Jet stream Role on the Energy Budgets of two different cyclonic systems

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H. Abdel Basset, M.M. Ibrahim and A.M. Lasheen

Department of Astronomy and Meteorology, Faculty of Science, Al-Azhar University, Cairo, Egypt.

ABSTRACT

Analysis of the kinetic energy budgets for two developing winter-type cyclones is presented. The first case represents a middle latitude cyclone that developed significantly north of the Mediterranean Sea. The development occurred as cold fresh air is advected to the rear of the system. The second situation represents typical middle latitude-tropical wave interaction. The event occurred in the area between a middle latitude cyclone located over Spain and a tropical disturbance west of Africa. The middle latitude cyclone is developed after the interaction. This location is one of the known favorite areas for such interaction. The role of the polar and subtropical jets is discussed.

The major contribution to vertical kinetic energy integral comes out due to a persistent upper troposphereic jet stream throughout the period of each cyclone. A large increase in the kinetic energy of the total flow fields occurs during the period of maximum amalgamation between the polar and subtropical jets.

Dissipation of kinetic energy is an important source of energy during the life cycle of the two cases.

Generation of kinetic energy via cross- contour flow is acting as a source of energy in the second cyclone, while it makes as a persistent sink of energy in the first cyclone. Horizontal flux convergence may act as a sink of energy during the period of each cyclone.

1. Introduction

Changes in atmospheric energy are associated with meteorological phenomena of all scales. An understanding of the energy processes of various scales of motion should help to explain and forecast many weather events that are not adequately understood. It is apparent from numerous investigations (e.g., Smith, 1973; Ward and Smith, 1976; Chen and Bosart, 1977 and Fuelberg and Scoggins, 1978) that kinetic energy sources and sinks show considerable spatial variation within individual synoptic-scale waves. Such inhomogeneities are especially prominent in the presence of a strong westerly jet core, where both transport and baroclinic conversion processes are maximized.

In addition, highly variable energy fields are observed in the presence of intense prefrontal convection, which is often embedded within these jet flows. Although strong jet streams and convective regions are known to be energetically active, understanding of the processes within such flow regimes remains incomplete. This is primarily due to the fact that these regimes are strongly influenced by processes that are subgrid-scale with respect to the current upper air synoptic network.

The purpose of the present study is to examine the kinetic energy budgets of the two

developing winter cyclones. The first system represents a middle latitude cyclone that developed

significantly north of the Mediterranean mainly due to baroclinic effects. The second cyclone

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represents typical middle latitude-tropical wave interaction where the approach of the polar and subtropical jets has affect on the system development. Selection of these particular cases allows an examination of the differences between energetic processes in the region of each cyclone in association with strong activity of the polar and subtropical jets.

In the following sections, we discussed the kinetic energy equation, the data sources and method of analysis, the synoptic situation for each cyclone and the kinetic energy budgets in association with the role of subtropical and polar jets during the development of the two systems.

2. The kinetic energy equation

The kinetic energy equation given by Smith (1969) is applicable to hydrostatic, open systems. The equation in isobaric coordinates is

∂

∂ ω

∂ K

t 1

s g t

1 s g

1 s g 1

s g

≡ = − ∇ ⋅ −

− ⋅ ∇φ −

∫

∫ ∫ ∫ ∫ ∫

∫

S P

k Vk k

P

V D k

0 0 0

0

0 0 0

0

1

ds dP ( ) ds dP ( )

ds dP

ds dP ( ) , ( )

Where S is the area of computational domain, g is the acceleration due to gravity and Po is the surface pressure. On the right-hand side of (1), the first and second terms are the horizontal and vertical flux divergence of kinetic energy, the third term is the generation of kinetic energy due to the cross-contour flow and the last term D (k) is commonly called the "dissipation" term.

3. Data and computations A - Data

The data used in this study have been taken from the archives of the European Center for Medium- Range Weather Forecasts (ECMWF). It consists of the horizontal wind components (u- eastward, v- northward), the temperature (T) and the geopotential height (z) on regular latitude-longitude grid points resolution of 2.5ô x 2.5ô for the isobaric levels 1000, 850, 700, 500, 300, 200 and 100 hPa. The available data is only at 1200 GMT during the period 18 to 25 January 1981 for the first case and from 21 to 26 January 1991 for the second case. The domain of study of the first case (cyclone I) extends from 15ôW to 40ô E and from 15ô N to 60ô N while for the second case (cyclone II) extends from 40ô W to 40ô E and from 10ô N to 60ôN. Two inner domains are used for the calculations of the present study of the two synoptic cases. For cyclone I, the computational domain extends from 5ô W to 40ô E and from 20ô N to 55ô N. For cyclone II, the domain extends from 25ô W to 20ô E and from 15ô N to 50ôN.

B - Analytical procedures

The vertical wind component in the P-coordinate system, namely ω = dp/dt, was estimated using the kinematic method. However, due to errors in horizontal divergence estimates, accumulation of error in

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ω occurs away from the bottom of the atmosphere. To remove this bias a pressure-weighted correction for ω was adopted following O'Brien, 1970. This technique was employed to calculate grid point values of ω at all standard isobaric levels and at the midpoint of each sublayer. At the bottom and the top of the atmosphere ω was initially set to zero.

The energy variables are calculated at 1200 GMT. Therefore, time derivatives evaluated by central differences spanning 48h give a reasonable indication of the time variation of kinetic energy, which used to compute horizontal derivatives and all vertical derivatives except those at the boundaries. For each of wind analysis at 1000 hPa, energy variables at this level are obtained by linear extrapolation. Finally, the dissipation term is evaluated as a residual in equation (1) (Kung, 1966). Holopainen, (1973) warns the risk of attaching physical significance to the sign or magnitude of residual terms, but concedes that application of the residual technique may be meaningful in data-rich areas.

4. Synoptic discussion

The two cyclones selected are different where the first one represents a middle latitude cyclone that developed significantly north of the Mediterranean, while the second cyclone represents typical middle latitude-topical wave interaction. This two cases of cyclogenesis will be refereed to chronologically: Case I which developed from 1200 GMT 19 to 1200 GMT 24 January 1981, Case II which developed from 1200 GMT 22 to 1200 GMT 25 January 1991.

a. Case I:

1200 GMT 19- 24 January 1981

This case is a typical case of cyclogenesis in the Gulf of Genoa. It has long been recognized that cyclogenesis to the lee of the Alps occurs typically with cold air outbreaks crossing the massif from the north or northwest and that the primary influence upon cyclogenesis is orographic. This cyclone evolves between 1200 GMT 19- 24 January 1981, while a strong cyclogenesis occurred during 1200 GMT 20-22 January 1981 over the Mediterranean Sea. Figs. 1a-1f and 2a-2f show the 1000 hPa and 500 hPa geopotential analysis for the period 19 to 24 January respectively.

At 1200 GMT 19 January, Figs. 1a and 2a shows that a weak low pressure system with surface center of 60 geopotential meter (GPM) is located south of Italy and is associated with a baroclinic upper air trough. During the next 24 h, the centers of the low propagates slowly to the northeastward and deepen to 40 GPM (Fig. 1b). A corresponding cut-off low formed at 500 hPa at 20^thover north Italy with center of 5280 GPM. On the 21^st, Figs.1c and 2c show that the low pressure was deepened to -100 GPH and moved south east to a point just south of Greece. The development of the upper air trough was accompanied by a lee cyclogenesis that started on 20^th associated with a cut-off low formed at 500 hPa over the Gulf of Genoa at low levels with center of 5340 GPM. Meanwhile, the Siberian high extended to include most of the north east of Europe and appeared as a new high-pressure center developed over north France. On the 22^nd, Fig.1d, indicate a southeast movement of the cyclone with slight filling to become -60 GPM at 500 hPa,

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while the higher pressure area intensified to include most of north Europe as shown from the 1000 hPa analysis.

The evolution of the lee cyclogenesis was consistent at least in the second and third days, with the schematic processes outlined in Buzzi and Tibalidi (1978). The interaction of the cold front with the Alps produced the initial disturbances, which then grow as a baroclinic disturbance.

During the next two days (23 and 24 January) the depression started filling and its central pressure increased gradually. On the other hand the high pressure over Atlantic is extended with a major ridge the joints the Siberian high on 22 January, Fig.1d. In other wards no more cold advection is permitted from north to the cyclone. While the Siberian high pressure extended westward the horizontal extension of the cyclone decreased and moved slowly eastward, and it became stationary vortex rotating above the north east of Mediterranean. Finally the cyclone was drifted slowly northeastward and was out of the computational domain by 25 January.

b. Case II

: 1200 GMT 22- 25 January 1991

This case study occurred during 22 to 25 January 1991, where interaction between middle latitude wave approaching north west Africa came in phase with a tropical disturbance located over the Atlantic at 35ôW, 5ôN. A careful look to the synoptic charts indicate that the development occurred between the 23^rd and 24^th. Figs.3a-3d are the 1000 hPa geopotential analysis for the period 22 to 25 respectively. On the 22^th a distinct high pressure system with center located over England and a deep elongated ridge directed to the south-west at about 20ô N and 42ô W. This high pressure system forces the westerly wave that come from the west Atlantic to move on an abnormal track, north of Europe. On the other hand east of the high pressure over Morocco and Spain there was a weak low pressure system with center of 160 geopotential meter (GPM). Also one can recognize along the African west coast a trough that extended from the tropical region. On the 23^rd, Fig. 3b, the Atlantic high pressure deepened as a result of the warm advection by waves on the western side of the Atlantic anticyclone. Fig. 3b shows also that the low pressure area over Morocco and Spain deepened to 140 GPM. On the 24^th, Fig, 3c, the African low gets its minimum value of 120 GPM with deep trough that extends to the tropical disturbance at about 35ôW, 5ôN. On the 25^th (Fig. 3d) there was a west movement of this wave with slight filling as indicated by a decrease in the low pressure area over north-west Africa. The intensification of the high pressure, on the 23^rd shown on Fig. 3b, causes distinct pouring of cold air on its east side as indicated by the extension of the high pressure to the tropical region. As a result a cold trough just west of Africa and warm ridge in the middle Atlantic are formed, see the temperature field on the 1000 hPa on 23^rd (Fig. 3b).

In the upper air, 500 hPa level, similar patterns are indicated. Figs. 4a- d are the 500 hPa on 23^rd to on 25^th respectively. On 23^rd the northwest African cyclone, is horizontally tilting to the west with center of 5520 GPM located over southwest Spain, Fig, 4b. On 24^th the tilt of this depression is directed to the south-

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west, Fig. 4c. On 25^th, Fig. 4d, west movement of the cyclone with filling to 5580 GPM is observed. The above discussion suggest that the development occurred between the 23^rd and 24^th. Note that over north- West Africa there is a shallow warm (thermal) trough that has vertical depth of about 2km. This trough extends from the tropics to Morocco, see the 1000 hPa geopotential analysis. On the other hand, the upper airflow over this area displays a cold deep middle latitude trough. Fig. 4b. The trigger action that led to the development seems to be the pouring of the cold air far to the south in the tropical region. In general two synoptic situations can lead to such substantial deep cold advection. Frontal passage associated with deep trough and the development of a high pressure system that has, on its east side, strong northerly wind component digging to the south. The latter case represents the present synoptic situation. This is an abnormal situation that is associated with a blocking high condition deviating the track of the middle latitude waves north and/or south of its normal path. Also such situation is generally marked with strong southerly (northerly) winds on the east (west) side of the blocking anticyclone, Fig. 3b.

4. The behavior of the subtropical and polar jets during the development of the two cases

It is known that the subtropical (polar) jet has its maximum speed around 200 hPa (300 hPa). So, we display the 300 and 200 hPa isotach fields in the following discussion to show the behavior of the polar and subtropical jets during the development of our two cases.

a. Case I

Figs. 5 and 6 display the isotach (wind speed) at 300 and 200 hPa from 19 to 24 January 1981. They show the behavior of the subtropical and polar jets at 200 and 300 hPa levels during the life cycle of the first cyclone. On 19^th Jan. 1981 (Fig. 5a) the wind direction over north Africa is zonal and the maximum speed of the subtropical jet is 50 m/s and is located over northeast of Africa (over Libya, Egypt and north Red sea), its value at 200 hPa is greater than 60 m/s. The polar jet extended from northwest England to southeast Spain and north of Italy with a maximum wind greater than 60 m/s at 300 hPa, its extension at 200 hPa has a maximum wind greater than 50 m/s. On 20^th Jan. 1981, the subtropical jet moves slightly to northeastward and its maximum center becomes greater than 60 m/s at 300 and 200 hPa and was located over Egypt. While the polar jet is shifted eastward and moved southeastward to amalgamate with the subtropical jet and its maximum value becomes greater than 70 m/s at 300 and 200 hPa. On 21^st Jan. 1981, the subtropical jet was shifted to the south east. The front of the polar jet reaches north of Algeria and its jet maximum wind value is greater than 70 m/s at 300 and 200 hPa. The subtropical jet weakened at 300 hpa and became stronger at 200 hPa (>70 m/s) and moved eastward. This day (21^st) represent the maximum amalgamation between the two jets. Beginning with the day of 22 up to 24 Jan. 1981 the polar jet becomes very weak at 300 hPa and its extension on 200 hPa disappear. Also, we notice that the subtropical jet is moved eastward and was almost back to the normal distribution in both speed and direction.

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b. Case II

Figs. 7a- d displays the isotach (wind speed) at 300 hPa from day 22 to day 25 of January 1991 respectively. On 22^nd , Fig. 7a, the wind direction over north Africa is zonal and the maximum speed of the subtropical jet is 50 m/s and we can note that over Spain a northerly wind (the polar jet associated with the middle latitude wave approaching the area) with speed 45 m/s is directed towards the subtropical jet. On 23^rd, Fig.7b, the polar jet gets near Africa and on 24^th, Fig. 7c, the polar jet amalgamates with the subtropical jet. The consequence is a stronger subtropical jet, speed greater than 60 m/c, and backing in direction to be south-westerly instead of being westerly. This backing of wind with time is known to be due to cold advection. In fact the change in direction is the driving force for moisture advection from the towering clouds at the I.T.C.Z towards the subtropical regions. On 25^th, Fig. 7d, the maximum wind moves easterly and on 26^th (not shown) one can note that the subtropical jet was almost back to normal distribution in both speed and direction (Fig. 9). The 200 hPa isotach on the 23^rd is displayed on Fig. 8b, one can observe that the maximum speed of the subtropical jet is about 70 m/s. On 24^th, i.e. after amalgamation of both jets the maximum speed increases to more than 80 m/s (Fig.8c). Also a stronger south component east of 0^o longitude was developed. In summary, before interaction the subtropical jet is westerly while the polar jet that appears over Spain is northerly (a sign of cold air pouring to the south). The interaction causes an increase in wind speed and a change in wind direction, of the subtropical jet, from the zonal to southwesterly flow over west Africa.

6. Kinetic energy budgets

6.1. Kinetic energy time development

The energy budget in terms of the Eulerian kinetic energy equation (1) is evaluated in a domain which encloses each cyclone during its life cycle. The area-mean energy variables, integrated from 1000 hPa to 100 hPa at 1200 GMT are shown in Tables 1 and 2. Note that the vertical flux divergence was integrated to zero because of the solid boundary condition on ω, therefore, is not presented in Tables 1and 2.

Tables 1 and 2 shows that the kinetic energy increased during the growth period of the two cyclones, reaches a maximum at 1200 GMT 21 January for cyclone I and at 1200 GMT 24 January for cyclone II. This values of K decreases gradually at the decay period. The local variation of kinetic energy,

∂k/∂t, positive most of the growth period of the two cyclones except during the latter portion when the two cyclones tend to decay. The growth period of the two cases is affected not only by the persistent of the upper troposphere subtropical jet but also by the entrance of a strong polar jet in the south western and north western boundary areas of the computational domain (Figs. 5 and 6), therefore the kinetic energy increased.

Generation of kinetic energy is a prominent sink of energy in the first case (cyclone I) except at the first day. The magnitude of this term is evidence of widespread and persistent imbalance in the mass and wind fields. The negative values of the generation term on average indicate that the cross contour flow is down gradient in the vicinity of the cyclone. The maximum destruction of kinetic energy by this term

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occurs at 1200 GMT 21 January. For cyclone II, generation of kinetic energy represent a source of energy for the all period except at the first day. The horizontal flux convergence acted as a source of energy during the first two days of cyclone I and a sink of energy for the following days. This term acted as a persistence sink of energy for the all period of cyclone.

Dissipation of kinetic energy from grid to subgrid scales is an important process during the period of the two cases. The results in Table 1 and 2 reveal that grid/ subgrid scale energy exchanges are the same in both cases, where a net transfer of energy from subgrid to grid scales (D(k)>0) is most pronounced during the life cycle of the two cyclones. However, it should be noted that during the growth period positive D(k) values are quit prominent and in fact remains the major energy sources for case I and a principle source for cyclone II.

Table 1: kinetic energy budget (1000 to 100 hPa) for cyclone I.

Units are W m^-2 except for energy content which are 10^-5 Jm^-2.

Date/time K ∂K/∂t -V.∇φ -∇.kV D(K) Growth period

19-1/12 6.58 0.75 3.74 3.67 -6.67 20-1/12 7.61 1.16 -2.75 2.40 1.15 21-1/12 8.58 -2.60 -12.11 -1.66 13.51 22-1/12 7.17 -1.21 -9.86 -2.83 11.48 Decay period

23-1/12 6.49 -0.07 -7.33 -4.13 11.38 24-1/12 7.05 0.69 -1.70 -7.86 10.25 Time mean 7.25 -0.21 -5.00 -1.74 6.85

Table 2: kinetic energy budget (1000 to 100 hPa) for cyclone II.

Units are W m^-2 except for energy content which are 10^-5 Jm^-2.

Date/time K ∂K/∂t -V.∇φ -∇.kV D(K) Growth period

22-1/12 7.91 0.49 -0.75 -4.46 5.70 23-1/12 8.76 0.64 1.69 -7.81 6.76 24-1/12 9.02 -0.32 0.64 -9.41 8.54 Decay period

25-1/12 8.20 -0.47 4.55 -8.31 3.29 Time mean 8.47 0.09 1.53 -7.50 6.07

6.2. Vertical- time variations of budget quantities

Energetic processes in relation to the cyclogenesis region need further examination and were analyzed by means of vertical- time cross sections as represented in Figs. 10 and 11 for case I and case II respectively.

The major feature of the cyclogenesis region is the field of kinetic energy due to the persistence of

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the upper subtropical jet stream between 300- 200 hPa. The maximum value occurred during the growth period of the two cases specially when the polar jet amalgamated with the subtropical jet and consequently increasing the kinetic energy. This can be noticed clearly on 20^th and 21^st for the first case and 23^rd and 24^th for the second case (Figs. 10a and 11a respectively).

The local derivative term (Figs. 10b and 11b) indicates that the kinetic energy increase at all levels of both cases especially above 300 hPa and on the first two days of each case with the amalgamation of the polar and subtropical jets. After the first two days the local variation of kinetic energy decreases at all levels of cyclone I and only above 300 hPa of cyclone II. The maximum decreasing of kinetic energy occurs at 22^nd for cyclone I and 24^thfor case II between 300- 200 hPa.

In case I weak generation of kinetic energy occurs in the first day above 300 hPa (Fig. 10c) , while for the following period the major energy sink is the intense conversion of kinetic to potential energy by the generation term which reaches its maximum negative at 21^st and 22^nd above 200 hPa. The generation of kinetic energy (-V. ∇φ) for cyclone II is a prominent source of energy above 300 hPa while it acts as a sink of energy below 300 hPa throughout the period of case II (Fig. 11c).

Systematic changes, related to the life cycle of each case occur in the flux convergence terms. In case I (Fig. 10d), this term had a positive sign during the first two days reached its maximum between 500- 200 hPa. With the beginning of the third day, 21^st January 1981, there was a negative values of the horizontal flux convergence specially in upper half of the atmosphere. The maximum of these values (the maximum export of kinetic energy out of the region) occurred at 200 hPa throughout the period. In case II (Fig. 11d), a large amount of energy is transported out of the area by horizontal flux convergence (-∇.kV <

0) above 500 hPa specially near the level of the jet. Below 500 hPa, although the contribution of this term still small it may be considered as a source of energy.

The term, -∂(ωk)/∂P, indicate the vertical transport of kinetic energy, positive values indicating downward transport. Comparing the two cases, downward transport of kinetic energy is found for first case in the layer 850-300 hPa for the growth period (Fig. 10e). Above 300 hPa for the growth period and below 300 hPa for the decay period and also in the lower layer 1000-850 hPa the vertical flux is negative which indicate that the transport of kinetic energy aloft by the upward vertical motion was dominant throughout the period. This vertical transport acts as a source of kinetic energy to the middle troposphere and to the stratosphere. In case II (Fig. 11e), throughout the all period this term was positive below 200 hPa and negative above 200 hPa. Which explain that this term transport the energy above 200 hPa to the stratosphere, while below 200 hPa this vertical transport acts as a source of energy to the middle and lower troposphere. However, the magnitude of the vertical flux term is relatively small in our two cases.

Positive dissipation term is suggesting a transfer of energy from subgrid to grid scales of motion as an import source of energy during these periods (Figs. 10f and 11f). So, the large amount of energy is imported to the area by dissipation that acts as a source of energy at all levels with maxim near the level of the jet. The maximum positive dissipation values occurs at 200 hPa on the second day of strong

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development in our two cases, where in case I it appears on 21^st January 1981 while in case II on 24^th January 1991. The values of this term in case I was larger than these in case II. This is due to the dissipation term may be considered as the only energy sources for case I during its period. Positive values of this term have been reported by numerous other investigators (e.g., Ward and smith, 1976; Chen and Bosart, 1977;

and Tusi and Kung, 1977).

6.3. Horizontal distribution of energy terms

The relationships between the evolving synoptic features and the ensemble cyclogenesis are now examined by considering the spatial distribution of budget terms. All quantities are 1000 to 100 hPa integrals except for the kinetic energy content, which is restricted to the 200-500 hPa jet stream layer.

a. Case I

Fields of kinetic energy content and local change are presented in Figs. 12 and 13. During the first day two centers of maximum values of kinetic energy located on the northwest corner and west of the Mediterranean sea and continuos to propagate eastward (Fig. 12). The first center (> 50 x 10⁴ J m^-2) which is associated with the polar jet stream occurs over the north west of our domain (over England) while the second center (>35 x 10⁴ J m^-2) is associated with the subtropical jet and is located over the south part of Mediterranean (over the north of Libya).On the second day (20 January) the two centers were shifted southeastward and the maximum of the first weakened to about 45 x 10⁴ J m^-2 and it become located over France. On day 21^st (where the strong amalgamation between the tow jets occurred), the first center is waked and moved more to southeastward and was located over Tunis and its extension became small. The second center is shifted southerly. On 22^ndJanuary, after the amalgamation of both jet, the polar jet disappear and the maximum values of kinetic energy associated with the subtropical jet increase to more than 50 10⁴ J m^-2. On the last two days (23^rd and 24^th), where the subtropical jet is almost back to normal distribution in both speed and direction, its associated center was weakened and moved eastward.

The ∂k/∂t reflects the progression and reorientation of the kinetic energy fields. During the period of most active cyclogenesis (the growth period) the larger ∂k/∂t is located between the geometric center of cyclogenesis. Propagation of the subtropical and polar jets is reflected in the ∂k/∂t maximums. Increases kinetic energy greater than 8 W m^-2 occurred north west of the storms (Fig. 13), and there are also increase of Kinetic Energy greater than 6 W m^-2 to their southeast, corresponding to the speed maximum of the two jets (Fig. 13). The center of positive ∂k/∂t northwest of the cyclone is shifted southeastward, while the values of southeast center become negative. The most pronounced variation on 21 January was the decrease in energy associated with the exit of the polar jet.

Kinetic energy generation fields (Figs.14) are dominated by a broad region of strong conversion of kinetic to potential energy that propagates slowly eastward. The fields of –V.∇φ had two regions, the first which is located in the left side of the upper air trough (see Fig.2) has negative sign, while the second which

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is located in the right side of upper air trough is positive. The magnitude of the negative values is greater than of the positive ones except at the first day, so the destruction of kinetic energy is much greater than the generation. The maximum conversion of kinetic to potential energy occurs at the growth period, where maximum negative values greater than –55 W m^-2 are located north and west Europe at 20 and 21 January, while maximum positive value greater than 20 W m^-2 are northeast of our domain at the first three days.

Although in the second case horizontal flux convergence is the major budget sources as indicated by the statistics in Table 2 it acts as a kinetic energy sink in the most days of case I (Table 1). Figs. 15 show that the maximum centers of horizontal flux convergence occur just east of the kinetic energy content and jet maximum. It is interesting to note that the positive centers of -∇.kV at the northwest of our domain (above west of Europe) were found associated with the centers of maximum energy and with centers of maximum wind of the polar jet throughout the first three days (19- 20 January 1981). Also we notice on 20^th January that corresponding to the centers of maximum kinetic energy and the subtropical jet above northeast of Africa there are two centers of -∇.kV. The first was positive and located above northeast of Egypt and east of Mediterranean while the second was located west of the first. This two centers oscillate (west to east or east to west) and intensify in association with the oscillation and intensification of the subtropical jet throughout the period of our first cyclone. In general the horizontal flux convergence maxim are positioned just downstream from the jet maxim in the regions of difluent flow. As shown by Uccllini and johson (1979) supergeostrophic flow a head of a jet maximum may act through its circulation to reinforce the low-level jet, thus enhancing the differential moisture and thermal transport will maintain favorable conditions for development deep cyclogenesis.

The dissipation fields (Figs. 16) contain substantial regions of positive values, indicating subgrid- scale kinetic energy sources. Although the dissipation term is subject to computational uncertainty, positive D(k) values appear to be related to the presence of cyclogenesis. In our case a substantial portion of the cyclogenesis develops within regions of positive values, taking consideration those positive values weakened during the decay period. In this case of study, each dissipation field divided into two regions the first contained positive values and the second contained negative values. The regions containing positive values were located in the left side of our domain and oscillate eastward especially during the growth period, while the negative values regions was located in the right side. Strong association is observed between the dissipation region of positive values and the generation of negative values, and also between the dissipation regions of negative values with the generation regions of positive values. The association can be seen by comparing the distributions of D(k) in Fig. 16 to those in Fig.14 of -V.∇φ. The magnitude of the positive values is much greater than the magnitude of the negative values this indicates that the transfer of energy from the subgrid to the grid scale may have provided an important source of energy throughout the period of this case.

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b. Case II

The phase development is described in the synoptic discussion of this case is evident in the K and

∂k/∂t fields (Figs. 17 and 18). During the first day (22 Jan. 1991) the kinetic energy maximum associated with the polar jet moved from northeast to southeast (besides the entrance of the subtropical jet), while the maximum values of K associated with the subtropical jet propagate from southeast northeast over the North Africa. On the second day (23 Jan. 1991) the previous maximum of K which was associated with polar jet is disappeared while the maximum values above north Africa increases and continues to propagate to north east of Africa. Another increase of K occurred at 24^th especially at the region of the entrance of the subtropical jet. At the last day (25 Jan. 1991) the maximum of energy decreased and moved also to northeast. The ∂k/∂t values reflect this progression and reorientation of K fields. Comparison of ∂k/∂t fields with those of K reveals that regions of strongest kinetic energy gain contain the region of cyclogenesis and also reflect the progression and reorientation of the polar and subtropical jets.

Although -V.∇φ was the major budget source, as indicated by the statistics in Table 2, it was initially a kinetic energy sink as shown in Figs. 19. The region of conversion from kinetic to potential energy at the first two days (22- 23 Jan. 1991) was associated with the region of polar jet. The center of maximum generation of K was located northeast of Africa, it intensified and moved eastward throughout the period of our cyclone.

The horizontal flux convergence, -∇.kV, acted as a sink of energy throughout the period of this case. Generally, the negative centers of -∇.kV were found over the north of Africa corresponding to the centers of maximum of kinetic energy. Dissipation fields (Figs. 21) show evidence of both grid to subgrid and subgrid to grid energy exchange in the proximity of cyclogenesis and the jet streams. The primary center of positive values appeared initially over England and Spain and extended to the northwest corner of Africa, and the center moved at the second day to the southeast. On 24^th and 25^th^, each dissipation field is nearly divided into two regions the first contained positive values and the second contained the negative values. The region containing positive values were located in the left side of our domain and moved eastward.

7. Summary and conclusions

Kinetic energy budget of two different cyclone systems in the Mediterranean have been studied in terms of time area- average statistics, spatial distributions of vertical integrals and time-height cross sections. The first case is for 19- 24 January 1981 at 1200 GMT while the other is for 22- 25 January 1991 at 1200 GMT. The important results are as follows:

1- Both cases show similar behavior of local kinetic energy change.

2- Horizontal flux convergence acted as a sink of energy for both cases.

3- Generation of kinetic energy via cross- contour flow acted as energy source for the second case during the growth period of cyclone.

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4- The subgrid term D(k), in the first case, was the most important during the growth period of the cyclone.

5- The first case was relatively statically unstable compared to the second case. This is consistent with the role played by the subgrid term D(k).

6- The major contribution to vertical kinetic energy integral comes from a persistent upper troposphereic jet stream throughout the period of each cyclone. A large increase in the kinetic energy of the total flow fields occurs during the period of maximum amalgamation between the polar and subtropical jets.

REFERENCES

Buzzi, A. and S. Tibaldi, 1978: Cyclogenesis in the lee of the Alps: a case study. Q. J. R. Meteorol. Soc.

104, 271- 287.

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List of figures

Fig. 1: 1000 hPa height contours in 20 m intervals (solid) and temperature (dashed) in 5

^o

C Increments for 1200 GMT 19- 24 January 1981.

^o

C Increments for 1200 GMT 22- 25 January 1991.

Fig. 5: 300 hPa isotach (wind speed) during the period 1200 GMT 19- 24 January 1981.

Fig. 9: Subtropical jet stream for January (15 years mean from 1980 to 1995).

Fig. 10: Pressure time cross section of kinetic energy budget terms for cyclone I. Units: kinetic energy in 10

⁵

Jm

^-2

(100 hPa)

^-1

, kinetic energy changes in Wm

^-2

(100 hPa)

^-1

.

Fig. 11: Pressure time cross section of kinetic energy budget terms for cyclone II. Units: kinetic energy in 10

⁵

Jm

^-2

(100 hPa)

^-1

, kinetic energy changes in Wm

^-2

(100 hPa)

^-1

.

Fig. 12: Horizontal maps of kinetic energy content in the layer 200- 500 hPa during the period 1200 GMT 19- 24 January 1981. Units are Wm

^-2

.

Fig. 13: Horizontal maps of ∂k/∂t (1000-100 hPa integrated values) during the period 1200 GMT 19- 24 January 1981. Units are Wm

^-2

.

Fig. 14: Horizontal maps of –V. ∇φ (1000-100 hPa integrated values) during the period 1200 GMT 19- 24 January 1981. Units are Wm

^-2

.

Fig. 15: Horizontal maps of -∇. kV (1000-100 hPa integrated values) during the period 1200 GMT 19- 24 January 1981. Units are Wm

^-2

.

Fig. 16: Horizontal maps of D(k) (1000-100 hPa integrated values) during the period 1200 GMT 19- 24 January 1981. Units are Wm

^-2

.

Fig. 17: Horizontal maps of kinetic energy content in the layer 200- 500 hPa during the period

1200 GMT 22- 25 January 1991. Units are Wm

^-2

.

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Fig. 18: Horizontal maps of ∂k/∂t (1000-100 hPa integrated values) during the period 1200 GMT 22- 25 January 1991. Units are Wm

^-2

.

Fig. 19: Horizontal maps of –V. ∇φ (1000-100 hPa integrated values) during the period 1200 GMT 22- 25 January 1991. Units are Wm

^-2

.

Fig. 20: Horizontal maps of -∇. kV (1000-100 hPa integrated values) during the period 1200 GMT 22- 25 January 1991. Units are Wm

^-2

.

Fig. 21: Horizontal maps of D(k) (1000- 100 hPa integrated values) during the period 1200 GMT

22- 25 January 1991. Units are Wm

^-2

.