Editorial Type:
Article
Article Type:
Research Article

A Simple Coupled Model of the Wind–Evaporation–SST Feedback with a Role for Stability

Kristopher B. Karnauskas aDepartment of Atmospheric and Oceanic Sciences, University of Colorado Boulder
bCooperative Institute for Research in Environmental Sciences, University of Colorado Boulder

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Online Publication:
16 Mar 2022
Print Publication:
01 Apr 2022
DOI:
https://doi.org/10.1175/JCLI-D-20-0895.1
Page(s):
2149–2160
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Abstract

The wind–evaporation–SST (WES) feedback describes a coupled mechanism by which an anomalous meridional sea surface temperature (SST) gradient in the tropics evolves over time. As commonly posed, the (positive) WES feedback depends critically on the atmospheric response to SST anomalies being governed by a process akin to that argued by Lindzen and Nigam in 1987, and omits an alternative process by which SST anomalies modulate surface wind speed through vertical momentum mixing as proposed by Wallace et al. and Hayes et al. in 1989. A simple model is developed that captures the essential coupled dynamics of the WES feedback as commonly posed, while also allowing for momentum entrainment in response to evolving SST anomalies. The evolution of the coupled system depends strongly on which effects are enabled in the model. When both effects are accounted for in idealized cases near the equator, the initial anomalous meridional SST gradient grows over a time scale of a few months but is damped within one year. The sign and magnitude of the WES feedback depend on latitude within the tropics and exhibit hemispheric asymmetry. When constrained by realistic profiles of prevailing zonal wind, the model predicts that the WES feedback near the equator is stronger during boreal winter, while the domain over which it is positive is broader during boreal summer, and that low-frequency climate variability can also modulate the strength and structure of the WES feedback. These insights may aid in the interpretation of coupled climate behavior in observations and more complex models.

Significance Statement

Regional climate variability on time scales from months to decades, including El Niño, relies heavily on feedbacks between the atmosphere and the ocean in which some initial change in the environment is either amplified or damped over time. Several conceptual models for such feedbacks have been devised over the years to explain the coupled climate behavior seen in observations and computer simulations. A rather ubiquitous one is called the wind–evaporation–SST (WES) feedback, but the typical phrasing of it does not incorporate a potentially important influence of ocean temperature changes on the stability of the atmosphere above it. This study adds that effect to the WES feedback framework and examines climate variability through the lens of the augmented conceptual model.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kristopher B. Karnauskas, kristopher.karnauskas@colorado.edu

Abstract

The wind–evaporation–SST (WES) feedback describes a coupled mechanism by which an anomalous meridional sea surface temperature (SST) gradient in the tropics evolves over time. As commonly posed, the (positive) WES feedback depends critically on the atmospheric response to SST anomalies being governed by a process akin to that argued by Lindzen and Nigam in 1987, and omits an alternative process by which SST anomalies modulate surface wind speed through vertical momentum mixing as proposed by Wallace et al. and Hayes et al. in 1989. A simple model is developed that captures the essential coupled dynamics of the WES feedback as commonly posed, while also allowing for momentum entrainment in response to evolving SST anomalies. The evolution of the coupled system depends strongly on which effects are enabled in the model. When both effects are accounted for in idealized cases near the equator, the initial anomalous meridional SST gradient grows over a time scale of a few months but is damped within one year. The sign and magnitude of the WES feedback depend on latitude within the tropics and exhibit hemispheric asymmetry. When constrained by realistic profiles of prevailing zonal wind, the model predicts that the WES feedback near the equator is stronger during boreal winter, while the domain over which it is positive is broader during boreal summer, and that low-frequency climate variability can also modulate the strength and structure of the WES feedback. These insights may aid in the interpretation of coupled climate behavior in observations and more complex models.

Significance Statement

Regional climate variability on time scales from months to decades, including El Niño, relies heavily on feedbacks between the atmosphere and the ocean in which some initial change in the environment is either amplified or damped over time. Several conceptual models for such feedbacks have been devised over the years to explain the coupled climate behavior seen in observations and computer simulations. A rather ubiquitous one is called the wind–evaporation–SST (WES) feedback, but the typical phrasing of it does not incorporate a potentially important influence of ocean temperature changes on the stability of the atmosphere above it. This study adds that effect to the WES feedback framework and examines climate variability through the lens of the augmented conceptual model.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kristopher B. Karnauskas, kristopher.karnauskas@colorado.edu
Keywords: Tropics; Atmosphere-ocean interaction; Sea surface temperature; Coupled models

1. Introduction

Feedbacks involving wind and sea surface temperature (SST), including the wind–evaporation–SST (WES) feedback, are important to the maintenance of aspects of the mean tropical climate such as the northward-biased intertropical convergence zone (ITCZ) and other equatorial asymmetries (Emanuel 1987; Neelin et al. 1987; Xie and Philander 1994; Maloney and Sobel 2004; Xie 2004). The WES feedback has also been argued to be an important process in modes of internal climate variability including the Madden–Julian oscillation (MJO; DeMott et al. 2016), the Indian Ocean dipole mode (Li et al. 2003), meridional modes (Chiang and Vimont 2004), El Niño–Southern Oscillation (ENSO; Wang et al. 1999; Zhu et al. 2016), decadal variability (Chang et al. 1997; Xie and Tanimoto 1998), and tropical–extratropical interactions (Stuecker 2018; Amaya 2019), and in shaping the response of the mean climate to radiative forcing (Xie et al. 2010).

As commonly posed (e.g., Xie and Philander 1994), the WES feedback is positive (Fig. 1a); a positive meridional SST gradient induces a negative meridional sea level pressure (SLP) gradient, which induces a northward surface wind that is deflected differentially along the SLP gradient due to the dependence of the Coriolis parameter on latitude. The subsequent zonal wind anomalies superimpose differentially upon the mean prevailing winds, reducing (enhancing) latent heat flux over the warm (cold) SST anomaly, thereby amplifying the initial anomalous SST gradient. This mechanism depends critically on the surface wind response to the SST anomalies being governed by the hydrostatic adjustment of SLP in a well-mixed boundary layer (Lindzen and Nigam 1987; Back and Bretherton 2009); that is, warm (cold) SST anomalies force low (high) SLP anomalies, and the resulting gradient therein propels the low-level wind.

Fig. 1.
Fig. 1.

Schematic illustrations of the WES feedback in which the surface wind response to an anomalous meridional SST gradient is governed by (a) the LN87 mechanism (hydrostatic pressure, i.e., the common WES feedback) and (b) the WH89 mechanism (vertical momentum mixing). In both diagrams, time progresses from left to right following steps A through F (see main text). Note that the final state (step F) in (a) is an amplified version of the initial state (step A), thus representing a positive feedback, and vice versa for (b).

Citation: Journal of Climate 35, 7; 10.1175/JCLI-D-20-0895.1

Omitted from this formulation of the WES feedback is an alternative mechanism by which the surface wind field can respond to SST anomalies. Specifically, the potential for surface wind speed to be modulated by SST through vertical stratification and momentum mixing as proposed by Wallace et al. (1989) and Hayes et al. (1989) is not considered in the common WES feedback. Such a mechanism alone would also give rise to a feedback involving wind, evaporation, and SST—but a negative one (Fig. 1b). In that case, the warm (cold) SST anomaly would destabilize (stabilize) the atmospheric boundary layer by steepening (relaxing) its temperature lapse rate and therefore increase (decrease) the rate of vertical mixing of horizontal momentum. The result would be an increase (decrease) in surface wind speed and latent heat flux over the warm (cold) SST anomaly, thereby damping the initial anomalous meridional SST gradient.

Recognizing that the Lindzen and Nigam (1987) argument (hereafter the LN87 mechanism) and the Wallace et al. (1989) and Hayes et al. (1989) mechanism (hereafter the WH89 mechanism) need not be mutually exclusive, this study seeks to develop a simple yet useful model of the WES feedback that accounts for both. The intent is not to declare a winner, but to explore the degree to which the WES feedback as commonly posed may be improved upon when also considering the WH89 mechanism. The model is developed in the following section, with the results of some idealized experiments presented in section 3. The dependence of the magnitude and latitudinal structure of the WES feedback on low-frequency variations in mean climate is also explored, before offering some concluding remarks in section 4.

2. Model

In this section, a model is developed that includes only the essential physics involved in the WES feedback. Consider the SST tendency equation based on the ocean mixed layer heat budget neglecting advection and diffusion:
∂T′∂t=−Q′ρoCph,
where T′ is SST anomaly, Q′ is latent heat flux anomaly, ρo is a reference seawater density (1025 kg m−3), Cp is the specific heat capacity of seawater (3850 J kg−1 K−1), and h is the mixed layer depth. For the experiments conducted in this study, a constant mixed layer depth h of 50 m is assumed—a reasonable value for the tropical oceans (de Boyer Montégut et al. 2004). The latent heat flux anomaly Q′ is given by the bulk formula
Q′=ρaLυCLHΔq(|U¯+U′|−|U¯|),
where ρa is air density (1.3 kg m−3), Lυ is the latent heat of vaporization (2.3 106 J kg−1), CLH is a nondimensional transfer coefficient for latent heat (3 10−3), Δq is the specific humidity gradient at the sea surface (assumed here to be a constant 1 g kg−1), U¯ is the prevailing zonal wind, and U′ is the zonal wind anomaly. The latent heat flux anomaly Q′ will thus be modulated only by the anomalous magnitude of the zonal wind speed |U¯+U′|−|U¯|, with neglect of variations in Δq a sacrifice toward simplicity and isolating the influence of wind anomalies on evaporation—the crux of the WES feedback. A brief examination of the impact of allowing adjustments of Δq is, however, given in section 3.
To account for two mechanisms by which the surface wind will respond to SST anomalies, including meridional gradients thereof, the zonal wind anomaly U′ may be written as
U′=−1ρaf ΔP′Δy+dU¯T′,
where f is the Coriolis parameter 2Ωsinφ [where Ω is the rotation rate of Earth (7.292 10−5 s−1) and φ is latitude], the term ΔP′/Δy is a discretization of the anomalous meridional SLP gradient ∂P′/∂y, and d is an efficiency parameter for vertical mixing (or entrainment) of zonal momentum. The first term in (3) enables the LN87 mechanism by assuming the surface wind anomaly to be in quasigeostrophic balance with the anomalous horizontal pressure gradient, and constitutes an important mechanism embedded in the WES feedback as commonly posed. The SLP anomaly P′ is obtained by the simple relation
P′=−eT′,
where the parameter e is estimated to be 100 Pa K−1 from the solutions of LN87, which assumes a well-mixed planetary boundary layer in hydrostatic equilibrium. The second term in (3) enables the WH89 mechanism by assuming the (downward) mixing of zonal momentum is linearly proportional to the product of the SST anomaly T′ and the prevailing zonal wind U¯. It is assumed that a warm SST anomaly T′ > 0 would destabilize the atmospheric boundary layer by steepening its lapse rate and therefore increase the rate of vertical mixing of horizontal momentum, and that the mean prevailing wind U¯ scales with the horizontal momentum available in the free troposphere from which the mixing may draw. The coefficient d is thus the fraction of U¯ that will be transferred to U′ per SST anomaly (K−1). There is no doubt that this parameterization [the second term in (3)] is an oversimplification of boundary layer dynamics and turbulent mixing, but it may nonetheless prove useful here on the lowest rung of model hierarchy. In some respects, this model is similar to that used by Liu and Xie (1994) to study the annual cycle in the eastern tropical Pacific; theirs was also based on a LN87-type atmosphere (without inclusion of the WH89 mechanism), and a substantially more complex ocean mixed layer (including entrainment, wind-driven currents, and temperature advection). Furthermore, this model is conceptually similar to the Gulf Stream study of Takatama et al. (2012) in terms of diagnosing the role of these two mechanisms (LN87 and WH89), except that here the coupled system is considered.
Equations (1)–(4) represent a coupled system of physically based equations that allow for feedbacks between wind, evaporation, and SST. Their form and simplicity may be further exposed by grouping most of the physical constants and coefficients such that there are five parameters, a, b, c, d, and e (note that d and e are defined above). By letting
a=1ρoCph,
b=ρaLυCLHΔq, and
c=1ρafΔy,
the system of equations may be written simply as
∂T′∂t=−aQ′,
Q′=b(|U¯+U′|−|U¯|),
U′=−cΔP′+dU¯T′, and
P′=−eT′,
and by substitution, may be condensed into a single (albeit less simple) nonlinear partial differential equation for the time tendency of SST anomalies:
∂T′∂t=−ab(|U¯+ceΔT′+dU¯T′|−|U¯|)⋅

The following section presents several experiments conducted with this model. The model equations (8)–(11) are integrated with a one-day time step for two locations (denoted by subscripts N for north and S for south) separated by 10° latitude and initialized with SST anomalies T′N=+0.5 K and T′S=–0.5 K(ΔT′=1 K). The parameter d is nominally set to 0.25 K−1, but this choice is consequential; that sensitivity is also explored below. For experiments constrained by realistic profiles of prevailing zonal wind U¯, data from the NCEP–NCAR reanalysis (Kalnay et al. 1996) are used. A Pacific decadal oscillation (PDO; Mantua et al. 1997; Newman et al. 2016) index is used, which was obtained from https://psl.noaa.gov/pdo/; a decadal low-pass filter was applied to the seasonal-mean PDO time series to remove intraseasonal to interannual variations. One set of experiments is conducted with an example change in U¯ drawn from one climate model from phase 6 of the Coupled Model Intercomparison Project (CMIP6; Eyring et al. 2016). The Shared Socioeconomic Pathway 5 (SSP5–8.5) simulation of the Institut Pierre‐Simon Laplace (IPSL) Climate Model version 6A‐low resolution (CM6A‐LR; Boucher et al. 2020) is used, which spans 2015–2100, obtained from https://esgf-node.llnl.gov/search/cmip6/.

3. Results

a. Solutions with a constant and uniform background state

The first experiments to examine are idealized ones in which only the LN87 mechanism is enabled, only the WH89 mechanism is enabled, and both mechanisms are enabled. Each experiment is initialized with an anomalous meridional SST gradient of 1 K over 10° latitude antisymmetric about the equator (as described in section 2), the parameter d is set to 0.25 K−1, and the prevailing zonal wind U¯ is a uniform −5 m s−1. The evolution of SST, SLP, zonal wind, and latent heat flux anomalies in these three experiments over the course of one year (Fig. 2) clearly exhibits strong dependence on which mechanisms are enabled. In the LN87-only experiment (Fig. 2a), the anomalous meridional SST gradient ΔT′ grows rapidly to tenfold its initial value in approximately 7 months. Zooming in on the evolution of SST anomalies during the first two months (Fig. 3) reveals that the initial warm SST anomaly further warms for only about 20 days and then begins to cool (Fig. 3a), whereas the initial cool SST anomaly cools continuously (Fig. 3b). The inflection point for T′N at 23 days is determined by the time scale for the zonal wind anomaly U′ there to surpass twice the magnitude of U¯ and start to increase |U¯+U′| and thus Q′ > 0. Unsurprisingly, the evolution of the WH89-only experiment (Figs. 2b and 3) is very different, characterized by a negative feedback on the initial ΔT′. Zonal wind anomalies, drawing from U¯ at a rate determined by the product of d and T′, immediately damp the SST anomalies through latent heat flux. As the SST anomalies weaken over time, so too does the damping and hence T′N, T′S, and ΔT′ asymptote on zero.

Fig. 2.
Fig. 2.

Solutions to the WES model in which (a) the LN87 mechanism is enabled, (b) the WH89 mechanism is enabled, and (c) both the LN87 and WH89 mechanisms are enabled. Shown for each solution is the SST anomaly (T′; K), sea level pressure anomaly (P′; mb; 1 mb = 1 hPa), zonal wind anomaly (U′; m s−1), and latent heat flux anomaly (Q′; W m−2) for the northern box (thin solid line), southern box (dashed line), and their difference (ΔT′; heavy solid line).

Citation: Journal of Climate 35, 7; 10.1175/JCLI-D-20-0895.1

Fig. 3.
Fig. 3.

Solutions to the WES model for SST anomaly (T′; K) in (a) the northern box, (b) the southern box, and (c) their difference (ΔT′; K), in which the LN87 mechanism is enabled (thin solid line), the WH89 mechanism is enabled (dashed line), and both the LN87 and WH89 mechanisms are enabled (heavy solid line).

Citation: Journal of Climate 35, 7; 10.1175/JCLI-D-20-0895.1

The behavior of the model in which both the LN87 and WH89 mechanisms are enabled (Fig. 2c) is quite intriguing over course of the first year of integration. The value of ΔT′ is roughly quadrupled at 4 months and is then reduced to 1% of its initial value by the end of one year. Comparing the results of this experiment (Fig. 2c) with those of the LN87-only experiment (Fig. 2a) suggests that enabling the WH89 mechanism facilitates the eventual damping of an otherwise obviously unrealistic (ceaseless) growth of SST anomalies—strictly through the dynamics of the coupled system (i.e., without requiring a Newtonian damping term). In reality, of course, there is a thermal damping of this coupled system through adjustment of surface heat flux (Frankignoul and Kestenare 2002; Myers and Mechoso 2020) including variations in the air–sea specific humidity difference Δq (which has thus far been held constant). If the model is rephrased such that Δq is allowed to adjust during model integration (Fig. 4), a steady-state solution for ΔT′ is reached by about day 120 (Fig. 4c), and that final anomaly ΔT′ is about 11% smaller in the model that includes the WH89 mechanism in addition to LN87.

Fig. 4.
Fig. 4.

(a),(b) As in the left columns of Figs. 2a and 2c, i.e., combining SST and zonal wind anomaly results from the LN87-only model (red lines) and the model with both LN87 and WH89 mechanisms enabled (black lines). (c),(d) As in (a) and (b), but for a version of the model with interactive air–sea specific humidity difference Δq. In the latter version, it is necessary to specify additional parameters defining the background state including a mean SST (26°C) and sea level pressure (1013.25 mb) (to calculate the saturation specific humidity at the sea surface), and the mean near-surface specific humidity (0.016 kg kg−1); all other model parameters and initial conditions remain unchanged.

Citation: Journal of Climate 35, 7; 10.1175/JCLI-D-20-0895.1

The sensitivity of this model solution to varying all of the parameters and initial conditions by 20% reveals some dependencies to be expected based on climate physics (e.g., increasing the mixed layer depth h slows SST change without changing the amplitude of the feedback), but a general insensitivity of the overall character of the solution as described above (Fig. 5). An additional sensitivity of the model solution with the LN87 mechanism enabled is on the meridional distance between the two points at which T′N and T′S are specified, such that a distance greater (less) than 10° latitude will yield a stronger (weaker) positive WES feedback with a longer (shorter) time scale via the Coriolis parameter (not shown). Again zooming in on the first few months of the simulation, the initially warm T′N actually grows slightly faster with both mechanisms than with LN87 alone (Fig. 3a), but the initially cold T′S grows more slowly and by a greater margin than for T′N, and consequently the growth of the anomalous gradient ΔT′ is reduced by about 0.25 K (7%) at day 60, and by 1.7 K (30%) at day 120, due to the inclusion of the WH89 mechanism. In most of the subsequent analyses, the time frame of 60 days is highlighted due to the presence of meaningful and qualitatively representative differences between simulations, and a relative insensitivity to modest variation of model parameters at that time scale.

Fig. 5.
Fig. 5.

Solutions to the WES model (for ΔT′) in which both the LN87 and WH89 mechanisms are enabled (i.e., as in Fig. 2c), but with each model parameter and initial condition changed by 20%. The thick gray line is for nominal values as indicated in the main text. The solid red line is for the prevailing easterlies U¯ strengthened from −5 to −6 m s−1. The dashed red line is for the initial SST anomalies T′ strengthened from ±0.5 to ±0.6 K. The solid blue line is for the mixed layer depth h increased from 50 to 60 m. The dashed blue line is for the specific humidity gradient at the sea surface Δq increased from 1 to 1.2 g kg−1. The solid black line is for the parameter d increased from 0.25 to 0.30 K−1. The dashed black line is for the parameter e increased from 100 to 120 Pa K−1.

Citation: Journal of Climate 35, 7; 10.1175/JCLI-D-20-0895.1

The chosen value of d = 0.25 K−1 is of course quite arbitrary and is apparently not large enough to eliminate the positive feedback inherent to the common WES feedback in this experiment. How large would d need to be for the tendency of the WH89 mechanism to damp the initial meridional SST gradient to override the tendency of the LN87 mechanism to amplify it? Setting U′ = 0 and rearranging, (3) becomes
1ρaf ΔP′Δy=dU¯T′,
and solving for d yields
d=ΔP′ρafΔyU¯T′,
which indicates that the “break-even” value of d is state dependent—it scales with the inverse of the prevailing zonal wind U¯. For values of each variable in (14) as initialized in this experiment, it appears that a coefficient d of 2.2 K−1 allows the WH89 mechanism to exactly balance the LN87 mechanism in the WES feedback at the equator, yielding a steady-state solution with no change in T′N, T′S, or ΔT′ over time. Examining the sensitivity of the solution to the WES model to d as a function of latitude under uniform U¯ (Fig. 6a) indicates that this break-even value also applies near 10°N, and otherwise varies strongly as a function of latitude throughout the tropics. Near the equator, it appears that for 0 < d ≤ 1, the mitigation of the positive feedback by the inclusion of the WH89 mechanism (i.e., relative to d = 0 K−1) is about 10% (Fig. 6b).
Fig. 6.
Fig. 6.

(a) Solutions to the WES model for anomalous meridional SST gradient (ΔT′; K) at day 60 as a function of central latitude with uniform prevailing easterlies ( U¯=–5 m s–1; blue line), in which the parameter of the WES model that controls the efficiency of the WH89 mechanism (d) is varied from 0 K−1 (blue line) to 2 K−1 (red line) in increments of 0.25 K−1. (b) Scatter diagram of the solutions in (a) at central latitude 0°N as a function of parameter d (filled circles). (c) As in (a), but for the WES model that includes a Rayleigh damping term to avoid singularities caused by the Coriolis parameter f approaching zero near the equator. The solutions in (c) at central latitude 0°N as a function of parameter d are also shown in (b) as open circles.

Citation: Journal of Climate 35, 7; 10.1175/JCLI-D-20-0895.1

Variation of the Coriolis parameter f is the root cause of the latitudinally dependent results shown in Fig. 6; all other model parameters are equal at different latitudes, and the simulations are run separately at each latitude using the same initial SST anomalies T′ including their meridional spacing Δy. Since the Coriolis parameter f (and its meridional gradient ∂/∂φ) is a nonlinear function of latitude φ, and ∂f/∂φ is maximum in the tropics, the extent to which the LN87-driven positive WES feedback in the presence of an initial positive ΔT′ (i.e., ∂T′/∂φ > 0) is strongly a function of latitude, which introduces latitudinally varying competition to the WH89 mechanism that would attempt to damp it. These latitudinally dependent evolving SST anomalies then modulate the efficiency of the WH89 mechanism by way of T′ in the second term of Eq. (3) ( dU¯T′).

As a means to avoid the singularity at ±5° evident in Fig. 6a, and thus shed further light on the latitudinal structure of the WES feedback, a Rayleigh damping term may be added to Eq. (3) [or term c as defined in Eq. (7)]. In that case, 1/f is simply replaced by f/(f2+A2), where the damping rate A is here set to 10−5 s−1. With Rayleigh damping invoked, there is less hemispheric asymmetry in the magnitude of the WES feedback (Fig. 6c), but asymmetry is still present in solutions to the model where d < 0.5 K−1. Moreover, while the mitigation of the WES feedback by the WH89 mechanism with Rayleigh damping invoked remains about 10% as d is increased from 0 to 0.25 K−1 (Fig. 6b), the mitigation does not then plateau to d = 1 K−1. Rather, the mitigation of the WES feedback scales approximately linearly with the value of parameter d until amplification by the LN87 mechanism is fully compensated by the WH89 mechanism at d = 1.5 K−1.

b. The role of variations in the background state

The remainder of this paper examines the potential influence of variations in background climate at seasonal, decadal, and centennial time scales on the magnitude and latitudinal structure of the WES feedback, particularly with both the LN87 and WH89 mechanisms enabled (d = 0.25 K−1). All subsequent experiments do not invoke Rayleigh damping, although it was checked that the overall conclusions of this paper (including retroactively; i.e., the solutions shown in Figs. 2 and 3) do not depend critically on whether term c as defined in Eq. (7) is treated with Rayleigh damping. For these experiments, realistic profiles of U¯ are based on the NCEP–NCAR reanalysis over 1948–2019, and zonal averages are taken only over the oceans. While this strategy is well motivated by previous experiments that have demonstrated a major role for variations in background winds in the WES feedback including its hemispheric asymmetry (Zhang et al. 2014), it is quite plausible that aspects of the time-varying background state other than U¯ can modulate the WES feedback. For example, some aspects of the WES feedback may be sensitive to changes in ITCZ characteristics (Martinez-Villalobos and Vimont 2016), mean meridional winds (Wang 2010), mixed layer depth h, and the near-surface specific humidity gradient Δq—the crudely estimated model parameters d and e may well also depend on the background thermodynamic state. The focus here is on temporal variations in U¯ since they are measurable, generally robust, and relatively easy to understand.

In the idealized experiments described above, U¯ was set to a uniform −5 m s−1, which is a reasonable magnitude but neglects the latitudinal structure of U¯ including its large seasonal variability (Fig. 7a). For example, the peak easterlies in the global zonal mean are found in the winter hemisphere—centered at ∼13°S during June through August (JJA) and at ∼13°N during December–February (DJF). Such seasonal variations do not only alter the latitudinal distribution of U¯; of potential importance here is also the introduction of its meridional gradient ∂U¯/∂φ. The solutions of the WES model for the JJA and DJF profiles U¯(φ) generally resemble the uniform U¯ case (i.e., Fig. 6a for d ≤ 1), but with some interesting differences (Fig. 7b). In both cases, the solution approaches zero (maximum negative feedback) as the central latitude approaches 5°S (or φN = 0°N), and the solution approaches infinity (unstable, maximum positive feedback) as the central latitude approaches 5°N (or φS = 0°N). The magnitude of the WES feedback on the equator, however, depends strongly on season, such that it is nearly zero (negligible change in ΔT′ from its initial value of 1 K after 60 days) during JJA and quite substantial during DJF (ΔT′ nearly tripling after 60 days). [Note that the magnitude of the WES feedback on the equator in JJA is only approximately zero in the global zonal mean; this is not necessarily so in regional zonal means such as in the eastern Pacific or Atlantic sectors (not shown).] Moreover, while the WES feedback may be stronger on the equator during boreal winter, the latitudinal domain over which it acts as a positive feedback under these circumstances is broader during boreal summer by about 5° into the Northern Hemisphere.

Fig. 7.
Fig. 7.

(a) Profiles of global zonal mean zonal surface wind (m s−1) from the NCEP–NCAR reanalysis (averaged 1948–2019) for boreal winter (DJF; blue line) and boreal summer (JJA; red line). (b) Solutions to the WES model for anomalous meridional SST gradient (ΔT′; K) at day 60 as a function of central latitude, with the prevailing zonal wind U¯ prescribed by the profiles in (a), in which both the LN87 and WH89 mechanisms are enabled (solid line) and only the LN87 mechanism is enabled (dashed line). Solutions for central latitude 0°N are indicated by filled circles, while the initial value of ΔT′ is indicated by an open black circle. (c) As in (b), but solutions ΔT′ in which both the LN87 and WH89 mechanisms are enabled (K) for each calendar month and zoomed close to the equator. (d) As in (c), but with only the LN87 mechanism enabled. In (c) and (d), the initial value of ΔT′ (1 K) is indicated by dashed contour. (e) The difference between (c) and (d), which exposes the contribution of the WH89 mechanism.

Citation: Journal of Climate 35, 7; 10.1175/JCLI-D-20-0895.1

The bulk of the seasonal results are fundamentally driven by the LN87 mechanism (i.e., the WES feedback as commonly posed) and are not qualitatively sensitive to whether the WH89 mechanism is enabled in the WES model. However, the introduction of the WH89 mechanism to the WES model does render the WES feedback near the equator slightly negative during August and September (Fig. 7c), whereas it is positive all year with only the LN87 mechanism enabled (Fig. 7d), so that the WH89 mechanism serves to amplify the annual cycle of the strength of the WES feedback by ∼0.25 K in ΔT′ on the equator at day 60 (Fig. 7e). The prevailing zonal wind U¯ (including its meridional gradient ∂U¯/∂φ) is different at different latitudes and seasons, which clearly introduces further complexity to the latitudinal structure above by modulating the second term in Eq. (3) ( dU¯T′). For example, one might expect the efficiency of the WH89 mechanism to damp the WES feedback (or to act as a net negative feedback in the absence of LN87) would be greater when (and where) the magnitude of the prevailing winds is stronger to the north ( ∂|U¯|/∂φ>0), given an initial positive ΔT′ (i.e., ∂T′/∂φ > 0).

Changes to the prevailing zonal wind U¯ owing to lower-frequency climate variations are typically more subtle than the seasonal cycle, but may take on a different character and are thus worth a brief examination. Solutions to the WES model with U¯(φ) defined by composite regional (east Pacific sector) zonal mean U¯ from intervals during which the PDO was in positive and negative phases (Fig. 8a) suggest that the PDO modulates the magnitude of the WES feedback by ∼7% at 60 days (Figs. 8b,c) and by ∼11% at 120 days (not shown). Specifically, persistent zonal wind anomalies associated with the positive phase of the PDO strengthen the WES feedback, representing a potential scale interaction (e.g., between PDO phase and ENSO amplitude) that should be examined in greater detail through future research.

Fig. 8.
Fig. 8.

(a) Profiles of zonal mean (eastern Pacific, 135°–125°W) zonal surface wind (m s−1) from the NCEP–NCAR Reanalysis (1948–2019) for boreal winters with PDO > 0.5 (heavy line) and PDO < −0.5 (thin line). (b) Solutions to the WES model for anomalous meridional SST gradient (ΔT′; K) at day 60 as a function of central latitude, with the prevailing zonal wind U¯ prescribed by the profiles in (a). Solutions for central latitude 0°N are indicated by filled circles, while the initial value of ΔT′ is indicated by an open black circle. (c) As in (b), but zoomed in on the results at the equator.

Citation: Journal of Climate 35, 7; 10.1175/JCLI-D-20-0895.1

Finally, the potential change in the magnitude and structure of the WES feedback due to anthropogenic radiative forcing can be examined using the projected change in U¯(φ) by fully coupled global climate models. There is sufficient reason to expect that climate change will include robust responses of the atmospheric general circulation including large-scale prevailing winds. For example, the meridional structure of U¯ is closely linked to the Hadley circulation, which may be widening globally (Grise et al. 2019) and at different rates in different sectors (Staten et al. 2019). Moreover, the zonal surface wind in the Pacific sector is defined by the Walker circulation, which ensembles of climate models have indicated will weaken under future global warming (Vecchi and Soden 2007a,b). As shown in Fig. 9a, the IPSL CM6A-LR model (of the CMIP6 generation) predicts a weakening of the equatorial easterlies in the Pacific sector by ∼1.5 m s−1, a strengthening of the off-equatorial peak easterlies by <1 m s−1, and an overall southward shift of the entire structure U¯(φ), which results in a very modest (3%) enhancement of the WES feedback on the equator at day 60 and a very slight northward shift of the latitudinal domain over which the feedback is positive. In the Atlantic sector, however, the projected change in U¯ is a roughly uniform weakening throughout the tropics (Fig. 9d), which leads to a 29% reduction of the WES feedback on the equator and a more substantial northward shift in the latitudinal domain over which the feedback is positive.

Fig. 9.
Fig. 9.

(a) Profiles of zonal mean (eastern Pacific, 135°–125°W) zonal surface wind (m s−1) from the NCEP–NCAR reanalysis (averaged 1948–2019) for boreal winter (thin line), and plus the centennial trend predicted by one CMIP6 climate model (heavy line). (b) Solutions to the WES model for anomalous meridional SST gradient (ΔT′; K) at day 60 as a function of central latitude, with the prevailing zonal wind U¯ prescribed by the profiles in (a). Solutions for central latitude 0°N are indicated by filled circles, while the initial value of ΔT′ is indicated by an open black circle. (c) As in (b), but zoomed in on the results at the equator. (d)–(f) As in (a)–(c), but for the Atlantic (30°–20°W).

Citation: Journal of Climate 35, 7; 10.1175/JCLI-D-20-0895.1

4. Summary and discussion

In light of the multiple and generally competing mechanisms by which SST anomalies can alter surface winds and hence guide the wind–evaporation–SST feedback, a simple coupled model was developed that enables exploration of such processes simultaneously. The atmospheric component of the model developed here accounts for both the hydrostatic adjustment of surface pressure to SST anomalies and the influence of SST anomalies on the stability of the boundary layer and hence vertical mixing of horizontal momentum from the free troposphere. Inclusion of the latter effect prevents the WES feedback from growing unstable beyond a few months, and damps its magnitude on the equator by order 10% for reasonable model parameters and cases [including with or without allowing for the (negative) heat flux feedback via adjustments in Δq]. This is not the first time the aperture on the WES feedback has been widened. A recent study, for example, uncovered an important role for a variable ocean mixed layer depth in shaping such feedbacks (Kataoka et al. 2019), and the WH89 mechanism could have interesting implications in that context as well.

Several other studies have employed a similar formulation of the ocean aspect of the coupled system to investigate the WES feedback (i.e., a slab ocean mixed layer with bulk formula for latent heat flux), but with substantially greater complexity in the atmosphere (e.g., Gill–Matsuno type), which of course leads to atmospheric Kelvin and Rossby wave propagation and consideration of horizontal mass convergence (e.g., Vimont 2010; Martinez-Villalobos and Vimont 2017)—processes that may well be necessary to fully resolve all of the implications of the WH89 mechanism for the WES feedback. Interestingly, the results of Takatama et al. (2012) suggest that the two mechanisms considered here (LN87 and WH89) may play different roles in terms of rendering surface convergence versus divergence—at least in the context of narrow frontal zones such as along western boundary currents. Additionally, the suitability of the WH89 mechanism to explain the correlation between SST and surface wind speed (positive in this model, by construction) may depend on proximity to, and the wind’s orientation relative to, the frontal transition between the warm and cold SST anomalies (Samelson et al. 2006; Spall 2007).

Hemispheric asymmetries in the strength of the WES feedback predicted by the simple model, even under uniform zonal winds, are consistent with previous studies that show that WES is more active in the Northern Hemisphere for the Atlantic meridional mode (Chang et al. 2000; Amaya et al. 2017). Model solutions for realistic cases, constrained by observed profiles of prevailing zonal wind, reveal the leading influence of seasonality on the strength and latitudinal structure of the WES feedback such that it is predicted to be much stronger near the equator during boreal winter than boreal summer, but active over a wider range of latitudes during boreal summer. Inclusion of the stability mechanism serves to amplify the annual cycle of the strength of the WES feedback by about 10%. Such seasonality of the efficiency of the WES feedback near the equator may contribute to its potential to play a role in ENSO development, and in particular ENSO’s observed phase locking to the annual cycle as previously argued by Wang et al. (1999).

This framework may be applied to lower-frequency variations in the background climate, including those arising due to anthropogenic forcing. It is important to be mindful that this is not a rigorous estimate of the forced change—nor is it intended to be. It is a demonstration using a single run by one climate model for a particular forcing scenario, and some nontrivial low-frequency natural variability may contaminate the trend. Liguori and Di Lorenzo (2018) analyzed output from a large ensemble of full complexity coupled GCM simulations driven by similar radiative forcing and calculated the so-called WES parameter to estimate the strength of the WES feedback post hoc using the model output. They concluded that the WES feedback in the PMM region (central northern tropical Pacific) exhibits an exponential increase in amplitude because of the nonlinear relationship between SST and evaporation in a warming mean climate. The simple model, when only driven by projected changes in zonal wind, predicts a more modest (∼3%) enhancement of the WES feedback in the east Pacific on the equator. North of the equator, however, the increase in WES feedback strength is quite stronger than this locally due to a northward shift in the latitude band in which WES is positive and effective. Despite very different models and with a large number of other caveats, one may conclude that these results are not inconsistent. The overarching conclusion is that temporal variability in the background climate state—forced and unforced alike—can alter the strength and structure of the WES feedback [as also shown by Okajima et al. (2003) by altering land distribution in a full-physics coupled model], and these insights may facilitate interpretation of coupled climate behavior in observations and more complex models.

Acknowledgments.

The author acknowledges support from NOAA Climate Program Office, Climate Variability and Predictability (CVP) Program (NA18OAR4310406) and a helpful discussion with Dr. Lei Zhang. The author also thanks three anonymous reviewers for insightful suggestions, and the editor for patience.

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  • Amaya, D. J., 2019: The Pacific meridional mode and ENSO: A review. Curr. Climate Change Rep., 5, 296–307, https://doi.org/10.1007/s40641-019-00142-x.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Amaya, D. J., M. J. DeFlorio, A. J. Miller, and S.-P. Xie, 2017: WES feedback and the Atlantic meridional mode: Observations and CMIP5 comparisons. Climate Dyn., 49, 1665–1679, https://doi.org/10.1007/s00382-016-3411-1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Back, L. E., and C. S. Bretherton, 2009: On the relationship between SST gradients, boundary layer winds, and convergence over the tropical oceans. J. Climate, 22, 4182–4196, https://doi.org/10.1175/2009JCLI2392.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Boucher, O., and Coauthors, 2020: Presentation and evaluation of the IPSL‐CM6A‐LR climate model. J. Adv. Model. Earth Syst., 12, e2019MS002010, https://doi.org/10.1029/2019MS002010.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Chang, P., L. Ji, and H. Li, 1997: A decadal climate variation in the tropical Atlantic Ocean from thermodynamic air–sea interactions. Nature, 385, 516–518, https://doi.org/10.1038/385516a0.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Chang, P., R. Saravanan, L. Ji, and G. C. Hegerl, 2000: The effect of local sea surface temperatures on atmospheric circulation over the tropical Atlantic sector. J. Climate, 13, 2195–2216, https://doi.org/10.1175/1520-0442(2000)013<2195:TEOLSS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Chiang, J. C. H., and D. J. Vimont, 2004: Analogous Pacific and Atlantic meridional modes of tropical atmosphere–ocean variability. J. Climate, 17, 4143–4158, https://doi.org/10.1175/JCLI4953.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • de Boyer Montégut, C., G. Madec, A. S. Fischer, A. Lazar, and D. Iudicone, 2004: Mixed layer depth over the global ocean: An examination of profile data and a profile‐based climatology. J. Geophys. Res., 109, C12003, https://doi.org/10.1029/2004JC002378.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • DeMott, C. A., J. J. Benedict, N. P. Klingaman, S. J. Woolnough, and D. A. Randall, 2016: Diagnosing ocean feedbacks to the MJO: SST‐modulated surface fluxes and the moist static energy budget. J. Geophys. Res. Atmos., 121, 8350–8373, https://doi.org/10.1002/2016JD025098.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Emanuel, K. A., 1987: An air–sea interaction model of intraseasonal oscillations in the tropics. J. Atmos. Sci., 44, 2324–2340, https://doi.org/10.1175/1520-0469(1987)044<2324:AASIMO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Eyring, V., S. Bony, G. A. Meehl, C. A. Senior, B. Stevens, R. J. Stouffer, and K. E. Taylor, 2016: Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) experimental design and organization. Geosci. Model Dev., 9, 1937–1958, https://doi.org/10.5194/gmd-9-1937-2016.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Frankignoul, C., and E. Kestenare, 2002: The surface heat flux feedback. Part I: Estimates from observations in the Atlantic and the North Pacific. Climate Dyn., 19, 633–647, https://doi.org/10.1007/s00382-002-0252-x.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Grise, K. M., and Coauthors, 2019: Recent tropical expansion: Natural variability or forced response? J. Climate, 32, 1551–1571, https://doi.org/10.1175/JCLI-D-18-0444.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Hayes, S., M. McPhaden, and J. Wallace, 1989: The influence of sea-surface temperature on surface wind in the eastern equatorial Pacific: Weekly to monthly variability. J. Climate, 2, 1500–1506, https://doi.org/10.1175/1520-0442(1989)002<1500:TIOSST>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437–471, https://doi.org/10.1175/1520-0477(1996)077<0437:TNYRP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Kataoka, T., M. Kimoto, M. Watanabe, and H. Tatebe, 2019: Wind–mixed layer–SST feedbacks in a tropical air–sea coupled system: Application to the Atlantic. J. Climate, 32, 3865–3881, https://doi.org/10.1175/JCLI-D-18-0728.1.

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    • Export Citation

  • Li, T., B. Wang, C. Chang, and Y. Zhang, 2003: A theory for the Indian Ocean dipole–zonal mode. J. Atmos. Sci., 60, 2119–2135, https://doi.org/10.1175/1520-0469(2003)060<2119:ATFTIO>2.0.CO;2.

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    • Search Google Scholar
    • Export Citation

  • Liguori, G., and E. Di Lorenzo, 2018: Meridional modes and increasing Pacific decadal variability under anthropogenic forcing. Geophys. Res. Lett., 45, 983–991, https://doi.org/10.1002/2017GL076548.

    • Crossref
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  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    Schematic illustrations of the WES feedback in which the surface wind response to an anomalous meridional SST gradient is governed by (a) the LN87 mechanism (hydrostatic pressure, i.e., the common WES feedback) and (b) the WH89 mechanism (vertical momentum mixing). In both diagrams, time progresses from left to right following steps A through F (see main text). Note that the final state (step F) in (a) is an amplified version of the initial state (step A), thus representing a positive feedback, and vice versa for (b).

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    Solutions to the WES model in which (a) the LN87 mechanism is enabled, (b) the WH89 mechanism is enabled, and (c) both the LN87 and WH89 mechanisms are enabled. Shown for each solution is the SST anomaly (T′; K), sea level pressure anomaly (P′; mb; 1 mb = 1 hPa), zonal wind anomaly (U′; m s−1), and latent heat flux anomaly (Q′; W m−2) for the northern box (thin solid line), southern box (dashed line), and their difference (ΔT′; heavy solid line).

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    Solutions to the WES model for SST anomaly (T′; K) in (a) the northern box, (b) the southern box, and (c) their difference (ΔT′; K), in which the LN87 mechanism is enabled (thin solid line), the WH89 mechanism is enabled (dashed line), and both the LN87 and WH89 mechanisms are enabled (heavy solid line).

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    (a),(b) As in the left columns of Figs. 2a and 2c, i.e., combining SST and zonal wind anomaly results from the LN87-only model (red lines) and the model with both LN87 and WH89 mechanisms enabled (black lines). (c),(d) As in (a) and (b), but for a version of the model with interactive air–sea specific humidity difference Δq. In the latter version, it is necessary to specify additional parameters defining the background state including a mean SST (26°C) and sea level pressure (1013.25 mb) (to calculate the saturation specific humidity at the sea surface), and the mean near-surface specific humidity (0.016 kg kg−1); all other model parameters and initial conditions remain unchanged.

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    Solutions to the WES model (for ΔT′) in which both the LN87 and WH89 mechanisms are enabled (i.e., as in Fig. 2c), but with each model parameter and initial condition changed by 20%. The thick gray line is for nominal values as indicated in the main text. The solid red line is for the prevailing easterlies U¯ strengthened from −5 to −6 m s−1. The dashed red line is for the initial SST anomalies T′ strengthened from ±0.5 to ±0.6 K. The solid blue line is for the mixed layer depth h increased from 50 to 60 m. The dashed blue line is for the specific humidity gradient at the sea surface Δq increased from 1 to 1.2 g kg−1. The solid black line is for the parameter d increased from 0.25 to 0.30 K−1. The dashed black line is for the parameter e increased from 100 to 120 Pa K−1.

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    (a) Solutions to the WES model for anomalous meridional SST gradient (ΔT′; K) at day 60 as a function of central latitude with uniform prevailing easterlies ( U¯=–5 m s–1; blue line), in which the parameter of the WES model that controls the efficiency of the WH89 mechanism (d) is varied from 0 K−1 (blue line) to 2 K−1 (red line) in increments of 0.25 K−1. (b) Scatter diagram of the solutions in (a) at central latitude 0°N as a function of parameter d (filled circles). (c) As in (a), but for the WES model that includes a Rayleigh damping term to avoid singularities caused by the Coriolis parameter f approaching zero near the equator. The solutions in (c) at central latitude 0°N as a function of parameter d are also shown in (b) as open circles.

  • <sc>Fig</sc>. 7.
    View in gallery
    Fig. 7.

    (a) Profiles of global zonal mean zonal surface wind (m s−1) from the NCEP–NCAR reanalysis (averaged 1948–2019) for boreal winter (DJF; blue line) and boreal summer (JJA; red line). (b) Solutions to the WES model for anomalous meridional SST gradient (ΔT′; K) at day 60 as a function of central latitude, with the prevailing zonal wind U¯ prescribed by the profiles in (a), in which both the LN87 and WH89 mechanisms are enabled (solid line) and only the LN87 mechanism is enabled (dashed line). Solutions for central latitude 0°N are indicated by filled circles, while the initial value of ΔT′ is indicated by an open black circle. (c) As in (b), but solutions ΔT′ in which both the LN87 and WH89 mechanisms are enabled (K) for each calendar month and zoomed close to the equator. (d) As in (c), but with only the LN87 mechanism enabled. In (c) and (d), the initial value of ΔT′ (1 K) is indicated by dashed contour. (e) The difference between (c) and (d), which exposes the contribution of the WH89 mechanism.

  • <sc>Fig</sc>. 8.
    View in gallery
    Fig. 8.

    (a) Profiles of zonal mean (eastern Pacific, 135°–125°W) zonal surface wind (m s−1) from the NCEP–NCAR Reanalysis (1948–2019) for boreal winters with PDO > 0.5 (heavy line) and PDO < −0.5 (thin line). (b) Solutions to the WES model for anomalous meridional SST gradient (ΔT′; K) at day 60 as a function of central latitude, with the prevailing zonal wind U¯ prescribed by the profiles in (a). Solutions for central latitude 0°N are indicated by filled circles, while the initial value of ΔT′ is indicated by an open black circle. (c) As in (b), but zoomed in on the results at the equator.

  • <sc>Fig</sc>. 9.
    View in gallery
    Fig. 9.

    (a) Profiles of zonal mean (eastern Pacific, 135°–125°W) zonal surface wind (m s−1) from the NCEP–NCAR reanalysis (averaged 1948–2019) for boreal winter (thin line), and plus the centennial trend predicted by one CMIP6 climate model (heavy line). (b) Solutions to the WES model for anomalous meridional SST gradient (ΔT′; K) at day 60 as a function of central latitude, with the prevailing zonal wind U¯ prescribed by the profiles in (a). Solutions for central latitude 0°N are indicated by filled circles, while the initial value of ΔT′ is indicated by an open black circle. (c) As in (b), but zoomed in on the results at the equator. (d)–(f) As in (a)–(c), but for the Atlantic (30°–20°W).

Fig. 1.

Schematic illustrations of the WES feedback in which the surface wind response to an anomalous meridional SST gradient is governed by (a) the LN87 mechanism (hydrostatic pressure, i.e., the common WES feedback) and (b) the WH89 mechanism (vertical momentum mixing). In both diagrams, time progresses from left to right following steps A through F (see main text). Note that the final state (step F) in (a) is an amplified version of the initial state (step A), thus representing a positive feedback, and vice versa for (b).
Fig. 2.

Solutions to the WES model in which (a) the LN87 mechanism is enabled, (b) the WH89 mechanism is enabled, and (c) both the LN87 and WH89 mechanisms are enabled. Shown for each solution is the SST anomaly (T′; K), sea level pressure anomaly (P′; mb; 1 mb = 1 hPa), zonal wind anomaly (U′; m s−1), and latent heat flux anomaly (Q′; W m−2) for the northern box (thin solid line), southern box (dashed line), and their difference (ΔT′; heavy solid line).
Fig. 3.

Solutions to the WES model for SST anomaly (T′; K) in (a) the northern box, (b) the southern box, and (c) their difference (ΔT′; K), in which the LN87 mechanism is enabled (thin solid line), the WH89 mechanism is enabled (dashed line), and both the LN87 and WH89 mechanisms are enabled (heavy solid line).
Fig. 4.

(a),(b) As in the left columns of Figs. 2a and 2c, i.e., combining SST and zonal wind anomaly results from the LN87-only model (red lines) and the model with both LN87 and WH89 mechanisms enabled (black lines). (c),(d) As in (a) and (b), but for a version of the model with interactive air–sea specific humidity difference Δq. In the latter version, it is necessary to specify additional parameters defining the background state including a mean SST (26°C) and sea level pressure (1013.25 mb) (to calculate the saturation specific humidity at the sea surface), and the mean near-surface specific humidity (0.016 kg kg−1); all other model parameters and initial conditions remain unchanged.
Fig. 5.

Solutions to the WES model (for ΔT′) in which both the LN87 and WH89 mechanisms are enabled (i.e., as in Fig. 2c), but with each model parameter and initial condition changed by 20%. The thick gray line is for nominal values as indicated in the main text. The solid red line is for the prevailing easterlies U¯ strengthened from −5 to −6 m s−1. The dashed red line is for the initial SST anomalies T′ strengthened from ±0.5 to ±0.6 K. The solid blue line is for the mixed layer depth h increased from 50 to 60 m. The dashed blue line is for the specific humidity gradient at the sea surface Δq increased from 1 to 1.2 g kg−1. The solid black line is for the parameter d increased from 0.25 to 0.30 K−1. The dashed black line is for the parameter e increased from 100 to 120 Pa K−1.
Fig. 6.

(a) Solutions to the WES model for anomalous meridional SST gradient (ΔT′; K) at day 60 as a function of central latitude with uniform prevailing easterlies ( U¯=–5 m s–1; blue line), in which the parameter of the WES model that controls the efficiency of the WH89 mechanism (d) is varied from 0 K−1 (blue line) to 2 K−1 (red line) in increments of 0.25 K−1. (b) Scatter diagram of the solutions in (a) at central latitude 0°N as a function of parameter d (filled circles). (c) As in (a), but for the WES model that includes a Rayleigh damping term to avoid singularities caused by the Coriolis parameter f approaching zero near the equator. The solutions in (c) at central latitude 0°N as a function of parameter d are also shown in (b) as open circles.
Fig. 7.

(a) Profiles of global zonal mean zonal surface wind (m s−1) from the NCEP–NCAR reanalysis (averaged 1948–2019) for boreal winter (DJF; blue line) and boreal summer (JJA; red line). (b) Solutions to the WES model for anomalous meridional SST gradient (ΔT′; K) at day 60 as a function of central latitude, with the prevailing zonal wind U¯ prescribed by the profiles in (a), in which both the LN87 and WH89 mechanisms are enabled (solid line) and only the LN87 mechanism is enabled (dashed line). Solutions for central latitude 0°N are indicated by filled circles, while the initial value of ΔT′ is indicated by an open black circle. (c) As in (b), but solutions ΔT′ in which both the LN87 and WH89 mechanisms are enabled (K) for each calendar month and zoomed close to the equator. (d) As in (c), but with only the LN87 mechanism enabled. In (c) and (d), the initial value of ΔT′ (1 K) is indicated by dashed contour. (e) The difference between (c) and (d), which exposes the contribution of the WH89 mechanism.
Fig. 8.

(a) Profiles of zonal mean (eastern Pacific, 135°–125°W) zonal surface wind (m s−1) from the NCEP–NCAR Reanalysis (1948–2019) for boreal winters with PDO > 0.5 (heavy line) and PDO < −0.5 (thin line). (b) Solutions to the WES model for anomalous meridional SST gradient (ΔT′; K) at day 60 as a function of central latitude, with the prevailing zonal wind U¯ prescribed by the profiles in (a). Solutions for central latitude 0°N are indicated by filled circles, while the initial value of ΔT′ is indicated by an open black circle. (c) As in (b), but zoomed in on the results at the equator.
Fig. 9.

(a) Profiles of zonal mean (eastern Pacific, 135°–125°W) zonal surface wind (m s−1) from the NCEP–NCAR reanalysis (averaged 1948–2019) for boreal winter (thin line), and plus the centennial trend predicted by one CMIP6 climate model (heavy line). (b) Solutions to the WES model for anomalous meridional SST gradient (ΔT′; K) at day 60 as a function of central latitude, with the prevailing zonal wind U¯ prescribed by the profiles in (a). Solutions for central latitude 0°N are indicated by filled circles, while the initial value of ΔT′ is indicated by an open black circle. (c) As in (b), but zoomed in on the results at the equator. (d)–(f) As in (a)–(c), but for the Atlantic (30°–20°W).
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