# Sensitivity of the Wave Field to High Time-Space Resolution Winds during a Tropical Cyclone

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Selected Event: Tropical Cyclone Isaac (2012)

#### 2.2. Model Configuration

#### 2.2.1. Hurricane Dynamic Atmospheric Model

#### 2.2.2. Waves Spectral Model

^{®}(WW3; [33]) is a third generation model operated by the National Oceanic and Atmospheric Administration (NOAA), together with the National Centers for Environmental Predictions (NCEP). The model WW3 describes the evolution of the wave directional spectrum based on the numerical solution of the spectral action balance equation. Most of the results analyzed here refer to a TC developed over deep waters. Under these conditions, the evolution of the directional spectrum is mainly controlled by three processes: the energy transfer between the atmosphere and the waves (wind input), the energy dissipation by deep water wave breaking (whitecapping) and the resonant quadruplet wave–wave interactions. This is treated in our model configuration using the ST6 package (see Table 3).

## 3. Results

#### 3.1. Characteristic Parameters of the TC

#### 3.1.1. Structure and Trajectory

#### 3.1.2. Fixed Observations

- (a)
- The determination coefficient,$${R}^{2}=\frac{{C}_{xy}}{{\sigma}_{x}{\sigma}_{y}},$$
- (b)
- The root mean squared error ($RMSE$),$$RMSE=\sqrt{\frac{1}{n}\sum _{i=1}^{n}{\left({y}_{i}-{x}_{i}\right)}^{2}},$$
- (c)
- Bias,$$S=\overline{y}-\overline{x},$$

#### 3.2. Effects of the Time Resolution of the Wind Field on the Wave Field

#### 3.2.1. Average Wind and $Hs$ Fields

#### 3.2.2. Mean Fields of Filtered Winds and the Corresponding Wind Waves

#### 3.2.3. Particular Case: Change from Tropical Storm to Hurricane

#### 3.3. Temporal Variability of the Wind and Significant Wave Height Fields

## 4. Discussion

## 5. Conclusions

- The wave field generated by the WaveWatch III model does not respond instantly to the variations in the wind field structure. More studies and specialized measurements are required to determine if the described behavior is either physically realistic, or is a deficiency of the wave model.
- The results indicate that the structure of the wave field is strongly determined by the extended fetch process, which leads to the occurrence of high waves over quadrants I and II of the storm. The high wave values over the frontal quadrant IV are related to a translation speed of the TC smaller than the group velocity of the waves generated in quadrants I and II.
- The wind field generated by parametric hurricanes successfully reproduces the wave field structure because the mean wind field has a tendency to produce a typical asymmetric spatial structure.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Spatial domains of the HWRF atmospheric model. The area covered by the pressure field indicates the extent of the fixed domain (D01), the black segmented line indicates the area covered by the second mobile domain (D02) and the red segmented line indicates the third mobile domain (D03).

**Figure 2.**(

**a**) Trajectory of hurricane Isaac reported by the NHC (solid black line) and the one obtained with the HWRF model (solid blue line). The colored dots represent the time of the simulation. The position of the NDBC buoys used here is denoted with triangle-shaped markers. (

**b**) Time series of the maximum sustained wind at 10 m, (

**c**) minimum pressure and (

**d**) translation speed of the TC. The blue dashed line in (

**b**) indicates the time at which the storm became a category 1 hurricane according to the model, whereas the date reported by the NHC is indicated with a gray dashed line. In (

**d**), the blue dashed line represents the fitting of the ${V}_{t}$ values computed by the HWRF.

**Figure 3.**Time evolution of ${U}_{10}$ and $Hs$ computed by HWRF and WW3 models, respectively, as well as the observations from the NDBC buoys 42001 (

**left panels**) and 42003 (

**right panels**).

**Figure 4.**Wind fields (

**left**) and mean significant wave height (

**right**) obtained with original data. ${U}_{10}$ (

**a**) and $Hs$ (

**b**) fields with an 18 h interval. Wind field (

**c**) and significant wave height (

**d**) for the moderate storm stage. Intensification stage for the wind field (

**e**) and significant wave height (

**f**).

**Figure 5.**Wind fields (

**left**) and mean significant wave height (

**right**) obtained with the 3 h running mean filtered data. ${U}_{10}$ (

**a**) and $Hs$ (

**b**) fields with an 18 h interval. Wind field (

**c**) and significant wave height (

**d**) for the moderate storm stage. Intensification stage for the wind field (

**e**) and significant wave height (

**f**).

**Figure 6.**Differences (in percentage) between the 97.5 percentile values of the $Hs$ calculated using the original winds minus those calculated using the filtered winds.

**Figure 7.**Average ${U}_{10}$ and $Hs$ fields for the 3 h period in which the storm reaches the category 1 hurricane stage. At the top panel, the wind (

**a**) and significant wave height (

**b**) average fields computed with the original data. At the lower panel, the wind (

**c**) and significant wave height (

**d**) average fields are computed with filtered data.

**Figure 8.**Evolution of the TC translation speed, and the wave’s average group velocity ($\u2329{C}_{g}\u232a$) using the original (light-blue solid line) and filtered results (light-blue dashed line).

**Figure 9.**Temporal variability of the wind field computed with the original (

**left**) and filtered (

**right**) data. The panel levels represent the 18 h scheme (

**top**), moderate storm (

**center**) and intensification (

**bottom**) stages. (

**a**) and (

**b**) show the average for the total period (18 h); (

**c**) and (

**d**) show the period of moderate storm (9 h), and (

**e**) and (

**f**) show the intensification period (9 h).

**Figure 10.**Temporal variability of the $Hs$ field computed with the original (

**left**) and filtered (

**right**) data. The panel levels represent the 18 h scheme (

**top**), moderate storm (

**center**) and intensification (

**bottom**) stages. (

**a**) and (

**b**) show the average for the total period (18 h); (

**c**) and (

**d**) show the period of moderate storm (9 h), and (

**e**) and (

**f**) show the intensification period (9 h).

**Figure 11.**Average temporal variability fields of ${U}_{10}$ (

**left**) and $Hs$ (

**right**) computed for the 3 h interval in which the storm becomes a category 1 hurricane. The top and bottom panels represent the results from the original (

**a**) and (

**b**) and filtered data (

**c**) and (

**d**), respectively.

**Table 1.**Characteristics of the grids used for the HWRF model configuration. The fixed grid is centered in the initial position of the tropical cyclone, whereas the mobile grids are centered in the instant position of the tropical cyclone eye.

Domain | Resolution | Grid |
---|---|---|

D01 | 80${}^{\circ}$ × 80${}^{\circ}$ (18 km) | Fixed |

D02 | 25${}^{\circ}$ × 25${}^{\circ}$ (6 km) | Mobile |

D03 | 8.3 ${}^{\circ}$ × 8.3${}^{\circ}$ (2 km) | Mobile |

Physical | Parameterization |
---|---|

Governing Equations | Primitive equations with non-hydrostatic option (NMM) |

Surface boundary layer | Geophysical Fluid Dynamics Laboratory (GFDL) [29] |

Cumulus parameterization | Simplified Arakawa–Schubert (SAS) [30,31] |

Microphysics | Ferrier–Aligo [32] |

Vortex tracking | Geophysical Fluid Dynamics Laboratory vortex tracker |

Vertical resolution | 61 vertical levels |

**Table 3.**Physical processes parameterizations and some resolution characteristics used in the implementation of the atmospheric model WW3 version 6.07 (ST6 according to the model nomenclature).

Physical | Parameterization |
---|---|

Wind input | Donelan et al. [34] |

Non-linear interactions | Discrete Interaction Approximation (DIA) |

Whitecapping | Rogers et al. [35], Zieger et al. [36] |

Microphysics | Ferrier–Aligo Ferrier [32] |

Resolution | |

Temporal resolution | 15 min |

Spatial resolution | 0.02${}^{\circ}$ |

Number of frequencies | 32 (0.0373–0.7159 Hz; $\Delta f/f=0.1$) |

Number of directions | 30 ($\Delta \theta $ = 12${}^{\circ}$) |

Maximum global time step | 180 s |

Maximum CFL time step for x-y | 60 s |

Maximum CFL time step for k-theta | 60 s |

Minimum source term time step | 15 s |

**Table 4.**Statistical validation for the wind intensity, ${U}_{10}$, and the significant wave height, $Hs$, computed by the models at the corresponding positions of the NDBC buoys 42001 and 42003.

Buoy | Variable | ${\mathit{R}}^{2}$ | $\mathit{RMSE}$ | S |
---|---|---|---|---|

42001 | ${U}_{10}$ [ms${}^{-1}$] | 0.75 | 0.98 | −0.22 |

$Hs$ [m] | 0.85 | 0.5 | 0.32 | |

42003 | ${U}_{10}$ [ms${}^{-1}$] | 0.2 | 5.4 | 3.2 |

$Hs$ [m] | 0.47 | 1.7 | 1.5 |

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## Share and Cite

**MDPI and ACS Style**

Pérez-Sampablo, L.; Osuna, P.; Esquivel-Trava, B.; Rascle, N.; Ocampo-Torres, F.J.
Sensitivity of the Wave Field to High Time-Space Resolution Winds during a Tropical Cyclone. *Oceans* **2023**, *4*, 92-113.
https://doi.org/10.3390/oceans4010008

**AMA Style**

Pérez-Sampablo L, Osuna P, Esquivel-Trava B, Rascle N, Ocampo-Torres FJ.
Sensitivity of the Wave Field to High Time-Space Resolution Winds during a Tropical Cyclone. *Oceans*. 2023; 4(1):92-113.
https://doi.org/10.3390/oceans4010008

**Chicago/Turabian Style**

Pérez-Sampablo, Laura, Pedro Osuna, Bernardo Esquivel-Trava, Nicolas Rascle, and Francisco J. Ocampo-Torres.
2023. "Sensitivity of the Wave Field to High Time-Space Resolution Winds during a Tropical Cyclone" *Oceans* 4, no. 1: 92-113.
https://doi.org/10.3390/oceans4010008