Recent high-resolution satellite observations have significantly helped the understanding of how the ocean and atmosphere interact, and have revealed that surface wind divergence and wind curl exhibit coherent structures across large-scale sea surface temperature (SST) fronts on monthly or longer timescales (see review by Xie, 2004; Chelton et al., 2004; Small et al., 2008; Chelton and Xie, 2010). Surface convergence found over western boundary currents can be an agent that connects atmospheric responses in the Marine Atmospheric Boundary Layer (MABL) and free troposphere. In particular, Minobe et al. (2010) demonstrated that surface wind convergence just over the Gulf Stream current axis is accompanied by enhanced rain, deep ascent in the mid-troposphere and frequent occurrences of high cloud tops.
There has been much debate on the mechanisms of surface wind divergence/convergence with respect to SST fronts. A widely accepted explanation (Xie et al., 2002; O'Neill et al., 2003) is the downward momentum mixing mechanism (Sweet et al., 1981; Wallace et al., 1989), in which the near-surface atmosphere destabilizes over warmer SSTs and the intensified downward momentum transport from aloft acts to accelerate the surface wind. According to this mechanism, the near-surface wind divergence should be proportional to the downwind SST gradient (Chelton et al., 2001). The other mechanism used for surface wind convergence/divergence (Small et al., 2003; Cronin et al., 2003; Song et al., 2006; Minobe et al., 2008, 2010; Tokinaga et al., 2009; Koseki and Watanabe, 2010) is the pressure adjustment mechanism (Lindzen and Nigam, 1987; Feliks et al., 2004), in which SST modifies boundary layer air-temperature, and the resultant relatively low (high) pressure anomalies produce wind convergence (divergence) over relatively warm (cold) SSTs. In this mechanism, the near-surface wind convergence is suggested to be proportional to the Laplacian of sea level pressures (SLPs; Minobe et al., 2008; Bryan et al., 2010; Shimada and Minobe, 2011). Both mechanisms have been suggested to be responsible for the surface wind convergence/divergence over the Gulf Stream based on empirical relationships such as linear regressions (Chelton et al., 2004; Minobe et al., 2008). Thus, it is important to evaluate dynamically the contributions of the two mechanisms. To address this task, we develop a new diagnostic method for near-surface wind and applied it to a regional atmospheric model output over the Gulf Stream.
2. Diagnostics and model
The present diagnostics explicitly separate the two roles of the turbulent stress discussed by Wallace et al. (1989), i.e. the downward momentum inputs, which play an essential role in their mechanism, and the damping due to the surface stress. The vertically and time averaged momentum equations, ignoring horizontal diffusion terms, from the sea surface to a certain height Z are written as
where x and y designate the zonal and meridional coordinates, respectively, (U, V) are the vertically averaged zonal and meridional momentum, respectively, f the Coriolis parameter, P the vertically averaged pressure, (τx(Z), τy(Z)) the downward momentum inputs at the height Z, consisting of the vertical diffusion and the vertical advection, (τx(0), τy(0)) the surface wind stresses and (Ax, Ay) the horizontal advections. O'Neill et al. (2010) also examined vertically averaged momentum, but for a thick layer (0–1200 m) for which downward momentum inputs from the top of the layer were ignored.
The two effects of the vertical stress were not separated for most of previous diagnostics, which analyzed the momentum equations at a certain height as reviewed by Small et al. (2008). Consider a simple momentum balance mainly between the forcing due to the downward momentum input and the damping due to the surface stress, as suggested by Hayes et al. (1989). The previous diagnostics at a single level can only evaluate the total stress, which is actually a residual from the main balance. Our diagnostics explicitly separate the main forcing due to the downward momentum input and the dumping due to surface stress.
A further consideration is needed for the surface stress. In contrast to the pressure gradients and the downward momentum flux terms in Equation (1), which express active roles, the surface stress always acts as the passive damping. Note that the surface friction is very important also for the pressure adjustment mechanism; without it, pressure driven winds are nondivergent (as in purely geostrophic flow). Therefore, for a proper understanding of the mechanism, the passive nature of the surface friction should be expressed properly, and such a formulation is that the surface wind stress is assumed to be a linear damping as suggested by Lindzen and Nigam (1987) and Wallace et al. (1989), expressed as
where ε(x, y) is the proportional linear damping coefficient. Then, Equation (1) can be solved for U and V, and the momentum convergence can be written as
where M1 = [ε/(ε2 + f2)]x + [−f/(ε2 + f2)]y and M2 = [f/(ε2 + f2)]x + [ε/(ε2 + f2)]y. Consequently, the momentum convergence can be expressed by the sum of contributions from the pressure gradient, the downward momentum input at the top of the analysis layer, and the horizontal advection. The first and second terms represent the pressure adjustment and the downward momentum mixing mechanism, respectively, and the last term indicates the contribution of the horizontal advection.
The atmospheric model used in this study is the International Pacific Research Center (IPRC) Regional Climate model, which uses E–ε turbulent closure scheme for vertical diffusion and modified Monin–Obukhov scheme for turbulent fluxes at the ocean surface (Wang, 2003 for detail). The model domain covers the western North Atlantic (5°–65°N, 100°–20°W) with 0.5°× 0.5° horizontal grid and 28 vertical sigma levels. We used the National Center for Environmental Prediction (NCEP) reanalysis 1, with 2.5° resolution at 6-h intervals (Kalnay et al., 1996) as initial and lateral boundary conditions, and NCEP Real Time Global SST with 0.5° resolution (Gemmill et al., 2007) as the daily surface boundary condition. The model was integrated for 5 years (from December 2001 to November 2006) after 1-month spinup. The present integration time is one to two orders of magnitude longer than those used in previous diagnostics of atmospheric responses to SST fronts (Small et al., 2003; Song et al., 2006; O'Neill et al., 2010). The horizontal and vertical momentum advections are calculated through the model integration at every time step, and then are averaged for the analysis period. The height Z is set as 100 m so that the diagnosed layer is suitable for near-surface winds. This height roughly corresponds to the top of the surface layer, which occupies approximately one tenth of the MABL, since annual-mean MABL height is between 700 and 1200 m in the model.
The coefficient ε is determined from annual-mean wind stresses and vertically averaged momentum as , and is relatively large over the Gulf Stream (not shown), which is probably associated with a more unstable condition due to larger air-sea temperature difference (Liu et al., 2007). However, the spatial change of ε seems insignificant in this analysis: the first terms of the pressure adjustment and the downward momentum mixing mechanisms explain the most of the convergence/divergence as described below, and the terms with M1 and M2, directly related to the change of ε, are relatively small. Moreover, if the typical value of ε, determined by a least square method as 2.0 × 10−4 s−1 (about twice larger than f), is used for the whole region, the diagnosed convergence is almost same as that with spatially varying ε (spatial correlation is 0.96).
We first examine the regional model performance for the major features of surface wind response around the Gulf Stream, by comparing the simulated annual-mean climatology of neutral 10-m wind convergence with observations from the QuikSCAT satellite (Liu et al., 2002) on a 0.5°× 0.5° grid available at Jet Propulsion Laboratory. As shown by previous studies (Chelton et al., 2004; Minobe et al., 2008), satellite observations exhibit surface wind convergence (divergence) on the warm (cold) flank of the Gulf Stream SST front. These features are successfully captured by the model, as the spatial correlation in the Gulf Stream region (parallelogram area shown in Figure 1) between the model and satellite data is high (r = 0.91). Although the simulated magnitudes of wind divergence/convergence are somewhat weaker than observed ones (the spatial regression coefficient of the simulated convergence on the observed one is 0.64), we believe that the present diagnostics still provide useful information for a better understanding as discussed below.
The divergence/convergence of 0–100 m averaged momentum in the model (lhs of Equation (3); Figure 2(a)) is almost identical to the diagnosed total divergence/convergence (rhs of Equation (3); Figure 2(b)). The spatial correlation coefficient between them is 0.94, and the regression coefficient of the rhs onto the lhs is 1.00. This ascertains the validity of assumption of Equation (2). Also, the diagnosed divergence/convergence shares the aforementioned major features of the 10-m wind divergence/convergence, confirming that the surface winds are well represented by the vertically averaged momentum. In the following analysis, the region where the vertically averaged momentum is less than 2 kg m s−1 is excluded from the diagnostics because the ε is not stably determined.
The division of the diagnosed convergence (Figure 2(b)) into three components due to the pressure adjustment (Figure 2(c)), the downward momentum mixing mechanism (Figure 2(d)) and the contribution of horizontal advection (not shown) indicates that the convergence due to the pressure adjustment mechanism is generally larger than those due to the other mechanisms. Contributions from each mechanism can be measured with a spatial regression within the parallelogram. The spatial regression coefficient of the convergence due to the pressure adjustment mechanism onto the total diagnosed divergence is 0.69, that due to the downward momentum mixing is 0.34 and that due to the advection is − 0.03. Consequently, the pressure adjustment (downward momentum mixing) mechanism predominantly (secondarily) works in the Gulf Stream region, explaining about 70% (30%) of the total divergence/convergence in the present model. The one-order smaller of magnitude contribution of advection is ignored hereafter.
The spatial pattern of the convergence/divergence due to the pressure adjustment mechanism is characterized by the convergence (divergence) on the warm (cold) flank of the SST front, consistent with a short term (less than a day) regional model experiment for the Gulf Stream (Warner et al., 1990; Song et al., 2006). A further division of the contribution of the pressure adjustment mechanism using Equation (3) indicates that the first term with the pressure Laplacian is dominant. Indeed, the SLP Laplacian essentially explains the convergence pattern due to this mechanism (Figure 3(a)) consistent with Minobe et al. (2008). The positive SLP Laplacian has a similar pattern to a negative SST Laplacian along the Gulf Stream (not shown), over which vast ocean-to-atmosphere turbulent heat fluxes (more than 250 W m−2 to the west of 60°W) warm the MABL and cause relative low pressures. Consistent with the present result, Minobe et al. (2010) found relative low SLPs on the warmer flank of the Gulf Stream SST front using historical marine meteorological observations, and Bryan et al. (2010) reported a striking similarity between the SLP Laplacian and the wind convergence using an extremely high-resolution air-sea coupled general circulation model (0.25° for the atmosphere).
The downward momentum mixing mechanism, on the other hand, contributes to the divergence mainly over the meridionally running eastern Gulf Stream (east of 60°W) and the convergence around the Grand Banks (Figure 2(d)). This divergence/convergence pattern is well represented by positive and negative downwind SST gradient, v10·∇T, where v10 is the 10-m wind vectors and T is the SST, as suggested by previous studies (Chelton et al., 2004). Furthermore, the simulated sign-inversed downwind SST gradient (Figure 3(b)) is similar to the estimation based on QuikSCAT winds and Real Time Global SST, though the observed positive values corresponding to the wind convergence around the Grand Banks are much weaker than those in the simulation (Figure 3(c)).
Note that over the Gulf Stream west of 60°W the sign-inversed downwind SST gradient is mostly negative in model and observations (Figure 3(b,c)), suggesting that downward momentum mixing does not effectively produce the wind convergence here, as confirmed by the diagnosis shown in Figure 2(d). It follows that the underestimation of the wind convergence over the Gulf Stream west of 60°W (Figure 1) in the model is likely due to the underestimation of the pressure adjustment mechanism. Although the relative contributions may depend on the model used (Song et al.2009) reported that the boundary layer parameterization is important in improving the strength of the downward momentum mixing mechanism), it is clear that the prominent convergence along the western Gulf Stream axis is mainly due to the pressure adjustment mechanism.
4. Concluding remarks
The importance of the pressure adjustment mechanism for near-surface convergence over the Gulf Stream is generally consistent with previous studies. Numerical studies focusing on atmospheric responses over the Gulf Stream (Wai and Stage, 1989; Warner et al., 1989; Song et al., 2006) found the primary role of this mechanism. Although the idealized modeling studies using large eddy simulations showed the dominant role of the downward momentum mixing (Skyllingstad et al., 2007), the small numerical domains may not capture the full spatial extent (especially in the vertical) of the air-temperature change, which is essential for the pressure adjustment mechanism (Spall et al., 2007; Small et al., 2008).
Applications of the present diagnostics to other models and to other regions should be valuable to understand nature of atmospheric responses to SST fronts. Signatures of the pressure adjustment mechanism were reported not only for the Gulf Stream region but also for other western boundary current regions based on in situ and satellite observations (Tokinaga et al., 2009; Minobe et al., 2010; Shimada and Minobe, 2011) and numerical simulation (Bryan et al., 2010). The pressure-relating terms in Equation (3) can be evaluated from standard outputs of numerical models, and thus it is possible to evaluate at least the role of this mechanism in a wide range of numerical studies.
We thank J. M. Wallace and T. P. Mitchell for helpful discussions. This work was supported by Grant-in-Aid for Scientific Research defrayed by the Ministry of Education, Culture, Sports, Science and Technology of Japan. M. Inatsu was supported by the Global Environmental Research Fund S-5-3 of the Ministry of the Environment of Japan.