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Keywords:

  • convection;
  • air–sea interactions;
  • midlatitude climate variability

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Motivation: a criterion for the occurrence of deep (surface-to-tropopause) moist convection in midlatitude baroclinic waves
  5. 3. Application to the ERA interim dataset
  6. 4. Conclusions
  7. Acknowledgements
  8. References

The role of moist convection in ‘transferring’ upward surface ocean conditions throughout the troposphere is studied using reanalysis data for the extratropical Northern and Southern Hemispheres in winter. It is found that conditions for the development of a convective air column from the sea surface to the tropopause are met frequently over all major western boundary currents and their extension in the oceanic interior (sometimes for as much as 50% of the time). These frequent occurrences are shown to be jointly controlled by oceanic advection of warm waters and, on the atmospheric side, the downward displacement of the tropopause associated with synoptic weather systems.

Based on these results, it is proposed that the oceans can influence the atmosphere directly through convection in midlatitudes, as is commonly thought to occur in the Tropics. Analysis of the Richardson number Ri found at low levels suggests that moist symmetric instability (0 < Ri ≤ 1) is a key process involved in linking surface ocean temperatures to atmospheric lapse rates, in addition to standard upright convection. These low Ri processes are not currently parametrized in climate models, which raises the possibility that the extratropical oceanic influence on climate might be underestimated in the current generation of models. Copyright © 2011 Royal Meteorological Society


1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Motivation: a criterion for the occurrence of deep (surface-to-tropopause) moist convection in midlatitude baroclinic waves
  5. 3. Application to the ERA interim dataset
  6. 4. Conclusions
  7. Acknowledgements
  8. References

The current generation of climate models shows a clear-cut behaviour regarding the role of ocean–atmosphere interactions in generating climate variability. On the one hand, the models need the interaction between the ocean and the atmosphere in order to simulate large-scale climate variability in the Tropics (El Niño events). On the other hand, the dominant (annular) modes of extratropical climate variability do not owe their existence to such two-way interactions between the ocean and the atmosphere. They are found to behave realistically in atmosphere-only simulations, and the extratropical oceans seem to respond primarily passively to their time fluctuations (Czaja et al., 2003).

The response of atmospheric general circulation models (hereafter GCMs) to basin-scale extratropical sea-surface temperature (hereafter SST) anomalies has indeed shown to be elusive, sometimes appearing localized and baroclinic, sometimes appearing in the form of equivalent barotropic wavetrains. In their review of the subject, Kushnir et al. (2002) emphasized the complex dependence of the response of atmospheric GCMs to details of the background mean flow and the intrinsic low-frequency variability of the model. More recently, however, global satellite observations of surface wind stress and sea-surface temperature have suggested a larger oceanic influence on the atmosphere on spatial scales of equation image 100 km in midlatitudes (Chelton et al., 2004), an impact possibly not limited to the atmospheric boundary layer but reaching to greater heights in the atmosphere (Minobe et al., 2008).

In this contribution, we investigate whether moist convective processes could be instrumental in coupling ocean and atmosphere in midlatitudes, as they are thought to be in the Tropics. This hypothesis is encouraged by the studies mentioned in the previous paragraph, but is also motivated by the recent suggestion that moist convection plays a role in setting the thermal stratification of the extratropical atmosphere (Juckes, 2000; Korty and Schneider, 2007; Pauluis et al., 2008). Korty and Schneider (2007) showed convincing evidence that neutrality to moist convection is often observed over the extratropical oceans in winter, and it is the purpose of this note to assess whether this observation allows us to link surface ocean conditions to atmospheric lapse rates, maybe up to the tropopause level.

This note is structured as follows. In section 2, we introduce a conceptual model of a baroclinic wave and how, under certain conditions, it can develop a convective column from the sea surface to the tropopause. The occurrence of these conditions is then tested using the ERA interim data (Berrisford et al., 2009) in section 3. A discussion and conclusions are offered in sections 4 and 5, respectively.

2. Motivation: a criterion for the occurrence of deep (surface-to-tropopause) moist convection in midlatitude baroclinic waves

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Motivation: a criterion for the occurrence of deep (surface-to-tropopause) moist convection in midlatitude baroclinic waves
  5. 3. Application to the ERA interim dataset
  6. 4. Conclusions
  7. Acknowledgements
  8. References

Undulations of the height of the tropopause are routinely observed in synoptic weather maps, travelling eastward around the globe in the midlatitudes (Hoskins etal., 1985). When the tropopause is anomalously low, a positive tropospheric potential vorticity (PV) anomaly is created, reflecting the much higher values of PV in the stratosphere than in the troposphere. This PV anomaly induces cyclonic winds decaying towards the Earth's surface (Juckes, 1994), which, to the east of the displaced tropopause, advect warm and moist air from lower latitudes poleward and upward (Figure 1).

thumbnail image

Figure 1. Schematic of conditions possibly leading to surface-to-tropopause convection in a growing baroclinic wave. The tropopause is indicated by the dashed black line, while cyclonic circulations are depicted by the grey curved arrows. At mid-to-upper levels, warm and moist air of subtropical origin is brought to saturation by poleward and upward advection (grey arrow). At low levels, cold and dry air is brought to saturation by surface evaporation over the ocean (black arrow). The entropies stp (tropopause), sst (subtropical) and ssb (surface boundary) referred to in the text are also indicated.

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A consequence of these motions is that the displaced subtropical air mass can become saturated and, if its entropy is larger than that of the air at the tropopause, this air mass can become convectively unstable. Indeed, a saturated atmosphere is unstable to vertical displacements when the (moist) buoyancy frequency equation image, which occurs when specific entropy s decreases with height z (Emanuel, 1994):*

  • equation image(1)

(in this expression Γm > 0 is the moist adiabatic lapse rate). To grow, the upper-level cyclonic circulation must be coupled to a surface cyclone, but the latter must be to the east of the former (Eady, 1949). This leads, ahead of the depressed tropopause, to poleward advection at upper levels and equatorward advection below (Figure 1). When this happens near the western boundary of ocean basins, the low-level air is of continental origin and its advection over the warm ocean leads to large upward sensible and latent heat fluxes at the air–sea interface: as the upper air mass is brought to saturation, so is the low-level air mass (so long as the moistening effect dominates over the rise in temperature in setting high relative humidity). If the entropies of air near the surface ocean boundary (ssb), air near the tropopause (stp) and the midlevel subtropical air mass (sst) satisfy stp< sst< ssb, a convective instability from the sea surface to the tropopause can occur.

The above idealized model suggests that when the previous inequalities are satisfied, sea-surface temperature conditions can be communicated throughout the depth of the troposphere via moist convective processes. To test whether this occurs frequently in midlatitudes or not, next a thermodynamic analysis of the ERA interim dataset is conducted, poleward of 20° in the Northern and Southern Hemispheres.

3. Application to the ERA interim dataset

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Motivation: a criterion for the occurrence of deep (surface-to-tropopause) moist convection in midlatitude baroclinic waves
  5. 3. Application to the ERA interim dataset
  6. 4. Conclusions
  7. Acknowledgements
  8. References

3.1. Data and methods

The ERA interim dataset is a reanalysis of the global atmosphere covering the data-rich period since 1989, and continuing in real time (Berrisford et al., 2009). It uses 60 levels in the vertical and a spectral truncation of T255 (the reduced Gaussian grid has a equation image 79 km spacing for surface and other grid-point fields). Even though this resolution is higher than that of most climate models, convection is still heavily parametrized, following the mass-flux scheme of Tiedtke (1989). This situation is not ideal for our purpose, but has to be weighted against the large number of observations that constrain the model through time. Note that other studies have used renalysis data with success to study the impact of extratropical moist convection on atmospheric dynamics (Korty and Schneider, 2007; Pauluis et al., 2008).

Daily (1200 UTC) fields of temperature (T), specific humidity (qv), water-vapour pressure (e), total pressure (P), total water content (qT) and relative humidity (RH) were used to compute the specific entropy of moist air s according to (Emanuel, 1994)

  • equation image(2)

in which To = 273.15 K is a reference temperature, Pdo = 1000 mb a reference pressure, cl is the specific heat capacity of liquid water, cpv that of water vapour at constant pressure, Rd and Rv the gas constants for dry air and vapour, respectively, and lv the enthalpy of vaporization for water vapour, approximated as lv = lv(T) = lvo − (clcpv)(TTo) with lvo = 2.5 × 106 J kg−1.

The tropopause was tracked as a surface of constant potential vorticity (PV = 2 PV units was chosen, following Hoskins et al., 1985). The entropy stp was estimated by first computing the values of T,P,e,qv,qT and RH along the 2 PV unit surface and then using those values in (2).

The criterion developed in the preceding section (stp< sst< ssb) is not ideally suited to a direct application to observations. First, the calculation of sst is not as straightforward as that of stp because it requires an estimate of the meridional scale of the parcel's displacement driven by a low tropopause event (or a Lagrangian trajectory calculation in order to track the exact origin and entropy of the subtropical air parcel ‘entrained’ in the synoptic system). In addition, even if it were satisfied somewhere in the atmosphere at a given time, the associated air column would quickly overturn and reach a nearly uniform entropy profile with height: put simply, unstable conditions are unlikely to be observed. An alternative to the previous inequalities could thus be to check for weak vertical entropy gradients, proceeding from the sea surface upward, but we opted instead for a simpler approach, which is to look for profiles satisfying stp< so, in which so is the entropy that an air parcel would have if it were (1) at the same temperature as the surface ocean, (2) at the pressure found at the sea surface and (3) at a relative humidity of 80% (note that the SST from the ERA interim data is used for the calculation of so). The rationale for this choice is that so thus defined is an upper bound on the entropy possibly found at low levels and so satisfying stp< so is a necessary condition for convective events of the type described in section 2 to occur. Accordingly, we classify a grid point on a given daily map as potentially unstable to deep (surface to tropopause) moist convection if, at that grid point

  • equation image(3)

3.2. Results

The fraction of days during which the criterion (3) is satisfied is shown for the Northern Hemisphere winter of 2003–2004 (December–February) in Figure 2(a) and for the Southern Hemisphere winter of 2004 (June–August) in Figure 2(b). Over vast stretches of ocean it is seen that the criterion is only rarely met, typically less than 10% of the time (note that neither land nor sea-ice covered grid points are considered in these plots). Over the western sides of ocean basin, however, the situation is very different, with the fraction exceeding 50% of the time in some locations.

thumbnail image

Figure 2. Fraction of days (in percent) for which the criterion stpso < 0 is met poleward of 20° for (a) the Northern winter of 2003–2004 and (b) the Southern hemisphere winter of 2004. The calculation was not carried out over continent (black) and sea-ice (fraction of days set to zero) covered grid points. This figure is available in colour online at wileyonlinelibrary.com/journal/qj

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Besides this western intensification, there are two very interesting features in Figure 2 that need further discussion. First, although the largest values of so are found at low latitudes, where the SST is largest,§ these regions are not those dominating in Figure 2. The reason is that the tropopause height is large (low pressure), with only weak time variations over these regions, and as a result stp is systematically larger than so. Put differently, the key feature explaining Figure 2 is the high occurrence of low tropopause events over the major storm-track systems: a low tropopause has low entropy because of the upward advection of low potential temperature surfaces below it (Hoskins et al., 1985). In a calculation in which stp is fixed to its wintertime mean value rather than varying daily, the frequent occurrences in Figure 2 disappear (not shown).

The second interesting feature is the imprint of the ocean circulation. Rather than displaying a broad land–sea contrast-type pattern, the maps in Figure 2 capture the structure of the major western boundary-current systems. This is particularly pronounced over the Gulf Stream, where the thin ribbon associated with advection of warm waters from lower latitudes is clearly visible in Figure 2(a). The ocean circulation's imprint is also seen in the asymmetry between the high latitudes of the North Atlantic and the high latitudes of other ocean basins: in the North Pacific and the Southern ocean, the occurrences found in Figure 2 do not exceed 10% poleward of 50° of latitude, whereas they reach 20–30% poleward of 50°N in the North Atlantic. In a calculation in which SSTs are uniformly lowered by 2°C in the North Atlantic (while keeping the same daily values of stp), occurrences drop below 10% in most of the northwestern Atlantic (not shown). This suggests that the presence of the North Atlantic drift, and its associated transport of warm waters to high latitudes, is an important contributor to the high occurrences found in Figure 2. The low occurrences found at high latitudes of the Southern Ocean show less sensitivity to uniform changes in SST: it would take a warming of at least 5°C to increase the occurrences to 20–30% poleward of 50°S (not shown).

To illustrate what happens on a given day when the criterion (3) is satisfied, meridional–height sections of entropy and vertical velocity are shown in Figure 3(a) and (b) respectively. The section chosen is along 55°W, a longitude at which stp< so is satisfied at 40°N for the day considered. The broad distribution of entropy shows the expected low values at high latitudes in each hemisphere and high (and more uniform) values in the Tropics (Figure 3(a)). At 40°N, entropy is nearly constant from the surface to the tropopause (indicated by the thick black line) and the relative humidity reaches 100% throughout this layer (not shown), as envisioned in section 2. The occurrence of deep convection at (55°W, 40°N) on that day is confirmed by an inspection of vertical velocities in Figure 3(b), which shows a meridionally narrow but vertically broad (from the surface to the tropopause, the latter being indicated by the thick black line on the figure) region of ascent at 40°N. The magnitude of the ascent is large, of the order of 1 Pa s−1 (about a thousand mb in one day), a value only matched at that longitude and time within the intertropical convergence zone a few degrees south of the Equator.

thumbnail image

Figure 3. Latitude–pressure (in mb) sections at 55°W on 10 February 2004 at 1200 UTC. (a) Specific entropy (in Jkg−1 K−1, contoured every 25Jkg−1 K−1 for s ≤ 300Jkg−1 K−1 and 50Jkg−1 K−1 for s ≥ 300Jkg−1 K−1) and (b) pressure vertical velocity (in Pa s−1, contoured every 0.5 Pa s−1, continuous when negative i.e. upwards). In both panels the tropopause location (2 PVU surface) is indicated by the thick black line. The black blocks indicate orography.

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More insight into the mechanisms involved when the convective potential is realized, as in Figure 3, is provided in Figure 4. The latter displays the probability distribution function of the Richardson number Ri computed at 700 mb according to

  • equation image(4)

in which |U700/∂z|2 measures the vertical shear of the horizontal velocity vector at 700 mb and equation image was introduced in (1). The calculation displayed in Figure 4 was only carried out over the portion of the North Atlantic where the stpso < 0 condition is met for more than 25% of the time and the surface-to-tropopause averaged relative humidity exceeds 80%. The distribution peaks at Ri = 0, characteristic of standard, upright convection, but another peak is found near Ri = 1, the critical value marking the onset of moist symmetric instability (or ‘slantwise’ convection–see Bennetts and Hoskins, 1979; Emanuel, 1983a). The integrated distribution over the 0 < Ri ≤ 1 interval is twice as large as that corresponding to the peak centred at Ri = 0, suggesting that slantwise convection dominates the dynamics at low levels. This result is in agreement with the analysis of Korty and Schneider (2007, comparing their figures 9 and 10).

thumbnail image

Figure 4. Probability distribution function of the Richardson number at 700 mb over ‘moist’ Gulf Stream profiles during the 2003–2004 winter. See text for details.

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Finally, in order to link atmospheric thermodynamic conditions near the sea surface more explicitly to those at mid-to-upper levels over the Gulf Stream region, the density temperature of an air parcel lifted adiabatically and reversibly (i.e. without exchange of heat with the surroundings and conserving its total water content qT and entropy s) from 950 mb is compared with that of its environment over the 900–300 mb layer (Figure 5). Each dot on the scatterplot indicates the result of the calculation on a given day, averaging on that day the thermodynamic properties over the region of the Gulf Stream where the condition stpso < 0 is met for more than 25% of the time. In addition, since low static stability is expected for low-pressure systems only, a grid point of that region on that day was considered in the averaging only if its surface pressure was lower than its wintertime mean.

thumbnail image

Figure 5. Comparison of daily density temperatures (in K) averaged over the 900–300 mb layer (≡< Tρ >) for Gulf Stream cyclones during the 2003–2004 winter. On the y-axis, < Tρ > corresponds to the layer-averaged density temperature of a parcel lifted adiabatically and reversibly from 950 mb (upright in black, slanted in grey). On the x-axis, the actual < Tρ > is given. See text for details.

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The black circles indicate the result of the calculation when the parcel is lifted vertically upward, thereby testing the stability of the air column to standard upright convection. It is seen that the environment is typically more buoyant than the parcel by a few degrees K, the circles falling to the right of the ‘moist neutral diagonal’ (the x = y curve shown as the black continuous line). As expected, the root-mean-square (rms) difference between the density temperature of the parcel and that of its environment increased when considering high-pressure rather than low-pressure systems (from 4.9K to 8.9 K) but, more interestingly, the correlation seen in Figure 5 (black circles) also deteriorated as a result (not shown). This indicates more coherence between low and mid-to-upper levels in cyclones than in anticyclones, and supports the idea that moist neutrality is approached in low-pressure systems (Juckes, 2000).

The Richardson number analysis in Figure 4 showed that slantwise convection, in addition to standard upright convection, is also involved in air–sea interactions near the Gulf Stream. The buoyancy calculation above was thus repeated for slanted, rather than upright, displacement of air parcels (grey circles in Figure 5).|| The circles now fall even more closely onto the ‘moist neutral’ diagonal, with the rms difference between the density temperature of the parcel and that of the environment being 3.1 K instead of 4.9 K in the upright case. Overall, the buoyancy calculations in Figure 5 suggest that low-level (950 mb) thermodynamic conditions over the Gulf Stream are indeed communicated over a deep layer (900–300 mb) via convective processes.

3.3. Discussion

The physical picture of a column convecting from the sea surface to the tropopause (section 2) is admittedly a crude representation of the complex mechanisms found in extratropical weather systems (Browning, 1986). Indeed, the latter move eastward and, as they do so, entrain air masses of different geographical origins (Green et al., 1966). For the local picture adopted in this study to hold, the time-scale for the convective processes must be less than the time taken for the system to cross the western boundary-current regions. Inspection of daily maps of tropopause heights suggests that low tropopause anomalies take a couple of days to make this crossing, consistent with an eastward extension of the western boundary-current regions of about equation image 1000 km and a system displacement velocity of equation image 10 m s−1. This time is less than those for moist symmetric instability (of the order of the local inertial period f−1equation image 3 h at 40°N – see Emanuel, 1983a) and standard upright convection (an hour or so). We thus suggest that the physical picture of section 2 is relevant to air–sea interactions near the western boundary-current regions, a view clearly reinforced by the buoyancy calculations in Figure 5.

If the convective potential stpso < 0 was realized as frequently as depicted in Figure 2, the troposphere would find itself under the direct influence of the ocean (sequation imageso from the sea surface to the tropopause) for as much as 50% of the time over the western boundary-current regions in winter. Analysis of alternative criteria (column-averaged relative humidity, vertical velocities) suggests however that the potential is only achieved about 10% of the time (not shown), leaving the ocean a one-week ‘window’ to the troposphere every winter. It is not clear at present what controls whether the convective potential is realized or not. The results of Korty and Schneider (2007) suggest that baroclinic waves are efficient at stratifying the 700–800 mb layer (see their figure 8(c)). This could prevent unstable conditions near the sea surface from developing further vertically, thereby providing an overall ‘break’ in the mechanism schematized in Figure 1. Further work is needed to test this hypothesis.

Finally, a striking feature of the analysis presented here is its emphasis on the western boundary-current regions. This contrasts with the study by Korty and Schneider (2007), the results of which showed western intensification at low levels but not aloft (their figure 9). A possible explanation could be the use of a fixed-level analysis in Korty and Schneider (2007), while the analysis presented here follows the tropopause. However, after repeating the calculation of Figure 2 using the entropy at 300 mb rather than that at the tropopause, the same western intensification was found (not shown). It is more likely that the difference reflects the emphasis on surface conditions considered here (testing the stability of air columns to upward displacements from the sea surface) as opposed to conditions in the bulk of the atmosphere in Korty and Schneider (saturation PV in a given volume of air). In other words, a possible physical interpretation of the difference between this study and that of Korty and Schneider (2007) is that convection is rooted in the boundary layer over western boundary-current regions, while this is less so elsewhere. This is an interesting question which requires further work to elucidate fully.

4. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Motivation: a criterion for the occurrence of deep (surface-to-tropopause) moist convection in midlatitude baroclinic waves
  5. 3. Application to the ERA interim dataset
  6. 4. Conclusions
  7. Acknowledgements
  8. References

In this note we have investigated a mechanism by which the distribution of sea-surface temperature can affect the extratropical atmosphere. The physical picture is simple and reminiscent of that often invoked in the Tropics, whereby oceanic temperature conditions are transmitted vertically up to the tropopause through moist convective processes. The introduction and analysis of a new measure of convective potential over the oceans shows that the wintertime occurrence of convectively neutral situations (1) can be found from the sea surface to the tropopause, though the latter must be anomalously low (i.e. closer to the sea surface than on average), and (2) is primarily found over western boundary-current regions of the Southern and Northern Hemispheres, where advection of warm waters maintains a large thermodynamic imbalance with the atmosphere.

The convective mechanism is appealing because it bypasses the difficulties associated with wave mean-flow interactions that lie at the core of understanding how sea-surface temperature conditions affect the atmospheric circulation in the extratropics (Kushnir et al., 2002). It is, however, not clear at present how much of this ‘vertical influence’ translates into a climatic influence away from the western boundary-current regions. A possibility is that the occurrence of moist neutral conditions over the western boundary-current regions helps maintain a high Eady growth rate there (i.e. low dry stratification), thereby being instrumental in setting the location of the storm track. This line of thought was first proposed by Hoskins and Valdes (1990), who invoked the baroclinic response of the atmosphere to the diabatic heating associated with land–sea contrast, rather than moist neutrality. Hoskins and Valdes (1990) were not able to show convincingly a role for ocean currents, as the heat lost in winter by the oceans could be regained the following summer. Our results, however, clearly point towards ocean currents as the key ingredients allowing moist neutral conditions to be achieved, as is evident from the oceanic dynamical structures in Figure 2.

The importance of ocean currents and western boundary-current regions found here is reminiscent of the recent study by Nakamura et al. (2008)–see also Booth et al. (2010). They proposed that air–sea heat exchanges at oceanic fronts are responsible for restoring the baroclinicity of the atmosphere at low levels. This mechanism of ocean–atmosphere coupling is complementary to the one discussed here in that it emphasizes the role of the ocean in restoring horizontal temperature gradients in the atmosphere at low levels (their study), as opposed to restoring vertical temperature profiles to a moist adiabat over a deep tropospheric layer (this study).

Finally, it was found that moist symmetric instability (Richardson number of unity or less) was an important mechanism to ‘transmit’ oceanic conditions vertically. This instability is not parametrized in the current generation of climate models, which suggests that the extratropical oceanic influence on climate, and its associated predictability, might currently be underestimated in climate models. This exciting prospect deserves further consideration.

Acknowledgements

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Motivation: a criterion for the occurrence of deep (surface-to-tropopause) moist convection in midlatitude baroclinic waves
  5. 3. Application to the ERA interim dataset
  6. 4. Conclusions
  7. Acknowledgements
  8. References

N. Blunt was funded by a bursary from the Nuffield foundation. Discussions with B. Hoskins and R. Hide helped in focusing the ideas presented in this note. Comments from an anonymous reviewer and Rob Korty helped to improve the manuscript.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Motivation: a criterion for the occurrence of deep (surface-to-tropopause) moist convection in midlatitude baroclinic waves
  5. 3. Application to the ERA interim dataset
  6. 4. Conclusions
  7. Acknowledgements
  8. References
  • *

    Small terms depending on the total water content were neglected in Emanuel's equation (6.2.10).

  • An anonymous reviewer suggested that this state of affairs is relevant to the Gulf Stream but less so to the Kuroshio extension. It is plausible that the ocean thermal front itself plays this role in the North Pacific.

  • This is because low-level air has a temperature lower than the SST and a relative humidity below 80%. Only far from wintertime continental boundaries would this temperature and relative humidity be reached.

  • §

    The effect of surface pressure on so is weak.

  • The density temperature Tρ of a sample of air is defined as Tρ = T(1 −qTqvRv/Rd), using the notation from section 3.1. At fixed pressure, Tρ is inversely proportional to density and thus provides a measure of buoyancy (Emanuel, 1994).

  • ||

    Following Emanuel (1983b), the ascent was computed along a surface of constant angular momentum Mfx + vT in which vT is the velocity perpendicular to the thermal wind vector, f is the Coriolis parameter and x is the distance in the direction perpendicular to the thermal wind vector. The latter was estimated as the average of the vertical shear at 700 and 400 mb. Note that the calculation was only performed when those two shear vectors differed by less than 10 degrees in direction in order to satisfy the assumption of two-dimensionality implicit in the theory of slantwise convection–see Emanuel (1983b).