-performing VTSP with τ = 1 h performs comparably or only slightly worse than ENS240. The best-performing VTSM with τ = 3 h even shows more accurate track forecasts than ENS240, likely contributed to by its better sampling of timing and/or phase errors for cases with small ensemble track spread.

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