Mechanisms controlling the SST air-sea heat flux feedback and its dependence on spatial scale

Abstract

The turbulent air-sea heat flux feedback ($\alpha$, in $\text {W m}^{-2}\text { K}^{-1}$) is a major contributor to setting the damping timescale of sea surface temperature (SST) anomalies. In this study we compare the spatial distribution and magnitude of $\alpha$ in the North Atlantic and the Southern Ocean, as estimated from the ERA-Interim reanalysis dataset. The comparison is rationalized in terms of an upper bound on the heat flux feedback, associated with “fast” atmospheric export of temperature and moisture anomalies away from the marine boundary layer, and a lower bound associated with “slow” export. It is found that regions of cold surface waters ($\le$10 $^\circ \,$C) are best described as approaching the slow export limit. This conclusion is not only valid at the synoptic scale resolved by the reanalysis data, but also on basin scales. In particular, it applies to the heat flux feedback acting as circumpolar SST anomaly scales are approached in the Southern Ocean, with feedbacks of $\le$10 $\text {W m}^{-2}\text { K}^{-1}$. In contrast, the magnitude of the heat flux feedback is close to that expected from the fast export limit over the Gulf Stream and its recirculation with values on the order of ≈40 $\text {W m}^{-2}\text { K}^{-1}$. Further analysis suggests that this high value reflects a compensation between a moderate thermodynamic adjustment of the boundary layer, which tends to weaken the heat flux feedback, and an enhancement of the surface winds over warm SST anomalies, which tend to enhance the feedback.

Appendices

Appendix 1: Estimating the heat flux feedback

The heat flux feedback $\alpha$ as defined in (2) is estimated from timeseries of turbulent heat fluxes Q and SST T using lagged covariance analysis, as introduced by Frankignoul et al. (1998). Here we follow the method for seasonal feedback estimation described by Hausmann et al. (2016, i.e. as used to construct their Fig. 6). As therein major sources of low frequency variability (linear seasonal ENSO signals and trends) are removed from anomaly time series before the analysis. The feedback is then obtained for each month of the year as the $T'$ $Q'$ covariance function, weighted by the $T'$ autocovariance

$$\begin{aligned} \alpha = \frac{\overline{T'(t)Q'(t+1 \delta t)}}{\overline{T'(t)T'(t+1 \delta t)}}, \end{aligned}$$

(12)

in which $\delta t$ is one month and t is taken only in certain months of the year. For example, the February (F) feedback $\alpha$(F) is obtained taking t only in January and February (JF), that is from the response of February and March (FM) heat fluxes to JF SST, weighted by the latter’s own decay into FM: $\alpha (F) = \frac{\overline{T'(JF)Q'(FM)}}{\overline{T'(JF)T'(FM)}}$. The annual-mean feedback displayed in Fig. 2 is then obtained as the average of the feedbacks estimated separately for each month of the year.

Appendix 2: Decomposition of the heat flux feedback into thermodynamic and dynamic components

The turbulent heat flux feedback can be written as $\alpha = \alpha _{upper} + d\alpha$, and $d\alpha$ (mapped in Fig. 3) is further decomposed as (11). Therein the thermodynamic component, $d\alpha _{thdyn}$, reflects the contribution to the feedback, in departure from its upper bound, by thermal and moisture adjustments to SST anomalies (with the other properties of the MABL held fixed). It is given by the sum of the 2nd terms on the rhs of Eqs. (3) and (4), i.e.

$$\begin{aligned} d\alpha _{thdyn} = - \left( \overline{\rho ^a u^a c_S c_p^a}\ {\partial \left\langle {T^a}'\right\rangle }/{\partial T'}\ + \overline{\rho ^a u^a c_L L}\ {\partial \left\langle {q^a}'\right\rangle }/{\partial T'} \right) . \end{aligned}$$

(13)

To estimate (13) from data, ${\partial \left\langle {T^a}'\right\rangle }/{\partial T'}\,$and ${\partial \left\langle {q^a}'\right\rangle }/{\partial T'}\,$are obtained for each month of the year by applying the same lagged covariance analysis method as used for $\alpha$ (see Appendix 1), which gives ${\partial \left\langle X'\right\rangle }/{\partial T'}$ with $X = Q$, to $X = T^a$ and $q^a$. The other variables in (13) are estimated from monthly air-sea climatology, as in the estimate of the bounds in Sect. 3a. To capture seasonal correlations, the products in (13) are evaluated for each month of the year, before annually averaging. The result is mapped in Fig. 6a, b.

At the level of approximation used in Sect. 2,

$$\begin{aligned} d\alpha _{thdyn} \approx d\alpha _{therm} + d\alpha _{rhum}, \end{aligned}$$

(14)

in which the thermal adjustment contribution ($d\alpha _{therm}$, mapped in Fig. 5c, d) is given by the sum of the 2nd terms on the rhs of (3) and (8) as:

$$\begin{aligned} d\alpha _{therm} = \overline{\rho ^a u^a} \left( \overline{c_S c_p^a} + \overline{c_L L}\overline{r_H}\frac{d q_{sat}}{dT}\left| _{\overline{T^a}\,}\right) \ {\partial \left\langle {T^a}'\right\rangle }{/\partial T'}\right. , \end{aligned}$$

(15)

and the relative humidity adjustment contribution is given by the 3rd term on the rhs of (8) as:

$$\begin{aligned} d\alpha _{rhum} = -\overline{\rho ^a u^a c_L L}q_{sat}(\overline{T^a}\,)\ {\partial \left\langle {r_H}'\right\rangle }/{\partial T'}. \end{aligned}$$

(16)

Estimation of these terms reveals that the residual of the approximation (14) lies within ±0.5 $\text {W m}^{-2}\text { K}^{-1}\,$ everywhere in NA and SO (not shown). Differences between $d\alpha _{thdyn}$ (Fig. 6a, b) and $d\alpha _{therm}$ (Fig. 5c, d) are thus accounted for by the relative humidity adjustment contribution $d\alpha _{rhum}$ (not shown).

The dynamical coupling contribution to the feedback, solely reflecting wind speed adjustments to SST anomalies ${\partial \left\langle {u^a}'\right\rangle }/{\partial T'}$, is obtained by evaluating (2) while keeping all MABL properties but $u^a$ fixed, and then subtracting $\alpha _{upper}$, with the result:

$$\begin{aligned} d\alpha _{dyn} = \left( \overline{\rho ^a c_S c_p^a} \left( \overline{T}- \overline{T^a}\right) +\overline{\rho ^a c_L L}\,\left( q_{sat}(\overline{T}) - \overline{q^a}\,\right) \right) \ {\partial \left\langle {u^a}'\right\rangle }/{\partial T'}. \end{aligned}$$

(17)

The remaining contribution $d\alpha _{res}$ is then estimated as residual of the terms quantified in Eq. (11), that is as:

$$\begin{aligned} d\alpha _{res} = \alpha - (\alpha _{upper} + d\alpha _{thdyn} + d\alpha _{dyn}). \end{aligned}$$

(18)