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Craig S. Schwartz and Zhiquan Liu

Abstract

Analyses with 20-km horizontal grid spacing were produced from parallel continuously cycling three-dimensional variational (3DVAR), ensemble square root Kalman filter (EnSRF), and “hybrid” variational–ensemble data assimilation (DA) systems between 0000 UTC 6 May and 0000 UTC 21 June 2011 over a domain spanning the contiguous United States. Beginning 9 May, the 0000 UTC analyses initialized 36-h Weather Research and Forecasting Model (WRF) forecasts containing a large convection-permitting 4-km nest. These 4-km 3DVAR-, EnSRF-, and hybrid-initialized forecasts were compared to benchmark WRF forecasts initialized by interpolating 0000 UTC Global Forecast System (GFS) analyses onto the computational domain.

While important differences regarding mean state characteristics of the 20-km DA systems were noted, verification efforts focused on the 4-km precipitation forecasts. The 3DVAR-, hybrid-, and EnSRF-initialized 4-km precipitation forecasts performed similarly regarding general precipitation characteristics, such as timing of the diurnal cycle, and all three forecast sets had high precipitation biases at heavier rainfall rates. However, meaningful differences emerged regarding precipitation placement as quantified by the fractions skill score. For most forecast hours, the hybrid-initialized 4-km precipitation forecasts were better than the EnSRF-, 3DVAR-, and GFS-initialized forecasts, and the improvement was often statistically significant at the 95th percentile. These results demonstrate the potential of limited-area continuously cycling hybrid DA configurations and suggest additional hybrid development is warranted.

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Zhiquan Liu, Craig S. Schwartz, Chris Snyder, and So-Young Ha

Abstract

The impact of assimilating radiance observations from the Advanced Microwave Sounding Unit-A (AMSU-A) on forecasts of several tropical cyclones (TCs) was studied using the Weather Research and Forecasting Model (WRF) and a limited-area ensemble Kalman filter (EnKF). Analysis/forecast cycling experiments with and without AMSU-A radiance assimilation were performed over the Atlantic Ocean for the period 11 August–13 September 2008, when five named storms formed. For convenience, the radiance forward operators and bias-correction coefficients, along with the majority of quality-control decisions, were computed by a separate, preexisting variational assimilation system. The bias-correction coefficients were obtained from 3-month offline statistics and fixed during the EnKF analysis cycles. The vertical location of each radiance observation, which is required for covariance localization in the EnKF, was taken to be the level at which the AMSU-A channels’ weighting functions peaked.

Deterministic 72-h WRF forecasts initialized from the ensemble-mean analyses were evaluated with a focus on TC prediction. Assimilating AMSU-A radiances produced better depictions of the environmental fields when compared to reanalyses and dropwindsonde observations. Radiance assimilation also resulted in substantial improvement of TC track and intensity forecasts with track-error reduction up to 16% for forecasts beyond 36 h. Additionally, assimilating both radiances and satellite winds gave markedly more benefit for TC track forecasts than solely assimilating radiances.

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Craig S. Schwartz, Zhiquan Liu, Yongsheng Chen, and Xiang-Yu Huang

Abstract

Two parallel experiments were designed to evaluate whether assimilating microwave radiances with a cyclic, limited-area ensemble adjustment Kalman filter (EAKF) could improve track, intensity, and precipitation forecasts of Typhoon Morakot (2009). The experiments were configured identically, except that one assimilated microwave radiances and the other did not. Both experiments produced EAKF analyses every 6 h between 1800 UTC 3 August and 1200 UTC 9 August 2009, and the mean analyses initialized 72-h Weather Research and Forecasting model forecasts. Examination of individual forecasts and average error statistics revealed that assimilating microwave radiances ultimately resulted in better intensity forecasts compared to when radiances were withheld. However, radiance assimilation did not substantially impact track forecasts, and the impact on precipitation forecasts was mixed. Overall, net positive results suggest that assimilating microwave radiances with a limited-area EAKF system is beneficial for tropical cyclone prediction, but additional studies are needed.

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Craig S. Schwartz, Zhiquan Liu, and Xiang-Yu Huang

Abstract

Dual-resolution (DR) hybrid variational-ensemble analysis capability was implemented within the community Weather Research and Forecasting (WRF) Model data assimilation (DA) system, which is designed for limited-area applications. The DR hybrid system combines a high-resolution (HR) background, flow-dependent background error covariances (BECs) derived from a low-resolution ensemble, and observations to produce a deterministic HR analysis. As DR systems do not require HR ensembles, they are computationally cheaper than single-resolution (SR) hybrid configurations, where the background and ensemble have equal resolutions.

Single-observation tests were performed to document some characteristics of limited-area DR hybrid analyses. Additionally, the DR hybrid system was evaluated within a continuously cycling framework, where new DR hybrid analyses were produced every 6 h over ~3.5 weeks. In the DR configuration presented here, the deterministic backgrounds and analyses had 15-km horizontal grid spacing, but the 32-member WRF Model–based ensembles providing flow-dependent BECs for the hybrid had 45-km horizontal grid spacing. The DR hybrid analyses initialized 72-h WRF Model forecasts that were compared to forecasts initialized by an SR hybrid system where both the ensemble and background had 15-km horizontal grid spacing. The SR and DR hybrid systems were coupled to an ensemble adjustment Kalman filter that updated ensembles each DA cycle.

On average, forecasts initialized from 15-km DR and SR hybrid analyses were not statistically significantly different, although tropical cyclone track forecast errors favored the SR-initialized forecasts. Although additional studies over longer time periods and at finer grid spacing are needed to further understand sensitivity to ensemble perturbation resolution, these results suggest users should carefully consider whether SR hybrid systems are worth the extra cost.

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Kathryn M. Newman, Craig S. Schwartz, Zhiquan Liu, Hui Shao, and Xiang-Yu Huang

Abstract

This study examines the impact of assimilating Microwave Humidity Sounder (MHS) radiances in a limited-area ensemble Kalman filter (EnKF) data assimilation system. Two experiments spanning 11 August–13 September 2008 were run over a domain featuring the Atlantic basin using a 6-h full cycling analysis and forecast system. Deterministic 72-h forecasts were initialized at 0000 and 1200 UTC for a comparison of forecast impact. The two experiments were configured identically with the exception of the inclusion of the MHS radiances (AMHS) in the second to isolate the impacts of the MHS radiance data. The results were verified against several sources, and statistical significance tests indicate the most notable differences are in the midlevel moisture fields. Both configurations were characterized by high moisture biases when compared to the European Centre for Medium-Range Weather Forecasts interim reanalysis (ERA-Interim, also known as ERA-I) specific humidity fields, as well as precipitable water vapor from an observationally based product. However, the AMHS experiment has midlevel moisture fields closer to the ERA-I and observation datasets. When reducing the verification domain to focus on the subtropical and easterly wave regions of the North Atlantic Ocean, larger improvements in midlevel moisture at nearly all lead times is seen in the AMHS simulation. Finally, when considering tropical cyclone forecasts, the AMHS configuration shows improvement in intensity forecasts at several lead times as well as improvements at early to intermediate lead times for minimum sea level pressure forecasts.

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Xiaoshi Qiao, Shizhang Wang, Craig S. Schwartz, Zhiquan Liu, and Jinzhong Min

Abstract

A probability matching (PM) product using the ensemble maximum (EnMax) as the basis for spatial reassignment was developed. This PM product was called the PM max and its localized version was called the local PM (LPM) max. Both products were generated from a 10-member ensemble with 3-km horizontal grid spacing and evaluated over 364 36-h forecasts in terms of the fractions skill score. Performances of the PM max and LPM max were compared to those of the traditional PM mean and LPM mean, which both used the ensemble mean (EnMean) as the basis for spatial reassignment. Compared to observations, the PM max typically outperformed the PM mean for precipitation rates ≥5 mm h−1; this improvement was related to the EnMax, which had better spatial placement than the EnMean for heavy precipitation. However, the PM mean produced better forecasts than the PM max for lighter precipitation. It appears that the global reassignment used to produce the PM max was responsible for its poorer performance relative to the PM mean at light precipitation rates, as the LPM max was more skillful than the LPM mean at all thresholds. These results suggest promise for PM products based on the EnMax, especially for rare events and ensembles with insufficient spread.

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Tae-Kwon Wee, Ying-Hwa Kuo, Dong-Kyou Lee, Zhiquan Liu, Wei Wang, and Shu-Ya Chen

Abstract

The authors have discovered two sizeable biases in the Weather Research and Forecasting (WRF) model: a negative bias in geopotential and a warm bias in temperature, appearing both in the initial condition and the forecast. The biases increase with height and thus manifest themselves at the upper part of the model domain. Both biases stem from a common root, which is that vertical structures of specific volume and potential temperature are convex functions. The geopotential bias is caused by the particular discrete hydrostatic equation used in WRF and is proportional to the square of the thickness of model layers. For the vertical levels used in this study, the bias far exceeds the gross 1-day forecast bias combining all other sources. The bias is fixed by revising the discrete hydrostatic equation. WRF interpolates potential temperature from the grids of an external dataset to the WRF grids in generating the initial condition. Associated with the Exner function, this leads to the marked bias in temperature. By interpolating temperature to the WRF grids and then computing potential temperature, the bias is removed. The bias corrections developed in this study are expected to reduce the disparity between the forecast and observations, and eventually to improve the quality of analysis and forecast in the subsequent data assimilation. The bias corrections might be especially beneficial to assimilating height-based observations (e.g., radio occultation data).

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Feng Gao, Zhiquan Liu, Juhui Ma, Neil A. Jacobs, Peter P. Childs, and Hongli Wang

Abstract

A variational bias correction (VarBC) scheme is developed and tested using regional Weather Research and Forecasting Model Data Assimilation (WRFDA) to correct systematic errors in aircraft-based measurements of temperature produced by the Tropospheric Airborne Meteorological Data Reporting (TAMDAR) system. Various bias models were investigated, using one or all of aircraft height tendency, Mach number, temperature tendency, and the observed temperature as predictors. These variables were expected to account for the representation of some well-known error sources contributing to uncertainties in TAMDAR temperature measurements. The parameters corresponding to these predictors were evolved in the model for a two-week period to generate initial estimates according to each unique aircraft tail number. Sensitivity experiments were then conducted for another one-month period. Finally, a case study using VarBC of a cold front precipitation event is examined. The implementation of VarBC reduces biases in TAMDAR temperature innovations. Even when using a bias model containing a single predictor, such as height tendency or Mach number, the VarBC produces positive impacts on analyses and short-range forecasts of temperature with smaller standard deviations and biases than the control run. Additionally, by employing a multiple-predictor bias model, which describes the statistical relations between innovations and predictors, and uses coefficients to control the evolution of components in the bias model with respect to their reference values, VarBC further reduces the average error of analyses and short-range forecasts with respect to observations. The potential impacts of VarBC on precipitation forecasts were evaluated, and the VarBC is able to indirectly improve the prediction of precipitation location by reducing the forecast error for wind-related synoptic circulation leading to precipitation.

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Craig S. Schwartz, Zhiquan Liu, Xiang-Yu Huang, Ying-Hwa Kuo, and Chin-Tzu Fong

Abstract

The Weather Research and Forecasting Model (WRF) “hybrid” variational-ensemble data assimilation (DA) algorithm was used to initialize WRF model forecasts of three tropical cyclones (TCs). The hybrid-initialized forecasts were compared to forecasts initialized by WRF's three-dimensional variational (3DVAR) DA system. An ensemble adjustment Kalman filter (EAKF) updated a 32-member WRF-based ensemble system that provided flow-dependent background error covariances for the hybrid. The 3DVAR, hybrid, and EAKF configurations cycled continuously for ~3.5 weeks and produced new analyses every 6 h that initialized 72-h WRF forecasts with 45-km horizontal grid spacing. Additionally, the impact of employing a TC relocation technique and using multiple outer loops (OLs) in the 3DVAR and hybrid minimizations were explored.

Model output was compared to conventional, dropwindsonde, and TC “best track” observations. On average, the hybrid produced superior forecasts compared to 3DVAR when only one OL was used during minimization. However, when three OLs were employed, 3DVAR forecasts were dramatically improved but the mean hybrid performance changed little. Additionally, incorporation of TC relocation within the cycling systems further improved the mean 3DVAR-initialized forecasts but the average hybrid-initialized forecasts were nearly unchanged.

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Dale Barker, Xiang-Yu Huang, Zhiquan Liu, Tom Auligné, Xin Zhang, Steven Rugg, Raji Ajjaji, Al Bourgeois, John Bray, Yongsheng Chen, Meral Demirtas, Yong-Run Guo, Tom Henderson, Wei Huang, Hui-Chuan Lin, John Michalakes, Syed Rizvi, and Xiaoyan Zhang

Data assimilation is the process by which observations are combined with short-range NWP model output to produce an analysis of the state of the atmosphere at a specified time. Since its inception in the late 1990s, the multiagency Weather Research and Forecasting (WRF) model effort has had a strong data assimilation component, dedicating two working groups to the subject. This article documents the history of the WRF data assimilation effort, and discusses the challenges associated with balancing academic, research, and operational data assimilation requirements in the context of the WRF effort to date. The WRF Model's Community Variational/Ensemble Data Assimilation System (WRFDA) has evolved over the past 10 years, and has resulted in over 30 refereed publications to date, as well as implementation in a wide range of real-time and operational NWP systems. This paper provides an overview of the scientific capabilities of WRFDA, and together with results from sample operation implementations at the U.S. Air Force Weather Agency (AFWA) and United Arab Emirates (UAE) Air Force and Air Defense Meteorological Department.

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