# Can We Improve Parametric Cyclonic Wind Fields Using Recent Satellite Remote Sensing Data?
## Data and Methods
### Methodology  
The methodology adopted in this study is summarized in the flowchart given in Figure 1. Three main steps are involved:  
* First, the biases between CYGNSS/ASCAT data and wind speeds inferred from the ensemble mean parametric winds (i.e., averaged over all formulas) are computed for different cyclone categories and distances to the center, to identify the cases for which CYGNSS and/or ASCAT could be good proxies for wind speeds. Due to the relatively large number of independent parametric formulations we consider (seven), individual errors are indeed expected to be trimmed down in such an ensemble mean.
* Second, based on assumptions about CYGNSS/ASCAT data, the biases of individual parametric models are computed to check whether our hypotheses enable reproduction of the findings of previous studies in terms of performance for wind gradient profiles.
* Third, we investigate whether our assumptions about CYGNSS/ASCAT data allow for identification of relevant parametric models for a specific case study: The category 5 hurricane Maria.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Main Reference** & **Formula** \\ \hline E11 & [PERSON] and [PERSON] [36] & \(V(r)=\frac{2r\left(R_{m}V_{m}+0.5 fK_{m}^{2}\right)}{R_{m}^{2}+r^{2}}-\frac{fr} {2}\) \\ \hline E04 & [PERSON] [46] & \(V(r)=V_{m}\frac{R_{m}\cdot r}{R_{0}-R_{m}}\left(\frac{r}{R_{m}}\right)^{m} \left(\frac{(1+b)(n+m)}{n+m\left(\frac{r}{R_{m}}\right)^{2(n+m)}}+\frac{b(1+2m )}{1+2m\left(\frac{r}{R_{m}}\right)^{2n+1}}\right)^{0.5}\) \\  & with \(b=0.25\), \(m=1.6\), \(n=0.9\), \(R_{0}=420\) km \\ \hline [PERSON] & [PERSON] et al. [47] & \(V(r)=\frac{2 rR_{m}V_{m}}{R_{m}^{2}+r^{2}}\) \\ \hline H80 & Holland [33] & \(V(r)=\sqrt{\left(\frac{R_{m}}{r}\right)^{\beta}\frac{B\Delta Pexp\left(- \left(\frac{R_{m}}{r}\right)^{\beta}\right)}{\rho}+\frac{r^{2}\rho}{4}}-\frac {fr}{2}\) \\  & with \(B=\frac{V_{m}^{2}\rho+fV_{m}R_{m}\rho}{\Delta P}\), \(\rho=1.15\), \(e=\exp(1)\) \\ \hline H80c & Holland [33] with cyclostrophic approximation & \(V(r)=\sqrt{\left(\frac{R_{m}}{r}\right)^{B}\frac{B\Delta Pexp\left(-\left( \frac{R_{m}}{r}\right)^{\delta}\right)}{\rho}}\) \\  & with \(B=\frac{V_{m}^{2}exp}{\Delta P}\), \(\rho=1.15\), \(e=\exp(1)\) \\ \hline M16 & [PERSON] et al. [37] & \(V(r)=V_{m}\left(\frac{2 rR_{m}}{(R_{m}^{2}+r^{2})}\right)^{n}\) with \(n=3/5\) \\ \hline W06 & [PERSON] et al. [38] & For \(0\leq r\leq R_{m}\): \(V(r)=V_{m}\left(\frac{r}{R_{m}}\right)^{n}\) with \(n=0.79\) \\  & & For \(r\geq R_{m}\):\(V(r)=V_{m}exp\left(-\frac{r-R_{m}}{X}\right)\) with \(X=243\) km \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parametric wind models considered in this study. For all of them, an empirical surface wind reduction factor [39], SWRF = 0.9, is used. Comparisons are only made for data within a distance of 200 km from the cyclone center. The translation vector is reduced by a factor of \(\alpha\) = 0.56 and rotated counter-clockwise by an angle of \(\beta\) = 19.2\({}^{\circ}\), according to the findings of [PERSON] and [PERSON] [17]. Here, \(V_{m}\) and \(R_{m}\) are the maximum wind speed and the radius of maximum winds. \(r\) refers to the distance to the TC center, and \(f\) to the Coriolis parameter.