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- Author or Editor: Alexey V. Fedorov x
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Abstract
Physical processes that control ENSO are relatively fast. For instance, it takes only several months for a Kelvin wave to cross the Pacific basin (Tk ≈ 2 months), while Rossby waves travel the same distance in about half a year. Compared to such short time scales, the typical periodicity of El Niño is much longer (T ≈ 2–7 yr). Thus, ENSO is fundamentally a low-frequency phenomenon in the context of these faster processes. Here, the author takes advantage of this fact and uses the smallness of the ratio ε k = Tk /T to expand solutions of the ocean shallow-water equations into power series (the actual parameter of expansion also includes the oceanic damping rate). Using such an expansion, referred to here as the low-frequency approximation, the author relates thermocline depth anomalies to temperature variations in the eastern equatorial Pacific via an explicit integral operator. This allows a simplified formulation of ENSO dynamics based on an integro-differential equation. Within this formulation, the author shows how the interplay between wind stress curl and oceanic damping rates affects 1) the amplitude and periodicity of El Niño and 2) the phase lag between variations in the equatorial warm water volume and SST in the eastern Pacific. A simple analytical expression is derived for the phase lag. Further, applying the low-frequency approximation to the observed variations in SST, the author computes thermocline depth anomalies in the western and eastern equatorial Pacific to show a good agreement with the observed variations in warm water volume. Ultimately, this approach provides a rigorous framework for deriving other simple models of ENSO (the delayed and recharge oscillators), highlights the limitations of such models, and can be easily used for decadal climate variability in the Pacific.
Abstract
Physical processes that control ENSO are relatively fast. For instance, it takes only several months for a Kelvin wave to cross the Pacific basin (Tk ≈ 2 months), while Rossby waves travel the same distance in about half a year. Compared to such short time scales, the typical periodicity of El Niño is much longer (T ≈ 2–7 yr). Thus, ENSO is fundamentally a low-frequency phenomenon in the context of these faster processes. Here, the author takes advantage of this fact and uses the smallness of the ratio ε k = Tk /T to expand solutions of the ocean shallow-water equations into power series (the actual parameter of expansion also includes the oceanic damping rate). Using such an expansion, referred to here as the low-frequency approximation, the author relates thermocline depth anomalies to temperature variations in the eastern equatorial Pacific via an explicit integral operator. This allows a simplified formulation of ENSO dynamics based on an integro-differential equation. Within this formulation, the author shows how the interplay between wind stress curl and oceanic damping rates affects 1) the amplitude and periodicity of El Niño and 2) the phase lag between variations in the equatorial warm water volume and SST in the eastern Pacific. A simple analytical expression is derived for the phase lag. Further, applying the low-frequency approximation to the observed variations in SST, the author computes thermocline depth anomalies in the western and eastern equatorial Pacific to show a good agreement with the observed variations in warm water volume. Ultimately, this approach provides a rigorous framework for deriving other simple models of ENSO (the delayed and recharge oscillators), highlights the limitations of such models, and can be easily used for decadal climate variability in the Pacific.
Abstract
How unstable is the tropical ocean–atmosphere system? Are two successive El Niño events independent, or are they part of a continual (perhaps weakly damped) cycle sustained by random atmospheric disturbances? How important is energy dissipation for ENSO dynamics? These closely related questions are frequently raised in connection with several climate problems ranging from El Niño predictability to the impact of atmospheric “noise” on ENSO. One of the factors influencing the system’s stability and other relevant properties is the damping (decay) time scale for the thermocline anomalies associated with the large-scale oceanic motion. Here this time scale is estimated by considering energy balance and net energy dissipation in the tropical ocean and it is shown that there are two distinct dissipative regimes: in the interannual frequency band the damping rate is approximately (2.3 yr)−1; however, in a near-annual frequency range the damping appears to be much stronger, roughly (8 months)−1.
Abstract
How unstable is the tropical ocean–atmosphere system? Are two successive El Niño events independent, or are they part of a continual (perhaps weakly damped) cycle sustained by random atmospheric disturbances? How important is energy dissipation for ENSO dynamics? These closely related questions are frequently raised in connection with several climate problems ranging from El Niño predictability to the impact of atmospheric “noise” on ENSO. One of the factors influencing the system’s stability and other relevant properties is the damping (decay) time scale for the thermocline anomalies associated with the large-scale oceanic motion. Here this time scale is estimated by considering energy balance and net energy dissipation in the tropical ocean and it is shown that there are two distinct dissipative regimes: in the interannual frequency band the damping rate is approximately (2.3 yr)−1; however, in a near-annual frequency range the damping appears to be much stronger, roughly (8 months)−1.
Abstract
Ocean general circulation models (GCMs), as part of comprehensive climate models, are extensively used for experimental decadal climate prediction. Understanding the limits of decadal ocean predictability is critical for making progress in these efforts. However, when forced with observed fields at the surface, ocean models develop biases in temperature and salinity. Here, the authors ask two complementary questions related to both decadal prediction and model bias: 1) Can the bias be temporarily reduced and the prediction improved by perturbing the initial conditions? 2) How fast will such initial perturbations grow? To answer these questions, the authors use a realistic ocean GCM and compute temperature and salinity perturbations that reduce the model bias most efficiently during a given time interval. The authors find that to reduce this bias, especially pronounced in the upper ocean above 1000 m, initial perturbations should be imposed in the deep ocean (specifically, in the Southern Ocean). Over 14 yr, a 0.1-K perturbation in the deep ocean can induce a temperature anomaly of several kelvins in the upper ocean, partially reducing the bias. A corollary of these results is that small initialization errors in the deep ocean can produce large errors in the upper-ocean temperature on decadal time scales, which can be interpreted as a decadal predictability barrier associated with ocean dynamics. To study the mechanisms of the perturbation growth, the authors formulate an idealized model describing temperature anomalies in the Southern Ocean. The results indicate that the strong mean meridional temperature gradient in this region enhances the sensitivity of the upper ocean to deep-ocean perturbations through nonnormal dynamics generating pronounced stationary-wave patterns.
Abstract
Ocean general circulation models (GCMs), as part of comprehensive climate models, are extensively used for experimental decadal climate prediction. Understanding the limits of decadal ocean predictability is critical for making progress in these efforts. However, when forced with observed fields at the surface, ocean models develop biases in temperature and salinity. Here, the authors ask two complementary questions related to both decadal prediction and model bias: 1) Can the bias be temporarily reduced and the prediction improved by perturbing the initial conditions? 2) How fast will such initial perturbations grow? To answer these questions, the authors use a realistic ocean GCM and compute temperature and salinity perturbations that reduce the model bias most efficiently during a given time interval. The authors find that to reduce this bias, especially pronounced in the upper ocean above 1000 m, initial perturbations should be imposed in the deep ocean (specifically, in the Southern Ocean). Over 14 yr, a 0.1-K perturbation in the deep ocean can induce a temperature anomaly of several kelvins in the upper ocean, partially reducing the bias. A corollary of these results is that small initialization errors in the deep ocean can produce large errors in the upper-ocean temperature on decadal time scales, which can be interpreted as a decadal predictability barrier associated with ocean dynamics. To study the mechanisms of the perturbation growth, the authors formulate an idealized model describing temperature anomalies in the Southern Ocean. The results indicate that the strong mean meridional temperature gradient in this region enhances the sensitivity of the upper ocean to deep-ocean perturbations through nonnormal dynamics generating pronounced stationary-wave patterns.
Abstract
Variations in the strength of the Atlantic meridional overturning circulation (AMOC) are a major potential source of decadal and longer climate variability in the Atlantic. This study analyzes continuous integrations of tangent linear and adjoint versions of an ocean general circulation model [Océan Parallélisé (OPA)] and rigorously shows the existence of a weakly damped oscillatory eigenmode of the AMOC centered in the North Atlantic Ocean and controlled solely by linearized ocean dynamics. In this particular GCM, the mode period is roughly 24 years, its e-folding decay time scale is 40 years, and it is the least-damped oscillatory mode in the system. Its mechanism is related to the westward propagation of large-scale temperature anomalies in the northern Atlantic in the latitudinal band between 30° and 60°N. The westward propagation results from a competition among mean eastward zonal advection, equivalent anomalous westward advection caused by the mean meridional temperature gradient, and westward propagation typical of long baroclinic Rossby waves. The zonal structure of temperature anomalies alternates between a dipole (corresponding to an anomalous AMOC) and anomalies of one sign (yielding no changes in the AMOC). Further, it is shown that the system is nonnormal, which implies that the structure of the least-damped eigenmode of the tangent linear model is different from that of the adjoint model. The “adjoint” mode describes the sensitivity of the system (i.e., it gives the most efficient patterns for exciting the leading eigenmode). An idealized model is formulated to highlight the role of the background meridional temperature gradient in the North Atlantic for the mode mechanism and the system nonnormality.
Abstract
Variations in the strength of the Atlantic meridional overturning circulation (AMOC) are a major potential source of decadal and longer climate variability in the Atlantic. This study analyzes continuous integrations of tangent linear and adjoint versions of an ocean general circulation model [Océan Parallélisé (OPA)] and rigorously shows the existence of a weakly damped oscillatory eigenmode of the AMOC centered in the North Atlantic Ocean and controlled solely by linearized ocean dynamics. In this particular GCM, the mode period is roughly 24 years, its e-folding decay time scale is 40 years, and it is the least-damped oscillatory mode in the system. Its mechanism is related to the westward propagation of large-scale temperature anomalies in the northern Atlantic in the latitudinal band between 30° and 60°N. The westward propagation results from a competition among mean eastward zonal advection, equivalent anomalous westward advection caused by the mean meridional temperature gradient, and westward propagation typical of long baroclinic Rossby waves. The zonal structure of temperature anomalies alternates between a dipole (corresponding to an anomalous AMOC) and anomalies of one sign (yielding no changes in the AMOC). Further, it is shown that the system is nonnormal, which implies that the structure of the least-damped eigenmode of the tangent linear model is different from that of the adjoint model. The “adjoint” mode describes the sensitivity of the system (i.e., it gives the most efficient patterns for exciting the leading eigenmode). An idealized model is formulated to highlight the role of the background meridional temperature gradient in the North Atlantic for the mode mechanism and the system nonnormality.
Abstract
This study investigates the excitation of decadal variability and predictability of the ocean climate state in the North Atlantic. Specifically, initial linear optimal perturbations (LOPs) in temperature and salinity that vary with depth, longitude, and latitude are computed, and the maximum impact on the ocean of these perturbations is evaluated in a realistic ocean general circulation model. The computations of the LOPs involve a maximization procedure based on Lagrange multipliers in a nonautonomous context. To assess the impact of these perturbations four different measures of the North Atlantic Ocean state are used: meridional volume and heat transports (MVT and MHT) and spatially averaged sea surface temperature (SST) and ocean heat content (OHC). It is shown that these metrics are dramatically different with regard to predictability. Whereas OHC and SST can be efficiently modified only by basin-scale anomalies, MVT and MHT are also strongly affected by smaller-scale perturbations. This suggests that instantaneous or even annual-mean values of MVT and MHT are less predictable than SST and OHC. Only when averaged over several decades do the former two metrics have predictability comparable to the latter two, which highlights the need for long-term observations of the Atlantic meridional overturning circulation in order to accumulate climatically relevant data. This study also suggests that initial errors in ocean temperature of a few millikelvins, encompassing both the upper and deep ocean, can lead to ~0.1-K errors in the predictions of North Atlantic sea surface temperature on interannual time scales. This transient error growth peaks for SST and OHC after about 6 and 10 years, respectively, implying a potential predictability barrier.
Abstract
This study investigates the excitation of decadal variability and predictability of the ocean climate state in the North Atlantic. Specifically, initial linear optimal perturbations (LOPs) in temperature and salinity that vary with depth, longitude, and latitude are computed, and the maximum impact on the ocean of these perturbations is evaluated in a realistic ocean general circulation model. The computations of the LOPs involve a maximization procedure based on Lagrange multipliers in a nonautonomous context. To assess the impact of these perturbations four different measures of the North Atlantic Ocean state are used: meridional volume and heat transports (MVT and MHT) and spatially averaged sea surface temperature (SST) and ocean heat content (OHC). It is shown that these metrics are dramatically different with regard to predictability. Whereas OHC and SST can be efficiently modified only by basin-scale anomalies, MVT and MHT are also strongly affected by smaller-scale perturbations. This suggests that instantaneous or even annual-mean values of MVT and MHT are less predictable than SST and OHC. Only when averaged over several decades do the former two metrics have predictability comparable to the latter two, which highlights the need for long-term observations of the Atlantic meridional overturning circulation in order to accumulate climatically relevant data. This study also suggests that initial errors in ocean temperature of a few millikelvins, encompassing both the upper and deep ocean, can lead to ~0.1-K errors in the predictions of North Atlantic sea surface temperature on interannual time scales. This transient error growth peaks for SST and OHC after about 6 and 10 years, respectively, implying a potential predictability barrier.
Abstract
A salient feature of paleorecords of the last glacial interval in the North Atlantic is pronounced millennial variability, commonly known as Dansgaard–Oeschger events. It is believed that these events are related to variations in the Atlantic meridional overturning circulation and heat transport. Here, the authors formulate a new low-order model, based on the Howard–Malkus loop representation of ocean circulation, capable of reproducing millennial variability and its chaotic dynamics realistically. It is shown that even in this chaotic model changes in the state of the meridional overturning circulation are predictable. Accordingly, the authors define two predictive indices which give accurate predictions for the time the circulation should remain in the on phase and then stay in the subsequent off phase. These indices depend mainly on ocean stratification and describe the linear growth of small perturbations in the system. Thus, monitoring particular indices of the ocean state could help predict a potential shutdown of the overturning circulation.
Abstract
A salient feature of paleorecords of the last glacial interval in the North Atlantic is pronounced millennial variability, commonly known as Dansgaard–Oeschger events. It is believed that these events are related to variations in the Atlantic meridional overturning circulation and heat transport. Here, the authors formulate a new low-order model, based on the Howard–Malkus loop representation of ocean circulation, capable of reproducing millennial variability and its chaotic dynamics realistically. It is shown that even in this chaotic model changes in the state of the meridional overturning circulation are predictable. Accordingly, the authors define two predictive indices which give accurate predictions for the time the circulation should remain in the on phase and then stay in the subsequent off phase. These indices depend mainly on ocean stratification and describe the linear growth of small perturbations in the system. Thus, monitoring particular indices of the ocean state could help predict a potential shutdown of the overturning circulation.
Abstract
Westerly wind bursts (WWBs)—brief but strong westerly wind anomalies in the equatorial Pacific—are believed to play an important role in El Niño–Southern Oscillation (ENSO) dynamics, but quantifying their effects is challenging. Here, we investigate the cumulative effects of WWBs on ENSO characteristics, including the occurrence of extreme El Niño events, via modified coupled model experiments within Community Earth System Model (CESM1) in which we progressively reduce the impacts of wind stress anomalies associated with model-generated WWBs. In these “wind stress shaving” experiments we limit momentum transfer from the atmosphere to the ocean above a preset threshold, thus “shaving off” wind bursts. To reduce the tropical Pacific mean state drift, both westerly and easterly wind bursts are removed, although the changes are dominated by WWB reduction. As we impose progressively stronger thresholds, both ENSO amplitude and the frequency of extreme El Niño decrease, and ENSO becomes less asymmetric. The warming center of El Niño shifts westward, indicating less frequent and weaker eastern Pacific (EP) El Niño events. Removing most wind burst–related wind stress anomalies reduces ENSO mean amplitude by 22%. The essential role of WWBs in the development of extreme El Niño events is highlighted by the suppressed eastward migration of the western Pacific warm pool and hence a weaker Bjerknes feedback under wind shaving. Overall, our results reaffirm the importance of WWBs in shaping the characteristics of ENSO and its extreme events and imply that WWB changes with global warming could influence future ENSO.
Abstract
Westerly wind bursts (WWBs)—brief but strong westerly wind anomalies in the equatorial Pacific—are believed to play an important role in El Niño–Southern Oscillation (ENSO) dynamics, but quantifying their effects is challenging. Here, we investigate the cumulative effects of WWBs on ENSO characteristics, including the occurrence of extreme El Niño events, via modified coupled model experiments within Community Earth System Model (CESM1) in which we progressively reduce the impacts of wind stress anomalies associated with model-generated WWBs. In these “wind stress shaving” experiments we limit momentum transfer from the atmosphere to the ocean above a preset threshold, thus “shaving off” wind bursts. To reduce the tropical Pacific mean state drift, both westerly and easterly wind bursts are removed, although the changes are dominated by WWB reduction. As we impose progressively stronger thresholds, both ENSO amplitude and the frequency of extreme El Niño decrease, and ENSO becomes less asymmetric. The warming center of El Niño shifts westward, indicating less frequent and weaker eastern Pacific (EP) El Niño events. Removing most wind burst–related wind stress anomalies reduces ENSO mean amplitude by 22%. The essential role of WWBs in the development of extreme El Niño events is highlighted by the suppressed eastward migration of the western Pacific warm pool and hence a weaker Bjerknes feedback under wind shaving. Overall, our results reaffirm the importance of WWBs in shaping the characteristics of ENSO and its extreme events and imply that WWB changes with global warming could influence future ENSO.
Abstract
Variations in the warm water volume (WWV) of the equatorial Pacific Ocean are considered a key element of the dynamics of the El Niño–Southern Oscillation (ENSO) phenomenon. WWV, a proxy for the upper-ocean heat content, is usually defined as the volume of water with temperatures greater than 20°C. It has been suggested that the observed variations in WWV are controlled by interplay among meridional, zonal, and vertical transports (with vertical transports typically calculated as the residual of temporal changes in WWV and the horizontal transport divergence). Here, the output from a high-resolution ocean model is used to calculate the zonal and meridional transports and conduct a comprehensive analysis of the mass balance above the 25 kg m−3 σθ surface (approximating the 20°C isotherm). In contrast to some earlier studies, the authors found that on ENSO time scales variations in the diapycnal transport across the 25 kg m−3 isopycnal are small in the eastern Pacific and negligible in the western and central Pacific. In previous observational studies, the horizontal transports were estimated using Ekman and geostrophic dynamics; errors in these approximations were unavoidably folded into the estimates of the diapycnal transport. Here, the accuracy of such estimates is assessed by recalculating mass budgets using the model output at a spatial resolution similar to that of the observations. The authors show that errors in lateral transports can be of the same order of magnitude as the diapycnal transport itself. Further, the rate of change of WWV correlates well with wind stress curl (a driver of meridional transport). This relationship is explored using an extended version of the Sverdrup balance, and it is shown that the two are correlated because they both have the ENSO signal and not because changes in WWV are solely attributable to the wind stress curl.
Abstract
Variations in the warm water volume (WWV) of the equatorial Pacific Ocean are considered a key element of the dynamics of the El Niño–Southern Oscillation (ENSO) phenomenon. WWV, a proxy for the upper-ocean heat content, is usually defined as the volume of water with temperatures greater than 20°C. It has been suggested that the observed variations in WWV are controlled by interplay among meridional, zonal, and vertical transports (with vertical transports typically calculated as the residual of temporal changes in WWV and the horizontal transport divergence). Here, the output from a high-resolution ocean model is used to calculate the zonal and meridional transports and conduct a comprehensive analysis of the mass balance above the 25 kg m−3 σθ surface (approximating the 20°C isotherm). In contrast to some earlier studies, the authors found that on ENSO time scales variations in the diapycnal transport across the 25 kg m−3 isopycnal are small in the eastern Pacific and negligible in the western and central Pacific. In previous observational studies, the horizontal transports were estimated using Ekman and geostrophic dynamics; errors in these approximations were unavoidably folded into the estimates of the diapycnal transport. Here, the accuracy of such estimates is assessed by recalculating mass budgets using the model output at a spatial resolution similar to that of the observations. The authors show that errors in lateral transports can be of the same order of magnitude as the diapycnal transport itself. Further, the rate of change of WWV correlates well with wind stress curl (a driver of meridional transport). This relationship is explored using an extended version of the Sverdrup balance, and it is shown that the two are correlated because they both have the ENSO signal and not because changes in WWV are solely attributable to the wind stress curl.
Abstract
A model of surface waves generated on deep water by strong winds is proposed. A two-layer approximation is adopted, in which a shallow turbulent layer overlies the lower, infinitely deep layer. The dynamics of the upper layer, which is directly exposed to the wind, are nonlinear and coupled to the linear dynamics in the deep fluid. The authors demonstrate that in such a system there exist steady wave solutions characterized by confined regions of wave breaking alternating with relatively long intervals where the wave profiles change monotonically. In the former regions the flow is decelerated; in the latter it is accelerated. The regions of breaking are akin to hydraulic jumps of finite width necessary to join the smooth “interior” flows and have periodic waves. In contrast to classical hydraulic jumps, the strongly forced waves lose both energy and momentum across the jumps. The flow in the upper layer is driven by the balance between the wind stress at the surface, the turbulent drag applied at the layer interface, and the wave drag induced at the layer interface by quasi-steady breaking waves. Propagating in the downwind direction, the strongly forced waves significantly modify the flow in both layers, lead to enhanced turbulence, and reduce the speed of the near-surface flow. According to this model, a large fraction of the work done by the surface wind stress on the ocean in high winds may go directly into wave breaking and surface turbulence.
Abstract
A model of surface waves generated on deep water by strong winds is proposed. A two-layer approximation is adopted, in which a shallow turbulent layer overlies the lower, infinitely deep layer. The dynamics of the upper layer, which is directly exposed to the wind, are nonlinear and coupled to the linear dynamics in the deep fluid. The authors demonstrate that in such a system there exist steady wave solutions characterized by confined regions of wave breaking alternating with relatively long intervals where the wave profiles change monotonically. In the former regions the flow is decelerated; in the latter it is accelerated. The regions of breaking are akin to hydraulic jumps of finite width necessary to join the smooth “interior” flows and have periodic waves. In contrast to classical hydraulic jumps, the strongly forced waves lose both energy and momentum across the jumps. The flow in the upper layer is driven by the balance between the wind stress at the surface, the turbulent drag applied at the layer interface, and the wave drag induced at the layer interface by quasi-steady breaking waves. Propagating in the downwind direction, the strongly forced waves significantly modify the flow in both layers, lead to enhanced turbulence, and reduce the speed of the near-surface flow. According to this model, a large fraction of the work done by the surface wind stress on the ocean in high winds may go directly into wave breaking and surface turbulence.
Abstract
Global climate models frequently exhibit cold biases in tropical sea surface temperature (SST) in the central and eastern equatorial Pacific. Here, Lagrangian particle back trajectories are used to investigate the source regions of the water that upwells along the equator in the IPSL climate model to test and confirm the hypothesis that the SST biases are caused by remote biases advected in from the extratropics and to identify the dominant source regions. Water in the model is found to be sourced primarily from localized regions along the western and eastern flanks of the subtropical gyres. However, while the model SST bias is especially large in the northwestern subtropical Pacific (about −5°C), it is found that the eastern subtropics contribute to the equatorial bias the most. This is due to two distinct subsurface pathways connecting these regions to the equator. The first pathway, originating in the northwestern subtropical Pacific, has relatively long advection time scales close to or exceeding 60 yr, wherein particles recirculate around the subtropical gyres while descending to approximately 500 m before then shoaling toward the equatorial undercurrent. The second pathway, from the eastern subtropics, has time scales close to 10 yr, with particles following a shallow and more direct route to the equator within the upper 200 m. The deeper and longer pathway taken by the western subtropical water ensures that vertical mixing can erode the bias. Ultimately, it is estimated that relatively confined regions in the eastern subtropics of both hemispheres control approximately half of the equatorial bias.
Abstract
Global climate models frequently exhibit cold biases in tropical sea surface temperature (SST) in the central and eastern equatorial Pacific. Here, Lagrangian particle back trajectories are used to investigate the source regions of the water that upwells along the equator in the IPSL climate model to test and confirm the hypothesis that the SST biases are caused by remote biases advected in from the extratropics and to identify the dominant source regions. Water in the model is found to be sourced primarily from localized regions along the western and eastern flanks of the subtropical gyres. However, while the model SST bias is especially large in the northwestern subtropical Pacific (about −5°C), it is found that the eastern subtropics contribute to the equatorial bias the most. This is due to two distinct subsurface pathways connecting these regions to the equator. The first pathway, originating in the northwestern subtropical Pacific, has relatively long advection time scales close to or exceeding 60 yr, wherein particles recirculate around the subtropical gyres while descending to approximately 500 m before then shoaling toward the equatorial undercurrent. The second pathway, from the eastern subtropics, has time scales close to 10 yr, with particles following a shallow and more direct route to the equator within the upper 200 m. The deeper and longer pathway taken by the western subtropical water ensures that vertical mixing can erode the bias. Ultimately, it is estimated that relatively confined regions in the eastern subtropics of both hemispheres control approximately half of the equatorial bias.
