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 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)
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 − (cl − cpv)(T − To) 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
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.
Figure 2. Fraction of days (in percent) for which the criterion stp − so < 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.
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
in which |∂U700/∂z|2 measures the vertical shear of the horizontal velocity vector at 700 mb and was introduced in (1). The calculation displayed in Figure 4 was only carried out over the portion of the North Atlantic where the stp − so < 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).
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 stp − so < 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.
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.
If the convective potential stp − so < 0 was realized as frequently as depicted in Figure 2, the troposphere would find itself under the direct influence of the ocean (sso 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.