Modeling the Atmospheric Boundary Layer Wind …rms/ms/MOW_all_Oct13.pdfModeling the Atmospheric Boundary Layer Wind Response to Mesoscale Sea Surface Temperature Natalie Perlin1,2,
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Modeling the Atmospheric Boundary Layer Wind
Response to Mesoscale Sea Surface Temperature
Natalie Perlin1,2
, Simon P. de Szoeke2, Dudley B. Chelton
2, Roger M. Samelson
2,
Eric D. Skyllingstad2, and Larry W. O’Neill
2
October 2013
(Submitted to Monthly Weather Review)
1 – corresponding author, nperlin@coas.oregonstate.edu
2 – College of Earth, Ocean and Atmospheric Sciences, Oregon State University,
104 CEOAS Admin Bldg, Corvallis, OR 97331-5503
2
ABSTRACT
The wind speed response to mesoscale SST variability is investigated over the Agulhas
Return Current region of the Southern Ocean using Weather Research and Forecasting (WRF)
and COAMPS atmospheric models. The SST-induced wind response is assessed from eight
simulations with different widely used subgrid-scale vertical mixing parameterizations. The
simulations are validated using satellite QuikSCAT scatterometer winds and NOAA sea surface
temperature (SST) observations on 0.25° grid. The observations produce a coupling coefficient
of 0.42 m s-1
°C-1
for wind to mesoscale SST perturbations. The eight model configurations
produce coupling coefficients varying from 0.31 to 0.56 m s-1
°C-1
. A WRF simulation with a
recent implementation of the Grenier-Bretherton-McCaa (GBM) boundary layer mixing scheme
yields 0.40 m s-1
°C-1
, most closely matching the QuikSCAT coupling coefficient. Relative
model rankings based on coupling coefficients for wind stress and SST, or for spatial
derivatives of wind/wind stress and of SST, are similar but not identical to that based on the
wind-SST coupling coefficient.
The atmospheric potential temperature response to SST variations decreases gradually
with height through the boundary layer (0-1.5 km). In contrast, the wind speed response to SST
perturbations decreases rapidly with height to near-zero at 150-300m, is weakly negative around
300 m, and decreasing upward toward zero above 600-800m. The wind speed coupling
coefficient is found to correlate well with the height-average turbulent eddy viscosity
coefficient estimated by boundary layer mixing schemes. The vertical structure of the eddy
viscosity depends on both the absolute magnitude of local SST perturbations, and the
orientation of the surface wind relative to the SST gradient.
3
1. Introduction
Positive correlations of local surface wind anomalies with mesoscale ocean sea surface
temperature (SST) anomalies, in contrast to negative correlations at large spatial scales, suggest
that the ocean is influencing atmospheric surface winds at the mesoscales (10-1000 km). These
correlations (Chelton et al., 2004; Xie, 2004; Small et al., 2008) are based on estimates of
surface ocean winds by SeaWinds scatterometer aboard the QuikSCAT satellite, a microwave
radar instrument that allows nearly daily measurements and resolution of ocean mesoscales
(25-km gridded global product), and SST from satellite measurements by passive microwave
and infrared radiometers.
The boundary layer response to mesoscale SST variability has been the subject of a
number of modeling studies in recent years. Evaluation of mechanisms for the boundary layer
wind response have centered largely on details of the relative roles of the turbulent stress
divergence and pressure gradient responses to spatially varying SST forcing. The pressure
gradient is driven by the SST-induced variability of planetary boundary layer (PBL)
temperature, PBL height, and entrainment of free-tropospheric temperature. There are some
differences among previous modeling as to the relative roles of these forcing terms in driving
the boundary layer wind response to SST. A primary goal of the present study is to investigate
the sensitivity of the surface wind response to SST on PBL mixing schemes, a possible
contributor to differences found in previous modeling studies.
The PBL turbulent mixing parameterizations are specifically designed to represent sub-
grid fluxes of momentum, heat, and moisture in numerical models through specification of
flow-dependent mixing coefficients. Subgrid-scale mixing affects the vertical turbulent stress
divergence, as well as the pressure gradient, through vertical mixing of temperature and
4
regulation of PBL height and entrainment. PBL parameterizations are especially important near
the surface where intense turbulent exchange takes place on scales much smaller than the grid
resolution. Song et al. (2009), O’Neill et al. (2010) reported superior performance of a boundary
layer scheme based on Grenier and Bretherton (2001, GB01 further in text) implemented in a
modified local copy of the Weather Research and Forecast (WRF) model, for estimating the
average SST-induced wind changes. The present study extends this model comparison to
evaluate the prediction of ocean surface winds by a number of PBL schemes in the WRF
atmospheric model, including an implementation in WRF of the Grenier-Bretherton-McCaa
PBL scheme (Bretherton et al, 2004; GBM PBL), which follows and improves upon that of
Song et al. (2009), as well as by COAMPS atmospheric model. For this comparison, we
performed month-long simulations over the Agulhas Return Current region in the Southern
Ocean, a region characterized by sharp SST gradients and persistent mesoscale ocean eddies,
with boundary SST conditions specified from a satellite-derived product (Reynolds et al., 2007).
Our general goal is to advance understanding of the atmospheric response to ocean
mesoscale SST meanders and eddies. Particularly, we evaluate the role of different planetary
boundary layer (PBL) sub-grid scale turbulent mixing parameterizations, and thereby the
dynamics that they represent. First, we assess the near-surface wind response to the small-scale
ocean features. We diagnose models to identify important mechanisms of BL momentum and
thermal adjustment to the SST boundary condition. We also analyze the vertical extent of SST
influence on the atmospheric boundary layer. We evaluate metrics of several PBL boundary
layer parameterizations in two atmospheric models, with the objective of identifying how
differences between the schemes influence simulations of surface wind.
5
2. Methods
2.1 Numerical atmospheric models and experimental setup
The Weather Research and Forecasting (WRF) Model is a 3-D nonhydrostatic
mesoscale atmospheric model designed and widely used for both operational forecasting and
atmospheric research studies (Skamarock et al., 2005). The Advanced Research WRF (ARW)
version 3.3 (hereafter simply WRF), was used in the present study simulations. The COAMPS
atmospheric model based on a fully compressible form of the nonhydrostatic equations (Hodur,
1997), and its Version 4.2 was used in the current research study. Of particular importance for
this study are the corresponding model PBL parameterizations, which are discussed in Section
2.2.
Numerical simulations with both models were conducted on two nested domains
centered over the Agulhas Return Current (ARC) in the South Atlantic (Fig.1). The area
features numerous mesoscale ocean eddies and warm core rings a few hundred kilometers in
size, with strong associated local SST gradients. This mesoscale structure is superimposed onto
strong large-scale meridional SST gradients between the Indian Ocean and the Antarctic
Circumpolar Current. The model simulation and analysis period is July 2002, a winter month in
the Southern Hemisphere, and is characterized by several synoptic systems passing through the
area with strong wind events. Thus, the effects of mesoscale SST features are investigated here
under a variety of atmospheric conditions. Domain settings are practically identical in WRF and
COAMPS. The outer domain has 75-km grid boxes extending about 72o and 33
o in the
longitudinal and latitudinal directions, respectively. The nested inner domain has a 25-km grid
with corresponding sizes of about 40o lon. x 17
o lat. The vertical dimension is discretized with a
6
scaled pressure ( ) coordinate grid with 49 pressure levels (or 50 full- levels), progressively
stretched from the lowest level at 10 m above the surface up to about 18 km; 22 levels are in the
lowest 1000m. The models are initialized and forced with global NCEP FNL Operational
Global Analysis data on 1.0x1.0 degree grid, available at 6-h intervals
(http://rda.ucar.edu/datasets/ds083.2/). This is the product from the Global Data Assimilation
System (GDAS) and NCEP Global Forecast System (GFS) model.
We use daily sea surface temperature (SST) data from the NOAA Reynolds Optimum
Interpolation (OI) 0.25o daily analysis Version 2 (Reynolds et al., 2007) as the lower boundary
condition for the atmospheric model simulations, and for estimation of the coupling coefficients
in conjunction with QuikSCAT winds (see Section 3.1). The optimum interpolation combines
two types of satellite observations, the Advanced Microwave Scanning Radiometer (AMSR-E)
and Advanced Very-High Resolution Radiometer (AVHRR), and includes a large-scale
adjustment of satellite biases with respect to the in-situ data from ships and buoys. AMSR-E
retrieves SST on grid spacing of about 25 km with coverage regardless of clouds, whereas the
AVHRR produces a 4-km gridded product, but cannot see through clouds. Missing AMSR-
AVHRR SST values in the interior of the nested model domain that occur due to land
contamination by small islands are interpolated using surrounding values. This small adjustment
of the model’s topography to eliminate small islands avoided orographic wind effects in the
models, providing more consistency for studying the marine boundary layer response to
mesoscale SST forcing.
The models were integrated forward for 1 month, 0000 UTC 1 July – 0000 UTC 1
August 2002. Model output was saved at 6-hourly intervals and was used to derive time
averages. A model spin up of 1 day was discarded, and the subsequent 30 days were used for
7
the analysis presented in this study. The month-long simulation period and time-averaging
statistics were sufficient to obtain a robust statistical relationship between the time-averaged
SST and winds. Analysis of the simulations was carried out primarily using the model results
from the inner domain.
2.2 Sub-grid Scale parameterizations
2.2.1. PBL parameterizations in WRF and COAMPS
Planetary Boundary Layer schemes (also called vertical mixing schemes) in atmospheric
models provide means of representing the unresolved, sub-grid scale turbulent fluxes of
modeled properties. The eight experiments performed with various widely-used boundary layer
parameterization schemes available in WRF and COAMPS models are listed in Table 1: six
schemes or their variations for the WRF model, and two PBL scheme variations in COAMPS
model. Experiment names are formed from the model name (WRF or COAMPS), an
underscore, and the PBL scheme name or reference.
Turbulent mixing terms result for the mean variables in a turbulent flow from Reynolds
decomposition of Navier-Stokes equations, in which the variables are split into mean and
fluctuating components. For example, for property and vertical velocity , the mean vertical
flux , where and are the fluctuating departures from the respective
means and . The schemes often parameterize vertical turbulent flux of any variable C as
proportional to the local vertical gradient (local-K approach; Louis, 1979),
,
where is a scalar proportionality parameter with units of velocity times distance. A counter-
gradient term is added in some PBL schemes to account for the possibility of turbulent transport
by larger-scale eddies not dependent on the local gradient.
8
Four of the WRF experiments and both COAMPS model experiments in the present
study use PBL parameterizations based on so-called Mellor-Yamada type (Mellor and Yamada,
1974; Mellor and Yamada, 1982), 1.5-order turbulence closure, level 2-2.5 schemes. The term
“order closure” refers to the highest order of a statistical moment of the variable for which
prognostic equations are solved in a closed system of equations (Stull, 1988, Chapter 6, see
Table 6-1). In a 1.5-order closure, some but not all the second-moment variables are
parameterized. For most of the 1.5-order schemes considered here, an additional prognostic
equation for the turbulent kinetic energy (TKE),
2
'''
2
2222 wvuq , is solved, but the other
second moments (the Reynolds fluxes of form ) are parameterized using the local gradient
approach, as in a first-order closure. The turbulent eddy transfer coefficients qMHK ,, are further
parameterized using the prognostic q value, as follows:
qHMqHM SqlK ,,,, , (1)
where l is master turbulent length scale, and qHMS ,, is a dimensionless parameter. The latter
could be set to a constant value (such as often set for qS ), or determined based on stability and
wind shear parameters. In Eq.(1), the subscripts M,H, and q indicate momentum, heat, and TKE
diffusivities, respectively.
A general form of the prognostic equation for the TKE is the following:
bsq PP
q
zK
z
q
Dt
D
22
22
, (2)
where Dt
D is the material derivative following the resolved motion, horizontal turbulent
diffusion is neglected, sP and bP are shear production and buoyant production of turbulent
9
energy, respectively, and is the dissipation term. Different approximations to Eq.(2) follow
from assumptions of production-dissipation balance or choices of empirical closure constants
in a given parameterization scheme, which determine different possible forms of how the
functions HMS , are calculated. For example, GBM PBL in WRF uses Eq. (24-25) in Galperin et
al. (1988) solution that assumes production-dissipation balance, 1 bs PP , for the purpose
of estimating of stability functions only; TKE is still calculated prognostically using the
transport equation. This method also restricts the dependence of HMS , the on wind shear,
resulting in simpler but more robust quasi-equilibrium model. Our implementation of the GBM
PBL in WRF 3.3 followed Song et al. (2009), with some minor corrections, and is now publicly
available as a part of WRF 3.5. MYJ PBL follows Janjić (2002), Eqs. (2.5, 2.6, 3.6, 3.7),
employing an analytical solution to determine HMS , , with a certain choice of closure constants
and dependence on both static stability and wind shear. MYNN PBL 2.5 level scheme uses a
revised set of Mellor and Yamada (1982) closure constants. UW PBL scheme is a heavily
modified version from GB01 parameterization, to improve its numerical stability for the use in
climate models with longer time steps; it adapts an approach where TKE is diagnosed, rather
than being prognosed, which may qualify it as lower than 1.5-order scheme. COAMPS PBL
schemes (ipbl=1,2) are again 1.5-order, level 2.5 schemes based closely on Mellor and Yamada
(1982) and Yamada (1983), and use Eq. (16-17) in Yamada (1983) to determine the stability
functions, which include dependence on the flux Richardson number with the imposed limits.
The COAMPS PBL option (ipbl=2) includes some improvements and code fixes, and is now
the recommended option. GBM PBL and UW PBL schemes also include explicit entrainment
closure for convective layers that modifies the expression for MK .
10
Furthermore, the stability function for TKE could take different forms. It is considered a
constant equal to 0.2 in Mellor and Yamada (1982) and Janjić (2002), but is tuned to be qS =5
in the MYJ PBL scheme numerical implementation, and qS = 3 in COAMPS schemes. The
GBM PBL assumes Mq SS 5 . The MYNN PBL scheme has Mq SS 2 in Nakanishi and Niino
(2004) reference, or tuned to Mq SS 3 in the numerical code of this scheme. The representation
of the turbulent master length scale, l, and the boundary layer height if this is included in
calculations of the length scale, are different in all of the PBL schemes as well. Additionally,
each numerical implementation of the PBL parameterization may contain specific restriction
conditions or tuning parameters that are not included in major scheme references to ensure
numerical stability of the scheme, and may or may not include a counter-gradient term. Thus,
different PBL schemes based on the same Mellor-Yamada 1.5-order closure approach could
perform differently due to numerous implementation details.
The YSU PBL scheme in WRF is the only one that is not a 1.5-order Mellor-Yamada-
type scheme. It is based on Hong and Pan (1996) and Hong et al. (2006), using non-local-K
approach (Troen and Mahrt, 1986). The scheme diagnoses the PBL height, considers
countergradient fluxes, and constrains the vertical diffusion coefficient HMK , to a fixed profile
over the depth of the PBL. The eddy viscosity coefficient within the boundary layer is
formulated as
2
1
h
zzkwK sM
, (3)
where k is von Karman constant (0.4), z is the height from the surface, sw is the mixed-layer
velocity scale, and h is the boundary layer height. The eddy diffusivity for temperature and
11
moisture are computed from MK in Eq.(4) using the Prandtl number. The local- K approach for
calculations of eddy diffusivities is used in the free atmosphere above the boundary layer, based
on mixing length, stability functions, and the vertical wind shear. The YSU PBL scheme also
includes explicit treatment of entrainment processes at the top of the PBL.
Distinctions between the WRF and COAMPS atmospheric model solutions could also
be expected due to the use of distinct combinations of other physical parameterizations
(convective schemes, for example), different numerical discretization schemes, horizontal
diffusion schemes, lateral boundary condition, and other factors not related to a choice of a PBL
scheme. For example, the differences in vertical discretization in models affect the calculations
of vertical gradients, and consequently, near-surface properties and lower boundary conditions
for the TKE equation.
2.2.2 Surface flux schemes
The lower boundary condition for fluxes of momentum, heat, and moisture between the
lowest atmosphere level and the surface are estimated by surface flux schemes. PBL mixing
schemes are sometimes configured and tuned with specific surface flux schemes. A total of
three different surface flux schemes were used in the simulations (Table 1). The two surface
flux schemes used in the WRF simulations are both based on Monin-Obukhov similarity theory
(Monin and Obukhov, 1954); they are referred to as “MM5 similarity” (sf_sfclay_physics=1 in
Table 1), or “Eta similarity” (sf_sfclay_physics=2). The MM5 similarity scheme uses stability
functions from Paulson (1970), Dyer and Hicks (1970), and Webb (1970) to compute surface
exchange coefficients for heat, moisture, and momentum; it considers four stability regimes
following Zhang and Anthes (1982), and uses the Charnock relation to determine roughness
12
length to friction velocity over water (Charnock, 1955). The Eta similarity scheme is adapted
from Janjić (1996, 2002), and includes parameterization of a viscous sub-layer over water
following Janjić (1994); the Beljaars (1994) correction is applied for unstable conditions and
vanishing wind speeds. Fluxes are computed iteratively in the Eta similarity surface scheme. To
investigate the influence of the differences in surface flux scheme, we modified the original
MYJ PBL scheme in WRF to be used with the same surface flux scheme as GBM PBL; this
simulation was named WRF_MYJ_SFCLAY, and is identical to WRF_MYJ except for the
different surface flux scheme. The COAMPS model uses a bulk scheme for surface fluxes
following Louis (1979), Uno et al. (1995); surface roughness over water follows the Charnock
relation; and stability coefficients over water are modified to match the COARE2.6 algorithm
(Fairall et al, 1996; Wang et al 2002).
2.3. Observations
Satellite observations of vector winds in rain- and ice-free conditions from the
microwave scatterometer aboard QuikSCAT satellite on a 0.25o grid were used for this study
(version 4; Wentz, 2006; Ricciardulli and Wentz, 2011). The SeaWinds scatterometer acquires
high-resolution radio-frequency backscatter from the sea surface, which are used to retrieve 10-
m equivalent neutral stability winds (ENS winds, Liu and Tang, 1996). These are the winds that
would be observed at 10 m, were the lower 10 m of the atmosphere neutrally stratified. For the
corresponding comparison with the QuikSCAT wind product, model 10-m ENS winds are
derived from surface momentum flux (friction velocity, *u ), under the assumption of neutral
stratification,
0
*10
10ln
zk
uU mN , where k is the von Karman constant, and 0z is the roughness
length over the water. NOAA Reynolds Optimum Interpolation (OI) SST on a 0.25o grid
13
(Reynolds et al., 2007) was used to derive the monthly-average SST field and along with
QuikSCAT winds, to estimate SST-wind coupling coefficients (see Section 3.1).
2.4. Spatial Filtering
A two-dimensional spatial loess smoother based on locally-weighted polynomial
regression was applied to the observed and modeled fields to separate the mesoscale signal from
the larger-scale signal (Cleveland and Devlin 1988; Schlax and Chelton, 1992). ENS winds or
wind stresses and SST were processed using a loess 2-D filter having an elliptical window with
a half-span of 30o
longitude and 10o latitude. These high-pass filtered fields are also referred to
as perturbations. Similar high-pass filtering was applied to SST fields on a 0.25o grid.
The filter window is comparable to the size of the nested grid of the models. To avoid
edge effects on the large loess filter window, filtering was done over the entire model domain
using data from both the nested and the outer grid. Data from the outer model domain were
interpolated onto a 0.25o grid outside the nested domain. The resulting perturbation fields were
analyzed in the region of the nested grid only.
Calculations of the derivative fields, such as ENS wind divergence and vorticity,
crosswind and downwind SST gradients, and wind stress curl and divergence, were performed
as follows. The instantaneous derivative fields were computed first from modeled or observed
SST and wind fields. These fields were then averaged over the month or 30 days and processed
using the loess filter with half-span parameters of 12o longitude x 10
o latitude.
14
3. Results
3.1. Observed coupling coefficients
We adopt the wind speed magnitude coupling coefficient, sU, which measures the
surface winds speed response to SST anomalies, as the primary metric for estimating air-sea
coupling, because it is simple and relatively invariant to the seasonal variations and background
wind speed (O’Neill et al., 2012). The wind speed coupling coefficient was computed as the
slope of a linear regression of bin-averaged surface wind perturbations on SST perturbations.
Perturbations of equivalent neutral stability (ENS) 10-m winds are used for the analysis of
surface winds. SST perturbations bins were 0.2 oC; mean wind perturbations and their standard
deviations were computed for each SST bin.
For completeness and for comparison with other studies that use a variety of metrics, we
present a total of 6 different coupling coefficients that measure wind stress and wind speed
derivative responses to SST perturbations and derivatives. The coefficient for wind stress
magnitude response to to SST perturbations (sstr) is a widely used quantitative estimate of air-
sea coupling as well. Despite the quadratic dependence of wind stress on the wind speed, the
wind stress and wind speed coupling coefficients both exhibit approximately linear dependence
on the SST perturbations (O’Neill et al., 2012). These coupling coefficients are often
qualitatively similar, but may also vary geographically and seasonally. Coupling coefficients
based on derivative fields have also been widely used (Chelton et al., 2001; O’Neill, 2005;
Chelton et al., 2004, 2007; Haack et al., 2008; Song et al., 2009; Chelton and Xie, 2010;
O’Neill et al., 2010; O’Neill et al., 2012). These metrics are computed for the following pairs of
high-pass filtered variables: 10-m ENS wind curl (vorticity) and cross-wind SST gradient (sCu);
15
10-m ENS wind divergence and downwind SST gradient (sDu); wind stress curl and cross-wind
SST gradient (sCstr); wind stress divergence and downwind SST gradient (sDstr).
Figure 2(a,b) demonstrates high visible correspondence between high-pass filtered fields
of monthly average quantities of observed wind/wind stress derivatives and SST derivatives
(left columns). Approximate linear relationship between the bin-averaged pairs of variables
allows to estimate the coupling coefficient from a linear regression (right columns, see Figure
caption for details). Coupling coefficients sU = 0.42 m/s per oC, and sstr= 0.022 N/m
2 per
oC
(Fig.2a-b, top right) are similar to 7-year estimates for the Agulhas Return Current region from
O’Neill et al. (2012; their Fig. 4) that reported values of 0.44 m/s per oC and 0.022 N/m
2 per
oC,
correspondingly.
3.2. Model surface winds and coupling coefficients
3.2.1. Mean winds
The study period of July 2002 is an austral winter, and was characterized by westerlies
and several strong synoptic weather systems propagating eastward through the area. The
monthly averages of the modeled and observed ENS 10-m winds (Fig. 3, shaded) indicate broad
similarity, with slight notable differences between QuikSCAT observations and model
estimates. Particular simulations vary in wind strength and in details of spatial structure of the
average wind fields. Visual examination of the mean winds indicate that the WRF models using
three 1.5-order turbulence closure schemes: GBM, MYNN2, UW, as well as WRF_YSU
scheme (refer to Table 1) seem to agree with QuikSCAT more than others in predicting the
maximum wind in the eastern part of the domain; other simulations seem to underestimate the
winds, and show less spatial variability. We will assess spatial variability of the surface winds
16
in response to underlying mesoscale SST changes. Note, however, that the strongest wind in the
domain is found in the east rather than aligned with the strong meridional gradient of SST along
42°S in Fig. 1.
3.2.2. Spatial scales of variability
Zonal power spectral density (PSD) estimate of mean July 2002 SST and wind
perturbations (Fig. 4) show a secondary peak in both variables at wavelengths about 300 km
(mesoscale), while the primary peak is at scales 1000 km and greater (closer to synoptic scale).
WRF_GBM simulation appears to be in a better agreement with QuikSCAT in synoptic-to-
mesoscale range, for wavelengths of ~200km and greater. COAMPS ipbl=2 is underestimating
the PSD at wavelengths between 500-1000km. Other models tend to either overestimate or
underestimate the PSD at all scales, except for WRF YSU that is close to QuikSCAT estimates
at about 400km wavelength.
3.2.3.Wind – SST coupling coefficients
2-D picture of mesoscale variability of the average ENS 10-m winds and average SST
fields (Fig. 5) indicates that contours of SST perturbations are consistently aligned with positive
and negative perturbations of the winds. Visual inspection of the amplitudes of maximum and
minimum wind perturbations reveals that WRF_MYNN2 and WRF_UW seem to overestimate
the amplitudes, WRF_MYJ seems to underestimate them. Others, e.g. WRF_GBM visually
agree better with QuikSCAT.
Quantitative estimates using linear regression and resulting coupling coefficients of ENS
wind magnitude and SST perturbations for QuikSCAT and the models (Fig.6) confirm the
initial comparative assessment: WRF GBM produced sU = 0.40 m/s per oC, the value closest to
17
QuikSCAT estimate (0.42 m/s per oC), followed by COAMPS ipbl=2, COAMPS ipbl=1, and
WRF_YSU (0.38, 0.36, and 0.35m/s per oC, respectively). Excessive sU resulted for
WRF_MYNN2 and WRF_UW (0.56 and 0.53 m/s per oC, respectively), and weakest sU = 0.31
m/s per oC resulted for WRF_MYJ.
Our attempts to minimize the differences between the experiments, and allow for
identical surface flux scheme to be used along with different PBL mixing schemes prompted to
modify the WRF_MYJ experiment that uses “Eta similarity” surface scheme, to
WRF_MYJ_SFCLAY that uses “MM5 similarity” surface flux scheme similarly to WRF_GBM
and others (refer to Table 1). That modification for WRF_MYJ_SFCLAY slightly increased the
sU from 0.31 to 0.34 m/s per oC, but was still almost 20% below the QuikSCAT estimates.
Additional test was performed for WRF_UW simulation, where Zhang-McFarlane
cumulus parameterization (cu_physics = 7; Zhang and McFarlane, 1995) and shallow
convection scheme (shcu_physics=2; Bretherton and Park, 2009), both adapted from
Community Atmospheric Model (CAM) were used along with the UW_PBL mixing scheme
that had been adapted from CAM as well. Such an adjustment of physical options that were
known to work well together in CAM, resulted in only slight reduction of sU = 0.51 m/s per oC,
compared with 0.53 in WRF_UW.
Another vertical mixing scheme in WRF, GFS_PBL (Hong and Pan, 1996), a non-local-
K profile scheme and a predecessor of YSU_PBL (Hong et al., 2006), was tested in our
numerical experiments and yielded sU = 0.23 m/s per oC. Because it produced the weakest
coupling coefficient among the rest of the experiments, GFS_PBL was not used for further
analysis.
18
3.2.4. Relation of large scale wind to mesoscale wind-SST coupling
Seeing significant variety (O 10%), among the model mean wind speeds and among
their mesoscale wind-SST coupling coefficients, we wanted to eliminate the possibility that the
large scale was influencing the mesoscale statistics. We found that strong mean ENS 10-m
winds in the simulations do not imply strong mesoscale wind variability. For example, both
COAMPS simulations produce reasonable sU, but tend to underestimate the mean wind. In an
attempt to separate the contribution of the average wind response and mesoscale perturbations
of the wind in the models, the total SST and wind speed (U, T) are partitioned into spatial
means ( U and T ), large-scale parts, and perturbations ( 'U and 'T ) by the loess spatial
filter. If N is the number of spatial locations, the overbar operator represents the average over
the entire inner domain
. The covariance of the mean speed and SST,
cov(U,T), can could then be written:
. (4)
After opening the parentheses in the above equation, rearranging the resulting nine
terms, and noting that small-scale averages ( ',' TU ) over the entire domain are numerically
negligible, the covariance in Eq.(5) is represented by four individual components as follows:
. (5)
I II III IV
The left-hand side of the Eq.(5) is the spatial co-variability of the temporal mean quantities. The
Term I on the right-hand side (RHS) is the covariance of large-scale (lowpass filtered) U and T
fields, cross Terms II and III evaluate the co-variability of large scale quantity with the
perturbation scale of the other variable. The last term IV represents the mesoscale co-variability
19
of the wind and SST that is proportional to the regression slope sU. This decomposition of
covariance into four components places the mesoscale co-variability into the context of the total
and large-scale co-variability. Covariances and variances (σ2) of different U and T variables and
pairs from Eq.(5) are given in Table 2, and the correlation coefficients
, for the
corresponding terms are shown in Fig. 7.
As found in previous studies, negative co-variability results for the time-average wind and
SST fields (LHS of Eq.5), the covariance of their large-scale components (Term I)
corresponding the large-scale product, and corresponding correlations for these terms. This
result supports the observations of negative correlations between winds and SST found on
larger scales (Liu et al., 1994), consistent with increased evaporative cooling of the ocean
surface, in a thermodynamic process where the atmosphere drives the ocean. All the RHS terms
involving the perturbations have positive covariance (data columns 3-5 in Table 2). The
resulting correlations, however, depend on the standard deviations of the terms. Term II,
, represents stronger larger-scale wind speeds at the locations of the positive small-
scale SST perturbations, and is small. The co-variability of mesoscale wind perturbations with
the large-scale SST changes (Term III), , results in consistent positive contribution.
The estimates of Term III for different models are comparable (50-100%) to the contributions
from the mesoscale co-variability explained by Term IV, . The positive
correlations of the mesoscale perturbations are the strongest (Fig. 7). Mesoscale
perturbations and their co-variability are the focus of the present study. Numerical atmospheric
models used in the study are also particularly designed and well-suited to resolve and simulate
mesoscale and smaller-scale features.
20
3.2.5. What determines the coupling coefficient?
The coupling coefficient sU , can be expressed approximately as the regression slope
'
'''
T
UTUUs
, (6)
where ''TU is the correlation coefficient, and 'U , 'T are the corresponding standard
deviations of the wind and SST perturbation fields, respectively, estimated for the fields shown
in Fig. 5. (The actual calculations of the coupling coefficients use a binned regression as
described in Section 3.1.) Note that correlation coefficients ''TU are generally high for all the
models, and fall within a small range (0.86 to 0.92, as shown in Fig. 7). The standard deviation
of temperature 'T = 1.1°C is nearly identical in both models as it is prescribed by the imposed
surface forcing. Variations in wind perturbation 'U thus determine the strength of the sU.
Indeed, Fig 8b shows the correlation among the models of wind perturbation variance 2
'U to sU
is 0.996. In contrast, no statistically significant correlation among the models and QuikSCAT
(Fig 8a) results between the domain-average wind speed and the sU. Spatial variances of time-
mean wind speed and mesoscale wind speed perturbations over the nested domain (Fig. 8c) are
found to be highly correlated at ρ=0.94, suggesting that the same process of mesoscale wind
response contributes to the total spatial variability of the wind field.
3.2.6. Coupling coefficients for other quantities
To facilitate comparisons with earlier estimates of mesoscale air-sea coupling, we
present coupling coefficients for wind stress, and derivatives of wind, wind stress, and SST.
Table 3 shows a summary of six different coefficients, discussed in Section 3.1, and the ratios
of each coupling coefficient to its corresponding QuikSCAT estimate. Modeled wind stress and
21
SST derivatives were computed from 6-h output of instantaneous model variables, then
averaged over 30 days, and high-pass filtered. Despite absolute differences between different
types of correlation coefficients, there is overall general agreement on whether a given
simulation overestimates, underestimates, or is close to QuikSCAT.
3.3. Boundary layer structure
3.3.1. Wind and thermal profiles
In addition to examining the response of the surface wind to SST, we analyzed the
vertical structure of the model atmospheric boundary layer in the simulations. Profiles of
average wind speed for all the simulations over the nested domain (Fig. 9a) have maximum
differences of 1.1 m/s near the ground, and about 1.0-1.4 m/s at 150-1500 m. Average profiles
of potential temperatures (Fig. 9b) differ by up to 1.3K near the ground, over 2.0K around
600m, and less than 1.0K at 1500 m elevations and higher. Average profiles indicate that
models differ in their simulation of near-surface wind shear and stability in the boundary layer,
which both affect the transfer of momentum. The WRF_UW experiment yields the most stable,
nearly linear, potential temperature profile, and strongest wind shear near the ground below
400m. Vertical profiles of the wind speed coupling coefficients (Fig. 9c), estimated with a
simplified way using Eq.(6), indicate a dipole structure, in which highest wind speed sensitivity
to SST near the ground (0.19-0.44 m/s per oC) rapidly reduce to near-zero at 150-300 m for
most models, and then become negative peaking near 300m. There is not much sensitivity of the
wind speed to SST above 600-800m for all of the models. Coupling coefficients of potential
temperature to SST (Fig. 9d) show a significantly different picture, in which high surface values
(0.38-0.50 K per oC) in all of the experiments gradually decrease to zero at 1000-1400m.
22
Fig. 10 shows composite profiles of the wind response to SST, for different SST
perturbation ranges. In agreement with the high sensitivity found primarily near the surface
(Fig. 9c), the strongest positive wind perturbations are found over warmer areas, and the
strongest negative wind perturbations (weakest winds) over colder patches within the lowest
few hundred meters. Above 150-400m and in the remaining part of the boundary layer, the
models predict stronger winds over the coldest SST patches (< -1.5oC), but not over the
intermediate range of cooler SST perturbations (-1.5oC ≤ SST '≤ -0.5
oC). There is less
agreement between the models on weakening of winds in the middle and upper part of the
boundary layer over the warmest SST perturbations (> 1.5oC). The lack of symmetrical
response between the warm and cold patches is evident in all of the simulations, primarily
originating from a differential response of turbulent mixing to modified stability over SST
perturbations. This is a direct result of mixing coefficient KM depending on non-linear stability
function SM (Eq.1) in Mellor-Yamada-type schemes, or non-linear Richardson number-
dependent mixing in non-local-K type scheme.
The modeled weakening of near-surface winds over cold water is expected if increased
static stability permits an even more strongly sheared layer in the lowest 400m, depleted of
momentum at the surface (Samelson et al., 2006). Some models have an excess of momentum
above the stable layer, due to the anomalous reduction of drag, analogous to mechanism
producing nocturnal low-level jets (Small et al., 2008, Vihma et al., 1998).
3.3.2. Vertical turbulent diffusion
To test the hypothesis that the variability in wind simulated by the models using
different boundary layer schemes reflects differences in vertical mixing of momentum, we show
23
profiles of model eddy viscosity, KM. Average profiles (Fig. 11a) for eight main experiments
show elevated maxima at ~350-500m, varying from 45 m2/s to less than 80 m
2/s for most of the
models, and notably greater maximum of almost 140 m2/s in WRF_UW simulation at elevation
around 1500m. The spatial standard deviations of the time-average KM perturbations (high-pass
filtered at each level in a manner similar to the winds, Fig. 11b) look similar to the average eddy
viscosity profile. The standard deviation of KM seems to roughly scale with the mean KM itself.
Correlations between 0-600m height-averaged eddy viscosity KM (Fig. 11c) and sU resulted in
correlation coefficient of ρ=0.83 for the eight basic experiments.
We carried out an additional experiment based on WRF_GBM simulation, in which the
turbulent eddy transfer coefficients (KM and KH) were set constant in time and horizontal
domain, and identical to the average profile for nested grid (WRF_GBM in Fig. 11 a). In this
simulation turbulent mixing therefore was invariant to the actual atmospheric stability, resulting
in a low coupling coefficient of only 0.15 m/s per oC (Km, Kh fixed in Fig. 11 c).
Song et al. (2009) reported strong dependence on stability of vertical diffusion in WRF
GB01-based PBL scheme (earlier version of GBM) as compared to the WRF MYJ PBL
scheme. Turbulent eddy coefficients HMHM lqSK ,, (Eq.1), are linearly proportional to
corresponding stability functionsHM SS , . A reduced stability factor Rs was introduced by Song
et al (2009) to influence the stability on turbulent eddy mixing coefficients, where Rs=0
corresponded to neutral conditions and Rs=1 equivalent to GB01 scheme. Modified stability
functions result by scaling with a stability factor Rs as follows
)(~ N
s
N SSRSS , (7)
where S are the stability functions for momentum or heat evaluated by the model scheme for
the prevailing conditions estimated (Eq. (24)-(25) from Galperin et al., 1988); NS are the same
24
functions for neutral stability conditions. Modified stability functions MS~
and HS~
are then used
in the equations for turbulent eddy coefficient for momentum and heat. Reduced stability
parameter consistently lowered coupling coefficients; attempts to increase the Rs, however,
rapidly led to too strong mixing and unstable model behavior.
Similarly reducing the effect of stability, we analyzed average eddy viscosity KM
profiles for different Rs in WRF GBM experiments; Fig. 11(a) shows the profiles for Rs =0, for
Rs =1 (being equivalent to WRF GBM), and for Rs =1.1. Other profiles of KM for Rs = 0.1, 0.3,
0.5, 0.7, and 0.9 vary gradually between those with Rs = 0 and Rs =1, and showed a single
elevated maximum. Increased stability with Rs =1.1 produced excessive mixing in the boundary
layer with secondary maximum between 1000-1200m. Examination of the individual KM
profiles suggests that models with stronger maximum also have higher wind coupling
coefficient. Correlations between height-averaged eddy viscosity and sU (Fig. 11c) for the
sensitivity experiments resulted in consistently higher coupling coefficients as Rs increased and
the static stability had more influence on the vertical mixing. Our results showed that for Rs = 1
the coupling coefficients for 10-m ENS winds were closer to QuikSCAT estimates, and for
Rs =0.0, coupling coefficients decreased by almost 60%.
Sensitivity of the eddy viscosity to the SST (Fig.12) is studied next in the two different
ways for the WRF_GBM experiment. In first method, average KM perturbations grouped by the
local SST perturbations (Fig. 12, left panel); monthly-average perturbations were used for this
method. In the second method, we grouped the KM anomalies depending on the orientation of
surface wind relative to the SST gradient (Fig. 12, right panel). Because the wind changes
direction over the 30 day simulations, the calculations were done for every individual time
25
record in the second method, and then averaged for each group. KM anomalies were defined as
deviations of the modeled values from their temporal and spatial average at each vertical level.
In the first analyzed method, the warmest patches (>1.5 oC) resulted in over 60%
increase in peak values compared with the average profile, found at about 350-400m. Coldest
SST patches (<-1.5 oC) yielded a reduction of close to 50% from the peak average values.
Consistent increase in vertical mixing over warmest patches occurs over the upper portion of
the boundary layer as well, between 1000-2000m, which could be due to the deepening of the
boundary layer over the warmest SST perturbations. Reduction in mixing is less defined for the
cold patches.
The analysis using the second method indicated clear tendency of increased vertical
mixing and higher Km by about 30% (at ~300m), when surface winds blow predominantly along
the SST gradient towards warmer SST, and about 25% decrease of peak Km, when winds blow
in the opposite direction. No significant changes in eddy viscosity profile were found for the
cases of cross-wind SST gradients. The effect of relative direction on the profiles is mostly
below 1400m.
Because of the strong effect of local SST changes on vertical mixing (Fig. 12 left), we
further quantified the sensitivity of turbulent eddy viscosity to SST perturbations for various
models (Fig. 13). Most sensitive height-average KM perturbations to local SST variations
results for WRF_GBM, WRF_MYNN2, and WRF_UW simulations, with the latter having
relatively extreme sensitivity. Less sensitivity resulted for COAMPS_ipbl=2 and WRF_YSU
runs, and much weaker sensitivity for WRF_MYJ. The variability between the models is
substantial not only in the rate of KM increase per perturbation oC, but also in the standard
deviation of KM perturbations. For most of the experiments except WRF_MYJ, rate of increase
26
is slightly slower for negative SST perturbation, and higher for positive SST perturbations.
This is in agreement with Fig. 12 (left) , in which warmer SST patches produced eddy viscosity
gain not only in the lower levels where the KM peaks, but in the upper portion of the boundary
layer (between 1000-2000m) as well.
4. Summary and Discussion
Our numerical modeling study explores sensitivity and atmospheric boundary layer
response to mesoscale SST perturbations in the region of Agulhas Return Current (ARC) in
terms of wind speed-SST coupling coefficients. Simulations from eight experiments using state-
of-the-art boundary layer mixing schemes in two distinct mesoscale atmospheric models were
analyzed. Satellite QuikSCAT scatterometer measurements of equivalent neutral stability (ENS)
winds produced coupling coefficients (CC) of 0.42 m/s per oC for the study region. Modeled
ENS winds at 10-m height derived from surface momentum flux under assumption of neutral
stability resulted in coupling coefficients ranging 0.31-0.56 m/s per oC for different models
and/or boundary layer parameterizations.
Our improved Grenier-Bretherton-McCaa (GBM) boundary layer mixing scheme
produced wind speed coupling coefficient of 0.40 m/s per oC in WRF model, closest to
QuikSCAT estimates. COAMPS case with ipbl=2 boundary layer scheme produced slightly
lower value of 0.38 m/s per oC, second closest to QuikSCAT, but COAMPS simulations
underestimated average ENS winds as compared to the WRF simulation. Underestimation of
average quantities by COAMPS could be due to using different dataset for initial and boundary
conditions than the model is well adjusted and tested for, i.e., U.S. Navy’s Operational Global
Atmospheric Prediction System (NOGAPS) model. In all eight simulations presented in our
study, however, global NCEP FNL Reanalysis data were used for that purpose.
27
The UW PBL scheme is an implementation of the boundary layer mixing scheme based
on GB01 study as the GBM PBL, except simplified and adapted for the use in climate models.
Despite this similarity, the WRF_UW simulation produced wind speed coupling coefficient of
0.53 m/s per oC, notably higher than in WRF_GBM experiment. Note, however, that in the
different context of the CAM5 global model, the UW PBL has been found to produce the wind
speed coupling coefficients quite close to the observed, for the similar geographical area (Justin
Small, personal communication, 2013).
We investigated vertical structure of mesoscale wind and potential temperature from the
simulations, and their sensitivity to SST changes. The strong sensitivity of potential temperature
perturbations to SST perturbations near the surface (0.38-0.50 K per oC) gradually decreased
with elevation, vanishing at 1000-1400m. Wind speed sensitivity to SST near the ground (0.19-
0.44 m/s per oC) rapidly decreased to near-zero at 150-300m, and then become negative at about
150-500m for the experiments with Mellor-Yamada type PBL schemes. The diagnosed 0-600m
height-average turbulent eddy viscosity (KM) was found to be highly correlated (ρ=0.83) with
the coupling coefficients among the corresponding eight model simulations, indicating the
importance of mixing the lower part of the boundary layer for the coupling coefficient.
Experiments with modified stability dependence in the WRF GBM mixing scheme showed the
effect of the stability dependence of KM on the surface wind speed mesoscale coupling
coefficient. Vertical profiles of eddy viscosity were found to be greatly dependent on
underlying mesoscale SST variability: warmest SST patches for SST perturbations > 1.5oC
resulted in profiles of positive KM perturbations (+60%), implying increased mixing in the
presence of shear below 350-400m. Colder patches (<-1.5oC of SST perturbations) resulted in
close to 50% decrease in KM at the peak level, with the most pronounced decrease in mixing in
28
the lower 1000-1200m. Relative orientation of the surface wind and underlying SST gradient
affected vertical mixing profiles as well; higher KM anomalies within the boundary layer of up
to 30% resulted for the flow from cold to warm water (with the SST gradient), and up to 25%
decrease resulted for flow from warm to cold water.
We attempted to identify the key parameters in boundary layer mixing schemes that
would affect the atmospheric response to the SST variability in different schemes. Static
stability, wind shear parameters (used in calculations of stability functions SM and SH),
turbulent kinetic energy (TKE), turbulent master length scale l, eddy transfer coefficient for
TKE in Mellor-Yamada type schemes (Kq), all showed notable variations between the model
simulations, but no single crucial parameter was identified.
The coupling coefficient took on a wide variety of values for the different schemes, so
we diagnosed the ensemble of simulations for emergent properties related to the wind response
to mesoscale SST. Due to the variety in mesoscale wind speed coupling behavior among
models, we advocate the wind speed coupling coefficient as a metric that can be assessed
against wind observations. The wind speed coupling coefficient is relatively insensitive to
seasonal and large-scale changes in the background mean wind (O’Neill et al., 2012).
The WRF GBM scheme best reproduced the wind speed coupling coefficient compared
to QuikSCAT observation. We have provided the Grenier-Bretherton-McCaa boundary layer
mixing scheme to the WRF code repository, distributed now with WRF version 3.5.
29
Acknowledgements
This research has been supported by the NASA Grant NNX10AE91G.
We thank Richard W. Reynolds (NOAA) for guidance to obtain AMSR-AVHRR SST data used
for lower boundary condition in numerical simulations. We are grateful to Justin Small (NCAR)
for methodical discussions about the coupling coefficients and for sharing the findings of his
group.
30
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35
TABLES
Table 1. List and summary numerical experiments. Name of the experiment contains the name of the atmospheric model
(WRF or COAMPS), and then by the conventional name of the boundary layer scheme used. In the WRFv3.3 release, MYJ
PBL scheme had to used only along with the “Eta similarity” surface layer scheme (sf_sfclay_physics=2). To ensure more
consistency between the physical option in WRF simulations, we developed WRF_MYJ_SFCLAY case, in which the MYJ
PBL was adapted to be used along with “MM5 similarity” surface scheme (sf_sfclay_physics= 1).
* - see Section 2.2.2 for details.
experiment name PBL type scheme PBL scheme reference sfc. flux scheme
(sf_sfclay_physics)
WRF_GBM 1.5-order closureGrenier and Bretherton (2001),
Bretherton et al. (2004)MM5 Similarity (1)
WRF_MYJ 1.5-order closure Janjić (1994, 2002) Eta Similarity (2)
WRF_MYJ_SFCLAY 1.5-order closure Janjić (1994, 2002) MM5 Similarity (1)
WRF_MYNN2 1.5-order closure Nakanishi and Niino (2006) MM5 Similarity (1)
WRF_UW 1-1.5-order closure * Bretherton and Park (2009) MM5 Similarity (1)
COAMPS_ipbl=1 1.5-order closureMellor and Yamada (1982),
Yamada (1983)
Louis (1979),
COARE-2.6 (water)
COAMPS_ipbl=2 1.5-order closureMellor and Yamada (1982),
Yamada (1983)
Louis (1979),
COARE-2.6 (water)
WRF YSU non-local-K Hong, Noh and Dudhia (2006) MM5 Similarity (1)
36
Database cov(U,T) cov(<U>,<T>) cov(<U>,T') cov(U',<T>) cov(U',T') σ2(U) σ2(<U>) σ2(U')
QuikSCAT v4 -0.63 -1.49 0.03 0.31 0.52 1.92 1.55 0.30
WRF GBM -1.58 -2.39 0.05 0.26 0.49 2.02 1.66 0.25
WRF MYJ -1.41 -2.13 0.06 0.28 0.28 1.54 1.26 0.15
WRF MYJ_SFCLAY -0.90 -1.67 0.07 0.29 0.41 1.41 1.10 0.18
WRF MYNN2 -1.06 -2.14 0.07 0.32 0.69 2.47 1.88 0.46
WRF UW -1.28 -2.32 0.05 0.33 0.66 2.22 1.72 0.43
WRF YSU -1.41 -2.16 0.05 0.27 0.43 1.57 1.29 0.19
COAMPS ipbl=1 -1.01 -1.82 0.06 0.30 0.45 1.42 1.15 0.21
COAMPS ipbl=2 -1.00 -1.81 0.06 0.28 0.48 1.47 1.15 0.23
Table 2. Covariances and variances (σ2) of the mean, large-scale (low-pass filtered), and mesoscale (high-pass filtered) ENS
winds from QuikSCAT and models, and sea surface temperatures. Units for covariances are oC m s
-1; units for variance of
wind variables are m2 s
-2. Variances of SST are generally similar because of the same database used, only slightly differ for
the models due to the model interpolation procedures.
Variances of NOAA SST are as follows: σ2(T) = 23.27 (oC)2 , σ2(<T>) = 20.49 (oC)2, and σ2(T’) =1.27 (oC)2.
Variances for WRF SST are σ2(T) = 23.79 (oC)2 , σ2(<T>) = 20.30 (oC)2, and σ2(T’) =1.22 (oC)2.
Variances for COAMPS SST are σ2(T) = 23.14 (oC)2 , σ2(<T>) = 20.56 (oC)2, and σ2(T’) =1.23 (oC)2.
37
Table 3. Summary for the coupling coefficients computed using six different methods (see Section 2.5): sU is for ENS wind – SST
perturbations (m s-1
oC
-1); sCu is for ENS wind relative vorticity – crosswind SST gradient (m s
-1 oC
-1); sDu is for ENS wind divergence
– downwind SST gradient (m s-1
oC
-1); sstr is for wind stress – SST perturbations (N m
-2 oC
-1), sCstr is for wind stress curl– crosswind
SST perturbations (100 * N m-2
oC
-1); sDstr is for wind stress divergence – downwind SST perturbations (100 * N m
-2 oC
-1). Ratios in
data columns 7 -12 are between the given coupling coefficient and its corresponding estimate from QuikSCAT (QuikSCAT + NOAA
IO SST, for derivative SST fields). Highlighted in bold and italic font are the row with QuikSCAT data and the column with sU
coupling coefficient; sU is chosen as a primary metric for air-sea coupling estimate in the present study. Rows are ordered by the
primary coupling coefficient.
Database s U s Cu s Du s str s Cstr s Dstr
WRF_MYJ 0.31 0.28 0.57 0.017 1.56 2.82 0.75 0.73 0.94 0.79 0.71 0.93
WRF_MYJ_SFCLAY 0.34 0.30 0.61 0.019 1.79 3.10 0.82 0.77 1.02 0.87 0.81 1.02
WRF_YSU 0.35 0.29 0.61 0.021 1.87 3.19 0.85 0.75 1.02 0.98 0.85 1.05
COAMPS_ipbl=1 0.36 0.40 0.68 0.016 1.83 2.78 0.85 1.05 1.13 0.73 0.83 0.91
COAMPS_ipbl=2 0.38 0.42 0.82 0.017 1.84 3.19 0.91 1.10 1.36 0.79 0.84 1.05
WRF_GBM 0.40 0.38 0.74 0.024 2.35 3.82 0.96 0.98 1.23 1.08 1.07 1.26
QuikSCAT v4 0.42 0.39 0.60 0.022 2.20 3.04 1.00 1.00 1.00 1.00 1.00 1.00
WRF_CAMUW 0.53 0.53 1.03 0.033 3.54 5.66 1.27 1.38 1.70 1.49 1.61 1.86
WRF_MYNN2 0.56 0.66 1.05 0.035 3.97 6.00 1.34 1.70 1.75 1.61 1.80 1.97
38
Figures
Figure 1. Monthly average of satellite SST estimate (oC) for July 2002, from NOAA
Reynolds optimum interpolation (OI) 0.25o daily sea surface temperature (SST) product,
based on Advanced Microwave Scanning Radiometer (AMSR) SST and Advanced Very
High Resolution Radiometer (AVHRR). Black rectangles outline WRF simulations
domains, outer and nested domains having 75km and 25km grid box spacing, respectively.
There are 50 vertical levels in each of the model grids, stretching from the ground to about
18km; 22 levels are in the lowest 1000m. Missing AMSR-AVHRR SST values in the
interior of nested domain d02 that occur due to land contamination by small islands, are
interpolated for the model lower boundary conditions updated.
39
Figure 2(a). (top left) July 2002 average of QuikSCAT 10-m ENS wind perturbations
(color) and satellite AMSR-E/ Reynolds OI SST perturbations (contours, interval 1oC, zero
contour omitted, negative dashed). (top right) Coupling coefficient sU is estimated as a
linear regression slope (red line) of bin-averaged wind perturbation (black dots) on SST
perturbations (shown in the left panel); shaded gray areas show plus/minus standard
deviation of wind perturbation for each SST bin. Dashed blue lines indicate SST bin
population (right blue y-axis). Estimates include range of SST perturbations of
approximately from -3oC to +3
oC (bins containing >50 data points). (middle row) Similar
to the top row, except for ENS wind curl (vorticity) – cross-wind SST gradient pair of
perturbation fields; contour intervals of SST gradients are 1oC/100km, with negative
contours dashed and zero omitted. Coupling coefficient sCu is marked on the right panel.
(bottom row) Similar to the middle row, except for ENS wind divergence – downwind
SST perturbations; coupling coefficient sDu is marked on the right panel.
40
Figure 2(b). (top row) Similar to Fig.2(a) top row, except for QuikSCAT wind stress –
SST derivative pair; coupling coefficient marked sstr on the right panel. (middle row)
Similar to the Fig. 2(a) middle row, except for wind stress – cross-wind SST gradient pair
of perturbation fields; coupling coefficient is marked sCstr on the right panel. (bottom row)
Similar to the middle row, except for wind stress divergence – downwind SST
perturbations; coupling coefficient is sDstr.
41
Fig
ure
3.
July
2002 m
ean 1
0-m
equiv
alen
t neu
tral
sta
bil
ity (
EN
S)
win
d s
pee
d (
m/s
), o
ver
the
mod
el n
este
d d
om
ain
area
, fr
om
Quik
SC
AT
v4
obse
rvat
ions
and m
odel
res
ult
s as
indic
ated
in l
ow
er l
eft
corn
er o
f ea
ch p
anel
.
42
Figure 4. Power spectral density estimate for the monthly mean SST (right y-axis), and
ENS 10-m winds (left y-axis), for the nested domain area. Spectral density
estimates were computed for individual latitudinal bands, and then averaged for
the region of the nested domain of the model. For consistency of comparison
between models and QuikSCAT, modeled fields were masked in the areas of
QuikSCAT data gaps.
43
Fig
ure
5.
July
2002
aver
age
of
10
-m E
NS
win
d p
ertu
rbat
ions
(colo
r),
and s
atel
lite
AM
SR
-E/
Rey
nold
s O
I
SS
T p
ertu
rbat
ions,
sim
ilar
to F
ig. 2a
top l
eft
pan
el.
Win
d p
ertu
rbat
ions
are
com
pute
d f
or
(top
lef
t) Q
uik
SC
AT
sate
llit
e w
ind p
roduct
(ver
sion 4
), s
moo
thed
wit
h 1
.25
o x
1.2
5o l
oes
s fi
lter
; (o
ther
pan
els)
model
s (W
RF
v3.3
or
CO
AM
PS
v3)
as i
ndic
ated
, w
ith v
ario
us
turb
ule
nt
mix
ing s
chem
es.
44
Fig
ure
6.
Coupli
ng c
oef
fici
ents
sU
(mar
ked
s i
n e
ach p
anel
) bet
wee
n E
NS
10
-m w
ind p
ertu
rbat
ions
and
SS
T p
ertu
rbat
ions
fiel
ds
show
n i
n F
ig.5
. S
imil
ar t
o F
ig. 2a
top r
ight
pan
el.
45
Figure 7. Correlation between the pairs of mean 10-m ENS winds and SST fields,
and their low-pass and high-pass components, from Eq.(3). Black open circles
indicate the coupling coefficient sU for each experiment/database (on x-axis, but in
m/s per oC).
46
a)
b)
47
Figure 8. Domain-wide mean statistics for the nested grid: (a) Coupling
coefficients for QuikSCAT and models mapped against the corresponding mean
ENS 10-m winds; (b) coupling coefficients vs. spatial variance of ENS wind
perturbations, 2
'U , and the correlation coefficient r computed between the nine
pairs of variables; (c) spatial variance of the mean ENS wind 2
U , vs. variance of
ENS winds perturbations 2
'U (i.e., variance of the fields shown in Fig. 3 vs.
corresponding fields from Fig.5), and the correlation coefficient between them for
nine points. Black dashed lines are given for the reference, passing through the
QuikSCAT estimates.
c)
48
Figure 9. Vertical profiles averaged for the nested domain of (a) average wind speed
and (b) potential temperature for the nested domain. Vertical profiles of the coupling
coefficients for (c) wind speed and (d) potential temperature to SST, estimated from
the high-pass filtered quantities using Eq.(6).
a) b)
c) d)
49
Figure 10. Average profile of high-pass filtered wind speed for ranges of SST
perturbations, as indicated on the legend, for the following simulations:
(a) WRF GBM, (b) WRF MYJ, (c) WRF MYNN2, (d) WRF UW, (e) COAMPS ipbl=2,
and (f) WRF YSU.
a) b) c)
d) e) f)
50
Fig
ure
11.
(a)
Month
ly a
ver
age
eddy v
isco
sity
coef
fici
ents
KM
for
the
nes
ted d
om
ain;
(b)
stan
dar
d d
evia
tions
of
month
ly
aver
age
per
turb
atio
n o
f K
M f
or
eight
model
sim
ula
tions.
(c)
Hei
gh
-av
erag
e K
M 0
-600m
vs.
coupli
ng c
oef
fici
ent.
Bla
ck l
ine
corr
esponds
to W
RF
GB
M s
imula
tions
wit
h m
odif
ied s
tabil
ity r
esponse
, R
s=0.0
, 0.1
0.3
, 0.5
, 0.7
, 0.9
. 1.0
, 1.1
(only
fir
st a
nd
last
num
ber
s ar
e m
arked
). C
yan
poin
t co
rres
pond
s to
the
sim
ula
tion u
sing
WR
F_G
BM
, but
the t
urb
ule
nt
eddy v
isco
sity
an
d
dif
fusi
vit
y p
rofi
les
invar
iant
and f
ixed
to t
he
dom
ain
-aver
age
pro
file
(K
M p
rofi
le s
how
n i
n t
he
(a)
pan
el).
a)
b)
c)
51
a) b)
I
II
III
IV wind
𝑛
𝑠
wind
I
II
II
IV
52
Figure 12. (left panel) Average profiles of eddy viscosity perturbations (MK ’) for
different SST perturbation ranges, from WRF GBM simulation. Anomaly of MK was
determined as a departure from the average at a given level. (right panel) Monthly mean
MK anomaly for different orientations of surface wind speed relatively to the SST gradient.
Anomaly was determined as a departure from the time- and domain- average MK at a given
level for each time record, after which the monthly mean was computed. s
and n
are unit
vectors in natural coordinate system, downwind and cross-wind, respectively (see insert for
details). Quadrants I, II, III, and IV are determined from downwind sSST / and cross-
wind nSST / components, as follows.
Quadrant I: sSST / >0 and nSSTsSST // (wind blows predominantly along
the SST gradient, from cold to warm water);
Quadrant II: nSST / >0 and sSSTnSST // (wind blows across the SST
gradient, warm water to the left of wind direction);
Quadrant III: sSST / <0 and nSSTsSST // ; (wind blows in the direction
opposite the SST gradient, from warm to cold water);
Quadrant IV: nSST / <0 and sSSTnSST // ; (wind blows across the SST
gradient, warm water to the right of wind direction).
s
n
53
Figure 13. Sensitivity of height-average eddy viscosity perturbations 'MK (0 – 600m) to
binned SST perturbations, for individual models as marked in each panel, computed
using a method similar to wind speed coupling coefficients. The errorbars indicate +/-
standard deviation from the mean value for each bin.
top related