## 4 Results
### Bogus Vortex Results  
Having obtained the TC center positions, we compute the scatterometer-derived 34-kt radius, which will be denoted as \(R_{34 kt}^{Scat}\). Meanwhile, [PERSON]'s Formula (1) uses \(P_{c}\), \(R_{out}\), \(R_{0}\), \(P_{out}\), and \(P_{\infty}\). Because \(P_{c}\), \(R_{out}\), and \(P_{out}\) come from IBTrACS, and \(P_{\infty}\) from ICOADS, \(R_{0}\) remains unknown. Past work approximated R\({}_{0}\) from best track R\({}_{34 kt}\) or model-based regressions [22]. Here, we derive \(R_{0}\) from R\({}_{34 kt}\) for Northwest Pacific TCs in 2022-2023. Figure 8 shows the best tracks during 2022 and 2023, with black symbols marking times missing in the MTCSWA dataset. Figure 9 plots \(P_{\infty}\) vs. \(P_{out}\) from ICOADS for four intensity categories: tropical storms, category-1, -2, and 3+ hurricanes. As expected, \(P_{\infty}>P_{\text{out}}\). Next, from Equation (2), we calculate \(R_{0}\) for each 6-h best track time. Figure 10 shows \(R_{0}\) vs. \(R_{34 kt}\), grouping the four categories. We find a linear fit: \(R_{0}=aR_{34 kt}+b\), with standard deviations ranging from -55 km for tropical storms to -22 km for 3+ hurricanes. As expected, the values of \(P_{\infty}\) are larger than the values of \(P_{\text{out}}\). Once we have \(P_{\infty}\), \(R_{0}\) can be calculated from the best track data using (2). We can then generate scatter plots of \(R_{0}\) versus \(R_{34 kt}\) for 2022 and 2023 Northwest Pacific tropical storms, category-1 hurricanes, category-2 hurricanes, and hurricanes with intensities stronger than category 2 (Figure 10). There are linear relationships between \(R_{0}\) and \(R_{34 kt}\). The larger the TC low-pressure system, the larger the wind radius of 34-kt. An empirical linear regression function, \(R_{0}=aR_{34 kt}+b\), is thus established for the four TC groups. The regression coefficients (\(a\), \(b\)) for the above four groups are (0.389, 71.854 km), (0.371, 34.588 km), (0.349, 9.398 km), and (0.283, \(-\)0.904 km), respectively. The standard deviations of the regression function for the four groups are 55.065, 34.644, 25.996, and 21.710 km, respectively. Figure 8: Spatial distribution of **(a)** 2022 and **(b)** 2023 Northwest Pacific TC best tracks at 6-h intervals. Times with missing MTCSWA data to derive \(R_{34 kt}^{Scat}\) are indicated by black symbols. We also compute the scatterometer-based \(R_{34 kt}^{Scat}\) and compare it with best-track R\({}_{34 kt}\). Figure 11 shows the comparison of R\({}_{34 kt}\) for the four categories. Again, a linear regression is applied: \(R_{34 kt}^{Scat}=cR_{34 kt}+d\). The regression coefficients (\(c\), \(d\)) for the above four groups are (0.411, 100.839 km), (0.206, 166.864 km), (0.709, 97.213 km), and (0.521, 149.350 km), respectively. The standard deviations of the regression function for the four groups are 55.927, 39.221, 52.441, and 48.176 km, respectively. Combining both relationships--\(R_{0}=aR_{34 kt}+b\) and \(R_{34 kt}^{Scat}=cR_{34 kt}+d\)-- gives a function \(R_{0}=a(R_{34 kt}^{Scat}-d)/c+b\). Figure 12 illustrates sample SLP profiles from Typhoons  
Figure 10: Scatter plots of \(R_{0}\) versus \(R_{34 kt}\) calculated from the best track data using Equation (2) for 2022 and 2023 Northwest Pacific tropical storms (gray cross), category 1 hurricanes (red cross), category 2 hurricanes (blue cross), and category 3 and above hurricanes (orange cross). The black solid line represents the best linear fitting line of \(R_{0}=aR_{34 kt}+b\) (Std = 55.065, 34.644, 25.996, and 21.710 km). The color convention is the same as in Figure 8.  
Figure 9: Scatter plots of sea level pressure at the radius of the outermost closed isobars (\(P_{\rm out}\)) and the sea level pressure at infinity (\(P_{\rm os}\)) for the 2022 and 2023 Northwest Pacific: (**a**) tropical storms (265 inverted triangles), (**b**) category 1 hurricanes (119 open circles), (**c**) category 2 hurricanes (81 squares), and (**d**) category 3 and above hurricanes (175 stars).