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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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Nicholas A. Gasperoni
and
Xuguang Wang

Abstract

The goal of this study is to improve an ensemble-based estimation for forecast sensitivity to observations that is straightforward to apply using existing products of any ensemble data assimilation system. Because of limited ensemble sizes compared to the large degrees of freedom in typical models, it is necessary to apply localization techniques to obtain accurate estimates. Fixed localization techniques do not guarantee accurate impact estimates, because as forecast time increases the error correlation structures evolve with the flow. Here a dynamical localization method is applied to improve the observation impact estimate. The authors employ a Monte Carlo “group filter” technique to limit the effects of sampling error via regression confidence factor (RCF). Experiments make use of the local ensemble transform Kalman filter (LETKF) with a simple two-layer primitive equation model and simulated observations. Results show that the shape, location, time dependency, and variable dependency of RCF localization functions are consistent with underlying dynamical processes of the model. Application of RCF localization to ensemble-estimated impact showed marked improvement especially for longer forecasts and at midlatitudes, when systematically verified against actual impact in RMSE and skill scores. The impact estimates near the equator were not as effective because of large discrepancies between the RCF function and the localization used at assimilation time. These latter results indicate that there exists an inherent relationship between the localization applied during the assimilation time and the proper localization choice for observation impact estimates. Application of RCF for automatically tuned localization is introduced and tested for a single observation experiment.

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Christopher A. Kerr
and
Xuguang Wang

Abstract

The potential future installation of a multifunction phased-array radar (MPAR) network will provide capabilities of case-specific adaptive scanning. Knowing the impacts adaptive scanning may have on short-term forecasts will influence scanning strategy decision-making in hopes to produce the most optimal ensemble forecast while also benefiting human severe weather warning decision-making. An ensemble-based targeted observation algorithm is applied to an observing system simulation experiment (OSSE) where the impacts of synthetic idealized supercell radial velocity observations are estimated before the observations are “collected” and assimilated. The forecast metric of interest is the low-level rotation forecast metric (0–1-km updraft helicity), a surrogate for tornado prediction. It is found that the ensemble-based targeted observation approach can reasonably estimate the true error variance reduction when an effective method that treats sampling error is applied, the period of model forecast is associated with less degrees of nonlinearity, and the observation information content relative to the background forecast is larger. In some scenarios, a subset of a full-volume scan assimilation produces better forecasts than all observations within the full volume. Assimilating the full-volume scan increases the number of potential spurious correlations arising between the forecast metric and radial velocity observation induced state perturbations, which may degrade the forecast metric accuracy.

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Xuguang Wang
and
Craig H. Bishop

Abstract

The ensemble transform Kalman filter (ETKF) ensemble forecast scheme is introduced and compared with both a simple and a masked breeding scheme. Instead of directly multiplying each forecast perturbation with a constant or regional rescaling factor as in the simple form of breeding and the masked breeding schemes, the ETKF transforms forecast perturbations into analysis perturbations by multiplying by a transformation matrix. This matrix is chosen to ensure that the ensemble-based analysis error covariance matrix would be equal to the true analysis error covariance if the covariance matrix of the raw forecast perturbations were equal to the true forecast error covariance matrix and the data assimilation scheme were optimal. For small ensembles (∼100), the computational expense of the ETKF ensemble generation is only slightly greater than that of the masked breeding scheme.

Version 3 of the Community Climate Model (CCM3) developed at National Center for Atmospheric Research (NCAR) is used to test and compare these ensemble generation schemes. The NCEP–NCAR reanalysis data for the boreal summer in 2000 are used for the initialization of the control forecast and the verifications of the ensemble forecasts. The ETKF and masked breeding ensemble variances at the analysis time show reasonable correspondences between variance and observational density. Examination of eigenvalue spectra of ensemble covariance matrices demonstrates that while the ETKF maintains comparable amounts of variance in all orthogonal and uncorrelated directions spanning its ensemble perturbation subspace, both breeding techniques maintain variance in few directions. The growth of the linear combination of ensemble perturbations that maximizes energy growth is computed for each of the ensemble subspaces. The ETKF maximal amplification is found to significantly exceed that of the breeding techniques. The ETKF ensemble mean has lower root-mean-square errors than the mean of the breeding ensemble. New methods to measure the precision of the ensemble-estimated forecast error variance are presented. All of the methods indicate that the ETKF estimates of forecast error variance are considerably more accurate than those of the breeding techniques.

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Samuel K. Degelia
and
Xuguang Wang

Abstract

The observation error covariance partially controls the weight assigned to an observation during data assimilation (DA). True observation error statistics are rarely known and likely vary depending on the meteorological state. However, operational DA systems often apply static methods that assign constant observation errors across a dataset. Previous studies show that these methods can degrade forecast quality when assimilating ground-based remote sensing datasets. To improve the impact of assimilating such observations, we propose two novel methods for estimating the observation error variance for high-frequency thermodynamic profilers. These methods include an adaptive observation error inflation technique and the Desroziers method that directly estimates the observation error variances using paired innovation and analysis residuals. Each method is compared for a nocturnal mesoscale convective system (MCS) observed during the Plains Elevated Convection at Night (PECAN) Experiment. In general, we find that these novel methods better represent the large variability of observation error statistics for high-frequency profiles collected by Atmospheric Emitted Radiance Interferometers (AERIs). When assimilating AERIs by statically inflating retrieval error variances, the trailing stratiform region of the MCS is degraded compared to a baseline simulation with no AERI data assimilated. Assimilating the AERIs using the adaptive inflation or Desroziers method results in better maintenance of the trailing stratiform region and additional suppression of spurious convection. The forecast improvements from these novel methods are primarily linked to increased error variances for some moisture retrievals. These results indicate the importance of accurately estimating observation error statistics for convective-scale DA and suggest that accounting for flow-dependence can improve the impacts from assimilating remote sensing datasets.

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Erin A. Jones
and
Xuguang Wang

Abstract

The current global operational four-dimensional ensemble-variational (4DEnVar) data assimilation (DA) system at NCEP adopts a background ensemble at a reduced resolution, which restricts the range of spatial scales that the ensemble background error covariance can resolve. A prior study developed a multi-resolution ensemble 4DEnVar method and determined that this approach can provide a comparable forecast to an approach using solely high-resolution members, while substantially reducing the computational cost. This study further develops the multi-resolution ensemble 4DEnVar approach to allow for a flexible number of low- and high-resolution ensemble members as well as varying localization length scales between the high- and low-resolution ensembles.

Three 4DEnVar experiments with the same computational costs are compared. The first has an 80-member high-resolution background ensemble with single-scale optimally-tuned localization (SR-High). The second and third utilize the multi-resolution background ensembles. One has 130 low-resolution and 40 high-resolution members (MR170) while the other has 180 low-resolution and 24 high-resolution members (MR204). Both multi-resolution ensemble experiments utilize differing localization radii with ensemble resolution. Despite having the same costs, both MR170 and MR204 improves global forecasts and decreases tropical cyclone track errors for up to five days in lead time compared to SR-High. Improvements are most apparent in larger-scale features, such as jet streams and the environmental steering flow of tropical cyclones. Additionally, MR170 outperforms MR204 in terms of global and tropical cyclone track forecasts, demonstrating the value of both increasing sampling at large scales and retaining substantial information at small scales.

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Nicholas A. Gasperoni
,
Xuguang Wang
, and
Yongming Wang

Abstract

A valid time shifting (VTS) method is explored for the GSI-based ensemble variational (EnVar) system modified to directly assimilate radar reflectivity at convective scales. VTS is a cost-efficient method to increase ensemble size by including subensembles before and after the central analysis time. Additionally, VTS addresses common time and phase model error uncertainties within the ensemble. VTS is examined here for assimilating radar reflectivity in a continuous hourly analysis system for a case study of 1–2 May 2019. The VTS implementation is compared against a 36-member control experiment (ENS-36), to increase ensemble size (3 × 36 VTS), and as a cost-savings method (3 × 12 VTS), with time-shifting intervals τ between 15 and 120 min. The 3 × 36 VTS experiments increased the ensemble spread, with largest subjective benefits in early cycle analyses during convective development. The 3 × 12 VTS experiments captured analysis with similar accuracy as ENS-36 by the third hourly analysis. Control forecasts launched from hourly EnVar analyses show significant skill increases in 1-h precipitation over ENS-36 out to hour 12 for 3 × 36 VTS experiments, subjectively attributable to more accurate placement of the convective line. For 3 × 12 VTS, experiments with τ ≥ 60 min met and exceeded the skill of ENS-36 out to forecast hour 15, with VTS-3 × 12τ90 maximizing skill. Sensitivity results demonstrate preference to τ = 30–60 min for 3 × 36 VTS and 60–120 min for 3 × 12 VTS. The best 3 × 36 VTS experiments add a computational cost of 45%–67%, compared to the near tripling of costs when directly increasing ensemble size, while best 3 × 12 VTS experiments save about 24%–41% costs over ENS-36.

Significance Statement

The purpose of this work is to study a valid time shifting method to improve the prediction of severe convective storm systems over the continental United States. This method improves ensemble-based radar reflectivity analyses by including ensemble member information at times before and after the analysis time, thereby increasing the ensemble size at just a fractional added computational cost. The results show the method can boost the accuracy of high-resolution convection prediction out to at least 12 h. This case study motivates future systematic testing in a real-time setting and potential implementation to enhance the U.S. operational ensemble-based convection-allowing forecast model and data assimilation system.

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Nicholas A. Gasperoni
,
Xuguang Wang
, and
Yongming Wang

Abstract

A gridpoint statistical interpolation (GSI)-based hybrid ensemble–variational (EnVar) scheme was extended for convective scales—including radar reflectivity assimilation—and implemented in real-time spring forecasting experiments. This study compares methods to address model error during the forecast under the context of multiscale initial condition error sampling provided by the EnVar system. A total of 10 retrospective cases were used to explore the optimal design of convection-allowing ensemble forecasts. In addition to single-model single-physics (SMSP) configurations, ensemble forecast experiments compared multimodel (MM) and multiphysics (MP) approaches. Stochastic physics was also applied to MP for further comparison. Neighborhood-based verification of precipitation and composite reflectivity showed each of these model error techniques to be superior to SMSP configurations. Comparisons of MM and MP approaches had mixed findings. The MM approach had better overall skill in heavy-precipitation forecasts; however, MP ensembles had better skill for light (2.54 mm) precipitation and reduced ensemble mean error of other diagnostic fields, particularly near the surface. The MM experiment had the largest spread in precipitation, and for most hours in other fields; however, rank histograms and spaghetti contours showed significant clustering of the ensemble distribution. MP plus stochastic physics was able to significantly increase spread with time to be competitive with MM by the end of the forecast. The results generally suggest that an MM approach is best for early forecast lead times up to 6–12 h, while a combination of MP and stochastic physics approaches is preferred for forecasts beyond 6–12 h.

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Jie Feng
,
Xuguang Wang
, and
Jonathan Poterjoy

Abstract

The local particle filter (LPF) and the local nonlinear ensemble transform filter (LNETF) are two moment-matching nonlinear filters to approximate the classical particle filter (PF). They adopt different strategies to alleviate filter degeneracy. LPF and LNETF localize observational impact but use different localization functions. They assimilate observations in a partially sequential and a simultaneous manner, respectively. In addition, LPF applies the resampling step, whereas LNETF applies the deterministic square root transformation to update particles. Both methods preserve the posterior mean and variance of the PF. LNETF additionally preserves the posterior correlation of the PF for state variables within a local volume. These differences lead to their differing performance in filter stability and posterior moment estimation. LPF and LNETF are systematically compared and analyzed here through a set of experiments with a Lorenz model. Strategies to improve the LNETF are proposed. The original LNETF is inferior to the original LPF in filter stability and analysis accuracy, particularly for small particle numbers. This is attributed to both the localization function and particle update differences. The LNETF localization function imposes a stronger observation impact than the LPF for remote grids and thus is more susceptible to filter degeneracy. The LNETF update causes an overall narrower range of posteriors that excludes true states more frequently. After applying the same localization function as the LPF and additional posterior inflation to the LNETF, the two filters reach similar filter stability and analysis accuracy for all particle numbers. The improved LNETF shows more accurate posterior probability distribution but slightly worse spatial correlation of posteriors than the LPF.

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Tyler Green
,
Xuguang Wang
, and
Xu Lu

Abstract

In this study, hourly data assimilation (DA) cycling is performed during a 24-h time period for Hurricane Matthew (2016), assimilating ground-based (GBR) and tail-Doppler radar (TDR) observations together, as well as separately using HWRF and its Hybrid 3DEnVar DA system. The objective is to examine the impacts of assimilating such data on the analysis and prediction of the weakening and re-intensification stages of the eyewall replacement cycle (ERC) of Matthew. Experiments assimilating GBR observations make quicker corrections to the initially inconsistent storm structure than does the TDR experiment, resulting in the primary and secondary eyewalls being realistically represented during the DA cycling period. The TDR experiment analyses show less-realistic concentric eyewall structure before, during, and after TDR observations become available. The forecasts from experiments assimilating GBR observations show more-realistic structural and point intensity changes for the ERC consistently throughout the cycling period when compared with the experiments assimilating TDR observations. Combined assimilation of GBR and TDR observations show similar ERC forecasts, on average, to the GBR experiment. The superior performance of the GBR experiments is shown to be tied to its earlier and longer availability despite its limited low-level coverage especially at the early stage of the cycling. The inferior performance of the TDR experiments even during the availability of TDR is hypothesized to be a result of rapidly changing 3D observational coverage during the high-frequency cycling. Brief mechanism diagnostics additionally suggest the need of properly initializing the TC concentric eyewalls to capture the ERC during the forecasts.

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