Upper-tropospheric downstream development leading to surface cyclogenesis in the central Mediterranean

Transcription

1 Meteorol. Appl. 6, 33 3 (999) Upper-tropospheric downstream development leading to surface cyclogenesis in the central Mediterranean Nicholas G Prezerakos, Helena A Flocas and Silas C Michaelides 3 General Department of Mathematics, TEI of Piraeus, Greece Department of Applied Physics, Laboratory of Meteorology, University of Athens, Greece 3 Meteorological Service, Nicosia, Cyprus In this study an attempt is made to investigate the upper-tropospheric downstream development over north-west Europe, which leads to surface cyclogenesis in the central Mediterranean. A case study is analysed to demonstrate that the upper-tropospheric downstream development could be closely related to the upper-tropospheric frontogenesis that appears upon the north-eastern flank of a blocking high. The frontogenesis is characterised by a jet streak within a strongly baroclinic zone and a tropopause folding associated with cold stratospheric air intrusion into the troposphere. According to this interpretation, the eddy ageostrophic divergence of eddy geopotential fluxes (dispersion and spreading of eddy kinetic energy), other than friction dissipation and barotropic conversion to the mean flow, is mainly responsible for the loss of kinetic energy from a decaying depression of synoptic scale that has passed the mature stage. This dispersed eddy kinetic energy accumulates in the vicinity of the aforementioned jet streak where it is transferred downstream and further triggers the generation or rejuvenation of a new disturbance.. Introduction The change of the zonal (high-index) atmospheric circulation to a meridional (low-index) circulation appears to be of crucial importance for operational meteorology and forecasting. Although this type of change was identified when upper-air charts were first used, the associated physical processes remained unknown for a long time. Later, Smagorinsky (969) claimed that the change of the zonal atmospheric circulation to a meridional one can be mainly attributed to the heat fluxes from the oceans to the atmosphere. These fluxes are difficult to predict accurately in space and time. The use of the numerical models coupling the ocean and atmosphere that are currently under development, for example at ECMWF (Palmer & Anderson, 994), is expected to yield a better insight into the understanding of the energy interaction between oceans and atmosphere; this should further contribute to the improvement in the monthly and seasonal weather forecasts. According to Smagorinsky (969) the change to the low-index circulation can cause the development of blocking anticyclones or downstream development. Downstream development can be defined as the intensification of a trough of a synoptic or larger-scale wave in the free upper troposphere which causes the intensification of another trough or the development of a new one far downstream, after the intensification of a preceding ridge. The downstream development occurs primarily during the change from the high-index circulation to a low one, and more rarely after the predominance of the low-index circulation. In an attempt to interpret downstream development over the Atlantic Ocean and western Europe, Miles (959) presented practical rules that relate the southwards extension of the hpa thickness troughs over the British Isles with the intensity of the southerly flow prevailing upstream ahead of a robust cyclogenesis over the Atlantic. Similarly, according to HMSO (969), Greek forecasters relate Mediterranean cyclogenesis to the downstream development over north-west Europe on the basis of the following practical rule: when an upper-level cyclonic development occurs on the western flank of a large-scale blocking high over the northern Atlantic Ocean causing strong warm air advection towards the ridge that extends over northwest Europe, an intense northerly flow is expected to form at the eastern flank of the blocking high. This type of flow controls the thermal energy budget in the region of the blocking high and contributes to cold air advection towards central and southern Europe. Under favourable low-level conditions, the upper-air advection of polar air masses towards the Mediterranean 33

2 N G Prezerakos, H A Flocas and S C Michaelides region frequently causes low-level cyclogenesis over the northern Mediterranean coast. The larger the cold air advection, the more intense the cyclogenesis is expected to be. The experience of Greek forecasters indicates that downstream development that occurs after the establishment a low index circulation is more likely associated with severe weather phenomena in the vicinity of Greece. The objective of this study is to investigate the dynamical processes involved in downstream development over north-west Europe leading to surface cyclogenesis over the central Mediterranean. Then, the proposed mechanism is tested for a case study associated with downstream development that occurred after the appearance of an omega block centred over the British Isles. Following the introduction, section investigates the upper-level conditions associated with downstream development from the theoretical point of view. The dynamics and the energetics of a case study leading to cyclogenesis over the Mediterranean region is analysed in section 3. Finally, section 4 summarises the main conclusions.. Theoretical approach Relatively recent observational and theoretical studies (e.g. Simmons & Hoskins, 979; Orlanski & Katzfey, 99; Orlanski & Chang, 993; Orlanski & Sheldon, 993; Chang, 993) consider downstream development to be the result of eddy kinetic energy fluxes being combined with local baroclinicity. These studies refer mainly to the process of dispersion of eddy kinetic energy by a growing unstable tropospheric system, which is more characteristic of high-frequency variability. This initiation of the downstream development is called downstream baroclinic development (DBD). Nevertheless, there are cases of downstream development that are associated with the dispersion of eddy kinetic energy by a packet of neutral barotropic waves, more characteristic of low-frequency variability (e.g. Namias & Clapp, 944; Cressman, 948; Hovmoller, 949). Synoptic-scale cyclogenesis over the northern coast of the central Mediterranean frequently can result from a mixed-type downstream development with a leaning towards the baroclinic one. Owing to large downstream energy fluxes in the upper troposphere, the disturbance initially develops at the upper levels and then, by converting the eddy available potential energy to eddy kinetic energy, quickly forces the low-level development. This type of cyclogenesis can be characterised as type B following Petterssen & Smebye (97). The most important factor in the downstream development over the North Atlantic and Europe is the jet 34 streak that appears on the north-eastern flank of a longwave omega or meridional block in the upper troposphere which is centred over the British Isles, as shown in Figure. While the stages of the development after the appearance of the jet streak over north-west Europe have been investigated from both the theoretical and synoptic points of view (Prezerakos & Flocas, 996, 997; Prezerakos et al., 996, 997), the physical mechanism responsible for the appearance of the jet streak on the northeastern flank of the blocking high has not yet been investigated. According to the pattern of ageostrophic motion, upper-level divergence and ascending motion are found in the right entrance and left exit of the jet causing cyclogenesis at the surface. On the other hand, at the left entrance and right exit of the jet, there is convergence and descending motion. In Figure a common situation is displayed where the isotherms lie parallel to the jet streak axis and therefore no advection occurs along the jet direction. If cold air advection occurs along the jet axis, then a shift of the vertical motion pattern is observed to the right side of the jet entrance and in the left side of the jet exit (Keyser & Shapiro, 986). Furthermore, the appearance of the jet streak is associated with the development of a relative vorticity maximum on the cold side and of a minimum on the warm side of the upper baroclinic zone. The vorticity can be partitioned into two components, one associated with wind shear and the other with curvature accounting for the horizontal divergence in the directions perpendicular and parallel to the jet, respectively. After the appearance of the jet streak, there are two possible, developments, depending on the characteris- Figure. Convergence divergence and vertical motion in the entrance and exit of the jet streak at the north-eastern flanks of an upper-air blocking high, when the isotherms are almost parallel to the wind direction.

3 Surface cyclogenesis in the central Mediterranean tics of the subsequent trough: (a) if the trough ahead of the jet streak is diffluent, with its axis orientated northwest to south-east, the trough will intensify; or (b) if the trough does not show these characteristics or does not exist at all, a part of the vorticity associated with wind shear is converted to vorticity associated with curvature while a smaller-scale wave forms upon the flank of the large-scale high where the jet streak is progressing. This wave moves very fast south-eastwards, intensifies and can cause surface cyclogenesis under favourable low-level conditions (Kurz, 994; Prezerakos & Flocas, ; Prezerakos et al., 997). The appearance of the jet streak in the region where the eddy kinetic energy, being dispersed upstream, has accumulated suggests the initiation of the upper-level frontogenesis. An extended review of the upper-level frontogenesis is presented by Keyser & Shapiro (986). Diagnostics of two cases of upper-level frontogenesis have been carried out by Lagouvardos & Kotroni (995). In these studies the solution of the two-dimensional Sawyer Eliassen equation (Sawyer, 956; Eliassen, 96) determines quantitatively the synopticscale vertical motion in the vicinity of frontal zones which results in the intrusion of cold stratospheric air into the troposphere, mainly in the jet entrance. This intrusion is characterised by high potential vorticity, which further supports the intensification of the frontal zone. Also, the synoptic experience provides evidence that the frontogenesis is characterised initially by a tropopause slope that evolves to a tropopause folding in the subsequent stages. This will be shown in the case studied in the next section. According to British studies in the 950s (Sumner, 954; Miles, 959) the downstream development is related to the movement of the jet streak that appears at the inflection point ahead of a trough just after its maximum development. The jet streak, accompanied by a relative vorticity maximum due to wind shear, moves downstream following the track of the absolute vorticity maximum at 500 hpa. This interpretation is more relevant when the circulation is of a high index. In the case of a low-index circulation, as prevails in the case study examined here, the jet streak disappears in the region just before the subsequent ridge and reappears on the northern or north-eastern flanks of the downstream large-scale ridge at an unknown time. Taking into account the aforementioned discussion, the downstream development can be interpreted from the synoptic point of view as follows: the development of the low pressure centre within a 500 hpa trough extending over Atlantic at an earlier time (see Figure (a)) and at the same time the progression of the jet streak at the inflection point in front of the trough favour the advection of warm air masses northwards, resulting in the intensification of the subsequent ridge and its expansion northwards (Figure (b)). Therefore, Figure. Interpretation of the downstream development from a synoptic point of view. (a) Day 0. The growing ridge creates area A; south-westerly jet backs and propagates northwards. ( b) Day. Growing high causes northerlies which push the trough southwards; north-westerly jet develops and veers causing thermal trough to extend. Full lines: hpa thickness. Dashed lines: mean sea level isobars. Arrows: jet stream at 500 hpa. L: surface low, H: surface high, A: anticyclonic development, C: cyclonic development. the thermal gradient intensifies in the region of the ridge where the cold air masses from the north meet the warm air masses from the south (Namias & Clapp, 949). Owing to the intensification of the thermal wind, the jet streak jumps from the western flank of the long-wave ridge to its north-eastern flank (Figure (b)). Since local energy budget analyses have proved to be a useful diagnostic tool for the dynamical processes involved in the development of atmospheric disturbances (e.g. Pierce, 974; Prezerakos & Michaelides, 989; Orlanski & Sheldon, 993) the downstream development, and especially the DBD, can be interpreted in terms of the energetics. The energy equation which is mainly associated with the downstream development is the eddy kinetic energy equation in pressure coordinates (Orlanski & Chang, 993). The wind at an isobaric level (V) is partitioned into a zonal mean, [V], and an eddy part, (V a ) : where [ V] V = [V] + (V a ) = V d 35

4 N G Prezerakos, H A Flocas and S C Michaelides Similarly, if Q is any scalar (including the vertical velocity ) then this can also be partitioned into its zonal mean and eddy parts: where Q = [Q] + (Q) Then following Orlanski & Katzfey (99), the quantity.[(v a ) (Φ) ], where V a is the ageostrophic departure of the wind and Φ is the geopotential, represents the dispersion of eddy kinetic energy (for more details see the Appendix). The integral of this quantity is given by where g is the gravitational acceleration and p 0 and p are the pressure at the bottom and top respectively of the atmospheric column with unit area. The distribution of this integral provides a clear picture of the geographical regions where the eddy kinetic energy can be dispersed or concentrated. The direction of the eddy kinetic energy dispersion, as defined by the first term on the right-hand side of equation (A) in the Appendix, is the same as the direction of (V), while its speed is determined by the relative group velocity (Orlanski & Katzfey, 99). Nevertheless it should be noted that a part of the atmospheric energy could be dispersed with a speed even greater than that determined by the group velocity (e.g. internal gravity waves). Following this discussion, downstream development can be comprehensively interpreted in terms of the eddy ageostrophic divergence of the eddy geopotential fluxes (dispersion and spreading of eddy kinetic energy) occurring downstream from a decaying vigorous atmospheric disturbance. This energy is often collected in the form of a jet streak and is then transferred farther downstream, triggering the initiation of the development of a new disturbance or the intensification of an existing one. It should be noted that after the formation of the jet streak upon the north-eastern flank of the large- scale ridge, the most important dynamical factors at the upper levels in the following stages of the development are: (a) the dynamically unstable ridge (Prezerakos & Flocas, 996), (b) the generation of a disturbance in the baroclinic flow due to orography (Eliassen, 977), (c) the asymmetrical distribution of the wind field in a diffluent trough (Prezerakos, 985; Prezerakos & Flocas, 997), and (d) the cyclonic and anticyclonic disruption 36 [ Q] p p0 = Q d [ Va Φ ].( ) ( ) dp g of long axis troughs (Prezerakos, 985). Since all these dynamical factors have already been studied, our investigation here is focused on the physical mechanism which leads to the appearance of the jet streak on the north-eastern flank of the blocking high. 3. Analysis of a case study 3.. Synoptic and dynamic overview A case of cyclogenesis occurred over the central Mediterranean on 6 December 99 followed by a deepening of the surface low-pressure centre over the Greek area in the following day. This low caused heavy precipitation in southern Greece and the Aegean Sea and a large temperature decrease in the whole Greek area (Prezerakos et al., 997). The data used in this study is obtained from ECMWF archived operational initialised analyses every hours at the surface, 000, 850, 700, 600, 500, 400, 300, 50, 00, 50 hpa in a.5 latitude longitude grid. According to Figure 3(a), at 00 UTC on 3 December the atmospheric circulation over the Atlantic and western Europe at 500 hpa is characterised by a low index as a blocking anticyclone has already formed, being centred over the British Isles. To the north of the blocking high, a wave packet can be detected with three troughs and three ridges. Trough is orientated northwest south-east and is associated with a low system centred at 5 N, 4 W over the western coast of the Atlantic. This trough is characterised by an asymmetrical wind distribution: on the western flank the northerly wind is in excess of 70 m s, while on the eastern flank the wind is south-westerly with a maximum speed of 5 m s. This type of wind distribution in conjunction with the observed cold air advection results in the continuous intensification of trough, while there is a reduction of the wind speed in the west and an increase in the east. Thus, by 0000 UTC on 4 December (see Figure 3(b)) a jet streak has formed in front of the trough with air speed in excess of 40 m s. The direction of the strong south-westerlies at the eastern flank of trough is almost perpendicular to the isotherms, causing intense warm air advection towards the region of ridge (Figure 3(b)). In the next hours, this ridge extends north-westwards along its axis while simultaneously moving north-eastwards (Figure 3(c)). Trough and its preceding ridge weaken, while trough 3 moves south-eastwards, veering by about 70. Owing to the extension of the high, the thermal gradient at its northern and north-eastern flanks has intensified considerably, producing a substantial increase of the thermal wind. Therefore, at 300 hpa the wind speed in the upstream side of trough 3 becomes as high as 50 m s at 00 UTC on 4 December (Figure 4(a)). Based on the tropopause analysis (Figure 5) at the same time,

5 Surface cyclogenesis in the central Mediterranean Figure 3. Geopotential height, every 4 gpdam (solid lines) and temperature, every C (dotted lines) at 500 hpa for: (a) 00 UTC on 3 December, (b) 0000 UTC on 4 December, (c) 00 UTC on 4 December and (d) 0000 UTC on 5 December 99. Also indicated are the axes of troughs and ridges numbered subsequently,, 3, following the text. Arrows indicate the wind velocity. The scale of the wind is in the upper-right corner of (a). the mean tropopause slope in the region of trough 3 between the highest and lowest points is estimated to be almost /50, which is the common slope of a warm front. Of course, in the vicinity of the jet streak a tropopause folding occurs. The maximum height of the tropopause is more than 80 hpa in the region between Greenland and the British Isles. Very cold stratospheric air below 70 C appears towards the right entrance of the jet streak to the north-east of Greenland. During the next hours the southernmost part of trough 3 at 500 hpa (Figure 3(d)) has moved eastwards about 6 in latitude whereas ridge has just passed Greenland, now orientated from north to south. The maximum wind speed at 300 hpa is found just ahead of ridge (Figure 4 (b)). As shown in Figure 6, the zonal part of the jet stream extends behind the 0 meridian and splits into two parts: one just above mid-latitude tropopause and the other just below the polar tropopause, indicating a tropopause folding. Thus, an accumulation of positive isentropic potential vorticity trough occurs in the entrance of the meridional part of the jet streak which extends equatorwards (Figure 7) and downwards (Figure 8). 37

6 N G Prezerakos, H A Flocas and S C Michaelides Figure 5. Subjective tropopause analysis at 00 UTC on 4 December 99. The continuous isopleths represent the tropopause height (every 0 hpa) while the dotted isopleths are the isotherms (every 5 C). Therefore, it is suggested that at 70 N, 7 E, where the jet streak turns to become meridional, cold stratospheric air starts penetrating in the troposphere owing to the vertical circulation pattern (Sawyer, 956; Eliassen, 96; Hoskins & Draghici, 977). This air, being characterised by high potential vorticity (PV) values, causes the intensification of the upper-level baroclinic zone (Figures 7 and 8). During 5 December at 500 hpa, the axis of ridge is oriented from north to south while the jet streak is located entirely on its eastern flank with values as high as 50 m s. The southernmost part of trough 3 disrupted when it moved equatorward past 50 N. Thus, a smaller-scale diffluent trough has formed corresponding to a secondary potential vorticity maximum, which Figure 4. Geopotential height, every 8 gpdam (thick lines) and isotachs (thin lines), every 0 m s at 300 hpa for (a) 00 UTC on 4 December, (b) 0000 UTC on 5 December and (c) 00 UTC on 5 December 99. The darkened region indicates values of wind speed greater than 60 m s. The scale of the wind velocity is in the upper-right corner of (a). 38 Figure 6. Vertical cross-section of the zonal wind along latitude 70 N at 0000 UTC on 5 December 99. The isotachs are every m s.

7 Surface cyclogenesis in the central Mediterranean greater than that implied by the westerlies. In this case, this is done through the dispersion of the eddy kinetic energy of the developing trough and its accumulation in the vicinity of the jet streak. If low-level baroclinicity exists, the propagation of the eddy kinetic energy towards trough 3 leads to its development. Trough 3 further intensifies by tapping the low-level baroclinicity through the conversion of the available eddy potential energy to the eddy kinetic energy. 3.. Energetics evidence Figure 7. Potential vorticity on the isentropic surface 330 K at 0000 UTC on 5 December 99. The isopleths are drawn every PVU. results from the equatorward and downward extension of the above-mentioned accumulation of positive potential vorticity in the entrance of the meridional part of the jet streak. This trough is associated with the surface cyclogenesis over the Greek area on 7 December. The dynamics of this case of cyclogenesis have been examined by Prezerakos et al. (997) and its energetics by Prezerakos et al. (996). The initial disturbance reached its maximum development on 3 December over the Atlantic, while four days later on 7 December a surface development occurred over Greece, 70 longitude to the east, as compared to the location of the initial disturbance, through the mechanism of the downstream development. Thus, the speed of the downstream amplification is estimated to be 7.5 per day. As this speed is much greater than the mean speed of the synoptic-scale waves, it seems that the atmosphere is able to transfer energy at a speed Figure 8. Vertical cross-section of the potential vorticity in PVU along latitude 70 N at 0000 UTC on 5 December 99. The isopleths are drawn every 0.4 PVU. In order (a) to get a better understanding of the dispersive nature of the atmospheric motion associated with the case study of downstream development and (b) show the collection of the dispersed eddy kinetic energy at the north-eastern flank of the omega blocking centred on the British Isles, an analysis in space and time of the eddy ageostrophic divergence/convergence of eddy geopotential is required, similar to that done by Orlanski & Sheldon (993). This is left for further research. Here, the boundary transfer of the eddy kinetic energy is estimated during the initial stages of the surface disturbance decay over the Atlantic at 0000 and 00 UTC on 4 December and the central Mediterranean development at 0000 and 00 UTC on 6 and 7 December 99. The eddy kinetic energy K e is integrated in an atmospheric volume extending horizontally in a quasi-rectangular region with dimensions of 5 latitude and longitude centred on the centre of the surface depression and vertically from 000 to 50 hpa. Unlike the traditional Eulerian method, which uses a steady volume and of course steady reference framework, a semi-langrangian method has been employed, which allows the integration volume to cover the disturbance during all the stages of its development. The mathematical expressions of the triple integrals that describe kinetic energy K e in J m and the boundary export import in W m within the atmospheric volume used in this paper are shown in the appendix. As this boundary transfer (export import) eddy kinetic energy is other than dissipation and barotropic conversion while steering by the eddy wind (as equation (A6) in the Appendix shows), it can be considered to include the dispersed and spread eddy kinetic energy. Thus, as a first approximation, this import/export of eddy kinetic energy given by equation (A6) can be used as an indication of dispersed eddy kinetic energy. It should be noted that the pressure work done by the boundaries, which could lead theoretically to the local production of kinetic energy, is not taken into account in the computations, since this process has appeared to yield quite unrealistic values when estimated numerically (Muench, 965). According to Table, the Atlantic disturbance exports eddy kinetic energy just after having reached its maximum development. This loss of K e, as mentioned above, could serve as an indication of dispersed K e. On 39

8 N G Prezerakos, H A Flocas and S C Michaelides Table. Eddy kinetic energy fluxes (W m 3 ) at certain stages of the Atlantic and central Mediterranean disturbances Hour/Date the other hand, the considered volume with its base centred at the centre of the central Mediterranean depression in the first stages of its development can be considered a receiver of K e at an increasing rate, which is maximised at the time of its maturity at 00 UTC on 7 December with a peak value of 3.76 W m (Table ). Eddy kinetic energy is also imported at an increasing rate in the same volume with its base centred at 7 N, 7 E, where the developing jet streak shifts to become meridional at 0000 UTC on 5 December. These rates for 00 UTC on 4 December and 0000 UTC on 5 December are.4 and.5 W m, respectively. This implies that the dispersed K e from the Atlantic region is collected in the region of the upper-level frontogenesis. Of course, the folding tropopause associated with the well-developed upper-level frontal zone is not a material surface but a region of active systematic transport of air between the stratosphere and troposphere resulting in the generation of potential vorticity at the level of maximum wind (Keyser & Shapiro, 986). It should be noted that the tropopause should be isolated in order for the collected K e to be distinguished. Nevertheless, the discussion above shows that well-known dynamic processes associated with the life cycle of the Atlantic disturbance are responsible for the creation of the jet streak. 4. Conclusions The intense surface cyclogenesis over the central Mediterranean, and especially its initiation, can be attributed to the downstream development, that is, the transfer of the eddy kinetic energy that has been collected in the upper troposphere over northwest Europe in the form of an intense jet streak curved anticyclonically. The appearance of the jet streak just ahead of a developing trough centred over the Atlantic favours the advection of warm air northwards, resulting in the intensification of the subsequent ridge and its expansion northwards. Therefore, the thermal gradient intensifies between the ridge in the south and a second trough further north owing to the approach of cold air 30 Eddy kinetic energy flux Atlantic Mediterranean disturbance disturbance 0000, 4 December.5 00, 4 December , 6 December.07 00, 6 December , 7 December.4 00, 7 December 3.76 from the north and warm air from the south. Owing to the intensification of the thermal wind, the jet streak moves from the western inflection point of the longwave trough to the northern or north-eastern flank of the ridge. The eddy kinetic energy has been radiated by the decaying disturbance over the Atlantic, by terms of the ageostrophic convergence of geopotential fluxes. Following this physical mechanism, the ageostrophic convergence of geopotential fluxes transfers downstream and further triggers the generation or rejuvenation of a new disturbance further to the east (here at a distance of 70 ) over the central Mediterranean. Calculations of the boundary transfer of the mean eddy kinetic energy of an open volume that extends horizontally 5 in longitude and latitude and vertically from 000 to 50 hpa support the idea of the dispersion collection transfer cycle of the eddy kinetic energy derived from an atmospheric wave packet. The downstream development can be a precursor of surface cyclogenesis during two stages: (a) strong development of a disturbance (trough) over the Atlantic and (b) intensification of a long wave (ridge), usually part of an omega block over the British Isles or farther to the west or to the east, along with the appearance of a jet streak at the north-eastern flank of the blocking high. The cyclogenesis over the central Mediterranean is likely to occur two days later under favourable low-level conditions. Appendix. Mathematical background of the energetics Following Orlanski & Katzfey (99) the eddy kinetic tendency equation can be written: K t e Ke {( ). ( ) }.( Ke) ( ω = V Φ V ) + residual (A) p where K e = (V) is the eddy kinetic energy, ω is the vertical velocity, Φ is the geopotential, t is time, and p is the atmospheric pressure. The second and third terms on the right-hand side of equation (A) represent the isobaric and vertical divergence of the eddy kinetic energy fluxes, respectively. The residual includes the terms (V).[((V). )(V) ] and (V).[((V). )[V] ] as well as dissipation. The first term on the right-hand side of equation (A) is particularly important for the examined case because it represents the dispersion of eddy kinetic energy when a constant Coriolis parameter is considered. Orlanski & Katzfey (99) showed that this term can be written as: [ ( ) ] ( V). ( ).[( V a ) ( ) ]+ ωα ω Φ Φ = Φ + p (A)

9 Surface cyclogenesis in the central Mediterranean where α is the specific volume and V a is the ageostrophic departure such that: (A) (A4). For any scalar, x, the quantity [x] φ is given by: where (V g ) = (V) (V g ) k ( ) = ( Φ) V g f 0 [ x] φ φ = xcosφddφ ( ) (sin φ sin φ ) φ where ([x] ) φ = [x] [x] φ. Note that ([x] ) φ is constant along a latitude circle from to longitude. and the Coriolis parameter f o is considered constant. Then, multiplied by (Φ), equation (A) becomes Since.[ f o k (Φ) ] = 0, equation (A3) yields:.[(v a ) (Φ) ] =.[(V) (Φ) ] (A4) Therefore, it is implied that if the Coriolis parameter is constant, the geopotential fluxes associated with the eddy ageostrophic departure (V a ) represent the divergence of the whole flux, (V) (Φ), as determined by the eddy velocity. The term ωα in equation (A) is the conversion of available eddy potential energy to eddy kinetic energy. Consequently, equations (A) and (A) can be applied in baroclinic atmospheric disturbances. The eddy kinetic energy (K e ) and the boundary exportimport (BK e ) can be written as (Reiter, 969; Prezerakos et al., 996): BK with p φ k ( ) ( Va ) ( Φ) = ( V) ( Φ) Φ f K e p [( V) ] = g p c g uv ( ( ) ) = d dp ϕ e + c p φ c (A3) where r is the earth s radius, u and v are the components of the horizontal wind along latitude and longitude circles, respectively, V is the wind speed, and the notation and other symbols are used as in equations φ 0 d p = r( )(sin φ sin φ ) c = r(sin φ sin φ ) (A5) g v V p V p ([ cos φ( ) ] ) d ([ ω( ) ] ) (A6) φ p g p ϕ ϕ p References Chang, K. M. (993). Downstream development of baroclinic waves as inferred from regression analysis. J. Atmos. Sci., 50: Cressman, G. P. (948). On the forecasting of long waves in the upper westerlies. J. Meteorol., 5: Eliassen, A. (96). On the vertical circulation in frontal zones. Geofys. Publ., 4: Eliassen, A. (977). Orographic waves and wave drag. In Parameterisation of the Physical processes in the Free Atmosphere. ECMWF Seminar Proceedings, Reading, UK, HMSO (96). Weather in the Mediterranean, MO 39, Vol., 36 pp Hoskins, B. J. & Draghici, I. (977). The forcing of ageostrophic motion according to the semi-geostrophic equations and in an isentropic coordinate model. J. Atmos. Sci., 34: Hovmoller, E. (949). The trough and ridge diagram. Tellus, : Keyser, D. & Shapiro, M. A. (986). A review of the structure and dynamics of upper frontal zones. Mon. Wea. Rev., 4: Kurz, M. (994). The role of diagnostic tools in modern weather forecasting. Meteorol. Appl., : Lagouvardos, K. & Kotroni, V. (995). Upper level frontogenesis: two case studies from the FRONTS 87 experiment. Mon. Wea. Rev., 3: Miles, M. K. (959). Factors leading to the meridional extension of thermal troughs and some forecasting criteria derived from them. Meteorol. Mag., 88: Muench, H. S. (965). On the dynamics of the wintertime stratosphere circulation. J. Atmos. Sci., : Namias, J. & Clapp, P. F. (944). Studies of the motion and development of long waves in the westerlies. J. Meteorol., : Namias, J. & Clapp, P. F. (949). Confluence theory of the high tropospheric jet stream. J. Meteorol., 6: Orlanski, I. & Katzfey, J. J. (99). The life cycle of a cyclone wave in the southern hemisphere. Part I: Eddy energy budget. J. Atmos. Sci., 48: Orlanski, I. & Chang, K. M. (993). Ageostrophic geopotential fluxes in downstream and upstream development of baroclinic waves. J. Atmos. Sci., 50: 5. Orlanski, I. & Sheldon, J. (993). A case of downstream baroclinic development over western North America. Mon. Wea. Rev., : Palmer, T. N & Anderson, D. L. T. (994). The prospects for seasonal forecasting. Technical. Report No. 70, Research Department, ECMWF, Reading, 49 pp, Pierce, R. P. (974). The design and interpretation of diagnostic studies of synoptic scale atmospheric systems. Q. J. R. Meteorol. Soc., 00:

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