# Can We Improve Parametric Cyclonic Wind Fields Using Recent Satellite Remote Sensing Data?

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## Abstract

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## 1. Introduction

- Validations of parametric wind models are generally performed using a limited number of “ground-truth” data. In-situ observations of surface wind speeds are relatively sparse for TCs, as they spend most of their lifetime over the oceans, where the density of buoys able to record extreme winds is relatively small. Besides, the wind recorded by meteorological stations can be biased because of terrestrial effects, which makes it difficult to compare observations with parametric values in a consistent way. Although these issues are offset to some extent in the North Atlantic and East Pacific thanks to aircraft reconnaissance, it remains a major problem in all oceanic basins;
- new proposed parametric models are generally compared with a limited number of existing gradient wind profiles. Except the work of Lin and Chavas [17], we are not aware of any study investigating parametric wind models over a wide range of parameters and methods. New proposed models are often compared to the Holland [33] or Jelesnianski and Taylor [35] approaches to assess their quality, and disregard more recent models, such as Willoughby et al. [38] or Emanuel and Rotunno [36]. It is thus difficult to assert that these new models really perform better than all existing approaches;
- new proposed parametric models are generally tested without considering all the available information on TC wind structure. As noted above, very few studies take into account all the available information about wind structure, such as the 34-kt, 50-kt, and 64-kt wind radii for each quadrant. Most of the time, only the radius of maximum winds or the hurricane-force (i.e., 64-kt) wind radii are used, which can potentially result in errors far from the cyclone center. It is thus unclear whether the discrepancies between the model and the observed data are due to the model itself, or to the fact that the model is not sufficiently constrained by available information (such as the 34-kt, 50-kt, and 64-kt wind radii); and
- some of the parameters used in parametric wind models are not always clearly specified. For example, the surface wind reduction factor (SWRF [39]), i.e., the empirical ratio between the surface and the top of the boundary layer, is rarely indicated, although it generally plays a significant role in the estimated parametric wind speeds [17].

## 2. Data and Methods

#### 2.1. CyclonesSelection

#### 2.2. Remote Sensing Data

- The “wind speed” (ws) product is derived from the best fit to both the normalized bistatic radar cross-section (NBRCS) and leading edge slope (LES) of the integrated delay waveform given by the delay-Doppler maps (DDM [42]), using the geophysical model function (GMF) appropriate for fully developed seas;
- the “yslf_les_wind_speed” (les) wind product is derived from only the LES of the DDM, using a young seas/limited-fetch GMF; and
- the “yslf_nbrcs_wind_speed” (nbrc) product is derived from only the NBRCS, using the young seas/limited-fetch GMF.

#### 2.3. Parametric Wind Models

- From the NHC advisories, the surface background wind relative to the cyclone translation velocity is estimated at the time of acquisition of the CYGNSS/ASCAT data point under consideration. Following the approach of Lin and Chavas [17], we assume that this wind is decelerated by a factor of α = 0.56 and rotated counter-clockwise by an angle of β = 19.2° from the free tropospheric wind.
- The translational portion of the wind speed is removed from the maximum observed wind velocity and the 34-, 50-, and 64-kt winds.
- Surface velocities given by the NHC are converted to velocities at the top of the atmospheric boundary layer by applying an empirical surface wind reduction factor, SWRF [39]. In the following sections, we use SWRF = 0.9. Other values were tested, but they did not change the conclusions of this paper. For the sake of brevity, these results are not presented here.
- The radii of maximum winds are estimated for the four quadrants, using the chosen parametric gradient wind profile, and the available wind radii information. For each quadrant, up to three radii of maximum winds are thus obtained: One estimated using the 64-kt wind radius (R
_{m}_{64}), another one from the 50-kt wind radius (R_{m}_{50}), and a third from the 34-kt wind radius (R_{m}_{34}). - Depending on the case, R
_{m}_{64}, R_{m}_{34}, or all the radii of maximum winds (R_{m}_{64}, R_{m}_{50}, and R_{m}_{34}) are computed for the data point azimuth, using a spline interpolation. - The parametric wind speed value at the CYGNSS/ASCAT data point is computed using the chosen parametric gradient wind profile. This step is straightforward if a single radius of maximum winds is considered. In the case where all the radii of maximum winds (R
_{m}_{64}, R_{m}_{50,}and R_{m}_{34}) are considered, the parametric wind speed is computed using a linear weighting approach similar to the one proposed by Hu et al. [45]. For example, for a CYGNSS/ASCAT point located at a distance, r, from the cyclone center larger than the 64-kt wind radius (r64), but lower than the 50-kt wind radius (r50), we:- (a) Compute V
_{Rm}_{64}, the parametric wind speed at the CYGNSS/ASCAT data point location obtained using R_{m}_{64}; - (b) compute V
_{Rm}_{50}, the parametric wind speed at the CYGNSS/ASCAT data point location obtained using R_{m}_{50}; and - (c) compute the final parametric wind speed, V, using the following equation:$$V=\frac{{V}_{Rm50}-{V}_{Rm64}}{r50-r64}\left(r-r64\right)+{V}_{Rm64}$$

This approach ensures that all the wind radii information are satisfied. - The velocity, V, is multiplied by SWRF to obtain the parametric wind speed at the surface.
- The wind speed obtained in the previous step is combined with the surface background wind computed in step 1 to get the final parametric wind speed at the CYGNSS/ASCAT data point considered.

#### 2.4. Methodology

- 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.

## 3. Comparison of CYGNSS and ASCAT Data

- ASCAT performs well for r > R34;
- ASCAT also performs well for R34 < r < R50 and category 3/5 cyclones (this product shows the lowest biases in these cases);
- none of the space-borne products tested here are reliable for smaller radii than R64 in the case of category 1 cyclones. We will not investigate these conditions in the next sections; and

## 4. Performance of Parametric Wind Models

- The inner region solution of Emanuel and Rotunno [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 Lin and Chavas [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 Chavas 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 Willoughby and Rahn [34]. This can 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 Lin and Chavas [17]. Our results suggest, however, that these wind speeds are generally not overestimated, and might better represent the wind decay as a function of the radius compared to other formulas;
- the results are generally much better when considering a family of profiles with two characteristic lengths, as proposed by Willoughby et al. [38]. For example, as stated above, the performance of the Holland model, H80, is significantly improved when both radii at 34-kt and 64-kt are prescribed; and

## 5. Comparison with In-Situ Oceanic Data

- Astronomic tidal potential over the whole domain (12 constituents);
- 26 tidal harmonic constituents at the open boundaries, provided by the global FES2012 model [51];
- parametric pressure fields [33]; and
- parametric winds blended with CFSR (Climate Forecast System Reanalysis [52]) wind data. The parametric winds are prescribed for smaller radii than R34, whereas CFSR data are imposed for r > 1.5 R34. In between, a smooth transition is ensured using a weighing coefficient, which varies linearly with radius r.

- E11 and H80, constrained using the 64-kt wind radii only (E11(R64) and H80(R64) in Figure 6);
- E11 and H80, constrained using all the wind radii information (E11(All) and H80(All) in Figure 6);
- E11H80, for which we choose to blend the wind speeds inferred from E11 for the inner core region with those given by H80 for the outer region (see the black contours in Figure 3); and
- M16b, a blend between wind speeds obtained from M16 constrained by R64 only and with all wind radii information (see black contours in Figure 4).

- H80 and E11 constrained only by the 64-kt wind radius (R64) give the worst results, with Hs generally significantly underestimated, and NRMS ranging between 20% and 50% (Table 3). This is consistent with the results of Figure 3 and Figure 4, which show large negative biases for H80 and E11 in the case of category 4–5 cyclones and wider radii than R64;
- constraining all the 34-kt, 50-kt, and 64-kt wind radii (All) results in better performance for E11, with reduced bias and NRMS (15% to 22% approximately), although significant wave heights are now overestimated. This is again consistent with the findings of Figure 3, which shows a positive bias at all radii for category 4 and 5 events;
- H80 constrained by all wind-radii information strongly overestimates Hs when Maria is closest to the storm. This is also consistent with the results of Figure 3 (and the findings of Willoughby and Rahn [34]), which show that H80 tends to overestimate wind speeds close to the center of strong (category 4–5) cyclones. The prediction is better when Maria moves further away, which is also expected and
- the best results are obtained for E11H80 and M16b, the two parametric models built to minimize the biases. NRMS values of the order of 9%–20% are obtained for significant wave heights, which is a good score considering the cyclone asymmetry due to the complexity of the area, characterized by a number of mountainous islands separated by just a few dozen kilometers.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Bias between the remote sensing data and the parametric winds averaged over all empirical models. Negative (resp. positive) values indicate that remote sensing data display lower (resp. higher) wind speeds compared to the mean parametric winds. Different categories of distance to the cyclone center (r) and cyclone intensities are considered. TS stands for tropical storms, H1, H2, H3, H4, and H5 to the Saffir-Simpson hurricane category (Cat 1, 2, 3, 4, and 5, respectively). R34, R50, and R64 are the radii for the 34-kt, 50-kt, and 64-kt winds. ws, nbrc, and les are three different CYGNSS products (see Section 2). The stars indicate which product has been selected as proxy for wind speeds in Section 4 and Section 5. The red box/cross shows the intensity/category class for which CYGNSS/ASCAT data are not expected to give adequate information about wind speeds.

**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.

**Figure 5.**Study area. The computational domain is depicted with the dashed red contour. The dashed white line represents the track of hurricane Maria. The location of the buoys used for comparison is given in the upper-right corner box. H3, H4, and H5 represent the Saffir-Simpson category of hurricane Maria along its trajectory.

**Figure 6.**Significant wave height time series for different parametric models. “R64” denotes a model constrained only by the 64-kt wind radius. “ALL” indicates a model constrained with all the available information (34-kt, 50-kt, and 64-kt wind radii). E11H80 corresponds to a blend of the model E11 (for the inner core region) and H80 (for the outer region). M16b is the result of a blend between wind speeds obtained from M16 constrained by R64 only and with all wind radii information. Results for Fort-de-France, 42060, and the Sainte-Lucie station are displayed in the upper, middle, and lower panels, respectively.

**Table 1.**List and characteristics of the 16 hurricanes considered in this study. The minimum and maximum radii at 34-kt, 50-kt, and 64-kts (R34, R50, and R64, respectively) are given in nautical miles at the time of peak intensity. WS stands for wind speed. The data sources are the best tracks provided by the National Hurricane Center (NHC).

Number | Name | Basin | Dates (Year 2017) | TCCategory (Max WS) | Min/Max R34 | Min/Max R50 | Min/Max R64 |
---|---|---|---|---|---|---|---|

1 | Dora | EP | 25/06 → 28/06 | 1 (80 kt) | 40/70 | 20/40 | 15/25 |

2 | Eugene | EP | 07/07 → 10/07 | 3 (100 kt) | 60/110 | 40/80 | 20/30 |

3 | Franklin | ATL | 07/08 → 10/08 | 1 (75 kt) | 60/130 | 30/50 | NA/30 |

4 | Gert | ATL | 13/08 → 17/08 | 2 (90 kt) | 50/120 | 15/60 | NA/30 |

5 | Harvey | ATL | 17/08 → 30/08 | 4 (115 kt) | 70/120 | 40/60 | 20/35 |

6 | Hilary | EP | 24/08 → 30/08 | 2 (90 kt) | 60/90 | 30/50 | 15/20 |

7 | Irma | ATL | 30/08 → 11/09 | 5 (160 kt) | 80/160 | 50/100 | 30/45 |

8 | Irwin | EP | 23/07 → 01/08 | 1 (80 kt) | 30/60 | 10/30 | NA/15 |

9 | Jose | ATL | 05/09 → 22/09 | 4 (135 kt) | 50/120 | 30/50 | 20/30 |

10 | Katia | ATL | 06/09 → 09/09 | 2 (90 kt) | 60/60 | 20/40 | 15/20 |

11 | Kenneth | EP | 19/08 → 23/08 | 4 (115 kt) | 60/90 | 30/50 | 15/25 |

12 | Lee | ATL | 16/09 → 30/09 | 3 (100 kt) | 60/80 | 40/50 | 25/30 |

13 | Maria | ATL | 16/09 → 30/09 | 5 (150 kt) | 100/150 | 60/80 | 35/50 |

14 | Max | EP | 13/09 → 15/09 | 1 (70 kt) | 30/40 | 20/20 | 10/10 |

15 | Norma | EP | 14/09 → 19/09 | 1 (65 kt) | 70/80 | 30/50 | NA/25 |

16 | Otis | EP | 16/09 → 19/09 | 3 (100 kt) | 40/60 | 20/40 | 10/20 |

**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 α = 0.56 and rotated counter-clockwise by an angle of β = 19.2°, according to the findings of Lin and Chavas [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.

Name | Main Reference | Formula |
---|---|---|

E11 | Emanuel and Rotunno [36] | $V\left(r\right)=\frac{2r\left({R}_{m}{V}_{m}+0.5f{R}_{m}^{2}\right)}{{R}_{m}^{2}+{r}^{2}}-\frac{fr}{2}$ |

E04 | Emanuel [46] | $V\left(r\right)={V}_{m}\frac{{R}_{0-r}}{{R}_{0}-{R}_{m}}{\left(\frac{r}{{R}_{m}}\right)}^{m}{\left(\frac{\left(1+b\right)\left(n+m\right)}{n+m{\left(\frac{r}{{R}_{m}}\right)}^{2\left(n+m\right)}}+\frac{b\left(1+2m\right)}{1+2m{\left(\frac{r}{{R}_{m}}\right)}^{2m+1}}\right)}^{0.5}$ with b = 0.25, m = 1.6, n = 0.9, R _{0} = 420 km |

J92 | Jelesnianski et al. [47] | $V\left(r\right)=\frac{2r{R}_{m}{V}_{m}}{{R}_{m}^{2}+{r}^{2}}$ |

H80 | Holland [33] | $V\left(r\right)=\sqrt{{\left(\frac{{R}_{m}}{r}\right)}^{B}\frac{B\u2206Pexp\left(-{\left(\frac{{R}_{m}}{r}\right)}^{B}\right)}{\rho}+\frac{{r}^{2}{f}^{2}}{4}}-\frac{fr}{2}$ with $B=\frac{{V}_{m}^{2}e\rho +f{V}_{m}{R}_{m}e\rho}{\u2206P}$, $\rho =1.15$, $e=\mathrm{exp}\left(1\right)$ |

H80c | Holland [33] with cyclostrophic approximation | $V\left(r\right)=\sqrt{{\left(\frac{{R}_{m}}{r}\right)}^{B}\frac{B\u2206Pexp\left(-{\left(\frac{{R}_{m}}{r}\right)}^{B}\right)}{\rho}}$ with $B=\frac{{V}_{m}^{2}e\rho}{\u2206P}$, $\rho =1.15$, $e=\mathrm{exp}\left(1\right)$ |

M16 | Murty et al. [37] | $V\left(r\right)={V}_{m}{\left(\frac{2r{R}_{m}}{\left({R}_{m}^{2}+{r}^{2}\right)}\right)}^{n}$ with $n=3/5$ |

W06 | Willoughby et al. [38] | For $0\le r\le {R}_{m}$: $V\left(r\right)={V}_{m}{\left(\frac{r}{{R}_{m}}\right)}^{n}$ with $n=0.79$ For $r\ge {R}_{m}$:$V\left(r\right)={V}_{m}exp\left(-\frac{r-{R}_{m}}{X}\right)$ with $X=243\mathrm{km}$ |

**Table 3.**Bias, root mean square error (RMS), and RMS normalized by the mean observed values (NRMS) obtained when comparing numerical simulations with in-situ significant wave heights.

Fort de France | St Lucie | 42060 | ||
---|---|---|---|---|

H80 (R64) | Bias | −0.74 m | −0.40 m | −1.18 m |

RMS | 0.81 m | 0.52 m | 1.29 m | |

NRMS | 37% | 23% | 30% | |

H80 (All) | Bias | 1.11 m | 0.83 m | 0.44 m |

RMS | 1.24 m | 1.03 m | 0.64 m | |

NRMS | 57% | 45% | 15% | |

E11 (R64) | Bias | −0.71 m | −0.38 m | −1.14 m |

RMS | 0.77 m | 0.50 m | 1.23 m | |

NRMS | 36% | 22% | 28% | |

E11 (All) | Bias | 0.62 m | 0.38 m | 0.13 m |

RMS | 0.72 m | 0.65 m | 0.56 m | |

NRMS | 33% | 29% | 13% | |

E11H80 | Bias | −0.04 m | 0.02 m | −0.64 m |

RMS | 0.41 m | 0.46 m | 0.75 m | |

NRMS | 19% | 20% | 17% | |

M16b | Bias | 0.06 m | −0.06 m | −0.28 m |

RMS | 0.25 m | 0.40 m | 0.40 m | |

NRMS | 11.5% | 17.4% | 9.1% |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Krien, Y.; Arnaud, G.; Cécé, R.; Ruf, C.; Belmadani, A.; Khan, J.; Bernard, D.; Islam, A.K.M.S.; Durand, F.; Testut, L.;
et al. Can We Improve Parametric Cyclonic Wind Fields Using Recent Satellite Remote Sensing Data? *Remote Sens.* **2018**, *10*, 1963.
https://doi.org/10.3390/rs10121963

**AMA Style**

Krien Y, Arnaud G, Cécé R, Ruf C, Belmadani A, Khan J, Bernard D, Islam AKMS, Durand F, Testut L,
et al. Can We Improve Parametric Cyclonic Wind Fields Using Recent Satellite Remote Sensing Data? *Remote Sensing*. 2018; 10(12):1963.
https://doi.org/10.3390/rs10121963

**Chicago/Turabian Style**

Krien, Yann, Gaël Arnaud, Raphaël Cécé, Chris Ruf, Ali Belmadani, Jamal Khan, Didier Bernard, A.K.M.S. Islam, Fabien Durand, Laurent Testut,
and et al. 2018. "Can We Improve Parametric Cyclonic Wind Fields Using Recent Satellite Remote Sensing Data?" *Remote Sensing* 10, no. 12: 1963.
https://doi.org/10.3390/rs10121963