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  • Climate Dynamics manuscript No. (will be inserted by the editor)

    Mechanisms controlling the SST air-sea heat flux feedback1

    and its dependence on spatial scale2

    Ute Hausmann · Arnaud Czaja · John3



    Manuscript submitted December 31, 20156

    Abstract The turbulent air-sea heat flux feedback (α, in W m−2 K−1) is a major7

    contributor to setting the damping timescale of sea surface temperature (SST)8

    anomalies. In this study we compare the spatial distribution and magnitude of9

    α in the North Atlantic and the Southern Ocean, as estimated from the ERA-10

    Interim reanalysis dataset. The comparison is rationalized in terms of an upper11

    bound on the heat flux feedback, associated with “fast” atmospheric export of12

    temperature and moisture anomalies away from the marine boundary layer, and a13

    lower bound associated with “slow” export. It is found that regions of cold surface14

    waters (≤10◦ C) are best described as approaching the slow export limit. This15

    conclusion is not only valid at the synoptic scale resolved by the reanalysis data,16

    U. Hausmann · J. Marshall

    Department of Earth Atmospheric and Planetary Sciences, Massachusetts Institute of Tech-

    nology, Cambridge, MA, USA

    E-mail: uhaus at mit dot edu

    A. Czaja

    Department of Physics, Imperial College London, UK

  • 2 Hausmann et al.

    but also on basin scales. In particular, it applies to the heat flux feedback acting17

    as circumpolar SST anomaly scales are approached in the Southern Ocean, with18

    feedbacks of ≤10 W m−2 K−1. In contrast, the magnitude of the heat flux feed-19

    back is close to that expected from the fast export limit over the Gulf Stream and20

    its recirculation with values on the order of ≈ 40 W m−2 K−1. Further analysis21

    suggests that this high value reflects a compensation between a moderate thermo-22

    dynamic adjustment of the boundary layer, which tends to weaken the heat flux23

    feedback, and an enhancement of the surface winds over warm SST anomalies,24

    which tend to enhance the feedback.25

    Keywords Sea surface temperature · air-sea interaction · feedback · variability ·26

    Southern Ocean · North Atlantic27

    1 Introduction28

    The rate at which sea surface temperature (SST) anomalies are damped to the29

    atmosphere is determined to a large extent by the air-sea heat flux feedback.30

    This quantity, hereafter denoted αnet (in W m −2 K−1), represents the change31

    in the net air-sea heat flux in response to a 1 K change in SST. It has been32

    established that it varies with location, time of the year and also with the spatial33

    scale of the SST anomaly (e.g., Frankignoul and Kestenare 2002). The heat flux34

    feedback has been found to be a crucial parameter for a realistic representation35

    of, for example, the ocean’s thermohaline circulation (Rahmstorf and Willebrand36

    1995) and the strength of decadal oscillations in the North Atlantic (NA), as37

    shown by, for example, Czaja and Marshall (2001). More recently, its magnitude38

    in the Southern Ocean (SO) has been identified as one of the primary sources of39

  • Mechanisms controlling the SST air-sea heat flux feedback 3

    differences between the climate response to stratospheric ozone forcing in coupled40

    models (Ferreira et al 2015).41

    Despite its important role, observational estimates of αnet are sparse, espe-42

    cially over the SO. In a recent study, Hausmann et al (2015) provide a benchmark43

    calculation for the circumpolar SO, thereby complementing the previous observa-44

    tional estimates of α for the midlatitude ocean basins of the Northern Hemisphere45

    and the low-latitude Southern Hemisphere (Frankignoul et al 1998; Frankignoul46

    and Kestenare 2002; Park et al 2005). These studies have highlighted marked vari-47

    ations in αnet over the world’s major current systems. Feedbacks of typically ≈ 4048

    W m−2 K−1 found over the major NH boundary current systems (Gulf Stream49

    and Kuroshio) stand in stark contrast with feedbacks of ≈ 10 W m−2 K−1 acting50

    along the Antarctic Circumpolar Current (ACC), falling to values as low as ≈ 551

    W m−2 K−1 in the region of seasonal sea ice in the summer time.52

    The above results are interesting but large uncertainties in estimates of αnet53

    limit their usefulness. Indeed, there are not only significant uncertainties in both54

    the turbulent and radiative components of the air-sea heat flux, but it is also55

    difficult to isolate the component of the heat flux which responds to SST variability56

    from that which forces it (Frankignoul et al 1998). These uncertainties provide57

    motivation to focus here on the mechanisms leading to the range of values cited58

    above. We will thereby focus only on the turbulent contribution (by latent and59

    sensible heat fluxes) to αnet = αturb+αrad. As established previously for both NH60

    and the SO (Hausmann et al 2015), αturb typically dominates the feedback. We61

    will simply denote it α in the following (dropping the subscript).62

    The approach taken here is to derive bounds on the magnitude of the air-sea63

    feedback. These provide a context for studying what sets observed spatial patterns64

  • 4 Hausmann et al.

    of α. The latter can arise as a result of regional variations in the background air-sea65

    state, but also as a result of different adjustment of the marine atmospheric bound-66

    ary layer (MABL) to the underlying SST anomalies. The bounds we derive help in67

    separating these two effects. In addition, we also partition the MABL adjustment68

    into dynamic (i.e., involving changes in surface winds) and thermodynamic (i.e.,69

    solely involving changes in air temperature and moisture fields) components, as70

    pioneered by Park et al (2005) for closed ocean basins. We expand on their study71

    and explore how the feedback and its driving mechanisms change as a function of72

    spatial scale, moving out from the scale of atmospheric synoptic disturbances to73

    that of ocean basins. We are particularly interested to contrast circumpolar and74

    gyre-like oceanic regimes, and so focus on the Southern Ocean (SO) and the North75

    Atlantic (NA) as two prototypes of these regimes, respectively.76

    The paper is structured as follows. In section 2, upper and lower bounds on77

    the air-sea heat flux feedback are derived using standard bulk formulae for the78

    air-sea fluxes. These bounds are estimated using reanalysis data and compared79

    to estimates of α in section 3. Mechanisms setting the actual heat flux feedback80

    are studied in section 4. Finally, section 5 provides a discussion of results and81


    2 Theoretical bounds on the heat flux feedback83

    Turbulent air-sea heat fluxes of sensible and latent heat (QS and QL, respectively,84

    measured positive upward, their sum being denoted Q) can be expressed via bulk85

  • Mechanisms controlling the SST air-sea heat flux feedback 5

    formulae (e.g., Gill 1982):86

    QS = ρ auacSc

    a p (T − Ta)

    QL = ρ auacLL (qsat(T )− qa). (1)

    Here ρa, cap, T a and qa are the density, specific heat capacity, temperature and87

    specific humidity of the surface atmosphere (usually evaluated 10 m above sea-88

    level), T and qsat are temperature and specific humidity of the (saturated) ocean89

    surface, L is the latent heat of evaporation, cS and cL are non dimensional transfer90

    coefficients for sensible and latent heat flux, respectively, and ua ≡ |uuua −uuu| is the91

    wind speed with respect to the moving ocean surface (with uuua & uuu denoting,92

    respectively, the surface vector wind & current).93

    The turbulent heat flux feedback arises from the response of these turbulent94

    fluxes to perturbations in SST. It can be expressed, in a general form, thus (e.g.,95

    Frankignoul 1985):96

    α ≡ αS + αL ≡ ∂ 〈 Q′ 〉

    ∂T ′

    ∣∣∣∣ T

    ≡ ∂ 〈 Q′S +Q

    ′ L

    〉 ∂T ′

    ∣∣∣∣ T

    . (2)

    In this, X ′ is the departure from the background seasonal state X of a variable97

    X, and 〈 〉 denotes ensemble averaging over many realizations of the same SST98

    anomaly. Note that the sign convention is thus that positive values of α correspond99

    to a negative feedback on the SST anomaly.100

    In the absence of dynamic adjustments to SST of the atmospheric boundary101

    layer (an assumption that is relaxed in section 4), the sensible and latent compo-102

    nents of the turbulent heat flux feedback (2) are given by103

    αS ≈ ρauacScap ∂ 〈 (T − Ta)′

    〉 ∂T ′

    , (3)

  • 6 Hausmann et al.


    αL ≈ ρauacLL ∂ 〈 (qsat(T )− qa)′

    〉 ∂T ′

    . (4)

    The latter expression can be further simplified using a Taylor expansion of qsat:105

    q′sat(T ) = qsat(T )− qsat(T ) ≈ dqsat dT

    ∣∣∣∣ T

    T ′, (5)

    and likewise,106

    q′sat(T a) = qsat(T

    a)− qsat(Ta ) ≈ dqsat dT

    ∣∣∣∣ Ta

    Ta ′ . (6)

    Furthermore intr