ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 22, NO. 3, 2005, 415–427 Assimilation and Simulation of Typhoon Rusa (2002) Using the WRF System GU Jianfeng∗1,2,3 (ï¸), Qingnong XIAO2, Ying-Hwa KUO2, Dale M. BARKER2, XUE Jishan1 (ÅVõ), and MA Xiaoxing3 (ê¡() 1Chinese Academy of Meteorological Sciences, Beijing 100081 2National Center for Atmospheric Research, Boulder, Colorado 80307, USA 3Shanghai Weather Forecast Center, Shanghai 200030 (Received 29 July 2004; revised 25 December 2004) ABSTRACT Using the recently developed Weather Research and Forecasting (WRF) 3DVAR and the WRF model, numerical experiments are conducted for the initialization and simulation of typhoon Rusa (2002). The observational data used in the WRF 3DVAR are conventional Global Telecommunications System (GTS) data and Korean Automatic Weather Station (AWS) surface observations. The Background Error Statistics (BES) via the National Meteorological Center (NMC) method has two different resolutions, that is, a 210-km horizontal grid space from the NCEP global model and a 10-km horizontal resolution from Korean operational forecasts. To improve the performance of the WRF simulation initialized from the WRF 3DVAR analyses, the scale-lengths used in the horizontal background error covariances via recursive filter are tuned in terms of the WRF 3DVAR control variables, streamfunction, velocity potential, unbalanced pressure and specific humidity. The experiments with respect to different background error statistics and different observational data indicate that the subsequent 24-h the WRF model forecasts of typhoon Rusa’s track and precipitation are significantly impacted upon the initial fields. Assimilation of the AWS data with the tuned background error statistics obtains improved predictions of the typhoon track and its precipitation. Key words: 3DVAR, data assimilation, background error statistics, numerical simulation, typhoon 1. Introduction ational (4DVAR, when time is included) data assim- ilation. The adjoint formalism was first proposed by The problem of determining a physically consis- Le Dimet (1982) for meteorological applications and tent and accurate snapshot of the atmosphere is cen- was then implemented by Derber (1985), Lewis and tral to numerical weather prediction (NWP). Nearly Derber (1985), Courtier (1985), Le Dimet and Tala- 50 years ago, in the period of scientific excitement and grand (1986), Talagrand and Courtier (1987), Navon challenge that followed the first successful numerical et al. (1992), Zupanski (1993), Zou et al. (1993a, weather prediction, the variational approach to mete- b), Li et al. (2000) and Xiao et al. (2002), among orological analysis was introduced by Sasaki (1958). others. However, 4DVAR has been known to be very In succeeding decades, with advances in both comput- time-consuming due to the adjoint nature of model ing power and optimization strategies, more sophisti- integration in iteratively searching for the optimal so- cated constraints and more diverse observations have lution (Li and Navon, 2001). In 3DVAR, since both been included in the problem. In the nomenclature of model integration and adjoint model integration are meteorology, this methodology has become known as not needed, it greatly simplifies the filtering processes three-dimensional variational (3DVAR, all space coor- with relatively cheaper adjoint operators for ingestion dinates but excluding time) and four-dimensional vari- of various observations (Rabier et al., 1997; Courtier *E-mail: [email protected] Current affiliation: Gu Jianfeng, Shanghai Weather Forecast Center, Shanghai 200030 416 ASSIMILATION AND SIMULATION OF TYPHOON RUSA (2002) USING THE WRF SYSTEM VOL. 22 et al., 1998). The main purpose of this paper is to demonstrate The Weather Research and Forecasting (WRF) the ability of the WRF 3DVAR in analyses of Typhoon project is a multi-institutional effort to develop an ad- Rusa (2002) and its surrounding atmosphere and to as- vanced mesoscale forecast and data assimilation sys- sess their impact on the subsequent the WRF model tem that is accurate, efficient, and scalable across a forecasts of the typhoon. The WRF 3DVAR analyses range of scales. The newest version (2.0) of the WRF for typhoon initialization are tuned by changing the model and the WRF 3DVAR were released in 2004. scale-lengths of horizontal Background Error Statis- The configuration of the WRF 3DVAR system is based tics (BES). Conventional Global Telecommunication on an incremental formulation producing a multivari- System (GTS) and Korean Automatic Weather Sta- ate incremental analysis in the WRF model space. The tion (AWS) observational data are used to enhance incremental cost function minimization is performed the 3DVAR analyses of the typhoon and surrounding in a preconditioned control variable space. The pre- atmosphere. Numerical forecasts of the typhoon track conditioned control variables we use in this study are and rainfall are conducted with the WRF model. This stream-function, velocity potential, unbalanced pres- paper is organized as follows. The next section briefly sure and specific humidity. Balance between mass and describes the WRF 3DVAR and the WRF modeling wind increments is achieved via a geostrophically and system. Section 3 gives a synoptic overview of ty- cyclostrophically balanced pressure derived from the phoon Rusa (2002). The preprocessing of the conven- wind increments. Statistics of differences between 24 tional GTS and Korean AWS observational data, and h and 12 h forecasts are used to estimate background the preparation of the WRF 3DVAR first-guess fields error covariances via the National Meteorological Cen- using National Centers for Environmental Prediction ter (NMC) method (Parrish and Derber, 1992). Rep- (NCEP) AVN data and the WRF standard initializa- resentation of the horizontal component of background tion (SI), will be presented in section 4. In section error is via horizontally isotropic and homogeneous 5, the scale-lengths of the WRF 3DVAR assimilation recursive filters. The vertical component is applied are tuned based on the root-mean-square errors and through projection onto climatologically averaged (in the single observation tests. Section 6 will describe time, longitude, and optionally latitude) eigenvectors our experimental design and list our data assimilation of vertical error estimated via the NMC method. Hor- and simulation experiments. In section 7, the numer- izontal/vertical errors are nonseparable in that hori- ical simulation results are presented. And finally, the zontal scales vary with vertical eigenvectors. A de- summary and conclusions are given in section 8. tailed description of the 3DVAR system can be found in Barker et al. (2004). 2. Brief description of the WRF 3DVAR and Numerical prediction of tropical cyclones has im- the WRF modeling system proved enormously over the past few decades. The difficulties in the numerical prediction of tropical cy- 2.1 The WRF 3DVAR clone track, intensity and inner-core structure are as- The basic goal of the WRF 3DVAR system is to sociated with insufficient observations over the oceans seek an “optimal” estimate of the true atmospheric and with the limitations of numerical models, such as state at analysis time through iterative solution of a low-resolution, crude physical parameterization, and prescribed cost-function: the inability to treat multiscale interaction. Recently, 1 T −1 tropical cyclone forecast models at high resolution J(x) = (x − xb) B (x − xb) have greatly improved as a result of advances in com- 2 puter resources. More sophisticated models have been 1 T −1 + (y − y0) O (y − y0) . (1) developed and used for tropical cyclone study and fore- 2 cast. To improve the tropical cyclone analysis and to The problem can be summarized as the iterative solu- produce an adequate initial condition for prediction tion of Eq. (1) to find the analysis state x that min- becomes an important procedure. In the recent stud- imizes J(x). This solution represents the estimate of ies of Zou and Xiao (2000), Xiao et al. (2000), and the true atmospheric state given the two sources of Zhang et al. (2003), the MM5 4DVAR data assimila- a priori data: the background (previous forecast) xb tion method was proposed to generate the structure of and observations y0 (Lorenc 1986). B and O are the a tropical cyclone and the adjacent synoptic features background and observation error covariance matri- with insufficient observations over the ocean in the ini- ces respectively. The observation operator H is used tial condition of the high-resolution mesoscale model to transform the gridded analysis x to observation MM5. The predictions of tropical cyclone track and space y = Hx for comparison against observations. intensity were improved in their studies. One practical solution to this problem is to perform NO. 3 GU ET AL. 417 a preconditioning via a control variable v-transform from eigenvectors and eigenvalues of a climatological defined by δx = Uv, where δx = x − xb. The trans- estimate onto model levels, and the physical variable T form U is chosen to approximately satisfy the rela- transformation Bp = U pU p converts control variables tionship B = UU T. Using the incremental formula- to model variables (e.g., u, v, T, p, q). tion (Courtier et al., 1994) and the control variable 2.2 The WRF model transform, Eq. (1) can be rewritten as: 1 1 The WRF model is a next-generation mesoscale J(v)= vTv+ (d−H0Uv)TO−1(d−H0Uv) , (2) 2 2 model that advances both the understanding and the prediction of mesoscale weather systems and