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Qingnong Xiao and Juanzhen Sun

Abstract

The impact of multiple–Doppler radar data assimilation on quantitative precipitation forecasting (QPF) is examined in this study. The newly developed Weather Research and Forecasting (WRF) model Advanced Research WRF (ARW) and its three-dimensional variational data assimilation system (WRF 3DVAR) are used. In this study, multiple–Doppler radar data assimilation is applied in WRF 3DVAR cycling mode to initialize a squall-line convective system on 13 June 2002 during the International H2O Project (IHOP_2002) and the ARW QPF skills are evaluated for the case. Numerical experiments demonstrate that WRF 3DVAR can successfully assimilate Doppler radial velocity and reflectivity from multiple radar sites and extract useful information from the radar data to initiate the squall-line convective system. Assimilation of both radial velocity and reflectivity results in sound analyses that show adjustments in both the dynamical and thermodynamical fields that are consistent with the WRF 3DVAR balance constraint and background error correlation. The cycling of the Doppler radar data from the 12 radar sites at 2100 UTC 12 June and 0000 UTC 13 June produces a more detailed mesoscale structure of the squall-line convection in the model initial conditions at 0000 UTC 13 June. Evaluations of the ARW QPF skills with initialization via Doppler radar data assimilation demonstrate that the more radar data in the temporal and spatial dimensions are assimilated, the more positive is the impact on the QPF skill. Assimilation of both radial velocity and reflectivity has more positive impact on the QPF skill than does assimilation of either radial velocity or reflectivity only. The improvement of the QPF skill with multiple-radar data assimilation is more clearly observed in heavy rainfall than in light rainfall. In addition to the improvement of the QPF skill, the simulated structure of the squall line is also enhanced by the multiple–Doppler radar data assimilation in the WRF 3DVAR cycling experiment. The vertical airflow pattern shows typical characteristics of squall-line convection. The cold pool and its related squall-line convection triggering process are better initiated in the WRF 3DVAR analysis and simulated in the ARW forecast when multiple–Doppler radar data are assimilated.

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Xiaolei Zou and Qingnong Xiao

Abstract

A bogus data assimilation (BDA) scheme is presented and used to generate the initial structure of a tropical cyclone for hurricane prediction. It was tested on Hurricane Felix (1995) in the Atlantic Ocean during its mature stage. The Pennsylvania State University–National Center for Atmospheric Research nonhydrostatic Mesoscale Model version 5 was used for both the data assimilation and prediction. It was found that a dynamically and physically consistent initial condition describing the dynamic and thermodynamic structure of a hurricane vortex can be generated by fitting the forecast model to a specified bogus surface low based on a few observed and estimated parameters. Through forecast model constraint, BDA is able to recover many of the structural features of a mature hurricane including a warm-core vortex with winds swirling in and out of the vortex center in the lower and upper troposphere, respectively; the eyewall; the saturated ascent around the eye and descent or weak ascent in the eye; and the spiral cloud bands and rainbands. Satellite and radar data, if available, can be incorporated into the BDA procedure. It was shown that satellite-derived water vapor winds have an added value for BDA—they can generate a more realistic initial vortex.

As a result of BDA using both a bogus surface low and satellite water vapor wind data, dramatic improvements occurred in the hurricane prediction of Felix. First of all, the initial fields of model variables describing the BDA initial vortex are well adapted to the forecast model. Second, the intensity forecast was greatly improved. The mean error of the central sea level pressure during the entire 72-h forecast period reduced from 25.9 hPa without BDA to less than 2.1 hPa with BDA. Third, the model captured the structures of the storm reasonably well. In particular, the model reproduced the ring of maximum winds, the eye, the eyewall, and the spiral cloud bands. Finally, improvement in the track prediction was also observed. The 24-, 48-, and 72-h forecast track errors with BDA were 76, 76, and 84 km, respectively, compared to the track errors of 93, 170, and 193 km without BDA.

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Chengsi Liu and Qingnong Xiao

Abstract

A four-dimensional ensemble-based variational data assimilation (4DEnVar) algorithm proposed in Part I of the 4DEnVar series (denoted En4DVar in Part I, but here we refer to it as 4DEnVar according to WMO conference recommendation to differentiate it from En4DVar algorithm using adjoint model) uses a flow-dependent background error covariance calculated from ensemble forecasts and performs 4DVar optimization based on an incremental approach and a preconditioning algorithm. In Part II, the authors evaluated 4DEnVar with observing system simulation experiments (OSSEs) using the Advanced Research Weather Research and Forecasting Model (ARW-WRF, hereafter WRF). The current study extends the 4DEnVar to assimilate real observations for a cyclone in the Antarctic and the Southern Ocean in October 2007. The authors performed an intercomparison of four different WRF variational approaches for the case, including three-dimensional variational data assimilation (3DVar), first guess at the appropriate time (FGAT), and ensemble-based three-dimensional (En3DVar) and four-dimensional (4DEnVar) variational data assimilations. It is found that all data assimilation approaches produce positive impacts in this case. Applying the flow-dependent background error covariance in En3DVar and 4DEnVar yields forecast skills superior to those with the homogeneous and isotropic background error covariance in 3DVar and FGAT. In addition, the authors carried out FGAT and 4DEnVar 3-day cycling and 72-h forecasts. The results show that 4DEnVar produces a better performance in the cyclone prediction. The inflation factor on 4DEnVar can effectively improve the 4DEnVar analysis. The authors also conducted a short period (10-day lifetime of the cyclone in the domain) of analysis/forecast intercomparison experiments using 4DEnVar, FGAT, and 3DVar. The 4DEnVar scheme demonstrates overall superior and robust performance.

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Chengsi Liu, Qingnong Xiao, and Bin Wang

Abstract

Applying a flow-dependent background error covariance (𝗕 matrix) in variational data assimilation has been a topic of interest among researchers in recent years. In this paper, an ensemble-based four-dimensional variational (En4DVAR) algorithm, designed by the authors, is presented that uses a flow-dependent background error covariance matrix constructed by ensemble forecasts and performs 4DVAR optimization to produce a balanced analysis. A great advantage of this En4DVAR design over standard 4DVAR methods is that the tangent linear and adjoint models can be avoided in its formulation and implementation. In addition, it can be easily incorporated into variational data assimilation systems that are already in use at operational centers and among the research community.

A one-dimensional shallow water model was used for preliminary tests of the En4DVAR scheme. Compared with standard 4DVAR, the En4DVAR converges well and can produce results that are as good as those with 4DVAR but with far less computation cost in its minimization. In addition, a comparison of the results from En4DVAR with those from other data assimilation schemes [e.g., 3DVAR and ensemble Kalman filter (EnKF)] is made. The results show that the En4DVAR yields an analysis that is comparable to the widely used variational or ensemble data assimilation schemes and can be a promising approach for real-time applications.

In addition, experiments were carried out to test the sensitivities of EnKF and En4DVAR, whose background error covariance is estimated from the same ensemble forecasts. The experiments indicated that En4DVAR obtained reasonably sound analysis even with larger observation error, higher observation frequency, and more unbalanced background field.

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Xin Qiu, Zhe-Min Tan, and Qingnong Xiao

Abstract

A high-resolution, full-physics model initiated with an idealized tropical cyclone–like vortex is used to simulate and investigate the secondary eyewall formation. The beta skirt axisymmetrization (BSA) hypothesis previously proposed is examined and the roles of axisymmetrizing vortex Rossby waves (VRWs) in the secondary eyewall formation are further investigated. During the formation period, convection outside the inner-core region is organized into an outer spiral rainband. The PV dipoles that are persistently generated by convective updrafts through tilting effect move along the rainband and inward toward inner-core region and are finally axisymmetrized in the preexisting beta skirt region. The formation of the secondary eyewall is preceded by a rapid intensification period, during which vortical hot towers, discrete VRWs, and sheared VRWs dominate the inner-core asymmetric structures. Sheared VRWs are repeatedly emanated from the outer edge of the eyewall and become more concentric when propagating outward, leading to the formation of a weak but nonnegligible secondary circulation near the VRWs’ stagnant radius. The mean tangential flow is accelerated by the low-level convergence associated with the secondary circulation and also by the wave–mean flow interaction mechanism, both of which are elucidated by absolute angular momentum budget calculation. The mean radial gradient of relative vorticity is enhanced across the stagnant radius, causing the extension of beta skirt to outer radii in the lower-tropospheric levels. Results from this study suggest that the stagnant radius mechanism and the BSA mechanism may work cooperatively in the sense that the former helps to establish an extensive beta skirt and the latter takes charge from then on.

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Qingnong Xiao, Xiaolei Zou, and Bin Wang

Abstract

The bogus data assimilation (BDA) scheme designed by Zou and Xiao to specify initial structures of tropical cyclones was tested further on the simulation of a landfalling hurricane—Hurricane Fran (1996). The sensitivity of the simulated hurricane track and intensity to the specified radius of maximum wind of the bogus vortex, the resolution of the BDA assimilation model, and the bogus variables specified in the BDA are studied. In addition, the simulated hurricane structures are compared with the available observations, including the surface wind analysis and the radar reflectivity captured onshore during Fran’s landfall.

The sensitivity study of the BDA scheme showed that the simulations of the hurricane track and intensity were sensitive to the size of the specified bogus vortex. Hurricanes with a larger radius of maximum sea level pressure gradient are prone to a more westward propagation. The larger the radius, the weaker the predicted hurricane. Results of the hurricane initial structures and prediction were also sensitive to the bogus variables specified in the BDA. Fitting the model to the bogused pressure data reproduced the hurricane structure of all model variables more efficiently than when fitting it to bogused wind data. Examining the initial conditions produced by the BDA, it is found that the generation and intensity of hurricane warm-core structure in the model initial state was a key factor for the hurricane intensity prediction.

Initialized with the initial conditions obtained by the BDA scheme, the model successfully simulated Hurricane Fran’s landfall, the intensity change, and some inner-core structures. Verified against the surface wind analysis, the model reproduced the distribution of the maximum wind streaks reasonably well. The model-predicted reflectivity field during the landfall of Hurricane Fran resembled the observed radar reflectivity image onshore.

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Xiaoyan Zhang, Qingnong Xiao, and Patrick J. Fitzpatrick

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Numerical experiments have been conducted to examine the impact of multisatellite data on the initialization and forecast of the rapid weakening of Hurricane Lili (in 2002) from 0000 UTC to landfall in Louisiana on 1300 UTC 3 October 2002. Fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) 4DVAR sensitivity runs were conducted separately with QuikSCAT surface winds, the Geostationary Operational Environmental Satellite-8 (GOES-8) cloud drift–water vapor winds, and Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) temperature–dewpoint sounding data to investigate their individual impact on storm track and intensity. The results were compared against a simulation initialized from a Global Forecast System background interpolated to the MM5 grid. Assimilating QuikSCAT surface wind data improves the analyzed outer-core surface winds, as well as the inner-core low-level temperature and moisture fields. Substantial adjustments of winds are noted on the periphery of the hurricane by assimilating GOES-8 satellite-derived upper-level winds. Both track forecasts initialized at 1200 UTC 2 October 2002 with four-dimensional variational data assimilation (4DVAR) of QuikSCAT and GOES-8 show improvement compared to those initialized with the model background. Assimilating Aqua MODIS sounding data improves the outer-core thermodynamic features. The Aqua MODIS data has a slight impact on the track forecast, but more importantly shows evidence of impacting the model intensity predicting by retarding the incorrect prediction of intensification. All three experiments also show that bogusing of an inner-core wind vortex is required to depict the storm’s initial intensity.

To properly investigate Lili’s weakening, data assimilation experiments that incorporate bogusing vortex, QuikSCAT winds, GOES-8 winds, and Aqua MODIS sounding data were performed. The 4DVAR satellite-bogus data assimilation is conducted in two consecutive 6-h windows preceding Lili’s weakening. Comparisons of the results between the experiments with and without satellite data indicated that the satellite data, particularly the Aqua MODIS sounding information, makes an immediate impact on the hurricane intensity change beyond normal bogusing procedures. The track forecast with the satellite data is also more accurate than just using bogusing alone. This study suggests that dry air intrusion played an important role in Lili’s rapid weakening. It also demonstrates the potential benefit of using satellite data in a 4DVAR context—particularly high-resolution soundings—on unusual cases like Hurricane Lili.

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Chengsi Liu, Qingnong Xiao, and Bin Wang

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An ensemble-based four-dimensional variational data assimilation (En4DVAR) algorithm and its performance in a low-dimension space with a one-dimensional shallow-water model have been presented in Part I. This algorithm adopts the standard incremental approach and preconditioning in the variational algorithm but avoids the need for a tangent linear model and its adjoint so that it can be easily incorporated into variational assimilation systems. The current study explores techniques for En4DVAR application in real-dimension data assimilation. The EOF decomposed correlation function operator and analysis time tuning are formulated to reduce the impact of sampling errors in En4DVAR upon its analysis. With the Advanced Research Weather Research and Forecasting (ARW-WRF) model, Observing System Simulation Experiments (OSSEs) are designed and their performance in real-dimension data assimilation is examined. It is found that the designed En4DVAR localization techniques can effectively alleviate the impacts of sampling errors upon analysis. Most forecast errors and biases in ARW are reduced by En4DVAR compared to those in a control experiment. En3DVAR cycling experiments are used to compare the ensemble-based sequential algorithm with the ensemble-based retrospective algorithm. These experiments indicate that the ensemble-based retrospective assimilation, En4DVAR, produces an overall better analysis than the ensemble-based sequential algorithm, En3DVAR, cycling approach.

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Xiaolei Zou, Qingnong Xiao, Alan E. Lipton, and George D. Modica

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The influence of Geostationary Operational Environmental Satellite (GOES) brightness temperature data on the numerical simulations of Hurricane Felix is investigated. Satellite data are included as an augmentation to a bogus data assimilation (BDA) procedure using a mesoscale adjoint modeling system. The assimilation of satellite data modified not only the environmental flow but also the structure of the initial vortex, which is located over a region devoid of satellite data. This modification resulted in a reduction of the 12-h forecast errors verified by radiosonde data. Despite the fact that the forecast using only the bogus surface low at the initial time was very good, track and intensity forecasts beyond 2 days of model integration were shown to be improved further by including satellite data in the initialization procedure. Differences in the prediction of Hurricane Felix with and without satellite data were also found in the prediction of the upper-level jet, the cold temperature trough ahead of the hurricane, the size of the hurricane eye, and the location of the maximum hydrometeor. Although the focus of this study is to assess the effect of the direct use of satellite brightness temperature data on hurricane prediction, it is also noted that the BDA experiment including only the bogus data shows a positive effect of the BDA vortex on the environmental flow during the forecast period, as verified by satellite observations.

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Qingnong Xiao, Xiaoyan Zhang, Christopher Davis, John Tuttle, Greg Holland, and Patrick J. Fitzpatrick

Abstract

Initialization of the hurricane vortex in weather prediction models is vital to intensity forecasts out to at least 48 h. Airborne Doppler radar (ADR) data have sufficiently high horizontal and vertical resolution to resolve the hurricane vortex and its imbedded structures but have not been extensively used in hurricane initialization. Using the Weather Research and Forecasting (WRF) three-dimensional variational data assimilation (3DVAR) system, the ADR data are assimilated to recover the hurricane vortex dynamic and thermodynamic structures at the WRF model initial time. The impact of the ADR data on three hurricanes, Jeanne (2004), Katrina (2005) and Rita (2005), are examined during their rapid intensification and subsequent weakening periods before landfall.

With the ADR wind data assimilated, the three-dimensional winds in the hurricane vortex become stronger and the maximum 10-m winds agree better with independent estimates from best-track data than without ADR data assimilation. Through the multivariate incremental structure in WRF 3DVAR analysis, the central sea level pressures (CSLPs) for the three hurricanes are lower in response to the stronger vortex at initialization. The size and inner-core structure of each vortex are adjusted closer to observations of these attributes. Addition of reflectivity data in assimilation produces cloud water and rainwater analyses in the initial vortex. The temperature and moisture are also better represented in the hurricane initialization.

Forty-eight-hour forecasts are conducted to evaluate the impact of ADR data using the Advanced Research Hurricane WRF (AHW), a derivative of the Advanced Research WRF (ARW) model. Assimilation of ADR data improves the hurricane-intensity forecasts. Vortex asymmetries, size, and rainbands are also simulated better. Hurricane initialization with ADR data is quite promising toward reducing intensity forecast errors at modest computational expense.

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