Century-long cooling trend in subpolar North Atlantic forced by atmosphere: an alternative explanation

Abstract

A well-known exception to rising sea surface temperatures (SST) across the globe is the subpolar North Atlantic, where SST has been declining at a rate of 0.39 ($\pm$ 0.23) K century⁻¹ during the 1900–2017 period. This cold blob has been hypothesized to result from a slowdown of the Atlantic Meridional Overturning Circulation (AMOC). Here, observation-based evidence is used to suggest that local atmospheric forcing can also contribute to the century-long cooling trend. Specifically, a 100-year SST trend simulated by an idealized ocean model forced by historical atmospheric forcing over the cold blob region matches 92% ($\pm$ 77%) of the observed cooling trend. The data-driven simulations suggest that 54% ($\pm$ 77%) of the observed cooling trend is the direct result of increased heat loss from the ocean induced by the overlying atmosphere, while the remaining 38% is due to strengthened local convection. An analysis of surface wind eddy kinetic energy suggests that the atmosphere-induced cooling may be linked to a northward migration of the jet stream, which exposes the subpolar North Atlantic to intensified storminess.

Appendix: Decomposition of \({Q}_{net}^{^{\prime}}\)

Air-sea heat flux anomaly (${Q}_{net}^{^{\prime}}={Q}_{SW}^{^{\prime}}-{Q}_{LW}^{^{\prime}}-{Q}_{SH}^{^{\prime}}-{Q}_{LH}^{^{\prime}}$) is a forcing mechanism on SSTA. However, due to its dependence on SSTA, it is also a damping mechanism (Stephens et al. 2012). For example, positive SSTA increases air-sea temperature and humidity differences, which induces a stronger sensible and latent heat flux from ocean to the atmosphere and thus restores the existing SSTA (i.e., a damping mechanism). The damping and forcing mechanism exerted by ${Q}_{net}^{^{\prime}}$ can be quantified as:

$${Q}_{net}^{^{\prime}}=-\alpha {T}^{^{\prime}}+{{Q}^{^{\prime}}}_{atmo}.$$

(A1)

On the right-hand side of Eq. (A1), the term $-\alpha T{^{\prime}}$ quantifies the damping mechanisms which represents the dependence of ${Q}_{net}^{^{\prime}}$ on existing SSTA. The other term ${Q{^{\prime}}}_{atmo}$ quantifies the forcing mechanism which is the anomalies in heat flux purely due to changes in atmospheric variables.

The decomposition presented in Eq. (A1) has been formulated by Li et al. (2020) based on bulk formula that relate the turbulent heat fluxes to surface wind speed ($\left|U\right|$), the air-sea temperature difference ($T-{T}_{a}$), and the air-sea humidity difference ($q-{q}_{a}$) as:

$${Q}_{SH}={\rho }_{a}{C}_{D}\left|U\right|{C}_{p}^{a}\left(T-{T}_{a}\right),$$

(A2)

$${Q}_{LH}={\rho }_{a}{C}_{D}\left|U\right|{L}_{v}\left(q-{q}_{a}\right).$$

(A3)

In Eqs. (A2) and (A3), ${\rho }_{a}=1.225\, \mathrm{kg }\,{\mathrm{m}}^{-3}$ is the density of air, ${C}_{D}=1.15\times {10}^{-3}$ is the transfer coefficient for sensible and latent heat, ${C}_{p}^{a}=1004 \text{ J Kg}^{-1} \text{ K}^{-1}$ is the specific heat of air, and ${L}_{v}=2.5\times {10}^{6}\,\mathrm{ J }\,{\mathrm{Kg}}^{-1}$ is the latent heat of vaporization. According to the Reynold’s decomposition ($\left|U\right|=\stackrel{-}{\left|U\right|}+{\left|U\right|}^{^{\prime}}; T-{T}_{a}=\left(\overline{T }-{\overline{T} }_{a}\right)+\left(T{^{\prime}}-{T}_{a}^{^{\prime}}\right)$, $q-{q}_{a}=\left(\overline{q }-{\overline{q} }_{a}\right)+\left(q{^{\prime}}-{q}_{a}^{^{\prime}}\right)$; where overbars are monthly climatology and primes are the deviation from climatology) and neglecting the second order terms, the turbulent heat flux anomalies can be quantified as:

$${Q}_{SH}^{^{\prime}}={\rho }_{a}{C}_{D}{C}_{p}^{a}\left\{\stackrel{-}{\left|U\right|}\left(T{^{\prime}}-{T}_{a}^{^{\prime}}\right)+\left|U\right|{^{\prime}}\left(\overline{T }-{\overline{T} }_{a}\right)\right\},$$

(A4)

$${Q}_{LH}^{^{\prime}}={\rho }_{a}{C}_{D}{L}_{v}\left\{\stackrel{-}{|U|}\left(q{^{\prime}}-{q}_{a}^{^{\prime}}\right)+{\left|U\right|}^{^{\prime}}\left(\overline{q }-{\overline{q} }_{a}\right)\right\}.$$

(A5)

As the atmosphere near the ocean surface is saturated, and the saturation humidity is a function of temperature, $q{^{\prime}}$ is determined solely by ${T}^{^{\prime}}$ and is formulated as ${q}^{^{\prime}}={\left.\frac{\partial q}{\partial T}\right|}_{\overline{T} }T{^{\prime}}$. Plug in the temperature dependence of $q{^{\prime}}$, Eq. (A5) can be expressed as:

$${Q}_{LH}^{^{\prime}}={\rho }_{a}{C}_{D}{L}_{v}\left\{\stackrel{-}{|U|}\left({\left.\frac{\partial q}{\partial T}\right|}_{\overline{T} }T{^{\prime}}-{q}_{a}^{^{\prime}}\right)+{\left|U\right|}^{^{\prime}}\left(\overline{q }-{\overline{q} }_{a}\right)\right\}.$$

(A6)

Equations (A4) and (A6) demonstrate that anomalies in sensible and latent heat fluxes are a function of SSTA ($T{^{\prime}}$) and atmospheric variables. Anomalies in the atmospheric variables ($\left|U\right|{^{\prime}}$, ${T}_{a}^{^{\prime}}$ and ${q}_{a}^{^{\prime}}$) may result from internal atmospheric variability or be the response to the underlying SSTA. To quantify the response of the atmospheric variables to SSTA, we further separate the anomalies in atmospheric variables into two components: anomalies due to SSTA (we assume a linear relationship) and a residual that is due to the atmospheric internal variability. With this separation, Eqs. (A4) and (A6) are expressed as:

$${Q}_{SH}^{^{\prime}}={\rho }_{a}{C}_{D}{C}_{p}^{a}\left\{\stackrel{-}{\left|U\right|}\left(T{^{\prime}}-\frac{\partial {T}_{a}}{\partial T}{T}^{^{\prime}}\right)+\frac{\partial \left|U\right|}{\partial T}T{^{\prime}}\left(\overline{T }-{\overline{T} }_{a}\right)\right\}+{Q}_{SH\_res}^{^{\prime}},$$

(A7)

$${Q}_{LH}^{^{\prime}}={\rho }_{a}{C}_{D}{L}_{v}\left\{\stackrel{-}{|U|}\left({\left.\frac{\partial q}{\partial T}\right|}_{\overline{T} }T{^{\prime}}-\frac{\partial {q}_{a}}{\partial T}{T}^{^{\prime}}\right)+\frac{\partial \left|U\right|}{\partial T}T{^{\prime}}\left(\overline{q }-{\overline{q} }_{a}\right)\right\}+{Q}_{LH\_res}^{^{\prime}}.$$

(A8)

In Eqs. A7 and A8, ${Q}_{SH\_res}^{^{\prime}}$ and ${Q}_{LH\_res}^{^{\prime}}$ are the residuals of the sensible heat flux and latent heat flux, respectively. Adding Eqs. A7 and A8, the turbulent heat flux anomalies are quantified as:

$${Q}_{SH}^{{^{\prime}}}+{Q}_{LH}^{{^{\prime}}}=\left\{\underset{{\alpha }_{self}}{\underbrace{{\rho }_{a}{C}_{D}\stackrel{-}{\left|U\right|}\left({C}_{p}^{a}+{L}_{v}{\left.\frac{\partial q}{\partial T}\right|}_{\overline{T} }\right)}}+\underset{{\alpha }_{\left|U\right|}}{\underbrace{{\rho }_{a}{C}_{D}\left[{C}_{p}^{a}\left(\overline{T }-\overline{{T }_{a}}\right)+{L}_{v}\left(\overline{q }-{\overline{q} }_{a}\right)\right]\frac{\partial \left|U\right|}{\partial T}}}\underset{{\alpha }_{thermal}}{\underbrace{-{\rho }_{a}{C}_{D}\stackrel{-}{\left|U\right|}\left({C}_{p}^{a}\frac{\partial {T}_{a}}{\partial T}+{L}_{v}\frac{\partial {q}_{a}}{\partial T}\right)}}\right\}{T}^{{^{\prime}}}+{Q}_{SH\_res}^{{^{\prime}}}+{Q}_{LH\_res}^{{^{\prime}}}.$$

(A9)

The dependence of turbulent heat flux on SSTA (term in brackets on the right-hand side of Eq. 10) provides an important SSTA damping mechanism, whose intensity can be quantified by a damping coefficient, $\alpha$. As shown in Eq. (A9), $\alpha = \alpha_{self} + \alpha_{\left| U \right|} + \alpha_{thermal}$, consists of three components: a direct response of sensible and latent heat flux to SSTA ($\alpha_{self}$), the response of wind speed to SSTA ($\alpha_{\left| U \right|}$), and the thermal adjustment of air temperature and humidity to SSTA ($\alpha_{thermal}$). The term ${ }\alpha_{self} = \rho_{a} C_{D} \overline{\left| U \right|} \left( {C_{p}^{a} + L_{v} \left. {\frac{\partial q}{{\partial T}}} \right|_{{\overline{T}}} } \right)$ is determined by the background wind speed ($\overline{\left| U \right|}$) and the sensitivity of saturation specific humidity to SSTA, which increases exponentially with background SST according to the Clausius–Clapeyron Equation. The terms $\alpha_{\left| U \right|} = \rho_{a} C_{D} \left[ {C_{p}^{a} \left( {\overline{T} - \overline{T}_{a} } \right) + L_{v} \left( {\overline{q} - \overline{q}_{a} } \right)} \right]\frac{\partial \left| U \right|}{{\partial T}}$ and $\alpha_{thermal} = - \rho_{a} C_{D} \overline{\left| U \right|} \left( {C_{p}^{a} \frac{{\partial T_{a} }}{\partial T} + L_{v} \frac{{\partial q_{a} }}{\partial T}} \right)$ depend on the partial derivatives of $\left| U \right|^{^{\prime}}$, $T_{a}^{^{\prime}}$, and $q_{a}^{^{\prime}}$ with respect to SSTA, which can be calculated based on the covariance between SSTA and $\left| U \right|^{\prime}$, $T_{a}^{^{\prime}}$, and $q_{a}^{^{\prime}}$ when the SSTA leads by one month, similar to Frankignoul et al. (1998), i.e.,

$$\frac{\partial \left| U \right|}{{\partial T}} = \frac{{cov\left( {\left| U \right|^{^{\prime}} ,T^{\prime}\left( { - 1} \right)} \right)}}{{var\left( {T^{\prime}\left( { - 1} \right)} \right)}}$$

(A10)

$$\frac{{\partial T_{a} }}{\partial T} = \frac{{cov\left( {T_{a}^{^{\prime}} ,T^{\prime}\left( { - 1} \right)} \right)}}{{var\left( {T^{\prime}\left( { - 1} \right)} \right)}}$$

(A11)

$$\frac{{\partial q_{a} }}{\partial T} = \frac{{cov\left( {q_{a}^{^{\prime}} ,T^{\prime}\left( { - 1} \right)} \right)}}{{var\left( {T^{\prime}\left( { - 1} \right)} \right)}}$$

(A12)

With the quantification of $\alpha$, the turbulent heat flux anomalies (Eq. A9) can be partitioned as:

$$- Q_{SH}^{^{\prime}} - Q_{LH}^{^{\prime}} = - \alpha T^{\prime} + Q_{res}^{^{\prime}} .$$

(A13)

The term $Q_{res}^{^{\prime}} = - Q_{SH\_res}^{^{\prime}} - Q_{LH\_res}^{^{\prime}}$ is the residual of turbulent heat flux anomalies from the damping mechanism, which is independent of SSTA and represents turbulent heat flux anomalies due to atmospheric variability. In addition, we assume that the radiative heat flux ($Q^{\prime}_{SW} - Q^{\prime}_{LW}$) is mainly determined by the atmosphere (Frankignoul and Kestenare 2002). Collecting terms, we quantify $Q_{atmo}^{^{\prime}} = Q_{sw}^{^{\prime}} - Q_{lw}^{^{\prime}} + Q_{res}^{^{\prime}}$ as the atmospheric contribution to the net surface heat flux anomaly.