Box Modeling of the Eastern Mediterranean Sea

Transcription

1 _ Box Modeling of the Eastern Mediterranean Sea Yosef Ashkenazy and Peter H. Stone Center for Global Change Science Department of Earth, Atmospheric and Planetary Sciences MIT, Cambridge, MA USA MASSACHUSETTS Center for Global Change Science INSTITUTE OF TECHNOLOGY Report No. 70 May 2003

2 The Earth s unique environment for life is determined by an interactive system comprising the atmosphere, ocean, land, and the living organisms themselves. Scientists studying the Earth have long known that this system is not static but changing. As scientific understanding of causal mechanisms for environmental change has improved in recent years there has been a concomitant growth in public awareness of the susceptibility of the present environment to significant regional and global change. Such change has occurred in the past, as exemplified by the ice ages, and is predicted to occur over the next century due to the continued rise in the atmospheric concentrations of carbon dioxide and other greenhouse gases. The Center for Global Change Science at MIT was established to address long-standing scientific problems that impede our ability to accurately predict changes in the global environment. The Center is interdisciplinary an d involves both research and education. This report is one of a series of preprints and reprints from the Center intended to communicate new results or provide useful reviews and commentaries on the subject of global change. See the inside back cover of this report for a complete list of the titles in this series. Ronald G. Prinn, Director Rafael L. Bras, Associate Director MIT Center for Global Change Science For more information contact the Center office. LOCATION: Center for Global Change Science Building 54, Room Massachusetts Avenue Massachusetts Institute of Technology Cambridge, MA USA ACCESS: Tel: (67) Fax: (67) cgcs@mit.edu Website: Printed on recycled paper

3 Box modeling of the Eastern Mediterranean sea Yosef Ashkenazy and Peter H. Stone Department of Earth Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 0239 Submitted to Journal of Physical Oceanography March 2003 corresponding author address: MIT Room 54-78, Cambridge MA phone: (67) , fax: (67)

4 Abstract Recently ( ) a new source of deep water formation in the Eastern Mediterranean was found in the southern part of the Aegean sea. Till then, the only source of deep water formation in the Eastern Mediterranean was in the Adriatic sea; the rate of the deep water formation of the new Aegean source is, three times larger than the Adriatic source. We develop a simple 3 box-model to study the stability of the thermohaline circulation of the Eastern Mediterranean sea. The 3 boxes represent the Adriatic sea, Aegean sea, and the Ionian sea. The boxes exchange heat and salinity and may be described by a set of nonlinear differential equations. We analyze these equations and find that the system may have one, two, or four stable flux states. We consider two cases for which the temperatures of the boxes are (i) fixed or (ii) variable. After setting the parameters to correspond to the Eastern Mediterranean we find that the system has two stable states, one with (i) two thermally dominant sources of deep water formation in the Adriatic and Aegean and the other with (ii) a salinity dominant source of deep water formation in the Adriatic and a thermally dominant source in the Aegean. While the Adriatic thermally dominant source is comparable to the observed flux of the Aegean source has much smaller flux than the observed value. This situation is analogous to the state of the thermohaline circulation pre 990 where the only source of deep

5 water formation was in the Adriatic. If we decrease the atmospheric temperature of the Aegean box by, in accordance with recent observations, we find that the deep water formation of the Aegean increases significantly to a value comparable to the recently observed flux. Our model also suggests that under a different scenario where the salinity flux of the Aegean box is positive instead of negative, the drop in atmospheric temperature over the Aegean may not result in the formation of a new source of deep water.. Introduction Recent observations of a major increase in the amount of bottom water formation and discharge from the Aegean sea (Roether et al. 996; Klein et al. 999; Malanotte- Rizzoli et al. 999) raise the possibility that the circulations in the Eastern Mediterranean are unstable and subject to sudden changes. The idea that density-driven circulations in the ocean could under a given set of boundary conditions display more than one equilibrium state, and therefore may have a behavior like that recently observed in the Aegean, was first put forth by Stommel (96). He illustrated the behavior with a very simple two-box model of the thermohaline circulation. The two equilibrium states that he found in his simple box model have since been found in simulations of the North Atlantic thermohaline circulation with the most sophisticated coupled atmosphere-ocean 2

6 general circulation models (e.g., Manabe and Stouffer (988, 993)). These recent results lend considerable credibility to Stommel s box model. However, there is nothing in his model that limits its applicability to large-scale circulations in the North Atlantic indeed in his paper he even suggested that it might be relevant to the Mediterranean. Here we apply the same basic ideas as Stommel s to develop a box model of the Eastern Mediterranean, and explore what the possible multiple equilibrium states are, and what their stability characteristics might be. The major change in the deep water formation in the Eastern Mediterranean sea occurred, basically, in the vicinity of the Adriatic-Aegean-Ionian seas (Klein et al. 999; Lascaratos et al. 999; Malanotte-Rizzoli et al. 997, 999; Roether et al. 996). Hydrographic surveys since early last century (Nielsen 92) indicated that the dominant source region for deep water over the entire Eastern Mediterranean, was the Adriatic sea. Water outflowing from the Adriatic were deposited in the bottom of the Ionian sea (Schlitzer et al. 99); then they spread southward and eastward (Wust 96; Malanotte-Rizzoli and Hecht 988). The deep water over-turning time was approximately 00 years with an average formation rate of (Roether and Schlitzer 99). An additional, much more dominant, source of deep water was found in a hydrographic survey during 995 (Roether et al. 996). The new source is located in the southern part of the Aegean sea and has an average outflow rate of about 3

7 Sv; the waters associated with this source are warmer then the old Adriatic source but more saline then the Adriatic source. A recent study suggested that the change in the thermohaline circulations of the Eastern Mediterranean sea actually started before October 99 (Malanotte-Rizzoli et al. 999). Several explanations have been suggested to understand the change in the deep water formation of the Eastern Mediterranean sea. One study suggested that enhanced net evaporation led to the formation of the new Aegean source (Zervakis et al. 2000). In addition, the north Eastern Mediterranean experienced some cold winters during the period; these cold winters have been associated with changes in the thermohaline circulation of the Eastern Mediterranean (Sur et al. 993; Theocharis et al. 999). However, the lack of oceanic data during makes it difficult to uncover the exact cause for the formation of the new Aegean source. Ocean General Circulation Models (OGCMs) have been used to better understand the possibilities which lead to the formation of the new Aegean source. For example, changes in the wind stress over the Aegean basin were related, using an OGCM, to the formation of the new Aegean source (Samuel et al. 999). Dry and cold winters of 987, , were also related, using an OGCM, to the formation of the new Aegean source (Lascaratos et al. 999). These studies based their numerical simulations on re-analysis data and didn t fully reproduce the entire Aegean source pattern. Wu et al. (2000), 4

8 on the other hand, have forced an OGCM by eight consecutive cold winters (from 987 to 995) over the Aegean basin. They showed that a decrease of the atmospheric temperature by leads to strong deep water formation over the Aegean; winter sea surface temperature over the Aegean sea was observed to be colder by up to from the climatological average (Marullo et al. 999). Recently, Stratford and Haines (2002) performed OGCM simulations and suggested that a combination of a few cold winters together with changes in the wind stress over the Eastern Mediterranean underlies the formation of the Aegean source. Here we propose a highly simplified conceptual box model to help pinpoint the possible causes for the recent changes in the thermohaline circulation of the Eastern Mediterranean sea. The simplicity of the model allows us to analytically analyze the steady states of the thermohaline circulation and the stability of these states. We show that the Aegean bottom water formation is mainly driven by cold atmospheric temperature and much less influenced by changes in the net evaporation over the Aegean. We however argue that under certain conditions the thermohaline circulation may remain unaffected even when the atmospheric temperature is significantly reduced. Our model also suggests that if the Aegean atmospheric temperature should return to its warmer climatological value, the Aegean source of deep water formation would drastically weaken after a time scale of 2-3 years. In our study we assume that the atmospheric 5

9 temperature over the Aegean basin was reduced by after 990 consistent with the observed cold winters in 987, (Lascaratos et al. 999), and with recent OGCM simulations (Wu et al. 2000). 2. Three box model of the Eastern Mediterranean Sea We represent the Adriatic sea, the Ionian sea, and the Aegean sea, by three boxes, respectively. All three boxes are forced by surface fluxes of heat and salinity and the boxes are assumed to be well mixed, so that their states can be described by a single temperature and salinity for each box. The flux between Box and Box is (representing Ionian-Adriatic flux) and the flux between Box and Box is (representing the Ionian-Aegean flux); see Fig.. The boxes interact through pipes with the fluxes and. The circulations between the boxes are assumed to be proportional to the density gradients between the boxes (Stommel 96), and with this parameterization the state of the system can be described by conservation equations for heat and salinity for each box, giving a total of six equations for the temperatures and salinities of the three boxes. The equations are nonlinear because of the nonlinear advection of heat and salinity between the boxes, and this nonlinearity give rise to the possibility of multiple 6

10 + + = = + A + + equilibrium states. The fluxes and are proportional to the density gradients between the boxes, () (2) where are the temperatures of the boxes, are the salinities of the boxes, and are the thermal and haline expansion coefficients, and are flux constants. The surface virtual salinity fluxes are "! and #$, and the upward surface heat fluxes are &%', &%)(, and &%*. We assume that the total salinity of the three boxes is conserved. We define the following variables and constants:,+ -,./..,, +, 0!!2, 0 $ $3, and 0 % '54 ( 4 * % '64 ( 4 *37 8)9;: ( 8 is the heat capacity per unit mass of water, 9<: is the average sea water density, and are the volumes of the boxes). Following (Stommel 96; Stone 997; Nakamura et al. 994) the salt and heat equations can be written as, =?> =D> 0?@! 0 $ BA A A C (3) (4) 7

11 = = A A A A = =D> 0?@! = 0 =D> %' = 0 =D> %* = 0 =?> %( A 0? $ A A A A ) A A A A (5) (6) (7) 6 (8) These equations describe the amount of salt and heat entering/leaving the boxes through the pipes plus the contribution of the surface fluxes. After a few algebraic operations the system reduces to four equations, = =?> 0?%)( = ( =?> 0?% =D> =D> 0 %' 0 %* 0 %( 0 %( DA A A 0 % ' 0 % * A A 0! 0D@! A A A A 0 $ A A A A 0 $ (9) (0) () A A (2) To obtain the fixed points of the system we set the left hand side to zero, i.e., = 7 =D> 8

12 A and = 7 =D>. From the temperature equations we then obtain 0 %( 0 % ' A A A A (3) 0 %( 0 % * A A A (4) Substituting for the surface heat fluxes in Eqs. () and (2), we obtain A A 0D A A (5) where. For there are two solutions, 0 (6) if 0 (7) For, there is one negative solution, 0 (8) 9

13 If the salinity flux is negative (0 ) just the solution is valid. In the above solutions we assume, consistent with the climatology, that the temperature gradients are positive; i.e., while. The solution is the salinity dominant stable flux state is the temperature dominant stable flux state. corresponds to sinking in boxes a and c while is an unstable state. corresponds to sinking in box b. As in Stommel s model In some cases the salinity flux 0 is relatively small, i.e., A 0 A (9) E.g., for the Eastern Mediterranean, the left hand side of Eq. (9) is at least five orders of magnitude smaller than the right hand side. Under this condition it is possible to simplify the flux steady states, 0 (20) (2) 0? (22) To explicitly know the flux solutions it is necessary to evaluate the temperature gradi- 0

14 ents and. In the following subsections we will consider two different scenarios: (i) The temperatures of the boxes are strongly coupled to the atmospheric apparent temperatures, i.e., the relaxation is assumed to be immediate and the temperatures of the boxes are thus assumed to be fixed and equal to the atmospheric temperatures. (ii) The temperatures of the boxes are assumed to be variable. a. Fixed temperatures As a first approximation we assume that the atmosphere is strongly coupled to the ocean. Thus, we assume that the temperatures of the different boxes are fixed and equal to the atmospheric (climatological) temperatures. The three box system in this special case has already been analyzed by Welander (986). In this case, the flux steady state solutions are given in Eqs. (5) where are constants. These are two independent solutions for and and each has either one or three solutions [Eqs. (6)-(8)]. It follows that the equilibrium states of the Adriatic and Aegean seas (boxes a and c) interact independently with the Ionian sea (box b), and in fact in equilibrium the model decouples into two separate two-box models, each identical to the original Stommel two-box model (Welander 986). Thus, for example, there are two possible stable states for the Adriatic, one with strong bottom water formation, and one without.

15 7 > > or All together there are either one, three, or nine fixed points; i.e.,, and, respectively. For the nine fixed points case, it is possible to show that (i) four of these fixed points are stable, i.e., are semistable (saddle points), i.e., i.e., and, (ii) four, and (iii) one is unstable,. In addition, there are no spiral modes in the system there is only simple damping or simple repelling of these fixed points. Although the fixed points of Eqs. (5) are independent of each other their stabilities depend on each other. To study the basin of attractions of the stable fixed points we first set (or 7 ) to zero and then find the dependence of on (or vice versa); a similar stability analysis, using different variables, was performed by Welander (986). The stability lines are the lines for which (or ) is minimal or maximal. In Fig. 2 we present two examples of the fixed points with their basins of attraction. Figure 2a shows the situation when the salinity flux forcing is weak and positive (0 ) for which there are 9 fixed points. Figure. 2b shows the situation when the salinity flux forcing of the Aegean box (box ) is weak but negative (0!, 0 $ ) for which there are 3 fixed points. We assume that the volume of the Ionian is ten times larger than the volume of the Aegean, and that the Aegean is twice the volume of the Adriatic. These ratios are approximately realistic, and illustrate some of the possible ways in which the basins can interact. In Fig. 2a (positive salinity flux) the four heavy dots 2

16 A indicate the stable equilibria of the system. One has strong bottom water formation in both the Adriatic and the Aegean; one has no bottom water formation in either (actually there is a slightly negative amount of bottom water formation in this state); and the other two have strong bottom water formation in one of the seas, but not the other. The shading indicates the attractor basin for each equilibrium. In the case with negative salinity flux forcing for the Aegean (Fig. 2b), two of the stable equilibria have disappeared, and two remain. In one there is strong bottom water formation only in the Aegean, and in the other there is strong bottom water formation in both basins. In effect, the negative salinity forcing of the Aegean has, in this case, eliminated the states with weak bottom water formation in the Aegean. Thus, changes in the salinity flux forcing of the basins may cause drastic changes in the stability of the different basins. In many cases it is useful to construct a pseudo-potential to describe the system. For the present case, it is possible to show that such a potential cannot be constructed. However, for the case for which (as for the present system), Eqs. (),(2) can be written in form of a pseudo-potential, A 0D@! A A 0? $ (23) 3

17 for which the time derivative of is = =D> (24) The potentials for the cases shown in Fig. 2 are shown in Fig. 3. b. Variable temperatures Here we assume that the ocean temperatures are not so strongly coupled to the atmospheric temperatures and that the relaxation time for the temperature of the different boxes is finite. Following Haney (97) we parametrize the heat flux of the boxes as, 0 % (25) where ; is the relaxation constant ( 7 ) (Haney 97), is the depth of the different boxes, and is the apparent atmospheric temperature of the different boxes. It follows from the equilibrium conditions [Eqs. (3),(4)] that A A A A.A A A A (26) (27) 4

18 After inserting into Eqs. (26),(27) the expressions for the fluxes and [Eqs. (6),(8)], we are left with two high order coupled equations for the equilibrium temperatures and. In the following we will use the approximations [Eqs. (20),(22)] to solve the temperature equations [Eqs. (26),(27)]. We will consider three cases: (i) both fluxes are salinity dominant, i.e., and is salinity dominant and the other is thermally dominant, e.g., both fluxes are thermally dominant, i.e.,, and. ; (ii) one of the fluxes, and ; (iii) i. Salinity dominant fluxes For the salinity dominant fluxes ( ) term in Eqs. (26),(27) may be approximated as 0 7 and the A [Eq. (22)]; i.e., A 0! 0D@! 0?$ (28) 0 $ (29) The second term on the right hand side is the correction to the apparent temperatures. Since the second term on the right hand side is generally much smaller than the first term on the right hand side, the most basic approximation is, i.e., the temperature of the boxes are equal to the apparent temperatures, as in the previous sub-section. 5

19 ii. Salinity dominant flux and thermally dominant flux We consider the case where one of the fluxes is salinity dominant and the other is thermally dominant, e.g., and. We approximate A A 0?"! 7 and A A [Eqs. (20),(22)]. From Eqs. (26),(27) we obtain 0D@! (30) where ' ( (3) ' ( * ( (32) * ( 7 ' ( (33) ' ( 7 * ( (34) * ( This is a quadratic equation with the solution 0! 7 (35) 6

20 Note that the larger solution for Eq. (30) is chosen to be consistent with the thermally dominant flux. Once is known it is possible to find all the other variables, [Eq. (20)], [Eqs. (22),(26)], and [Eq. (22)]. In the case where, it is possible to obtain the solution by replacing the subscript 2 by and vice and versa. iii. Thermally dominant fluxes The most complex case is when both the Adriatic and the Aegean have thermally dominant fluxes; i.e., we use the approximations A A and A A and. In that case [Eq. (20)]. Then Eqs. (26),(27) can be written as, (36) (37) where and are defined above [Eqs. (3)-(34)]. This leads to a fourth order equation for, (38) 7

21 This equation can be solved by neglecting the term! on the left hand side; we neglect this term since (i.e., the area of box is approximately equal to the area of box, as for the Eastern Mediterranean). Then we are left with a quadratic equation (39) with the solution, (40) where (4) (42) (43) In Eq. (40) we choose the the larger solution, i.e., with positive square-root, since it is closer to the apparent atmospheric temperature our assumption is that the box temperature relaxes to be as close as possible to the apparent forcing temperature. Eq. (40) is thus an approximation for the largest solution for the more complex Eq. (38); 8

22 see Fig. 4a. When there is no real solution to Eq. (39). However, the temperature gradient does exist in the more complex Eq. (38). We choose the temperature gradient at the minimum of the parabola of Eq. (39), 7, as the approximated solution for Eq. (38); see Fig. 4b. can be found in a similar way; i.e., by changing the subscript in Eqs. (4)-(43) to 2 and vice versa. Then, the fluxes can be obtain using the approximations, ( ). 3. Application to the Eastern Mediterranean Sea a. Parameter choices The parameter values used in our model are given in the Table I. The Ionian sea basin is taken to be between 5.5E-23E and 30N-40.5N, the Aegean basin between 23E-27E and 35N-4.5N, and Adriatic basin between 2E-20E 42N-46N and 5E-20E 40.5N- 42N; see Fig.. The dimensions (volume and depth) of the different boxes were measured using the Mediterranean bathymetry map (the Mediterranean Ocean Data-Base, MODB, The evaporation and precipitation over the boxes are based on the Dasilva 94 Atlas ( The river run-off to the boxes are based on the Global Runoff Data Center database ( 9

23 7 The virtual salinity fluxes,! and $, are approximated using the annual average precipitation plus river runoff minus evaporation,, over the different basins, :, (44) where : is the standard sea water salinity, is the depth of the box, and is a constant that balances the total salinity flux to zero (to conserve water/salt content). quantifies the salinity flux out of the box. The most critical parameters are and. We approximate and using the average temperature and salinity over the surface layer of depth; we use the climatological data of MODB to compute these averages. Since the average temperatures and salinities are based on climatological data they describe the situation prior to 990. The Adriatic-Ionian constant,, may be approximated by Eq. () using the observed flux of 0.3Sv. However, since the (small) Aegean-Ionian flux pre 990 is unknown we are unable to approximate. On the other hand, it was reported that the temperature over the Aegean basin dropped by during several winters after 990 (Theocharis et al. 999; Wu et al. 2000). This fact enables us to estimate the Aegean-Ionian constant,. We first decrease the climatological average temperature by and then use the reported Sv in Eq. (2) to compute. Thus is based on the post

24 conditions. Under the current setting, the Aegean constant is about.6 times larger than the Adriatic constant. The apparent temperatures used in Eq. (25) are approximated as the average temperatures over the surface layer of depth (using the MODB), in accordance with the strong coupling approximation. The apparent temperature of the Aegean box post 990 is decreased by with accordance with the cold winters post 990 (Theocharis et al. 999; Wu et al. 2000). b. Results Under the current (post 990) setting there are two possible stable states for the Eastern Mediterranean sea: (i) salinity dominant flux for the Adriatic and thermally dominant flux for the Aegean, and (ii) thermally dominant flux for both the Adriatic and Aegean seas. The Aegean-Ionian flux is always thermally dominated since the corresponding salinity flux is negative [see Eq. (6)]. Thus, the new source of deep water formation in the Aegean sea cannot be attributed to the transition between different states of the thermohaline circulation. On the other hand, changes in the salinity and heat fluxes Note that, and values are calculated based on the upper ocean temperature and salinity. Ideally one would like to consider the total volume temperature and salinity averages. However, this approach is not applicable for the Eastern Mediterranean since the Ionian box is much deeper than the Adriatic and the Aegean boxes and thus contains the more dense water. Using this greater density of the Ionian would lead to negative in Eqs. (), (2), i.e., deep water formation in the Ionian, in contrast with observations. 2

25 (due to changes in the state of the atmosphere) can enhance (or reduce) fluxes between the different basins. Such a change may have occured in the Aegean basin the winter atmospheric temperature was less for some winters after 990 (Sur et al. 993; Theocharis et al. 999; Wu et al. 2000). Such a cooling was associated with the new source of deep water formation in the Aegean sea (Theocharis et al. 999; Wu et al. 2000; Stratford and Haines 2002). In Tables 2-4 we present the temperature gradients, and, and the fluxes (Adriatic-Ionian flux) and (Aegean-Ionian flux). We consider the following cases, (i) the temperatures of the boxes are fixed [the analytical solutions Eqs. (6),(8) are given in Table 2] and (ii) the temperatures of the boxes are variable [the analytically approximated solutions Eqs. (35),(40) are given in Table 3 and the numerical solutions of Eqs. (3)-(8) are given in Table 4]. For each case we display the solution associated with the single dominant source of deep water formation in the Mediterranean (pre 990) and with two dominant sources of deep water formation (post 990). The model s estimate for the Adriatic source of deep water is (Tables 3,4); the deep water formation rate is almost the same before and after the change in the thermohaline circulation of the Mediterranean sea. This value is about 7 of the observed Adriatic rate of. The Aegean source of deep water formation, on the other hand, is increased drastically from before 990 to after 990. The Aegean 22

26 deep water formation rate after 990 is of the observed flux of while the rate before 990 is very small and practically zero. The differences between the observed flux values and the model s prediction are likely in part due to the simplicity of our model and in part due to inaccurate estimation of the model s parameters. Note that the fluxes obtained by assuming constant temperature of the boxes are more realistic (Table 2) 0.34Sv for the Adriatic and 0.66Sv for the Aegean post 990. This is most probably because the temperature gradients are not reduced as in Eqs. (26),(27). We repeated the calculations using the winter climatological values for the temperature and salinity instead of the annual climatological values. This is done since bottom water formation occurs mainly during winter when the sea surface temperature drops and surface water becomes denser and more easily sinks to depths. We find that the fluxes that are based on the winter climatological values are similar to the fluxes that are based on the annual climatological values. This similarity is due to the similarity between the temperature and salinity gradients, and, of winter and annual climatological values. We also studied the effect of seasonal variations in atmospheric temperature by adding a periodic function to the apparent temperatures with an amplitude of (the difference between the summer sea surface temperature and the winter sea surface temperature in the Eastern Mediterranean Sea is ). This seasonal variation led to seasonal changes in the volume fluxes 23 of around

27 the annual average fluxes. However, another study of the Mediterranean Sea suggests that the seasonal changes in the heat and moisture fluxes together with mixing effects do have an important role in the formation of deep water (Tziperman and Speer 994). Our results suggest that the new source of deep water formation in the Aegean is not really new but rather an enhanced existing source where its increased flux is mainly due to cooling of the atmospheric temperature in the vicinity of the Aegean sea. Our model predicts relatively large changes in the thermohaline circulation due to changes in temperature. Such changes, might also weaken or enhance the current deep water formation rate in the Adriatic as occurred in the Aegean. The salinity flux in the Eastern Mediterranean is relatively small [see Eq. (9)]. In the case of the Aegean sea, the salinity flux is negative and thus just one stable (thermally dominant) flux is associated with this basin [see Eq. (6)]. Small perturbations in the salinity flux due to increases in precipitation and river runoff to the Aegean basin might change the salinity flux to be positive. In this scenario, there will be two stable states related to the Aegean basin and a total of four stable states (as illustrated in Figs. 2a, 3a). In the next subsection we discuss the stability of the stable states of the model and how these states change when the apparent temperatures and the salinity fluxes are changed. 24

28 c. stability of the results It is easier to study the stability of the stable modes of the thermohaline circulation when the temperature of the boxes are fixed (Section 2.a.). In that case, it is possible to construct the region of stability for each stable mode; see Figs. 2,3. Our model suggests that the Eastern Mediterranean sea has two stable flux modes (i) a thermally dominant source for both the Adriatic and the Aegean and (ii) a salinity dominant flux for the Adriatic and a thermally dominant flux for the Aegean. A relatively large perturbation would be needed to switch from the thermally-thermally dominant flux solution to the salinity-thermally dominant flux solution. Perturbations of the stable flux states might arise due to changes in precipitation and river runoff (salinity flux) and due to changes in atmospheric temperature. To study the stability of the results due to changes in the salinity flux we adiabatically increase the salinity flux 0D"!4 $ until the thermally dominant flux collapses to the salinity dominant flux. Then we adiabatically decrease the salinity flux until this flux collapses back to the thermally dominant flux. The resulting curve is called the hysteresis curve and is usually used to explain how sudden changes in climate occur. We construct such curves for the Adriatic-Ionian and Aegean-Ionian fluxes using the numerical solution of the system [Eqs. (3)-(8)] and the solution for the case for which the boxes temperatures 25

29 are constant [Eqs. (6),(8)]; see Fig. 5. We display the curves corresponding to the Adriatic box (Fig. 5a), and the curves corresponding to the Aegean box, post (Fig. 5b) and pre (Fig. 5c) 990. The current salinity flux (indicated by the vertical dashed line) for the Adriatic and the Aegean post 990 is very small and a significantly large increase in the salinity flux is needed to switch from the thermally dominant flux to the salinity dominant flux. We thus regard the present state of the Eastern Mediterranean thermohaline circulation as a stable state to perturbation in salinity flux. The situation is different for the Aegean pre 990 hysteresis curve. Here, just a relatively small increase in the salinity flux may switch the thermally dominant state to the salinity dominant state. Thus, if for example, the salinity flux pre 990 increased causing a collapse to the salinity dominant state and just then the apparent temperature decreased adiabatically by, the resulting flux would remain salinity dominant with small (practically zero) flux. Therefore, a change in atmospheric temperature will not always result in enhanced deep water formation rate as occurred in the Eastern Mediterranean sea. If then the salinity flux decreased to be negative, the salinity dominant state would collapse rapidly to be thermally dominant one as in the current thermohaline circulation since for negative salinity flux there is just one thermally dominant state. Then it would be relatively stable to changes in the salinity flux. Since the current salinity flux is very 26

30 close to the transition point of the hysteresis curve, a small change in the salinity flux together with large change ( ) in the atmospheric temperature could, in some cases, cause a drastic change in the deep water formation rate and in other cases would hardly affect the deep water formation. Similar arguments are valid for the Adriatic sea as well, although it is relatively more stable. Changes in the apparent temperature of the different basins may result in increased (or decreased) flux. Since the salinity flux is small, the thermally dominant flux may be approximated as [ ; see Eq. (20)]. For the fixed temperature case, the flux linearly increases with temperature where the increase rate is 7 for the Adriatic sea (Fig. 6a) and 7 for the Aegean sea. For the variable temperature case, the flux is monotonically increasing with increasing apparent temperature where here a change of in the apparent temperature would result in a change of in the Adriatic-Ionian flux and in a change of in the Aegean-Ionian flux this increase is half of the increase predicted by the fixed temperature case. Thus, the strength of the thermohaline circulation of the Eastern Mediterranean is highly dependent on the apparent temperature of the different basins. Here we assume that the Ionian basin is warmer then the Adriatic and the Aegean. If, on the other hand, the Ionian was cooler than the Adriatic and the Aegean, the situation of the thermohaline circulation would have been much different. E.g., the source of 27

31 deep water formation would have been in the Ionian basin instead of the Adriatic or the Aegean [see Eqs. (6),(8)]. We note that the temperature of the Adriatic and Aegean will generally be much more variable than that of the Ionian because of their smaller volumes. It is possible to estimate the relaxation time to the stable state by linearization of the model s nonlinear equations [Eqs. (),(2)] assuming that the temperature of the boxes are constant. We find that the current relaxation time is, where. This relaxation time appears to be realistic since the change in the deep water formation in the Mediterranean sea took only a few years (Roether et al. 996). 4. Summary We model the recent change in the deep water formation of the Eastern Mediterranean using a 3 box model. The boxes represent the Adriatic, Ionian, and Aegean seas. The equations governing the dynamics are nonlinear and may have four, two, or one stable states. We consider two cases: (i) the temperatures of the boxes are fixed and (ii) the temperatures of the boxes are variable. For both cases, the Adriatic flux may be associated with either a thermally dominant state or a salinity dominant state, while the Aegean flux has a single thermally dominant state. Thus, in general, there are two 28

32 stable states for the Eastern Mediterranean, one with thermally dominant fluxes both in the Adriatic and in the Aegean and the other with salinity dominant flux for the Adriatic and thermally dominant flux for the Aegean. We relate the formation of a new Aegean source of deep water formation with a decrease in the atmospheric temperature of the Aegean sea; we conjecture that this state is not really a new source but rather an enhanced existing source. The model s Adriatic deep water formation rate (for the variable box temperature case) is which is quite close to the observed value. The model s Aegean deep water formation rate (for the variable box temperature case) is of the observed flux of. This offset may be attributed to the simplicity of the model and to an inaccurate estimation of the model s parameters. We also discuss the stability of the current thermohaline circulation of the Eastern Mediterranean. We show that in general the flux between the boxes is stable under changes in the salinity flux. However, we argue that under certain conditions small change in the salinity flux may result in a significant change in deep water formation rate. More specifically, when the salinity flux is negative there is just one thermally dominant state associated with the basin while for positive salinity flux there might be either two stable (thermally and salinity dominant) states or one salinity dominant state. The thermally dominant flux is, in general, much larger than the salinity dominant flux. When the temperature gradient between the Aegean (or Adriatic) and the 29

33 Ionian basin is small, a small change in the salinity flux can switch the state to be salinity dominant instead of thermally dominant and vice versa. If then the temperature gradient increases, the flux may remain unaffected if it is salinity dominant and will continue to be very small. On the other hand, the flux can be drastically increased due to the relative cooling of the basin if it is thermally dominant. Changes of -2 in the atmospheric temperatures of the small Aegean (or Adriatic) basin may occur because of the small volume of the basin. In addition, small changes in the salinity flux of the small Aegean (or Adriatic) basin may also occur due to changes in precipitation, evaporation, and river runoff. Thus, although the current thermohaline circulation of the Eastern Mediterranean is stable it might be drastically changed under certain circumstances discussed above where both changes in the salinity and heat fluxes may play an important role in this change. We also show that variations in the apparent temperature of the boxes may result in an enhanced or reduced fluxes. The current model highly simplifies the complex 3D dynamical circulation of the Eastern Mediterranean. This simplicity allows us to capture and easily model the possible cause of the recent change in the Eastern Mediterranean. However, our results are only suggestive of the possibilities, and much more complex 3D models of the Eastern Mediterranean ocean are necessary to fully understand the complex changes in the Eastern Mediterranean thermohaline circulation. 30

34 Acknowledgments YA thanks the Bikura fellowship for financial support. We thank P. Malanotte-Rizzoli for helpful discussions. References Haney, L. R.: 97, Surface boundary condition for ocean circulation models. J. Phys. Oceanogr.,, Klein, B., W. Roether, B. Manca, D. Bregant, V. Beitzel, V. Kovacevic, and A. Luchetta: 999, The large deep water transient in the eastern mediterranean. Deep Sea Res., 46, Lascaratos, A., W. Roether, K. Kittis, and B. Klein: 999, Recent changes in deep ocean formation and spreading in the eastern mediterranean sea. Prog. Oceanogr., 44, Malanotte-Rizzoli, P. and A. Hecht: 988, Large-scale properties of the Eastern Mediterranean: a review. Oceanologica Acta,, Malanotte-Rizzoli, P., B. Manca, M. d Alcala, A. Theocharis, A. Bergamasco, D. Bregant, G. Budillon, G. Civitarese, D. Georgopoulos, A. Michelato, E. Sansone, 3

35 P. Scarazzato, and E. Souvermezoglou: 997, A synthesis of the ionian sea hydrography circulation and water mass pathways during poem-phase i. Prog. Oceanogr., 39, Malanotte-Rizzoli, P., B. Manca, M. d Alcala, A. Theocharis, S. Brenner, G. Budillon, and E. Ozsoy: 999, The eastern mediterranean in the 80s and in the 90s: the big transition in the intermediate and deep circulations. Dyn. Atmos. Oceans, 29, Manabe, S. and R. J. Stouffer: 988, Two stable equilibria of a coupled ocean atmosphere model. J. Climate,, , Century-scale effects of increased atmospheric on the ocean-atmosphere system. Nature, 364, Marullo, S., R. Santoleri, P. Malanotte-Rizzoli, and A. Bergamasco: 999, The sea surface temperature field in the eastern mediterranean from advanced very high resolution radiometer (avhrr) data: Part ii. intermediate variability. J. Mar. Sys., 20, Nakamura, M., P. Stone, and J. Marotzke: 994, Destabilization of the thermohaline circulation by atmospheric eddy transports. J. Climate, 7,

36 Nielsen, J.: 92, Hydrography of the mediterranean and adjacent waters. Report of the Danish Oceanographic Expedition to the Mediterranean and Adjacent Waters, volume, Roether, W., B. Manca, B. Klein, D. Bregant, D. Georgopoulos, V. Beitzel, V. Kovacevic, and A. Luchetta: 996, Recent changes in eastern mediterranean deep waters. Science, 27, Roether, W. and R. Schlitzer: 99, Eastern mediterranean deep water renewal on the basis of chlorofluoromethans and tritium. Dyn. Atmos. Oceans, 5, Samuel, S., K. Haines, S. Josey, and P. Myers: 999, Response of the mediterranean sea thermohaline circulation to observed changes in the winter wind stress field in the period 993. J. Geophys. Res. - Oceans, 04, Schlitzer, R., W. Roether, H. Oster, H. Junghans, M. Hausmann, H. Johannsen, and A. Michelaton: 99, Chlorofluoromethane and oxygen in the eastern mediterranean. Deep Sea Res., 38, Stommel, H.: 96, Thermohaline convection with two stable regimes of flow. Tellus, 3, Stone, P.: 997, Global scale climate processes and climate sensitivity. Environmental 33

37 Dynamics Series V: Hydrometeorology and Climatology, M. Marani and R. Rigon, eds., Istituto Veeto di Scienze, Lettere ed Arti, Venice, Stratford, K. and K. Haines: 2002, Modelling changes in mediterranean thermohaline circulation J. Mar. Sys., 33, Sur, H., E. Özsoy, and U. Ünlüata: 993, Simultaneous deep and intermediate depth convection in the northern levantine sea, winter 992. Oceanologica Acta, 6, Theocharis, A., K. Nittis, H. Kontoyiannis, E. Papageorgiou, and B. E.: 999, Climatic changes in the aegean influence the eastern mediterranean thermohaline circulation ( ). Geophys. Res. Lett., 26, Tziperman, E. and K. Speer: 994, A study of water mass transformation in the mediterranean-sea analysis of climatological data and a simple 3-box model. Dyn. Atmos. Oceans, 2, Welander, P.: 986, Thermohaline effects in the ocean circulation and related simple models. Large-Scale Transport Processes in Oceans and Atmosphere, J. Willebrand and D. Anderson, eds., NATO ASI series, Reidel,

38 Wu, P., K. Haines, and N. Pinardi: 2000, Toward an understanding of deep-water renewal in the eastern mediterranean. J. Phys. Oceanogr., 30, Wust, G.: 96, On the vertical circulation of the Mediterranean Sea. J. Geophys. Res., 66, Zervakis, V., D. Georgopoulos, and P. Drakopoulos: 2000, The role of north aegean in triggering the recent eastern mediterranean climatic changes. J. Geophys. Res., 05,

39 Box a Box c Box b Box Modeling of Eastern Mediterranean Sea H S H Ta H S H Tb H S2 H Tc H S2 BOX a q BOX b q 2 BOX c Adriatic q Ionian q 2 Aegean Figure : Upper panel: The bathymetry map of the Eastern Mediterranean sea. The solid lines indicate the choice of the different boxes: Box a represents the Adriatic sea, Box b represents the Ionian sea, and Box c represents the Aegean sea. Lower panel: Illustration of the 3-box model of the Eastern Mediterranean sea. 36

40 2 (a) q (b) q q q Figure 2: (a) The basins of attraction of the 4 stable states (indicated by black circles). The gray circles indicate the semi-stable states and the white circle indicates the unstable state. The solid lines indicate the minima lines while the dashed lines indicate the maxima lines. This case resembles the case of weak and positive salinity flux forcing for which there are 4 stable states. The volumes of the boxes are:,, and in arbitrary units. (b) Same as (a) but for weak and negative salinity flux forcing for the Aegean ( $ ). Here there are just two stable states (units are non-dimensional). 37

41 (a) 0. φ q q (b) 0. 0 φ q q Figure 3: A pseudo-potential [Eq. (23)] of Fig. 2a,b for the case. The figure illustrates that a small change in salinity flux may result in different stability, e.g., a small perturbation is needed to switch from the minima to other minima but the minima are much more stable under perturbation. Under different choice of parameters the stability might be different. 38

42 (a) (b) 0 exact [Eq. (38)] approx. [Eq. (39)] Temperature T [ o C] Figure 4: (a) A comparison between the exact solution of Eq. (38) (solid black curve) and the approximated solution of Eq. (38) given by Eq. (39) (gray curve). The intersection between the solid curves and the horizontal dashed line are the possible solutions of Eqs. (38), (39). The right branch of the fourth order polynomial of Eq. (38) is approximated by a parabola given by Eq. (39). The arrow indicates the solution that we choose for Eq. (39); this solution is the closest to (and smaller than) the forcing apparent temperature. (b) In some cases the approximation of Eq. (39) doesn t have any real solutions since the polynomial is always larger than zero. In that case we choose T at the minimum of the parabola of Eq. (39) to be the solution this minimum is indicated by the arrow. [Fig. 5 appears on the following page] Figure 5: (a) Hysteresis curves for the Adriatic-Ionian flux q, (b) for the Aegean- Ionian flux q 2 post 990, and (c) for the Aegean-Ionian flux q 2 pre 990. The numerical solution of the model [Eqs. (3)-(8)] is indicated by the black solid line and the analytical solution of the case of constant temperature of the boxes [Eqs. (6),(8)] is indicated by the gray solid line. The dashed vertical lines indicate the current estimated salinity flux h S,2. The insets in Fig. (c) show an enlargement of the transition region. 39

43 (a) Adriatic-Ionian flux var. temp. const. temp. q [Sv] h S = Sv h S [Sv] Aegean-Ionian post 990 flux (b) var. temp. const. temp. q 2 [Sv] h S2 = Sv h S2 [Sv] Aegean-Ionian pre 990 flux q 2 [Sv] (c) h S2 = Sv q 2 [Sv] q 2 [Sv] var. temp. const. temp h S2 [Sv] h S2 [Sv] e-06 h S2 [Sv] 40

44 (a) Flux q [Sv] numerical analytical var. temp. analytical const. temp Apparent temperature T * [ o C] (b) post 990 Flux q 2 [Sv] 0.6 pre numerical analytical var. temp. analytical const. temp Apparent temperature T 2 * [ o C] Figure 6: The fluxes versus the apparent temperature (i) for the numerical solution of Eqs. (3)-(8) (solid line), (ii) for the analytical solution of variable boxes temperature Eq. (40) (long-dashed line), and (iii) for the analytical solution with constant boxes temperature Eq. (6) (dashed line). In (a) we decrease the Adriatic apparent temperature (and thus increase ) and in (b) we decrease the Aegean + apparent temperature (and thus increase ). The vertical dashed lines + indicate the apparent temperatures pre and post

45 42

46 Center for Global Change Science REPORT SERIES Massachusetts Institute of Technology 70. Box Modeling of the Eastern Mediterranean Sea, Y. Ashkenazy & P.H. Stone (5/03) 69. The 4 kyr World: Milankovitch s Other Unsolved Mystery, M. Raymo & K. Nisancioglu (9/02) 68. Reorganization of Miocene Deep Water Circulation in Response to the Shoaling of the Central American Seaway, K.H. Nisancioglu et al. (8/02) 67. Snowpack Model Estimates of the Mass Balance of the Greenland Ice Sheet and its Changes Over the 2st Century, V. Bugnion & P.H. Stone (/02) 66. The Production of Non-Methane Hydrocarbons by Marine Plankton, S. Shaw (9/0) 65. Optimal Determination of Global Tropospheric OH Concentrations Using Multiple Trace Gases, J. Huang (/00) 64. Measurement and Deduction of Emissions of Short-lived Atmospheric Organo-chlorine Compounds, G. Kleiman (9/99) 63. Construction of the Adjoint MIT Ocean GCM and Application to Atlantic Heat Transport Sensitivity, J. Marotzke et al. (5/99) 62. Terrestrial Sources and Sinks of Atmospheric Methyl Bromide: 3D Modeling of Tropospheric Abundance and Sensitivities, C. Jensen (4/99) 6. Inverse Modeling of Seasonal Variations in the North Atlantic Ocean, L. Yu & P. Malanotte-Rizzoli (8/98) 60. Interhemispheric Thermohaline Circulation in a Coupled Box Model, J. Scott, J. Marotzke & P. Stone (7/98) 59. Seasonal Measurements of Nonmethane Hydrocarbons in a Sub-tropical Evergreen Forest in Southern China, J. Graham (7/98) 58. Temporal Changes in Eddy Energy of the Oceans, D. Stammer & C. Wunsch (6/98) 57. On Convective Mixing and the Thermohaline Circulation, J. Marotzke (6/98) 56. The Importance of Open-Boundary Estimation for an Indian Ocean GCM-Data Synthesis, Q. Zhang & J. Marotzke (5/98) 55. Boundary Mixing and Equatorially Asymmetric Thermohaline Circulation, J. Marotzke & B.A. Klinger (4/98) 54. Impact of the Horizontal Wind Profile on the Convective Transport of Chemical Species, C. Wang & R. Prinn, (3/98) 53. Adjusting to Policy Expectations in Climate Change Modeling, S. Shackley et al. (3/98) 52. Open-Ocean Convection: Observations, Theory and Models, J. Marshall & F. Schott (/98) 5. Global Thermohaline Circulation: Parts I and II, X. Wang, P. Stone & J. Marotzke (0/97) 50. Destabilization of the Thermohaline Circulation by Atmospheric Transports: An Analytic Solution, Y. Krasovskiy & P. Stone (7/97) 49. The Global Ocean Circulation Estimated from TOPEX/POSEIDON Altimetry and the MIT GCM, D. Stammer, et al. (7/97) 48. Trapped Methane Volume and Potential Effects on Methane Ebullition in a Northern Peatland, E. Fechner-Levy & H. Hemond (5/97) 47. Seasonal Cycles of Meridional Overturning and Heat Transport of the Indian Ocean, T. Lee & J. Marotzke (3/97) 46. Analysis of the North Atlantic Climatologies Using a Combined OGCM/Adjoint Approach, L. Yu & P. Malanotte-Rizzoli (2/96) 45. Tracer Applications of Anthropogenic Iodine-29 in the North Atlantic Ocean, H.N. Edmonds (/96) 44. Boundary Mixing and the Dynamics of 3-Dimensional Thermohaline Circulations, J. Marotzke (8/96) 43. The Role of Aerosols in the Troposphere: Radiative Forcing, Model Response, and Uncertainty Analysis, W. Pan (5/96) 42. Development of a 3D Chemical Transport Model Based on Observed Winds and Use in Inverse Modeling of CFCl 3 F Sources, N. Mahowald (4/96) 4. The Role of Vegetation in the Dynamics of West African Monsoons, X. Zheng & E. Eltahir (3/96) 40. Inferring Meridional Mass and Heat Transports of the Indian Ocean by Fitting a GCM to Climatological Data, T. Lee & J. Marotzke (2/96) 39. Analysis of Thermohaline Feedbacks, J. Marotzke (2/95) 38. The Iron Hypothesis: Basic Research Meets Environmental Policy, S.W. Chisholm (2/95) 37. Hydrostatic, Quasi-Hydrostatic and Non-Hydrostatic Ocean Modeling, J. Marshall et al. (9/95) 36. A Finite-Volume, Incompressible Navier Stokes Model for Studies of the Ocean on Parallel Computers, J. Marshall et al. (9/95) Copies are available by request from the Center office. See inside front cover for contact numbers.