A WRF-Based Tool for Forecast Sensitivity to the Initial Perturbation: the Conditional Nonlinear Optimal Perturbations Versus Th
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JANUARY 2017 Y U E T A L . 187 A WRF-Based Tool for Forecast Sensitivity to the Initial Perturbation: The Conditional Nonlinear Optimal Perturbations versus the First Singular Vector Method and Comparison to MM5 a,b c,d a e f HUIZHEN YU, HONGLI WANG, ZHIYONG MENG, MU MU, XIANG-YU HUANG, g AND XIN ZHANG a Laboratory for Climate and Ocean–Atmosphere Studies, Department of Atmospheric and Oceanic Sciences, School of Physics, Peking University, Beijing, China b Qingdao Meteorological Bureau, Shandong, China c Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, Colorado d Global Systems Division, NOAA/Earth System Research Laboratory, Boulder, Colorado e Institute of Atmospheric Sciences, Fudan University, Shanghai, China f Centre for Climate Research Singapore, Meteorological Service Singapore, Singapore g IBM Research–China, Beijing, China (Manuscript received 12 September 2015, in final form 22 October 2016) ABSTRACT A forecast sensitivity to initial perturbation (FSIP) analysis tool for the WRF Model was developed. The tool includes two modules respectively based on the conditional nonlinear optimal perturbation (CNOP) method and the first singular vector (FSV) method. The FSIP tool can be used to identify regions of sensitivity for targeted observation research and important influential weather systems for a given forecast metric. This paper compares the performance of the FSIP tool to its MM5 counterpart, and demonstrates how CNOP, local CNOP (a kind of conditional nonlinear suboptimal perturbation), and FSV were detected using their evolutions of cost function. The column-integrated features of the perturbations were generally similar between the two models. More significant differences were apparent in the details of their vertical distribu- tion. With Typhoon Matsa (2005) in the western North Pacific and a winter storm in the United States (2000) as validation cases, this work examined the tool’s capability to identify sensitive regions for targeted obser- vation and to investigate important influential weather systems. The location and pattern of the sensitive areas identified by CNOP, local CNOP, and FSV were quite similar for both the Typhoon Matsa case and the winter storm case. The main differences were mainly in their impact on the growth of forecast difference and the details of their vertical distributions. For both cases, the wind observations might be more important than temperature observations. The results also showed that local CNOP was more capable of capturing the in- fluence of important weather systems on the forecast of total dry energy in the verification area. 1. Introduction analysis is targeted observation. Targeted observation is a method in which a special area is determined to The question of predictability in the atmospheric sci- gather extra observations that provide the optimal de- ences has received considerable attention since the work crease in error of a certain forecast metric through as- of Lorenz (1963, 1975). Sensitivity analysis, which ex- similating those extra observations. The method has amines, but is not limited to, the forecast response to a attracted considerable attention since it was first pro- change in the initial conditions, is one way to study posed by Snyder (1996; e.g., Aberson 2003, 2011; Peng predictability, and a potential application of sensitivity and Reynolds 2005, 2006; Wu et al. 2007, 2009b), and encouraging results have been obtained in a series of Denotes Open Access content. field experiments, such as the Fronts and Atlantic Storm Track Experiment (FASTEX; Bergot 1999) and the Corresponding author e-mail: Dr. Zhiyong Meng, zymeng@pku. North Pacific Experiment (NORPEX; Langland et al. edu.cn 1999). Targeting strategies can be roughly classified into DOI: 10.1175/JTECH-D-15-0183.1 Ó 2017 American Meteorological Society 188 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 34 two groups—one based on adjoint technology, such as precursors for some events. Wang et al. (2011) found singular vectors (SVs; Palmer et al. 1998), and the other that both CNOP and FSV were able to capture the areas encompassing ensemble-based methods, such as the of sensitivity for tropical cyclones at high levels. How- ensemble transform Kalman filter (Bishop et al. 2001). ever, the differences between CNOP and FSV in cap- A common limitation of most current targeting turing the weather systems that influence the forecast of strategies based on adjoint techniques is that the mag- typhoon were not examined. nitude of the initial perturbation needs to be sufficiently Most previous works on atmospheric predictability small to make sure the error propagation feature in the and targeted observation using the CNOP method were original nonlinear model can be approximated by the based on MM5 (Grell et al. 1995) and its tangent linear error propagation feature in the tangent linear model. and adjoint models (Zou et al. 1997). The MM5-CNOP/ The SV method is one such strategy and has been widely FSV optimization package was developed by Mu et al. used (Bergot 1999; Reynolds and Rosmond 2003). (2007) to study mesoscale predictability and targeted However, in the situations when the initial error is observations, and has since been applied in targeted large, the application of the adjoint methods to tar- observation and precursor studies (e.g., Mu et al. 2009; geted observation will break down. This issue is quite Wang 2009; Qin and Mu 2012; Jiang and Wang 2012). serious for mesoscale weather systems due to the sparse With the WRF Model (Skamarock et al. 2008) gradually observations. replacing MM5, Wang et al. (2011) developed a WRF- To take nonlinearity into account, Mu and Duan based CNOP method and compared it to FSV in two (2003) proposed the conditional nonlinear optimal tropical cyclone cases. Since the publication of that perturbation (CNOP) strategy. The CNOP method is work, WRF tangent linear and adjoint models have been essentially a nonlinear extension of the first singular redesigned and rewritten (Zhang et al. 2013), and suc- vector (FSV) method. CNOP is defined as the initial cessfully used in forecast sensitivity to observation perturbation whose nonlinear evolution attains the studies (e.g., Zhang et al. 2014) and the WRF 4DVAR maximum of a cost function under certain physical system (Zhang et al. 2015). Readers are referred to constraints over a chosen period (Mu and Duan 2003). Zhang et al. (2013) for details on the WRF tangent lin- This idea was also applied in the study of the transition- ear and adjoint models (called WRFPLUS). to-turbulence problem in fluid mechanics (Kerswell The aim of the work reported in this paper is to build a et al. 2014). user-friendly tool that can be used to perform forecast CNOP has been widely used to identify areas of sen- sensitivity to initial perturbation (FSIP) analysis (e.g., sitivity in targeted observations for mesoscale and identifying variables and/or weather systems that are tropical cyclone forecasts. The results showed that the more important to a given aspect of a forecast, using deployment of additional observations in the sensitive CNOP and/or FSV) based on a latest version of the area identified by CNOP had an overall positive influ- WRFPLUS package. The WRF users can apply the ence on typhoon track forecasts, and the degree of im- FSIP to their own cases through changing certain pa- provement was generally larger than that based on the rameters in a single namelist file. Relative to Wang et al. FSV method (Mu et al. 2007, 2009; Chen 2011; Qin and (2011), this work is unique in the following four aspects: Mu 2012; Chen et al. 2013; Qin et al. 2013). 1) A user-friendly WRF-based FSIP tool was con- Besides identifying the most sensitive area to add structed to perform sensitivity analyses with the FSV extra observations for initialization in numerical and CNOP methods using a new version of the weather prediction, sensitivity analysis can also be used WRFPLUS; 2) the FSIP tool was examined and vali- to identify precursors of a weather system or to examine dated by comparing to its MM5 counterpart; 3) the the possible interaction between different synoptic sys- performance of the FSIP tool was assessed not only in a tems (Wu et al. 2007, 2009a), which could be quite useful typhoon case in the western North Pacific but also in a for identifying key contributors to a weather event, es- winter storm case in the United States; and 4) the sen- pecially from an operational forecasting point of view. sitivities of the FSIP tool to different optimization win- The results of Wu et al. (2009b) showed that adjoint- dows were examined, revealing a number of differences based methods could capture the signal of the related between the CNOP and FSV methods in their capability dynamic systems that may affect typhoon movement or to capture the precursors of a weather event. evolution. CNOP has also been applied in the studies of Section 2 introduces the CNOP and FSV methods, weather and climate predictability (Mu and Duan 2003; how the FSIP tool was built, and the steps needed to Duan et al. 2004; Mu and Zhang 2006; Mu and Jiang calculate the WRF-based CNOP and FSV, as well as a 2008a,b; Mu et al. 2015). The results showed that the brief introduction to the two examined cases and the CNOP could be regarded as representing the optimal experimental design. The results from the validation of JANUARY 2017 Y U E T A L . 189 the FSIP tool in comparison to its MM5 counterpart are For simplicity, we let C1 5 C2 5 C. In this work, we presented in section 3. Further applications of the tool to defined a total dry energy (TDE) norm, which is a two validation cases for identifying sensitive areas for component of the total dry energy.