Modeling the Atmospheric Boundary Layer Wind. Response to Mesoscale Sea Surface Temperature

Transcription

1 Modeling the Atmospheric Boundary Layer Wind Response to Mesoscale Sea Surface Temperature Natalie Perlin 1, Simon P. de Szoeke, Dudley B. Chelton, Roger M. Samelson, Eric D. Skyllingstad, and Larry W. O Neill 17 October corresponding author nperlin@coas.oregonstate.edu

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 model simulations. The SST-induced wind response is assessed using a series of 8 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 winds or 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 m, is weakly negative around 300 m, and decreasing upward toward zero above m. 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 perturbation, and the orientation of the surface wind relative to the SST gradient. 2

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 ( 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 subgrid 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 3

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. 4

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 for 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 72 o and 33 o in the longitudinal and latitudinal directions, respectively. The nested inner domain has a 25-km grid with corresponding sizes of about 40 o lon. x 17 o lat. The vertical dimension is discretized with a 5

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 ( 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) 0.25 o 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 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 6

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 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 countergradient 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. 7

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 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), q u' v' w', is solved, but the other 2 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 K H M, q, are further parameterized using the prognostic q value, as follows: K M, H, q l q S M, H, q, (1) where l is master turbulent length scale, and S M H, q, is a dimensionless parameter. The latter could be set to a constant value (such as often set for S q ), 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: 2 D q Dt 2 K z q 2 q z 2 Ps P b, (2) where D Dt is the material derivative following the resolved motion, horizontal turbulent diffusion is neglected, P s and P b are shear production and buoyant production of turbulent 8

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 S, are calculated. For example, GBM PBL in WRF uses Eq. (24-25) in Galperin et M H al. (1988) solution that assumes production-dissipation balance, P 1 s P b, 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 S, the on wind shear, M H 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 S,, 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 M H closure for convective layers that modifies the expression for K M. 9

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 S q =5 in the MYJ PBL scheme numerical implementation, and S q = 3 in COAMPS schemes. The GBM PBL assumes S 5 q S M. The MYNN PBL scheme has S q 2S M in Nakanishi and Niino (2004) reference, or tuned to S q 3S M 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-Yamadatype 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 K, to a fixed profile m h over the depth of the PBL. The eddy viscosity coefficient within the boundary layer is formulated as 2 z K kw z 1, (3) m s h where k is von Karman constant (0.4), z is the height from the surface, ws is the mixed-layer velocity scale, and h is the boundary layer height. The eddy diffusivity for temperature and 10

11 moisture are computed from K m 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 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 11

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) Observations Satellite observations of vector winds in rain- and ice-free conditions from the microwave scatterometer aboard QuikSCAT satellite on a 0.25 o 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 u stratification, * 10 U 10 mn ln, where k is the von Karman constant, and z0 is the roughness k z 0 length over the water. NOAA Reynolds Optimum Interpolation (OI) SST on a 0.25 o grid 12

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) 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 30 o longitude and 10 o latitude. These high-pass filtered fields are also referred to as perturbations. Similar high-pass filtering was applied to SST fields on a 0.25 o 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 0.25 o 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 12 o longitude x 10 o latitude. 13

14 3. Results 3.1. Observed coupling coefficients We adopt the wind speed magnitude coupling coefficient, s U, 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 o C; 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 (s str ) is a widely used quantitative estimate of airsea 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 (s Cu ); 14

15 10-m ENS wind divergence and downwind SST gradient (s Du ); wind stress curl and cross-wind SST gradient (s Cstr ); wind stress divergence and downwind SST gradient (s Dstr ). 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 s U = 0.42 m/s per o C, and s str = N/m 2 per o C (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 o C and N/m 2 per o C, correspondingly Model surface winds and coupling coefficients 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 15

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 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-tomesoscale range, for wavelengths of ~200km and greater. COAMPS ipbl=2 is underestimating the PSD at wavelengths between km. 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 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 s U = 0.40 m/s per o C, the value closest to 16

17 QuikSCAT estimate (0.42 m/s per o C), followed by COAMPS ipbl=2, COAMPS ipbl=1, and WRF_YSU (0.38, 0.36, and 0.35m/s per o C, respectively). Excessive s U resulted for WRF_MYNN2 and WRF_UW (0.56 and 0.53 m/s per o C, respectively), and weakest s U = 0.31 m/s per o C 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 s U from 0.31 to 0.34 m/s per o C, 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 s U = 0.51 m/s per o C, 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 s U = 0.23 m/s per o C. Because it produced the weakest coupling coefficient among the rest of the experiments, GFS_PBL was not used for further analysis. 17

18 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 s U, but tend to underestimate the mean wind. In an attempt to separate the contribution of the average wind response and mesoscale perturbations to 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 ( U ', T ' ) 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 18

19 of the wind and SST that is proportional to the regression slope s U. 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 (σ 2 ) 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 smallscale 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. 19

20 What determines the coupling coefficient? The coupling coefficient s U, can be expressed approximately as the regression slope s U U ' U ' T ', (6) T ' where U 'T ' 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 U 'T ' are generally high for all the models, and fall within a small range (0.86 to 0.92, as shown in later 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 2 s U. Indeed, Fig 8b shows the correlation among the models of wind perturbation variance U ' to s U is In contrast, no statistically significant correlation among the models and QuikSCAT (Fig 8a) results between the domain-average wind speed and the s U. Spatial variances of timemean 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 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 20

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 Boundary layer structure 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 m/s at 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 ( m/s per o C) rapidly reduce to near-zero at m for most models, and then become negative peaking near 300m. There is not much sensitivity of the wind speed to SST above m for all of the models. Coupling coefficients of potential temperature to SST (Fig. 9d) show a significantly different picture, in which high surface values ( K per o C) in all of the experiments gradually decrease to zero at m. 21

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 m and in the remaining part of the boundary layer, the models predict stronger winds over the coldest SST patches (< -1.5 o C), but not over the intermediate range of cooler SST perturbations (-1.5 o C SST ' -0.5 o C). 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 (> 1.5 o C). 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 K m depending on non-linear stability function S M (Eq.1) in Mellor-Yamada-type schemes, or non-linear Richardson numberdependent 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) 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 22

23 profiles of model eddy viscosity, K M. Average profiles (Fig. 11, left panel) for eight main experiments show elevated maxima at ~ m, varying from 45 m 2 /s to less than 80 m 2 /s for most of the models, and notably greater maximum of almost 140 m 2 /s in WRF_UW simulation at elevation around 1500m. The spatial standard deviations of the time-average K M perturbations (high-pass filtered at each level in a manner similar to the winds, Fig. 11 center) look similar to the average eddy viscosity profile. The standard deviation of K M seems to roughly scale with the mean K M itself. Correlations between 0-600m height-averaged eddy viscosity K M (Fig. 11, right) and s U 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 (K M and K H ) 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 o C (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 K M H lqs M, H, (Eq.1), are linearly proportional to corresponding stability functions S, S M H. A reduced stability factor R s was introduced by Song et al (2009) to influence the stability on turbulent eddy mixing coefficients, where R s =0 corresponded to neutral conditions and R s =1 equivalent to GB01 scheme. Modified stability functions result by scaling with a stability factor R s as follows ~ N S s N S R ( S S ), (7) where S are the stability functions for momentum or heat evaluated by the model scheme for 23

24 the prevailing conditions estimated (Eq. (24)-(25) from Galperin et al., 1988); N S are the same functions for neutral stability conditions. Modified stability functions S ~ M and S ~ H 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 R s, however, rapidly led to too strong mixing and unstable model behavior. Similarly reducing the effect of stability, we analyzed average eddy viscosity K M profiles for different R s in WRF GBM experiments; Fig. 11(a) shows the profiles for R s =0, for R s =1 (being equivalent to WRF GBM), and for R s =1.1. Other profiles of K M for R s = 0.1, 0.3, 0.5, 0.7, and 0.9 vary gradually between those with R s = 0 and R s =1, and showed a single elevated maximum. Increased stability with R s =1.1 produced excessive mixing in the boundary layer with secondary maximum between m. Examination of the individual K M profiles suggests that models with stronger maximum also have higher wind coupling coefficient. Correlations between height-averaged eddy viscosity and s U (Fig. 11c) for the sensitivity experiments resulted in consistently higher coupling coefficients as R s increased and the static stability had more influence on the vertical mixing. Our results showed that for R s = 1 the coupling coefficients for 10-m ENS winds were closer to QuikSCAT estimates, and for R s =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 K M 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 K M 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 24

25 record in the second method, and then averaged for each group. K m 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 o C) resulted in over 60% increase in peak values compared with the average profile, found at about m. Coldest SST patches (<-1.5 o C) 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 m, 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 K m by about 30% (at ~300m), when surface winds blow predominantly along the SST gradient towards warmer SST, and about 25% decrease of peak K m, 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 K M 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 K M increase per perturbation o C, but also in the standard deviation of K M perturbations. For most of the experiments except WRF_MYJ, rate of increase 25

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 K M peaks, but in the upper portion of the boundary layer (between m) 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 stateof-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 o C 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 m/s per o C 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 o C 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 o C, 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. 26

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 o C, 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 ( K per o C) gradually decreased with elevation, vanishing at m. Wind speed sensitivity to SST near the ground ( m/s per o C) rapidly decreased to near-zero at m, and then become negative at about m for the experiments with Mellor-Yamada type PBL schemes. The diagnosed 0-600m height-average turbulent eddy viscosity (K M ) 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 K M 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 > 1.5 o C resulted in profiles of positive K M perturbations (+60%), implying increased mixing in the presence of shear below m. Colder patches (<-1.5 o C of SST perturbations) resulted in close to 50% decrease in K M at the peak level, with the most pronounced decrease in mixing in 27

28 the lower m. Relative orientation of the surface wind and underlying SST gradient affected vertical mixing profiles as well; higher K M 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 S M and S H ), turbulent kinetic energy (TKE), turbulent master length scale l, eddy transfer coefficient for TKE in Mellor-Yamada type schemes (K q ), 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

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. 29

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35 TABLES experiment name PBL type scheme PBL scheme reference WRF_GBM 1.5-order closure Grenier and Bretherton (2001), Bretherton et al. (2004) sfc. flux scheme (sf_sfclay_physics) 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 order closure * Bretherton and Park (2009) MM5 Similarity (1) COAMPS_ipbl=1 1.5-order closure Mellor and Yamada (1982), Yamada (1983) Louis (1979), COARE-2.6 (water) COAMPS_ipbl=2 1.5-order closure Mellor and Yamada (1982), Yamada (1983) Louis (1979), COARE-2.6 (water) WRF YSU non-local-k Hong, Noh and Dudhia (2006) MM5 Similarity (1) 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 for details. 35

36 Database cov(u,t) cov(<u>,<t>) cov(<u>,t') cov(u',<t>) cov(u',t') σ 2 (U) σ 2 (<U>) σ 2 (U') QuikSCAT v WRF GBM WRF MYJ WRF MYJ_SFCLAY WRF MYNN WRF UW WRF YSU COAMPS ipbl= COAMPS ipbl= Table 2. Covariances and variances (σ 2 ) 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 o C m s -1 ; units for variance of wind variables are m 2 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: σ 2 (T) = ( o C) 2, σ 2 (<T>) = ( o C) 2, and σ 2 (T ) =1.27 ( o C) 2. Variances for WRF SST are σ 2 (T) = ( o C) 2, σ 2 (<T>) = ( o C) 2, and σ 2 (T ) =1.22 ( o C) 2. Variances for COAMPS SST are σ 2 (T) = ( o C) 2, σ 2 (<T>) = ( o C) 2, and σ 2 (T ) =1.23 ( o C) 2. 36

37 Database s U s Cu s Du s str s Cstr s Dstr WRF_MYJ WRF_MYJ_SFCLAY WRF_YSU COAMPS_ipbl= COAMPS_ipbl= WRF_GBM QuikSCAT v WRF_UW WRF_MYNN Table 3. Summary for the coupling coefficients computed using six different methods (see Section 2.5): s U is for ENS wind SST perturbations (m s -1 o C -1 ); s Cu is for ENS wind relative vorticity crosswind SST gradient (s -1 o C -1 ); s Du is for ENS wind divergence downwind SST gradient (s -1 o C -1 ); s str is for wind stress SST perturbations (100 * N m -2 o C -1 ), s Cstr is for wind stress curl crosswind SST perturbations (100 * N m -3 o C -1 ); s Dstr is for wind stress divergence downwind SST perturbations (100 * N m -3 o C -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). Shading highlights the row with QuikSCAT data, and the column with s U coupling coefficient that is chosen to be a primary metric for air-sea coupling estimate in the present study. Rows are ordered by the primary coupling coefficient. 37

38 Figures Figure 1. Monthly average of satellite SST estimate ( o C) for July 2002, from NOAA Reynolds optimum interpolation (OI) 0.25 o 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. 38

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 1 o C, zero contour omitted, negative dashed). (top right) Coupling coefficient s U 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 -3 o C to +3 o C (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 1 o C/100km, with negative contours dashed and zero omitted. Coupling coefficient s Cu is marked on the right panel. 39

40 (bottom row) Similar to the middle row, except for ENS wind divergence downwind SST perturbations; coupling coefficient s Du is marked on the right panel. 40

41 Figure 2(b). (top row) Similar to Fig.2(a) top row, except for QuikSCAT wind stress SST derivative pair; coupling coefficient marked s str 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 s Cstr on the right panel. (bottom row) Similar to the middle row, except for wind stress divergence downwind SST perturbations; coupling coefficient is s Dstr. 41

42 Figure 3. July 2002 mean 10-m equivalent neutral stability (ENS) wind speed (m/s), over the model nested domain area, from QuikSCAT v4 observations and model results as indicated in lower left corner of each panel. 42

43 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

44 Figure 5. July 2002 average of 10-m ENS wind perturbations (color), and satellite AMSR-E/ Reynolds OI SST perturbations, similar to Fig. 2a top left panel. Wind perturbations are computed for (top left) QuikSCAT satellite wind product (version 4), smoothed with 1.25 o x 1.25 o loess filter; (other panels) models (WRF v3.3 or COAMPS v3) as indicated, with various turbulent mixing schemes. 44

45 Figure 6. Coupling coefficients su (marked s in each panel) between ENS 10-m wind perturbations and SST perturbations fields shown in Fig.5. Similar to Fig. 2a top right panel. 45