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Xuguang Wang
,
Chris Snyder
, and
Thomas M. Hamill

Abstract

Hybrid ensemble–three-dimensional variational analysis schemes incorporate flow-dependent, ensemble-estimated background-error covariances into the three-dimensional variational data assimilation (3DVAR) framework. Typically the 3DVAR background-error covariance estimate is assumed to be stationary, nearly homogeneous, and isotropic. A hybrid scheme can be achieved by 1) directly replacing the background-error covariance term in the cost function by a linear combination of the original background-error covariance with the ensemble covariance or 2) through augmenting the state vector with another set of control variables preconditioned upon the square root of the ensemble covariance. These differently proposed hybrid schemes are proven to be equivalent. The latter framework may be a simpler way to incorporate ensemble information into operational 3DVAR schemes, where the preconditioning is performed with respect to the background term.

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Aaron Johnson
,
Xuguang Wang
, and
Samuel Degelia

Abstract

Multiscale ensemble-based data assimilation and forecasts were performed in real time during the Plains Elevated Convection At Night (PECAN) field experiment. A 20-member ensemble of forecasts at 4-km grid spacing was initialized daily at both 1300 and 1900 UTC, together with a deterministic forecast at 1-km grid spacing initialized at 1300 UTC. The configuration of the GSI-based data assimilation and forecast system was guided by results presented in Part I of this two-part study. The present paper describes the implementation of the real-time system and the extensive forecast products that were generated to support the unique interests of PECAN researchers. Subjective and objective verification of the real-time forecasts from 1 June through 15 July 2015 is conducted, with an emphasis on nocturnal mesoscale convective systems (MCSs), nocturnal convective initiation (CI), nocturnal low-level jets (LLJs), and bores on the nocturnal stable layer. Verification of nocturnal precipitation during overnight hours, a proxy for MCSs, shows both greater skill and spread for the 1300 UTC forecasts than the 1900 UTC forecasts. Verification against observed soundings reveals that the forecast LLJs systematically peak, veer, and dissipate several hours before the observations. Comparisons with bores that passed over an Atmospheric Emitted Radiance Interferometer reveal an ability to predict borelike features that is greatly improved at 1-km, compared with 4-km, grid spacing. Objective verification of forecast CI timing reveals strong sensitivity to the PBL scheme but an overall unbiased ensemble.

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Craig H. Bishop
,
Bo Huang
, and
Xuguang Wang

Abstract

A consistent hybrid ensemble filter (CHEF) for using hybrid forecast error covariance matrices that linearly combine aspects of both climatological and flow-dependent matrices within a nonvariational ensemble data assimilation scheme is described. The CHEF accommodates the ensemble data assimilation enhancements of (i) model space ensemble covariance localization for satellite data assimilation and (ii) Hodyss’s method for improving accuracy using ensemble skewness. Like the local ensemble transform Kalman filter (LETKF), the CHEF is computationally scalable because it updates local patches of the atmosphere independently of others. Like the sequential ensemble Kalman filter (EnKF), it serially assimilates batches of observations and uses perturbed observations to create ensembles of analyses. It differs from the deterministic (no perturbed observations) ensemble square root filter (ESRF) and the EnKF in that (i) its analysis correction is unaffected by the order in which observations are assimilated even when localization is required, (ii) it uses accurate high-rank solutions for the posterior error covariance matrix to serially assimilate observations, and (iii) it accommodates high-rank hybrid error covariance models. Experiments were performed to assess the effect on CHEF and ESRF analysis accuracy of these differences. In the case where both the CHEF and the ESRF used tuned localized ensemble covariances for the forecast error covariance model, the CHEF’s advantage over the ESRF increased with observational density. In the case where the CHEF used a hybrid error covariance model but the ESRF did not, the CHEF had a substantial advantage for all observational densities.

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Jeffrey D. Duda
,
Xuguang Wang
, and
Ming Xue

Abstract

In this exploratory study, a series of perturbations to the land surface model (LSM) component of the Weather Research and Forecasting (WRF) Model was developed to investigate the sensitivity of forecasts of severe thunderstorms and heavy precipitation at 4-km grid spacing and whether such perturbations could improve ensemble forecasts at this scale. The perturbations (generated using a combination of perturbing fixed parameters and using separate schemes, one of which—Noah-MP—is new among the WRF modeling community) were applied to a 10-member ensemble including other mixed physics parameterizations and compared against an identically configured ensemble that did not include the LSM perturbations to determine their impact on probabilistic forecasts. A third ensemble using only the LSM perturbations was also configured.

The results from 14 (in total) 36-h ensemble forecasts suggested the LSM perturbations resulted in systematic improvement in ensemble dispersion and error characteristics. Lower-tropospheric temperature, moisture, and wind fields were all improved, as were probabilistic precipitation forecasts. Biases were not systematically altered, although some outlier members are present. Examination of near-surface temperature and mixing ratio fields, surface energy fluxes, and soil fields revealed tendencies caused by certain perturbations. A case study featuring tornadic supercells illustrated the physical causes of some of these tendencies. The results of this study suggest LSM perturbations can sample a dimension of model error not yet sampled systematically in most ensembles and should be included in convection-allowing ensembles.

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Yongzuo Li
,
Xuguang Wang
, and
Ming Xue

Abstract

An enhanced version of the hybrid ensemble–three-dimensional variational data assimilation (3DVAR) system for the Weather Research and Forecasting Model (WRF) is applied to the assimilation of radial velocity (Vr) data from two coastal Weather Surveillance Radar-1988 Doppler (WSR-88D) radars for the prediction of Hurricane Ike (2008) before and during its landfall. In this hybrid system, flow-dependent ensemble covariance is incorporated into the variational cost function using the extended control variable method. The analysis ensemble is generated by updating each forecast ensemble member with perturbed radar observations using the hybrid scheme itself. The Vr data are assimilated every 30 min for 3 h immediately after Ike entered the coverage of the two coastal radars.

The hybrid method produces positive temperature increments indicating a warming of the inner core throughout the depth of the hurricane. In contrast, the 3DVAR produces much weaker and smoother increments with negative values at the vortex center at lower levels. Wind forecasts from the hybrid analyses fit the observed radial velocity better than that from 3DVAR, and the 3-h accumulated precipitation forecasts from the hybrid are also more skillful. The track forecast is slightly improved by the hybrid method and slightly degraded by the 3DVAR compared to the forecast from the Global Forecast System (GFS) analysis. All experiments assimilating the radar data show much improved intensity analyses and forecasts compared to the experiment without assimilating radar data. The better forecast of the hybrid indicates that the hybrid method produces dynamically more consistent state estimations. Little benefit of including the tuned static component of background error covariance in the hybrid is found.

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Bo Huang
,
Xuguang Wang
, and
Craig H. Bishop

Abstract

The ensemble Kalman filter is typically implemented either by applying the localization on the background error covariance matrix (B-localization) or by inflating the observation error variances (R-localization). A mathematical demonstration suggests that for the same effective localization function, the background error covariance matrix from the B-localization method shows a higher rank than the R-localization method. The B-localization method is realized in the ensemble transform Kalman filter (ETKF) by extending the background ensemble perturbations through modulation (MP-localization). Specifically, the modulation functions are constructed from the leading eigenvalues and eigenvectors of the original B-localization matrix. Because of its higher rank than the classic R-localized ETKF, the B-/MP-localized ETKF is termed as the high-rank ETKF (HETKF). The performances of the HETKF and R-localized ETKF were compared through cycled data assimilation experiments using the Lorenz model II. The results show that the HETKF outperforms the R-localized ETKF especially for a small ensemble. The improved analysis in the HETKF is likely associated with the higher rank from the B-/MP-localization method, since its higher rank is expected to contribute more positively to alleviating the rank deficiency issue and thus improve the analysis for a small ensemble. The HETKF is less sensitive to the localization length scales and inflation factors. Furthermore, the experiments suggest that the above conclusion comparing the HETKF and R-localized ETKF does not depend on how the analyzed ensemble perturbations are subselected in the HETKF.

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Jeffrey D. Duda
,
Xuguang Wang
,
Yongming Wang
, and
Jacob R. Carley

Abstract

Two methods for assimilating radar reflectivity into deterministic convection-allowing forecasts were compared: an operationally used, computationally less expensive cloud analysis (CA) scheme and a relatively more expensive, but rigorous, ensemble Kalman filter–variational hybrid method (EnVar). These methods were implemented in the Nonhydrostatic Multiscale Model on the B-grid and were tested on 10 cases featuring high-impact deep convective storms and heavy precipitation. A variety of traditional, neighborhood-based, and features-based verification metrics support that the EnVar produced superior free forecasts compared to the CA procedure, with statistically significant differences extending up to 9 h into the forecast. Despite being inferior, the CA scheme was able to provide benefit compared to not assimilating radar reflectivity at all, but limited to the first few forecast hours. While the EnVar is able to partially suppress spurious convection by assimilating 0-dBZ reflectivity observations directly, the CA is not designed to reduce or remove hydrometeors. As a result, the CA struggles more with suppression of spurious convection in the first-guess field, which resulted in high-frequency biases and poor forecast evolution, as illustrated in a few case studies. Additionally, while the EnVar uses flow-dependent ensemble covariances to update hydrometers, thermodynamic, and dynamic variables simultaneously when the reflectivity is assimilated, the CA relies on a radar reflectivity-derived latent heating rate that is applied during a separate digital filter initialization (DFI) procedure to introduce deep convective storms into the model, and the results of CA are shown to be sensitive to the window length used in the DFI.

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Xuguang Wang
,
Craig H. Bishop
, and
Simon J. Julier

Abstract

New methods to center the initial ensemble perturbations on the analysis are introduced and compared with the commonly used centering method of positive–negative paired perturbations. In the new method, one linearly dependent perturbation is added to a set of linearly independent initial perturbations to ensure that the sum of the new initial perturbations equals zero; the covariance calculated from the new initial perturbations is equal to the analysis error covariance estimated by the independent initial perturbations, and all of the new initial perturbations are equally likely. The new method is illustrated by applying it to the ensemble transform Kalman filter (ETKF) ensemble forecast scheme, and the resulting ensemble is called the spherical simplex ETKF ensemble. It is shown from a multidimensional Taylor expansion that the symmetric positive–negative paired centering would yield a more accurate forecast ensemble mean and covariance than the spherical simplex centering if the ensemble were large enough to span all initial uncertain directions and thus the analysis error covariance was modeled precisely. However, when the number of uncertain directions is larger than the ensemble size, the spherical simplex centering has the advantage of allowing almost twice as many uncertain directions to be spanned as the symmetric positive–negative paired centering. The performances of the spherical simplex ETKF and symmetric positive–negative paired ETKF ensembles are compared by using the Community Climate Model Version 3 (CCM3). Each ensemble contains 1 control forecast and 16 perturbed forecasts. 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 accuracy of the ensemble means, the accuracy of predictions of forecast error variance, and the ability of the ETKF ensembles to resolve inhomogeneities in the observation distribution were all tested. In all of these test categories, the spherical simplex ETKF ensemble was found to be superior to the symmetric positive–negative paired ETKF ensemble. The computational expense for generating spherical simplex ETKF initial perturbations is about as small as that for the symmetric positive–negative paired ETKF. Also shown is that the seemingly straightforward centering method, in which centered perturbations are obtained by subtracting the average of the perturbations from each individual perturbation, is unsatisfactory because the covariance estimated by the uncentered perturbations is not necessarily conserved after centering.

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Jeffrey D. Duda
,
Xuguang Wang
,
Fanyou Kong
, and
Ming Xue

Abstract

Two approaches for accounting for errors in quantitative precipitation forecasts (QPFs) due to uncertainty in the microphysics (MP) parameterization in a convection-allowing ensemble are examined. They include mixed MP (MMP) composed mostly of double-moment schemes and perturbing parameters within the Weather Research and Forecasting single-moment 6-class microphysics scheme (WSM6) MP scheme (PPMP). Thirty-five cases of real-time storm-scale ensemble forecasts produced by the Center for Analysis and Prediction of Storms during the NOAA Hazardous Weather Testbed 2011 Spring Experiment were examined.

The MMP ensemble had better fractions Brier scores (FBSs) for most lead times and thresholds, but the PPMP ensemble had better relative operating characteristic (ROC) scores for higher precipitation thresholds. The pooled ensemble formed by randomly drawing five members from the MMP and PPMP ensembles was no more skillful than the more accurate of the MMP and PPMP ensembles. Significant positive impact was found when the two were combined to form a larger ensemble.

The QPF and the systematic behaviors of derived microphysical variables were also examined. The skill of the QPF among different members depended on the thresholds, verification metrics, and forecast lead times. The profiles of microphysics variables from the double-moment schemes contained more variation in the vertical than those from the single-moment members. Among the double-moment schemes, WDM6 produced the smallest raindrops and very large number concentrations. Among the PPMP members, the behaviors were found to be consistent with the prescribed intercept parameters. The perturbed intercept parameters used in the PPMP ensemble fell within the range of values retrieved from the double-moment schemes.

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Hristo G. Chipilski
,
Xuguang Wang
, and
David B. Parsons

Abstract

A novel object-based algorithm capable of identifying and tracking convective outflow boundaries in convection-allowing numerical models is presented in this study. The most distinct feature of the proposed algorithm is its ability to seamlessly analyze numerically simulated density currents and bores, both of which play an important role in the dynamics of nocturnal convective systems. The unified identification and classification of these morphologically different phenomena is achieved through a multivariate approach combined with appropriate image processing techniques. The tracking component of the algorithm utilizes two dynamical constraints, which improve the object association results in comparison to methods based on statistical assumptions alone. Special attention is placed on some of the outstanding challenges regarding the formulation of the algorithm and possible ways to address those in future research. Apart from describing the technical details behind the algorithm, this study also introduces specific algorithm applications relevant to the analysis and prediction of bores. These applications are illustrated for a retrospective case study simulated with a convection-allowing ensemble prediction system. The paper highlights how the newly developed algorithm tools naturally form a foundation for understanding the initiation, structure, and evolution of bores and convective systems in the nocturnal environment.

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