^{1}

^{*}

^{2}

In this study the effect of the surface waves over sea surface roughness (
z
_{0}) and drag coefficient (
C_{D}) is investigated by combining an ocean wave model and a simplified algorithm, which estimates
z
_{0} and
C_{D} with and without dependence on the sea state. This investigation was possible from several numerical simulations with the Wave-Watch-III (WW3) model for complex wind conditions. The numerical experiments were performed for idealized like-hurricanes with different translation speed (0, 5 and 10 m/s) and maximum wind speed (MWS) at the centre (35, 45 and 55 m/s). It is observed that
z
_{0} and
C_{D} are strongly dependent on the sea state, via substantial modification in Charnock parameterization (
z_{ch}). As the hurricane translation speed increases more discrepancies in
z
_{0} and
C_{D} are observed in opposite quadrants around the region of MWS. As for instance, higher, longer and older (or more developed) waves, located in the front-right quadrant, produce lower values of
z
_{0} and
C_{D}. In the rear-left quadrant, where the waves are lower, shorter and younger (or less developed), higher values of
z
_{0} and
C_{D} are observed. In addition the difference between values on opposite quadrants increases as the hurricane intensity increases, showing the hurricane intensification dependence. Interesting aspects are observed in scatter plotting wave age versus Charnock coefficient. It is also observed that
z_{ch}, which has a constant value of 0.0185, is modified by the sea state, where young waves produce higher values of
z_{ch}, while old waves are related to lower values of
z_{ch} when compared with
z_{ch} without dependence on sea state.

Ocean surface gravity waves are one manifestation of the interaction between the atmosphere and the ocean, which can have a significant impact on the transfer of momentum and enthalpy (heat) across the atmosphere- ocean interface [_{0}) is expressed in terms of the friction velocity (u_{*}), acceleration due to gravity (g), and a constant (z_{ch}), which is representative of an equilibrium sea. The parameter z_{ch} was based on measures from moderate to weak wind regimes (winds below 25 m/s). However, both observation and numerical modeling studies have indicated that the surface stress is also related to the sea state, in other words, it is dependent of the wind wave spectrum.

The presence of the waves cause significant changes in surface stress that influences directly or indirectly the planetary boundary layer over the oceans [

[_{10} and sea wave high (SWH). The authors pointed out that the increased friction in the region of intense air-sea interaction is the dominant feature of the two-way coupling that consequently produces a storm with diminished strength.

To evaluate the effect of surface waves on air-sea momentum flux over mature and growing seas [_{D}) and u_{*}. In cases of mature sea, their results showed that the Charnock coefficient is estimated to be about 0.01 - 0.02 and the drag coefficient increases as wind speed increases. With growing seas, for uniform winds less than 30 m/s, the drag coefficient is larger for younger seas, which agrees with previous theoretical and observational studies. However, for wind speed higher than 30 m/s their results show a different trend: very young waves yield less drag and drag increases as waves become older.

[_{D} strongly depends on the wave field. Moreover, hurricane intensity and translation speed are major factors that determine the spatial distribution of C_{D}. At strong winds above 30 m/s, the combined models predict significant reduction of C_{D} as the wind speed enhance.

[_{D}, u_{*}, z_{0}, and U_{10} in cases of Charnock and Smith relations (see Part I).

The main results of Part I showed that when the ocean is characterized by young waves, both z_{0} and C_{D} increases while U_{10} decreases. For old waves C_{D}, z_{0}, and U_{10} behave as in Charnock relation. Further, in cases of winds higher than 25 m/s C_{D} was higher to young waves than to old waves. For winds bellow 25 m/s there is a week tendency to a reduction of C_{D} for young waves. In the present study it is investigated the impact of the waves on the sea surface roughness length under hurricane wind conditions. Thus WW3 numerical model is combined in a one-way mode with a simple algorithm (Part I) to estimate C_{D}, u_{*}, z_{0}, and U_{10} under idealized hurricane wind conditions. A brief outline of the WW3, simplified algorithm, experimental design, and method used to investigate the impact of waves on sea surface roughness length under extreme wind conditions is introduced in Section 2. Section 3 describes results of the experiments with translation speed and intensity of the hurricane. The summary and conclusions are given in Section 4.

Results from theoretical and numerical modeling studies have shown that z_{0} (C_{D} or u_{*}) is a function of a single parameter called wave age defined as c_{p}/u_{*}, where c_{p} is the phase speed of the spectral peak frequency and u_{*} is the friction velocity. The wave age indicates the stage of wave development because the phase speed c_{p} increases progressively during wave growth [

To evaluate the impact of the waves on the sea surface roughness length it is used the WW3 numerical model joined with a very simple algorithm, which estimates C_{D}, u_{*}, z_{0}, and U_{10}, in one-way mode (not coupled). More detail about the WW3 and the simplified algorithm is given in Part I. The algorithm computes the surface parameters in two ways; in the first, no dependence with sea state is considered and the Charnock constant is used (z_{ch} = 0.0185). In the second, sea surface roughness length is dependent on the sea state and wave age takes the place of Charnock constant.

Momentum, heat, and moisture fluxes in the atmospheric boundary layer over the oceans are directly related to C_{D}. In the conventional theory of the boundary layer C_{D} is connected with surface roughness length, which is typically defined by Charnock relationship [_{*} and g,

Following [_{0} and the sea state can be expressed by two distinct forms: in terms of wave age dependence [

where _{w} denote, respectively, total stress and stress due to the presence of the waves. Results from [

At the frequency peak (f_{p}), c_{p} is computed according to the dispersion relation of the gravity wave,

where ω is the angular frequency and K is the wave number.

To evaluate the effect of hurricane translation speed (HTS) and its intensity, numerical simulations with WW3 model were designed (

The WW3 model runs for 72 hours from the rest (sea without waves) with time step and input wind speed of 1800 s, 24 directions (directional resolution), spatial resolution of 0.2˚ × 0.2˚, and 4000 meters depth. It extends 3000 km in the south-north direction and 1500 km in the east-west extent. The model grid is spatially regular on latitude-longitude grid.

In the following discussion, the results of all numerical experiments are presented after a spinup time of 56 hours, when a quasi steady state is achieved.

Exp name | Storm type | HTS (m/s) | Max wind speed (m/s) |
---|---|---|---|

Stationary | 0 | ||

Exp (A, B, C) | Typical speed | 5 | (35, 45, 55) |

Fast-moving | 10 |

Spatial distribution of SWH for different HTS produced by idealized experiments is shown in Figures 2(a)-(c). It can be seen that as the HTS increases, SWH in the front-right quadrant of the storm track become higher and longer, while those in the opposite quadrant become lower and shorter. [

Distributions of the input wave age representing the state of the growth of wind waves relative to local wind forcing are presented in

Figures 2(g)-(i) show that as HTS increases waves become lower, shorter, younger and rougher (high values of z_{0}) in the rear-left quadrant, whereas in the front-right quadrant z_{0} decreases. These results agree with observational and modeling studies, which show a strong inverse dependence between z_{0} and wave age. This means that, young waves produce rougher surface then older waves. The results show that the effect of waves on z_{0} values is more pronounced during developing sea. However, [_{0}, instead.

For stationary idealized tropical storm the values of C_{D} (Figures 2(j)-(l)) decrease symmetric and concentrically from the centre of the hurricane to its periphery. As the HTS increases, C_{D} also increases in the rear-left quadrant where waves are shorter, younger, and rougher. In this case, the spatial pattern suffers substantial modifications becoming more asymmetric. In the front-right quadrant, where waves are higher, longer, and older, C_{D} becomes lower than in the opposite quadrant. This asymmetric spatial pattern of C_{D} causes a no uniform hurricane wind velocity distribution (Figures 2(m)-(o)). It can be seen that wind speed (U_{10}) suffers a significantly reduction where waves are younger and rougher, while in the front-right quadrant, where waves are higher, longer, and older, U_{10 }experiences just slightly changes.

As the phase velocity of the waves become similar or near the HTS, winds act on surfaces with higher waves, unlike in the opposite quadrant. Other variables are sensible to those wind velocity differences, as for instance; wave age, z_{0}, C_{D}, U_{10} and u_{*}. Differences in those values cause spatial asymmetries in the structure of the atmospheric system at the surface, see Figures 2(a)-(o). As can be seen, from Figures 2(g)-(l), z_{0} and C_{D} suffers expressively modifications in its spatial pattern due to the asymmetry of the SWH. Higher values of those two quantities must cause a decrease in the moisture and mass convergence via diminishing the magnitude of the wind. The decrease in the magnitude of the wind, near surface, substantially, modifies the entire structure of the storm at surface [_{0} and U_{10}.

_{D} and z_{0} as function of the wave ages, as estimated from the idealized tropical storm experiments with different translation speeds and centre of maximum velocity, for all grid points. The results are color coded according to HTS at each grid point. For C_{D} (Figures 3(a)-(c)) the figure clearly shows that most of the increased C_{D} values are found in young waves (wave age less than 15) with maximum velocity at the centre of 55 m/s. In wave ages ranging from 15 to 35 the decrease of C_{D} with the increase of the wave age is less pronounced. In fact, for wave ages higher than 35, the values of C_{D} present a different trend, i.e. for wave age higher than 35 the values of C_{D} become slightly constant. This means that, in cases of young waves the sea acts more vigorously on C_{D} (and on z_{0}) than do old waves. This pattern can be more accentuated in cases of most intense storms, as observed in Figures 3(a)-(c). In fact, in cases of young waves, as the intensity of the hurricane increases C_{D} also increases. For example, we have a no dimensional value of C_{D} equal to 9 × 10^{−3} (6.8 × 10^{−3}) for wave age value of 5, in the case of MWS of 55 (35) m/s (_{D} is larger for young sea (wave age less than 15) than for old sea (wave age higher than 15). However, [_{D} decreases. Similar and interesting results are found in the case of z_{0} versus wave age (Figures 3(d)-(f)). Until the wave age threshold limit of 15, sea surface roughness length decreases as the waves become older. Above the threshold of 15 (old waves) it seems that the waves do not affect z_{0}, once its values hold constant with wave age. This result resembles to the behavior of the constant Charnock parameter (Part I).

In _{ch} is plotted against wave ages at all grid points as in _{ch}, for different MWS at the hurricane centre, is set in perspective with wave ages. Interesting aspects can be observed. Its well know that z_{ch} in the bulk parameterization is equal to 0.0185, which is used in most atmospheric numerical models. However, for MWS at the hurricane centre of 35 m/s (_{ch} undergoes modifications for different wave stages. In fact, young waves produce higher values of z_{ch} while old waves is related to lower values of z_{ch}. Moreover, it can be

0 m/s (35 m/s) | 5 m/s (35 m/s) | 10 m/s (35 m/s) | 0 m/s (45 m/s) | 5 m/s (45 m/s) | 10 m/s (45 m/s) | 0 m/s (55 m/s) | 5 m/s (55 m/s) | 10 m/s (55 m/s) | |
---|---|---|---|---|---|---|---|---|---|

H_{SIG} | 8.3/8.8 | 7.3/12 | 7.8/13.1 | 16.3/16.3 | 13.8/19 | 11.9/23 | 22/22 | 19.4/27.3 | 17.4/33.5 |

WA | 10.1/9.1 | 9/11.7 | 9/14.3 | 8.9/8.2 | 7.7/9.7 | 7.6/11.7 | 7.3/6.8 | 6.6/8 | 6.3/9 |

z_{0 } | 13.6/17.6 | 17/14.4 | 15/11.2 | 33.3/40.6 | 41.3/35.6 | 38.9/28.3 | 75.3/89 | 88.7/77.7 | 86/66 |

C_{D } | 3.7/3.9 | 4/3.7 | 3.8/3.4 | 4.9/5.3 | 5.3/5 | 5.2/4.6 | 6.7/7 | 7.2/6.8 | 7/6 |

U_{10 } | 27.7/28/7 | 28/30.3 | 27.2/30.7 | 34.9/35.9 | 35/37 | 34/38.2 | 40.8/41.4 | 40.8/43 | 39.7/44 |

u_{* } | 1.7/1.8 | 1.8/1.9 | 1.7/1.8 | 2.5/2.6 | 2.6/2.7 | 2.5/2.6 | 3.4/3.5 | 3.6/3.6 | 3.3/3.5 |

also seen that different HTS produce different behavior of z_{ch}. As can be seen from _{ch} than proposed by [_{ch} with the wave ages is higher as the intensity of the hurricane increases.

The effect of the surface waves over sea surface roughness length (z_{0}) and drag coefficient is investigated by combining an ocean wave model and a simplified algorithm. The combined model estimates z_{0}, C_{D}, U_{10} and u_{*}. Computations were done for two distinct conditions: in the first, the Charnock constant (z_{ch}) was applied to the algorithm, while in the second condition z_{ch} is computed from the wave age to include the effect from the sea. This investigation was possible through numerical simulations with the WW3 model for complex wind conditions. The numerical experiments were performed for idealized hurricanes with different translation speed (0, 5 and 10 m/s) and maximum wind speed at the centre (35, 45 and 55 m/s).

It can be observed that as the HTS increases SWH, in the front-right quadrant of the storm track become higher, longer and older (more developed waves), while those in the opposite quadrant become lower, shorter and younger (in the state of wave development). As the hurricane translations speed increases, lower, shorter and younger waves in the rear-left quadrant produce higher sea drag and sea surface roughness; higher, longer and old waves produce less drag and lower values of sea surface roughness. This results, which are in agreement with modeling and observational studies, suggest that sea drag and sea surface roughness are strongly related to the state of developing sea, or wave development. As the hurricane translation speed increases, from a stationary to a fast-moving condition, it causes more asymmetry in the spatial pattern of drag coefficient accentuating the discrepancy between values in the right-front and rear-left quadrants.

Other important result is that the wind velocity at 10 meters is strongly reduced in the rear-left quadrant where the waves cause more drag. More reduced wind speed is observed in the cases of fast hurricanes (Exps B and C). The reduction in the wind intensity is because younger waves induce more roughness and higher sea drag values. This reduction is strongly dependent on the HTS and the intensity of the hurricane. As for example, for the same HTS young waves will produce more drag (or z_{0}) in cases where the maximum wind velocity at the hurricane centre is higher. The results also show that this dependence between wave age and sea drag is less pronounced as the waves become older.

It was observed that z_{ch} must change for different wave stages. Young waves produce higher values of z_{ch}, while old waves are related to lower values of z_{ch}. However, the increase or decrease of z_{ch} depends on the HTS, where young waves in stationary hurricane (0 m/s) cause higher values of z_{ch} than young waves in moving hurricanes (5 and 10 m/s). In addition, there is just a slight increase in z_{ch} as the hurricane intensity increases. In all experiments, young waves overestimate z_{ch} values, when compared with the Charnock constant. In spite of old waves be related to underestimated values of z_{ch}, there is no a clear relationship between older waves and the Charnock constant.

These conclusions support the idea to use more complex model combined to the WW3 issuing the effects of the waves on the planetary boundary layer structure. One manner to do that is to use a simple planetary boundary layer model with a wave model. This kind of studies can bring more insight into the physical processes, which occur over ocean with different sea state conditions. An additional possibility is to couple atmospheric and ocean wave models to evaluate the feedback between waves and storm development, which has been done since the last two decades. We emphasize that despite idealized experiments are powerful tools to understand physical processes of isolated systems, more realistic experiments efforts including real data must be held, which is the authors future intention. Although modeling studies performed here do not use a more sophisticated model to estimate surface variables (C_{D}, z_{0}, U_{10} and u_{*}), they present similar results as compared with coupled experiments.

José Augusto P.Veiga,Mônica R.Queiroz, (2015) Impact of the Waves on the Sea Surface Roughness Length under Idealized Like-Hurricane Wind Conditions (Part II). Atmospheric and Climate Sciences,05,326-335. doi: 10.4236/acs.2015.53025