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# Wind Stress

When wind blows over the water, it exerts a shear stress at the water surface that transfers horizontal momentum vertically downward across the air–sea interface, driving circulation. In ADCIRC, wind stress is an input forcing term, with several different formats provided. See the NWS parameter for available formats. In most cases, the exact wind stress to be applied to the model is not provided, therefore ADCIRC must determine how to convert a given wind speed to the actual stress applied at the ocean surface. This page covers the various aspects of this process, as well as the options available to the user.

## Definition of Winds

The characteristics of wind forcing are often broken down in three ways:

1. Whether the winds are considered to be over-water (termed "marine exposure") or over-land
2. The elevation above the sea (or ground) surface of the winds
3. The time-averaging (if any) that has been applied

ADCIRC generally expects 10-meter, 10-minute winds at their actual exposure, although the exact expectations vary depending on the input type. For instance, when Holland-type wind inputs are provided (e.g. NWS=8 or NWS=20), the wind speed is expected to be the 1-minute maximum sustained wind at 10 meters elevation. If marine-exposure winds are provided, then surface roughness reductions may be needed [1] [2] . If winds are provided with a different averaging time, then an appropriate correction may be needed, though winds with averaging times of 10 to 60 minutes are generally considered to be quite similar; this is the so-called mesoscale gap. For recommendations on wind time-scale conversions not handled internally by ADCIRC, for tropical cyclones, see the WMO guidelines of Harper et al. [3]

## Roughness Reductions

Reductions in wind speed to convert to the appropriate exposure come from a logarithmic boundary layer formulation (see, e.g. [1] [2]) to determine a fraction ${\displaystyle f}$ to reduce the winds,

${\displaystyle f=\left({\frac {z_{0l}}{z_{0m}}}\right)^{0.0706}\left({\frac {\ln {\frac {10}{z_{0l}}}}{\ln {\frac {10}{z_{0m}}}}}\right)}$

for marine roughness length ${\displaystyle z_{0m}}$ and reduced ("land") roughness length ${\displaystyle z_{0l}}$. Wind speed is then reduced as,

${\displaystyle \mathbf {w} '=f\mathbf {w} =f[u,v]}$

for x- and y- wind vector components ${\displaystyle u}$ and ${\displaystyle v}$. The marine roughness length is,

${\displaystyle z_{0m}={\frac {0.018}{g}}c_{d}\left\Vert \mathbf {w} \right\|}$

for Charnock parameter ${\displaystyle 0.018}$, drag coefficient ${\displaystyle c_{d}}$ and acceleration due to gravity ${\displaystyle g}$. The wind drag coefficient is addressed below in this section. As previously noted, the reduced ("land") roughness length ${\displaystyle z_{0l}}$ is specified by the user via the surface roughness nodal attribute. The fraction ${\displaystyle f}$ is bounded on ${\displaystyle [0,1]}$, meaning the winds cannot be increased, nor change direction.

### Older Behavior

#### Interpolating Roughness Lengths Before v55

Comparison of output wind velocities using old and new methods.

Before version 55, the directional wind reductions were applied by determining which of the 12 directional bins the wind velocity (at each time step) fell into, and using that roughness reduction, i.e. nearest neighbor interpolation. Starting in version 55, the roughness length is linearly (in angle space) interpolated between directional bins. In testing, this has been found to generally have a very small effect on water levels, but a notable effect on wind speeds, since time evolution of winds is smoother. It can have large localized effects on water levels in rare cases in cases where there are large changes in neighboring roughness length bins coinciding with well-aligned winds, as in this test case with Hurricane Isaac.

#### Roughness Reduction Bug Before v54

Before version 54, there was a bug in this calculation. The mistake and its effects are addressed in this PDF document: ADD A LINK TO A PDF HERE YOOOOO.

## Converting Wind Velocity to Wind Stress

In ADCIRC, four formulations are available to convert wind velocities to the wind stresses applied in the momentum equations. Although there are several ways to control this, users are generally encouraged to use the metControl namelist in the fort.15 file. The default drag formulation is the Garratt [4] linear formula. An alternative for use with tropical cyclones is the Powell formulation, [5] which varies drag by the sector of the tropical cyclone. When ice coverage is included in the model, a wind drag formulation that accounts for this effect should be used. By default, if ice coverage input data are supplied, ADCIRC uses a cubic function of ice coverage, termed the "IceCube" drag formulation. Lastly, the "swell" drag law option allows users to utilize SWAN's drag formulation when employing the coupled model.

In all cases, the actual wind drag coefficients determined by ADCIRC can be output to a fort.63-type file named winddrag.173. Output settings (file format, output start/end times, and output interval) match those of either the fort.63 or fort.73/74 files, I think fort.73/74. Outputting of this file is enabled by setting outputWindDrag=.TRUE. in the &metControl namelist of the fort.15 file's namelist section.

### Garratt Drag Formulation

This is the default wind drag formulation in ADCIRC. From Garratt (1977)[4], the formula is,

${\displaystyle c_{d}=0.001\left(0.75+0.067\left\Vert \mathbf {w} \right\|\right)}$

By default, ADCIRC puts an upper bound on the drag coefficient of ${\displaystyle c_{d}\leq 0.0035}$. This upper bound WindDragLimit can be changed via the metControl fort.15 namelist.

### Powell Drag Formulation

CONTRIBUTOR NEEDED

### IceCube Drag Formulation

CONTRIBUTOR NEEDED

## References

1. Simiu, E., Scanlan, R.H., 1996. Wind effects on structures: fundamentals and applications to design, 3rd ed. ed. John Wiley, New York.
2. Simiu, E., Yeo, D., 2018. Wind effects on structures: modern structural design for wind, Fourth edition. ed. John Wiley & Sons, Hoboken, NJ.
3. Harper, B., Kepert, J., Ginger, J., 2010. Guidelines for converting between various wind averaging periods in tropical cyclone conditions (No. WMO/TD-No. 1555). WMO, Geneva, Switzerland.
4. Garratt, J.R., 1977. Review of Drag Coefficients over Oceans and Continents. Mon. Wea. Rev. 105, 915–929. https://doi.org/10.1175/1520-0493(1977)105<0915:RODCOO>2.0.CO;2
5. Powell, M.D., Vickery, P.J., Reinhold, T.A., 2003. Reduced drag coefficient for high wind speeds in tropical cyclones. Nature 422, 279–283. https://doi.org/10.1038/nature01481