# Can We Improve Parametric Cyclonic Wind Fields Using Recent Satellite Remote Sensing Data?
## 4 Performance of Parametric Wind Models  
Using the assumptions made in the previous section, we compute the bias in the various parametric models as a function of storm intensity, distance to the cyclone center, and calibration method (using only radii at 34-kt, only radii at 64-kt, and all radius information). The results are shown in Figures 3 and 4. Blue colors correspond here to small biases (in absolute value), and thus suggest that the parametric model should work well for the intensity/distance class considered. Conversely, red colors suggest that the model will perform poorly. First of all, it appears that the bias is significantly reduced in almost all cases when constraining the parametric models by R64, R50, and R34. This suggests that not only the \"mean\" parametric wind values computed in Section 3 are consistent with the CYGNSS/ASCAT data: Almost all of the parametric models, taken individually, are also consistent, as long as they are constrained by the observations (i.e., the 64-kt, 50-kt, and 34-kt wind radii given by the NHC). This finding further validates the assumptions made in Section 3. One notable exception arises for radii between R64 and R50 for category 1 cyclones, for which the biases amount to 5 m/s or more in absolute value for most gradient wind profiles, even when constraining the wind fields with all the wind radius information. This suggests that the remote sensing data considered here as a proxy for wind speeds may be less accurate in this particular case. Referring back to Figure 2, CYGNSS products are seen to give negative biases similar to ASCAT for this radius/intensity class. Since ASCAT is expected to underestimate wind speeds for values larger than about 17 m/s [48], CYGNSS data can also be expected to do so in this case. Figure 3: Diagrams displaying the bias between various parametric models and the surface wind speeds estimated by CYGNSS/ASCAT data for all the events considered here, as a function of storm intensity and distance to the cyclone center, as well as calibration method (using all radius information, or only radii at 64-kt and 34-kt, for the left, middle and right panels, respectively). The color bar shows the absolute bias. The values are displayed for each category/distance cell. The black contours indicate the category/distance classes for which we consider E11 or H80 to build the E11H80 model in Section 5. The strengths and weaknesses of each parametric formula can be investigated using the results shown in Figures 3 and 4. For example:  
* The inner region solution of [PERSON] and [PERSON] [36], E11, gives relatively small biases (hence, good results) close to the storm center, especially for intense and well defined cyclones. It is also found to underestimate wind speeds far from the center when constrained only by R64, as found in [PERSON] and [PERSON] [17]. E04 performs better for the outer region, but poorly near the center. E11 and E04 can thus be merged to develop a complete TC radial wind structure as proposed by [PERSON] et al. [49];
* when solely constrained by radii close to the cyclone center (here R64), the Holland profile (H80) underestimates the winds in the outer region, as noted by [PERSON] and [PERSON] [34]. This can  
Figure 4: Same as Figure 3, for four additional parametric models: H80c, J92, M16, and W06. The black contours indicate the model we consider for each category/distance class to build the M16b model (Section 5). also lead to broad wind maxima, and thus wind overestimations several dozens of kilometers from the center for strong cyclones, as can be seen also in Figure 3.
* J92 gives significantly higher wind speeds far from the center compared to most of the other parametric formulas, when constrained by R64 only. This is consistent with the findings of [PERSON] and [PERSON] [17].