GMDDGeoscientific Model Development DiscussionsGMDDGeosci. Model Dev. Discuss.1991-962XCopernicus GmbHGöttingen, Germany10.5194/gmdd-7-9063-2014On the wind stress formulation over shallow waters in atmospheric modelsJiménezP. A.DudhiaJ.National Center for Atmospheric Research, Research Applications Laboratory, Boulder, CO, USACIEMAT, División de Energías Renovables, Madrid, SpainNational Center for Atmospheric Research, Mesoscale and Microscale Meteorology Division, Boulder, CO, USAP. A. Jimenez (jimenez@ucar.edu)18December2014769063907726October201425November2014This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://gmd.copernicus.org/preprints/7/9063/2014/gmdd-7-9063-2014.htmlThe full text article is available as a PDF file from https://gmd.copernicus.org/preprints/7/9063/2014/gmdd-7-9063-2014.pdf
The wind stress formulation over shallow waters is investigated
using year-long observations of the wind profile within the first
100 m of the atmosphere and mesoscale simulations. The model
experiments use a range of planetary boundary layer
parameterizations in order to quantify the uncertainty related to
the turbulent closure assumptions, and thus isolate the dominant
influence of the roughness formulation. Results indicate that
a positive wind speed bias exists when the common open ocean
formulation for roughness is adopted. An alternative formulation
consistent with shallow water observations is necessary to reconcile
model results with observations, providing the first modeling
evidence supporting the increase of surface drag over shallow
waters. Including ocean bathymetry as static input data to
atmospheric models constitutes an area where further research should
be oriented.
Introduction
The roughness of the ocean is mainly controlled by the wave field
which is in turn determined to a large extent by the wind
. In general, the ocean surface is rougher for
increasingly higher winds. Over the open ocean, a modified version of
the Charnock relationship provides a good
representation of the feedback between the wind speed and the surface
roughness . However, data from field campaigns have
revealed that over shallow waters the roughness of the surface is
higher than the corresponding values over the open ocean
. In
spite of this differentiated behavior, atmospheric models apply the
same wind stress formulation regardless of the depth of the waters.
Here we show that a significant bias exists when compared to tower
data in shallow waters, and that an alternative formulation is
necessary to adequately reproduce the low-level wind speed
climatology. In particular, we found that increasing the surface drag
is necessary to reconcile model results with observations of the wind
profile within the first 100 m of the atmosphere. The
alternative formulation consists of a linear relationship between the
wind and the logarithm of the aerodynamic roughness length (z0) and
this increased drag is consistent with observations acquired over
shallow waters during the Humidity Exchange Over the Sea (HEXOS)
program . Our results demonstrate the
necessity of introducing a different representation of the surface
drag over shallow waters from the one over the open ocean; this being
the first modeling evidence supporting the increase of the ocean
roughness found in the field campaigns.
Observational evidence
Observational evidence indicates that the surface drag over the ocean
is a positive function of the wind speed . Using
non-dimensional arguments Charnock postulated
that z0 is proportional to the square of the friction velocity
(u∗), a variable that represents the intensity of the atmospheric
turbulent mixing of momentum associated with surface friction:
z0=agu∗2g is the gravity acceleration whereas the factor a is an empirical
constant known as the Charnock parameter. Subsequent field experiments
have reported a range of values for the parameter
. More
recent empirical evidence suggests a dependence of the Charnock
parameter on the wind speed , or even
on the sea state
. Nowadays, the
Coupled Ocean-Atmosphere Response Experiment (COARE) algorithm
provides the most widely used relationship. A satisfactory agreement
over the open ocean within the framework of the COARE algorithm has
been recently found using a Charnock parameter that is a function of
the wind speed .
There is an agreement that over shallow waters the sea is rougher than
over the open ocean for a given wind speed
. The
added drag over shallow waters is increasingly larger for higher winds
in comparison with the values over the open ocean. The physical
mechanism responsible for this effect is unclear, but it has been
speculated to be associated with the effects of the bottom of the
ocean that tends to slow down the phase speed of the waves which
become shorter and steeper in an effect known as shoaling
; or with form drag due to short (young) waves
. In spite of the different properties of the sea
surface, regional and global atmospheric models widely use a roughness
formulation such as Eq. (1) with a Charnock parameter valid for the open
ocean. We will show that models using the standard formulation are
systematically overestimating the lower level winds over regions with
shallow waters and hypothesize that this is because the drag over
these regions is higher in comparison with the open ocean. Since the
added drag is increasingly larger for higher winds, this explains why
the overestimation was an increasing function of the wind speed.
Experimental design
We have performed a series of modeling experiments with version 3.5.1
of the Weather Research and Forecasting (WRF) model
. WRF is a state of the art regional atmospheric
model designed for both operational and research needs. In order to
obtain statistically robust conclusions, we simulated the atmospheric
evolution over a coastal region during a complete year wherein
observations of the wind speed were available at a total of eight
levels within the first 100 m of the atmosphere. The
observations were acquired at the research platform FINO 1 located at
about 48 km from the German coast with a depth of about
30 m. The year of 2009 was selected due to the availability of
data at all the levels and its near climatological wind conditions.
The physical and dynamical settings used in the WRF simulations are
essentially the same as those used in previous studies . The model is initialized at 00:00 UTC of
each day and run for 48 h recording the output every hour. The first day is
discarded as a spin up of the model and the second day is retained as the
simulation for that day. The process is repeated until obtaining a simulation
for each day of the year of 2009. Data from the ERA-Interim reanalysis
are used as initial and boundary conditions. Sensitivity
experiments were performed to the horizontal resolution. Different
simulations were performed at 27, 9 and 3 km with very little
sensitivity in the wind speed distribution so the simulations herein
presented were performed at 27 km of horizontal resolution. A total
of 36 vertical levels were used in the vertical with 5 of them within the
first 200 m of the atmosphere.
Realizing the importance that the closure assumptions associated with the representation of the turbulent mixing within the planetary boundary layer (PBL) may exert on the results, we used a total of 4 different PBL parameterizations in each experiment to quantify the uncertainty related to the turbulence closure. The first one imposes the shape of the vertical profile of the eddy diffusivities (K-profile method) in a first order closure . The second one is based on a combination of a transilient approach with a local scheme and is also a first order closure . The third and fourth parameterizations impose a 1.5 order closure that resolve the turbulent kinetic energy equation to compute the eddy diffusivities . These two last parameterizations mainly differ in the turbulent length-scale formulation. This experimental design allows us to quantify the uncertainty related to the turbulent closure in order to isolate the effects of the roughness formulation. To avoid timing errors associated with the tails of the wind speed distribution that can mask systematic errors, we focus on the frequency distribution characteristics only.
Wind stress formulation
The comparison of the observed and simulated wind speed distributions
calculated with data corresponding to the 8760 h of 2009 is shown,
for the sensor located at 60 m, as a percentile-percentile
comparison in Fig. 1 (red area). Clearly, modeling results indicate
a progressive overestimation of the frequency of moderate-high wind
speeds. Data from all sensors are in close agreement with this
finding. The systematic overestimation for all the formulations of the
turbulent mixing points to limitations in the representation of the
ocean–atmosphere interactions as a potential source of the
discrepancies. Indeed, the overestimation can be understood in terms
of the z0 formulation used by WRF that consists of a Charnock
relationship, following Eq. (1) with a=0.0185,
consistent with values observed over the open ocean. Assuming a linear
dependence of the Charnock parameter with the wind speed as reported
to be more valid over the open ocean by the COARE algorithm
shows a small sensitivity compared to the previous
estimation (green, Fig. 1). In particular, this second experiment also
overestimates the frequency of moderate-high winds.
These findings support our working hypothesis that wind over shallow
waters will be overestimated, and therefore indicate the necessity of
improving the representation of the ocean roughness over these
regions. To further reinforce this statement, Fig. 2a shows the drag
coefficient (Cd) defined as the squared ratio of the
friction velocity and the wind speed at 10 m:
Cd=u∗2/u102. The symbols represent
observations recorded during the international HEXOS programme
that took place in the vicinity of the Dutch
Noordwijk platform with 18 m of ocean depth. HEXOS data has
been used due to the quality of the measurements and its relatively
close proximity to FINO1. The Cd values as a result of
assuming a neutral atmosphere and the standard WRF formulation (red
line) are in closer agreement with the open ocean formulation from the
COARE algorithm (green line) than with the shallow water data from the
HEXOS programme (symbols). Particularly, the drag is underestimated by
both formulations for moderate-high winds supporting our previous
expectations. Similar comments can be made regarding the friction
velocity (Fig. 2b) that shows how the two formulations (green and red
lines) are in agreement with the lower part of the observational
scattering with a clear underestimation of the recorded values at
moderate-high winds.
To provide complementary evidence of the importance of the roughness
formulation, we have performed an additional WRF experiment for the
year of 2009 modifying the z0-wind relation in order to suppress
the wind speed biases. The new formulation assumes that the logarithm
of the surface roughness is a linear function of the wind speed at the
first model level (15 m, u15):
log10(z0)=0.125u15-4.5
where the z0 values are consistent with the previous experiments
for low winds but reach significantly higher values for moderate-high
winds (Fig. 2c). A value of 0.01 m, equivalent to the z0
typical of grassland, is reached at 20 ms-1 giving drag
coefficient greater than 0.003 (blue, Fig. 2a). The parameters in the
linear relationship have been selected in such a way that this third
WRF experiment is successful in reducing the bias over the full range
(blue, Fig. 1). From a modeling perspective it is better to introduce
a relationship between z0 and u∗ to remove height
dependence and to add stability effects. If we assume a logarithmic
wind profile typical of neutral conditions and substitute the wind
speed with the one provided by the linear function (Eq. 2, blue line
in Fig. 2c) we obtain:
ln(z0)=(2.7u∗-14.4)(1.39+u∗)
which is now a stability-dependent formula imposed in the new WRF experiment.
The u∗ values obtained with this new formulation are also shown in
Fig. 2b (blue). The new formulation is in better agreement with the HEXOS
data for the moderate-high winds capturing the increase of the ocean
roughness observed over shallow waters. This result confirms that increasing
the z0 values over shallow waters in agreement with experimental data is
necessary and sufficient to remove the overestimation of the intensity of
moderate-high wind events by models (blue, Fig. 1).
To test the effect of this change on the profile for various stability
conditions, we show further in Fig. 3 the deviations from the
percentiles calculated with observations for this new experiment and
the experiment using the standard WRF formulation. Clearly, results
using the new formulation (Fig. 3b) are in better agreement with
observations than the standard formulation (Fig. 3a) at the three
vertical levels shown. The rest of the heights with wind records
available show virtually the same results indicating that increasing
drag, consistent with shallow water observations (Fig. 2a), improves
the replication of the whole observed wind profile. Figure 3c, d (3e, f) shows
the deviations subsetted for stable (unstable) conditions. The
overestimation of the high-wind frequency is improved under both
atmospheric stability conditions further reinforcing the attribution
of the overestimation to the ocean–atmosphere interactions. It is
noted that the previous high-wind overestimation was especially strong
in stable conditions and this was corrected well.
Conclusions
Our findings provide the first modeling evidence supporting the
increase of the surface drag over shallow waters in comparison with
the standard formulation derived from observations over the open
ocean. Results herein presented are valid for wind speeds up to
20 ms-1, and are statistically robust given the length of
the simulated period (1 year) and the consistency found
between the eight vertical levels. Although a more complicated
dependence of the roughness length may be anticipated, results from
this study constitute a starting point towards a better representation
of the ocean–atmosphere interactions in atmospheric models. For
example, including ocean bathymetry as static input data can be used
to discern the formulation used to represent the ocean roughness, and
depth can become a parameter of the roughness representation since the
drag coefficient has been shown to increase for increasingly shallower
waters e.g..
The impact that the increase in the friction velocity at high winds
(Fig. 2b) produces in the surface fluxes of heat and moisture also
requires additional investigation. Better wind estimations should be
reflected in improved surface-flux estimations, in a more accurate
coupling with ocean models that use the wind to derive the stress at
the ocean–atmosphere interface, or in improved surge estimations
that, for instance, should provide better estimations of storm impacts
at coastal locations. From a more applied point of view, the improved
wind simulations should have a direct benefit in the wind energy
industry since the number of offshore wind farms installed over
shallow waters has been increasing over the last few years. This work
represents an improvement in representing hub-height winds relevant to
this application.
P. A. Jiménez and J. Dudhia conceived the ideas
of the research, designed the experiment, and wrote the
manuscript. P. A. Jiménez performed the WRF simulations and did
all the calculations.
Acknowledgements
This work was supported by project ENE2012-38772-C02-01 and was
accomplished within Collaborative Agreement 09/490 between CIEMAT
and NCAR. NCAR is sponsored by the National Science
Foundation. J. Dudhia was supported by the National Science
Foundation through the National Center for Atmospheric Research and
by the Department of Energy through the Wind and Water Power
Technology Office (DE-EE0005373). Special thanks to Edward Patton
for constructive comments on an earlier version of this manuscript.
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Percentile-percentile plot of the observed and simulated wind
speed. The shaded areas comprise the results from the four different
turbulence closures used in each of the three experiments (colors)
performed with the WRF model: (red) standard WRF formulation, (green)
the ocean roughness formulation for the open ocean from the COARE
algorithm , and (blue) the alternative formulation
herein presented. The solid gray vertical line represents the median
of the observations whereas the dashed gray lines represent the 25th
and 75th percentile.
(a) Drag coefficient, (b) friction
velocity, and (c) roughness length as a function of the
10 m wind speed for the three different formulations of the
ocean roughness (see legend). The symbols in (a) and
(b) show the data recorded during the Humidity Exchange
over the Sea Main Experiment (HEXMAX) a field experiment of the
HEXOS programme . The squares are the data
recorded with a sonic anemometer whereas the circles were recorded
with a pressure anemometer.
Deviations from the observed percentiles (33, 60 and
90 m) for the standard WRF experiment (left column) and the
one using the shallow water formulation (right column): (first row)
all the dataset, (second row) stable conditions, (third row) unstable
conditions. The data used for each experiment corresponds with the
average of the 4 simulations using the different parameterizations
of the turbulence mixing.