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.

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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.