# Presentation: 535366

## Effect of Surface Waves on Air-Sea Momentum Flux in Tropical cyclones

**Isaac Ginis**
**Il Ju Moon**
**Tetsu Hara**
**Biju Thomas**
- 	**Graduate School of Oceanography**
**	****University of Rhode Island**

**Collaboration: **
**H. Tolman (EMC/NCEP)**
**E. Walsh (ETL/NOAA)**
**S. Belcher (UR, UK)**

## Air

**Air**

**Sea**

**Air-Sea Fluxes**

**Interface**

**Air**

**Water**

**C**

** ****C**

**Height**

- The vertical fluxes of any variable (c, i.e., wind speed) are assumed to be driven by the difference in variable across the air-sea interface with transport velocity, U

**T**

## Air-Sea Momentum Flux (Wind Stress)

**Air-Sea**** Momentum Flux (Wind Stress)**

-  **Air side controlled flux**
** ****The transport velocity is **
**  ****usually parameterized as**

**where *****U*****   is the mean horizontal wind speed at height 10m and *****C*****   is the bulk transfer coefficient (or ****drag coefficient****)**

*D*

**U**

- Height

- Wind Profile

- Water

**Air**

** ****U**

- 10

**= 0**

## Drag Coefficient & Surface roughness

**Using the logarithmic wind profile in neutral condition,**
**where z  is the ****surface roughness length**** and u  is the friction velocity (                  ) we obtain**

*****

**0**

**A non-dimensional roughness length is called the ****Charnock Coefficient**

**log(z)**

**Wind speed, U**

**Height**

## Simple Bulk Parameterization

- Drennan et al. (2003)

**Simple Bulk Parameterization**

**Wind Speed**

-  Drag coefficient is a function of wind speed
-  Charnock coefficient is constant** **

**Drag Coefficient, C****d**

**Most widely used in atmospheric and oceanic models**

## Parameterizations including wave age

** ****In real ocean, drag coefficient is not a simple function of wind speed.**
** ****This is mainly because the ****state of sea surface**** is not determined by local wind condition but by ****history of wind forcing**** (i.e. surface waves).**
** ****The most common way to find the relationship between momentum flux and surface waves is to use ****Charnock coefficient**** and ****wave age.**** **

**          ****is the phase speed of dominant waves (at the spectral peak) **
**  ****States of growth of wind waves relative to local wind forcing:**
**  ****Y****oung sea ****or growing sea, ****O****ld sea ****or mature sea**

**Wave age =**

## Charnock Coefficient vs Wave age

**Inverse wave age**

**Wind waves**

**Swell**

**Charnock coefficient**

**Laboratory**

**Field**

**Adapted from Jones & Toba (2001)**

-  **The relationship is far from conclusive!!!**

**0.0185**

## Numerical Investigation of the Effect of 

**Numerical Investigation of the Effect of **
**Surface Waves on Air-Sea Momentum Exchange  **

## Coupled Wave-Wind (CWW) Model

**High frequency part : ****Equilibrium Spectrum model**** of Hara and Belcher (2002)**

- 0

- 1

- 2

- 3

- 25

- - max

- -1

- High frequency part

- Near peak

**Coupled Wave-Wind (CWW) Model**

**Wave Boundary Layer (WBL) model**
** ****of Hara and Belcher (2004)**

**Two dimensional wave spectrum**

**Wind profile and drag coefficient**
**over any given seas**

- Explicitly calculates wave-induced stress

- Full wave spectrum

## 1. Uniform Wind Experiments

**1. Uniform Wind Experiments**

**Mean wave length**

**Significant wave height**

**Mature seas**

**At 72 h after the onset of wind**
**when wave field becomes fully developed and steady state**

**2. Growing seas**

**72h**

- 10 ~ 45 m/s

- 1500 km

- 3000 km

**Spatially homogeneous**** ****northward winds **

## Drag Coefficient vs Wind Speed

**Mature sea (+72h)**

**Young sea (+01h)**

**Constant Charnock**
** ****Coefficient (0.0185)**

**Observation-based formulas**

**C****d**** at mature sea increases with wind speed**

## Charnock Coefficient vs. Wave  age

**Charnock Coefficient vs. Wave  age**

**old**

**young**

**Wave age**

**Charnock Coefficient**

**Wind speed**

**     ****At mature seas**

**Constant : 0.01~0.02**
**Is true coefficient only**
**if waves are fully **
**developed!**

## 2. Hurricane Conditions

**A hurricane produces severe and complex ocean waves**

**2. Hurricane Conditions**

## Idealized Hurricane Experiments

**An axisymmetric hurricane wind moves northward with the translation speed of 0, 5, 10 m/s**

** ****Arrows:**
**wind direction**
** ****Contours: wind speed**
**Maximum wind speed: 45 m/s**
**	**

**Idealized Hurricane Experiments**

**After a spinup time of 72 h, a quasi steady state is achieved**

##      0 m/s      5 m/s      10 m/s

- 0 m/s                    5 m/s                       10 m/s

*     **0 m/s      5 m/s      10 m/s*

** ****Contour: Hs**
** ****Arrow : wave**
**            ****direction**
** ****Arrow length : **
**        ****wavelength**

**Significant wave height**

**Input wave age**

** ****Complex, multimodal spectrum **
** ****Peak freq. of the wind energy input **

**In ****the ****rear-lef****t ****quadrant  z****ch**** is reduced significantly as HTS increases.**** **

## +

- (i)

- (j)

*5 m/s                      10 m/s*

**Scatterplot of Drag Coefficient vs Wind Speed**

**+**

**Young seas**
**(uniform wind)**

**Mature seas**

** ****Drag in the ****front-right**** ****quadrant**** monotonically increases with the wind speed, which is similar to mature sea results of uniform wind.**
** ****Drag in the ****rear-left quadrant**** tends to level off or even decrease at high higher winds especially for the fast-moving hurricane. This trend is similar to the young sea results of uniform wind experiment. **

**Constant z****ch**** (0.0185)**

**Relative position from the storm center**

## Drag Coefficient in Different Models 

**CWW**

**Bulk**

**WW3**

**0 m/s**

**5 m/s**

**10 m/s**

## Comparisons with observations

** ****At high wind speeds, C****d**** levels off and even decrease with wind speed**

**Comparisons with observations**

**Upper and lower bounds of C****d**** from all earlier exp.**

- (Charnock Coefficient=0.0185)

## Wave-Wind Simulations in Real Hurricanes 

**Wave-Wind Simulations in Real Hurricanes **

## Scatterplot of Charnock Coefficient vs Wave Age

**Because of large scatter, it is difficult to find a unique relation ship between z****ch**** and w****age**

**Toba et al. (1990)**

**Scatterplot of Charnock Coefficient vs Wave Age**

## Scatterplot of Drag Coefficient vs Wind Speed

** ****D****rag coefficient ****levels off**** at very high wind speeds**
** ****This**** is ****consistent with**** recent field observations and the ****previous ****idealized hurricane simulations.**
** ****Under hurricane wind forcing waves are ****extremely young**** at high wind speeds and the young waves produce ****small drag****.**
** ****This explains why drag coefficient levels off ****at high wind speed****.**** **

**Scatterplot of Drag Coefficient vs Wind Speed**

## 3. Hurricane Wind Forecast Problem 

- The GFDL operational model underestimates winds in strong hurricanes

**Observations**

**Model**

## Computation of Momentum Flux in the GFDL hurricane model 

- Saturation mixing ratio, bulk Richardson number

- Iteration using Hicks functions (Hicks, 1975)
-  L (Monin-Obukhov length)
-  Drag Coefficient, *C**d*

- Roughness length

-  Updated roughness length
-  10-m Wind speed, *U(10)*

- stable

- Momentum flux

- unstable

**Computation of Momentum Flux in the GFDL hurricane model **

-  Universal function  of Hicks (1975)
-  Roughness length is computed using Charnock formula

**Constant **
**Charnock **
**Coefficient!**

## Scatterplot of Cd and Ch vs Wind Speed 

**Scatterplot of Cd and Ch vs Wind Speed **
**in the GFDL Operational Model**

**Cd**

**Ch**

## Developing a Coupled Hurricane-Wave-Ocean Model

**Hurricane Model**

**NCEP**
**WAVEWATCH III**

- Flux

- Wind &
- Air Temp.

**Atmosphere**

**Ocean**

**Waves**

- Currents,

**Wave Boundary Model**

- SST

-   Wave
-     Spectra

- Flux

**POM**
**(HYCOM)**

-   Wind &
- Air Temp.

- Flux

-   SST &
- Current

- Elevations,
- & SST

**Developing a Coupled Hurricane-Wave-Ocean Model**

-  GFDL model (black): C, M, F
-  POM (blue):  OW, OE
-  WAVEWATCH-III (red):  WL, WS** **

## (Very) Preliminary results

**(Very) Preliminary results**
**Hurricane Isabel : 06Z 12 Sept, 2003**

- Sea Surface Temperature

- Sea Surface Currents

- Surface Waves

- Surface Winds

- Surface Stresses

## Scatterplot of Cd and Ch vs Wind Speed 

**Scatterplot of Cd and Ch vs Wind Speed **
**in the Coupled Hurricane-Wave-Ocean Model**

**Cd**

**Ch**

## Spatial Distribution of the Drag Coefficient

**Difference**

**Wave fields**

**Coupled**

**Uncoupled**

## Spatial Distribution of the Drag Coefficient

**Difference**

**Wave fields**

**Coupled**

**Uncoupled**

**Spatial Distribution of the Drag Coefficient**

## Track and  Intensity Forecasts

** ****Hurricane Isabel: 06Z 12 Sep **

## Improvements in the Hurricane 

**Wind Structure Forecasts**

**Coupled**

**Uncoupled**

**Difference**

**HRD**
**Wind**

## Conclusions

** **
**1. ****Uniform Wind Experiments**** **
** ****Mature seas**** **
**The Charnock coefficient is estimated to be about 0.01 ******** 0.02 and the drag coefficient increases as wind speed increases, which are within the range of previous observational data.**

## Conclusions

**2. Idealized and real hurricane experiments**

** ****As the hurricane translation speed increases,**** ****higher, longer and more developed waves**** ****in the right front quadrant of the storm track produce higher sea drag;**** ****lower, shorter and younger waves**** ****in the rear left quadrant produce lower sea drag. **
** ****Drag coefficient**** ****levels off**** ****at high wind speeds under tropical cyclones. This tendency is consistent with the recent observations.**** **

**Conclusions**

## Conclusions

**3. Coupled Hurricane-Ocean-Wave experiments**

** ****We have developed ****a**** ****coupled hurricane-wave-ocean**** ****coupled model by coupling the GFDL hurricane model with the WAVEWATCH III wave model and a wave boundary layer model.**** **
** ****Preliminary ****simulations indicate that the hurricane intensity and structure can be significantly effected by explicit simulations of surface  waves.**

**Conclusions**

## Characteristics of wave model in coupled model

- 1. Use of high-resolution wind inputs in time/space near storm center
-  Every time step (12 min), wind is updated using GFDL wind
-  Spatial resolution of wave model : 1/12o by 1/12o
- 2. Continuously-moving ice coverage areas (for economical calculation)
-  Every time step (12 min), wave calculation areas (6o by 6o) that are not covered by ice are defined using storm center positions estimated from GFDL model.
-  Here, momentum fluxes of smaller areas (5o by 5o) are transferred to GFDL model.
- 3. Considering current-wave interactions
- Current and elevation data from ocean model will be used to consider current-wave interactions