Plan of the talk:

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Wind Wave Modeling within the Earth System

• Plan of the talk
• Wind waves
• Tools available for wave field computation
• Inputs and outputs
• Feedbacks and impacts
• Wave computation in the Mediterranean
• Trends and climate change in the Mediterranean Sea

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Restoring force
gravity
Surface tension
Coriolis
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Cartoon showing the waves at different stages of
their development. Parts a) and b) show the
beginning and the end of wave generation during a
storm c) e d) the beginning and end of wave
dispersion as they travel across the ocean, e)
dissipation due to wave breaking at the coast
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From the Fourier component of the surface
elevation
The wave spectrum is defined as
So that
and
Significant wave height is a measure of the
observed height and of the wave energy
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Wave models are grouped in 03 generations
- generation 0 Tables for SWH and fp
Spectrum distribution of energy as function of
frequency and direction
- generation 1 growth of the spectrum up to a
saturation level
- generation 2 Parametric spectral shape which
describes overshoot and growth of frequencies
that do not receive energy directly from the wind
- generation 3 parameterization of physical
processes responsible for the evolution of the
spectrum
WAM (Wave Model), WAMDI Group, JPO, 1987
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Generation 3 Energy balance equation
Source function
Sin Wind input
Divergence of the energy flux
Local Variation of the spectrum F
Snlnonlinear interactions
Sdsdissipation
Sbfbottom friction
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• Available wave models
• WAM
• WAVEWATCH
• SWAN

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WAM Model (operational at ecmwf) The original
WAM model software that has been developed over a
period of seven years (1985-1992) is fairly
general (WAMDIG 1988, Komen et al. 1994). .
Spectral resolution and spatial resolution are
flexible and the model can be run globally or
regionally with open and closed boundaries. Open
boundaries are important in case one wishes to
use results from a coarse resolution run as
boundary conditions for a fine mesh, limited area
run. Options such as shallow water, depth
refraction or current refraction may be chosen.
Since the 1990 there has been continuous
effort at ECMWF to streamline the software in
areas such as IO, archiving, vectorization and to
adapt the code to the new massive parallel
(vector) machines. Nevertheless, many of the
original features of the WAM model have been
retained.
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WAVEWATCH III (Tolman 1997, 1999a) is a third
generation wave model developed at NOAA/NCEP in
the spirit of the WAM model. It is available at
NOAA   WAVEWATCH III solves the spectral action
density balance equation for wavenumber-direction
spectra. The implicit assumption of this equation
is that properties of medium (water depth and
current) as well as the wave field itself vary on
time and space scales that are much larger than
the variation scales of a single wave. A further
constraint is that the parameterizations of
physical processes included in the model do not
address conditions where the waves are strongly
depth-limited. These two basic assumptions imply
that the model can generally by applied on
spatial scales (grid increments) larger than 1 to
10 km, and outside the surf zone.
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SWAN (simulating waves near shore) is a
third-generation wave model that computes random,
short-crested wind-generated waves in coastal
regions and inland waters. SWAN is supported by
Office of Naval Research (USA) and
Rijkswaterstaat (as part of the Ministry of
Transport, Public Works and Water Management, The
Netherlands). It can be downloaded from the DELFT
university SWAN accounts for the following
physics Wave propagation in time and space,
shoaling, refraction due to current and depth,
frequency shifting due to currents and
non-stationary depth. Wave generation by wind.
Three- and four-wave interactions.
White-capping, bottom friction and depth-induced
breaking. Wave-induced set-up. Propagation from
laboratory up to global scales. Transmission
through and reflection (specular and diffuse)
against obstacles. Diffraction.
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Wave models specifications
Input quantities Bathymetry Surface wind fields
(high space and time resolution) Output
quantities the following output quantities are
produced in numerical files containing tables,
maps and timeseries) one- and two-dimensional
spectra, significant wave height, mean and peak
wave periods, average wave direction and
directional spreading, Optional outputs one-
and two-dimensional spectral source terms,
root-mean-square of the orbital near-bottom
motion, dissipation, wave-induced force (based
on the radiation-stress gradients), set-up,
diffraction parameter, Feedbacks on the
atmospheric circulation
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Dependence of the drag coefficient on wave age
Reversed wave age
Young wind sea
Old wind sea
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Dependence of the roughness length on wave age
Young and growing windsea dominant wave gives a
small contribution
Labs and small lakes both equilibrium range and
dominant wave give a small contribution
Fully developed windsea dominant wave gives a
small contribution
From Makin and Kudryavtsev, 2003
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Wave sediment transport
From Falques 2005
The dynamics of the coastline is described by the
sediment conservation
Where Q is the sediment transport (which depends
on waves), and Xs the coordinate of the
perturbed coastline
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Waves in the Mediterranean
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WIND
WAVES
From Cavaleri et al.
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Which tools are available for evaluating SWH
climate trends
Wave buoys
Unfortunately time series are too sparse (and
actually rather short)
Satellite observations
Good coverage, but time series are short
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Reconstruction based on numerical simulations
Adapted from Lionello et al 2007
Quality of results is critically depending on
wind fields
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Model validation
monthly SWH index
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Model validation
Buoys
correlazione ERA 40-T213 .88 correlazione ERA
40-RON .84 correlazione RON-T213 .86
Satellite
Adapted from Lionello and Sanna 2005
correlazion ERA 40 SAT .72
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c)
d)
b)
a)
.Panel a) Comparison between monthly average SWH
for WAM-ERA40 (black), WW3-ERA40 (pink) modelling
configuration and satellite data (red). Panel
b) same as panel a), except it shows the
dimensionless index. Panel c) Same as panel a),
except it shows the model results with HIPOCAS
forcing. Panel d) Same as panel c), except it
shows the model results with HIPOCAS forcing
(green and blue line for WAM and WW3 models,
respectively). Values in meters (y-axis),
calendar months on the x axis.
From Galati et al, 2008
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Average SWH and dimensionless index for each
configuration and for satellite data, their
standard deviation and correlation (SWH values in
meters).
Adapted from Galati et al, 2008
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Scatter for the 4 modeling configurations
WAM-HIPOCAS
WAM-ERA40
model
model
obs
obs
WW3-HIPOCAS
WW3-ERA40
model
model
obs
obs
From Galati et al, 2008
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Mean SWH present trends
From Lionello and Sanna 2005
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Extreme events trends
Significant trends at 95
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Correlation with teleconnection patterns
Western Med
Eastern Med
Annual cycle (calendar months on the x-axis) of
the correlation between monthly average SWH field
and teleconnection pattern indexes. Only NAO, EA,
EP/NP, EA/WR, SCA are shown. Other patterns have
smaller and less relevant correlation values.
Thick bars denote value significant at the 95
confidence level. The two panels refer to the
western (top) and eastern (bottom) part of the
Mediterranean.
From Lionello and Galati 2007
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JAN correlation with EA-WR
SLP
SWH
low EA-WR
High EA-WR
January correlation of EA-WR index with SLP and
SWH, (a) and (b) panel, respectively. In the
color filled areas the correlation is significant
at the 95 confidence level. Panels (c) and (d)
composites of SWH (meters) during months with the
9 most high and low values of the EA-WR index,
respectively.
From Lionello and Galati 2007
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JAN correlation with EA
SLP
SWH
low EA
High EA
January correlation of EA index with SLP and
SWH, (a) and (b) panel, respectively. In the
color filled areas the correlation is significant
at the 95 confidence level. Panels (c) and (d)
composites of SWH (meters) during months with the
9 most high and low values of the EA index,
respectively.
From Lionello and Galati 2007
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CLIMATE CHANGE
Results are based on 30-year long simulations of
the wind-wave field in the Mediterranean Sea
carried out with the WAM model. Wave fields
have been computed for 2071-2100 period of the
A2, B2 emission scenarios and for 1961-1990
period of the present climate (REF). The wave
model has been forced by the wind field computed
by the RegCM regional climate model at a 50km
resolution
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REF simulation Comparison between satellite data
and model results. Annual cycles are plotted
separately for each decade of the simulation.
Vertical bars show the standard deviation. Values
in meters.
From Lionello et al 2008
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average SWH of REF, A2 and B2 scenario simulations
mean annual cycle vertical bars show the monthly
standard deviation (in meters)
single monthly values (in metres).
Mann-Whitney test ranks)
From Lionello et al 2008
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From Lionello et al 2008
WINTER
SWH (REF)
SWH A2-REF
U A2-REF
SLP A2-REF
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final message Wave models are a consolidated
tools for wind wave field simulations (hindcast,
forecast, projections). The quality of their
results depends strongly on that of the driving
wind fields ( and this is an issue in small
basins with complicated coastlines, such as the
Med) They provide information for coast
evolution and they may be used for the
computation of feedbacks on the atmospheric
circulation In the Mediterranean, present
evidence shows a trend towards milder climate.
Available climate projections suggest that this
trend will continue in future
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