## 1 Introduction  
The accuracy of numerical forecasts of tropical cyclones (TCs) depends on the realism of initial vortices embedded within model initial conditions. Because of scarce conventional observations over the oceans, TC observations rely heavily on infrared instruments [1, 2, 3] and microwave instruments [4, 5]. There is often uncertainty in key structural aspects of global large-scale analysis datasets [6]. The location and size characteristics can vary both among TCs and across a single TC's life cycle. Vortex initialization incorporates a bogus vortex into model initial conditions to improve forecasts of TCs. Realistic bogus vortices yield better vortex initialization. Traditional methods mainly rely on ships, buoys, and station observations, supplemented by aircraft reconnaissance [7]. However, the United States ended routine Northwest Pacific TC flights after 1987 [8]. Here, an objective scheme is developed to construct bogus vortices utilizing satellite sea surface wind observations. Microwave scatterometers have become the principal instruments for obtaining global sea surface wind data. Working essentially as radar systems, they measure backscattering coefficients related to sea surface roughness [9]. Due to their low observing frequencies, these scatterometer sea surface wind observations are usable under both clear and cloudy sky conditions. Since the launch of SeaSat by the United States in 1978 [10], multiple scatterometer-equipped satellites have been launched by different agencies, such as the European Space Agency's ERS series and MetOp satellites, Japan Aerospace Exploration Agency's ADEOS satellites, NASA's QuikSCAT, Indian Space Research Organization's OceanSat series, China's second-generation National Satellite Ocean Applications Center's Hai Yang-2 (HY-2) satellites, and Satellite Ocean Application Service Fengyun-3E (FY-3E) [11; 12; 13]. Constructing a bogus vortex for vortex initialization typically involves specifying an empirical radial profile of sea surface pressure [14] or tangential wind [15]. For example, [PERSON] [16] proposed an axisymmetric model in which the sea level pressure follows a parabolic function in the core region. [PERSON] [17] introduced another radial profile that better represents the periphery of a tropical cyclone. By merging both, [PERSON] [14] developed an empirical function with four parameters: the sea level pressure at the TC center position (P\({}_{\rm c}\)), the pressure at infinity of the typhoon (P\({}_{\infty}\)), the radius of the maximum radial gradient of sea level pressure (R\({}_{0}\)), and the radius of the outermost closed isobar (R\({}_{\rm out}\)). Thus, [PERSON]'s formula can represent a bogus vortex with realistic intensity and size. While P\({}_{\rm c}\) and R\({}_{\rm out}\) are often directly available from the best track data and P\({}_{\infty}\) can be approximated from large-scale analysis, R\({}_{0}\) is less certain. Earlier work replaced R\({}_{0}\) with the radius of maximum sustained wind, R\({}_{\rm max}\)[18; 19; 20; 21]. [PERSON] and [PERSON] [22] instead derived R\({}_{0}\) from the radius of 34-kt wind speed (R\({}_{\rm 34 kt}\)) in the best track data. Specifically, R\({}_{0}\) is regressed on R\({}_{\rm 34 kt}\) using 16 model-based vortices generated via 4D-Var data assimilation [18]. Their approach significantly improved the intensity prediction of Hurricane Bonnie (1998), due to the model capturing larger surface fluxes and latent heat release. Given the global coverage of microwave scatterometers, it is now possible to use satellite observations to establish a relationship between R\({}_{0}\) and R\({}_{\rm 34 kt}\) directly from observed data rather than from model forecasts. Moreover, scatterometers sea surface wind observations can pinpoint the TC center position [23], complementing brightness temperature-based methods that can suffer from cloud contamination [24]. Furthermore, the assimilation of post-processed scatterometer data significantly improved TC forecasting [25; 26; 27; 28].