The winter circulation of the Adriatic Sea

Deep-Sea Research, 1976, Vol. 23,

pp. 353

to 370. Pergamon Press. Printed in Great Britain.

The winter circulation of the Adriatic Sea MYRL C. HENDERSHOTT* and PAOLARIzzor.lt (Received 12 October 1973; in revised form 4 September

1975; accepted 10 September

1975)

Abstract-The winter circulation of the northern Adriatic Sea is examined in the light of 1965-1966 Bannock data. A vertically integrated numerical model of the flow is used to study the relative importance of evaporation, wind stress, coastal river runoff, and exchange with the southern Adriatic Sea for the wintertime fields of vertically integrated mass transport and density. A strong and sudden outbreak of cold, dry central Asian air over the Adriatic Sea during January, 1966, resulted in such rapid evaporation rates that water columns evidently overturned continuously. Changes in the density and temperature in the interior of the basin were dominated by surface heat fluxes. Initially sea temperatures were high and evaporation was rapid but as it continued, sea temperatures fell and the rate of evaporation decreased. Model calculations suggest that the strong horizontal density gradient set up by evaporation and coastal inflow of fresh water is an important source of the large scale wintertime circulation. This circulation, counterclockwise in the northern Adriatic Sea with a net transport of about 0.4 x 10’ m3 s-r, is closed upon itself in most of the model solutions because of the relief of the ocean bottom. Mass exchange with the southern Adriatic Sea appears to be of secondary importance for this circulation.

1.

WINTER

HYDROGRAPHY

NORTHERN

ADRIATIC

OF

THE

SEA

Sea is a long (- 800 km) and narrow (200 km) quasi-rectangular basin bounded by Italy to the west and north and by Jugoslavia to the east. The Italian coast is regular, offshore isobaths parallel it smoothly, and depth increases uniformly seaward. The Jugoslav coast is composed of many small islands and headlands rising abruptly from deep coastal water (Fig. 1). Mid-basin depths increase from the order of 30 m in the northern Gulf of Venice to a maximum of about 260 m in the Jabuka Pit; depths across the Gargano-Mjlet transect are of order 200 m or less. The hydrography of the Adriatic Sea has been discussed by ZORE-ARMANDA (1963) on the basis of data gathered during all seasons from 1911 to 1913 and during the winter of 1914 by the CicIope and the Najade, as well as on the basis of data gathered between 1956 and 1958 by various Jugoslav cruises (see ZORE-ARMANDA,1963, for references). During the winter of 1962, the Atlantis made a THE ADRIATIC

of stations in the southern and central Adriatic Sea. The Bunnock, under TROTTI(1970), completed two cruises in the northern Adriatic Sea during autumn of 1965 and winter of 1966, each time occupying more than 70 stations at roughly equal intervals along nine transects across the northern Adriatic Sea (Fig. 1). Our study is based almost entirely on these two cruises. During both autumn and winter, the coldest and freshest water appears in the northwest corner of the basin corresponding to runoff from the PO River delta (Figs. 2 and 3). This is the greatest single source of runoff, but other rivers and drainage basins also contribute significantly to the heat and salt budgets (Table 2). The river water is cold but fresh, and the runoff produces a rim of light water extending from the Gulf of Venice southward along the Italian coast (Fig. 4). The transition from coastal to mid-basin values of number

*Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California 92093, U.S.A. fLaboratorio per lo Studio della Dinamica delle Grandi Masse, Venice, Italy.

353

354 12~

MYRL C. HENDEI~HOTT and PAOLA RIZZOLI "14

12"

"16

J ,RtESTE I

14 °

16°

I

RAVENNA ..

,,,9,~.~_~_.~

'

"-3

~'~'f, . . ~ : : -~- \~ ' ~ l "~\', ,--"-..,.~',+'~.: ~ .. / "." . ' # ,~

l

L ,~

,,~ " . ' . . -.. ~ . . . .

..~o

AMENDOLA@I ~"P

I

~A~ANOi~

[

~

•

"~.h~ ~, .#",,~ y

a \",C_

®

• • \ . .

.-'--

I

I

Fig. 1. Place names, station locations (solid dots, irregularly numbered and distributed over basin along transects labeled A to D, standard locations (small squares) at which wind stress and evaporation are least square estimated (Section 3), and bathymetry (dotted lines labeled in m). In the text, stations are referenced by section and number, i.e. F40. Cross-basin variations are called east-west and axial variations are called north-south even though the axis of the Adriatic Sea is inclined about 30 ° to the meridians.

T and S occurs over a region a few tens of kilometers wide; the net of stations is too coarse to describe the details of the associated mixing. The stations are not generally close enough to the Jugoslav coast to reveal similar processes there, if they occur, although some evidence of runoff is visible on the Istrian side of section B (Fig. 5). Winter surface temperatures are lower than those in autumn by 2 to 3°C over the southern part of the region and by more than 5°C in the Gulf of Venice; surface (~t in winter is everywhere greater than in autumn (Fig. 4). The winter field of ~t is dominated by a mid-basin maximum stretching in attenuated form southward along the western side of the basin and bounded to the north and west by the rim of diluted runoff water. Vertical distributions may be summarized as follows: in the north (section A to D), T, S, and oxygen were notably uniform in the vertical during both autumn and winter except near the Italian or Istrian coasts (Fig. 5). Even at more southerly stations, where the depth often exceeds 200 m,

,

(a) 12"

45.

14°

16"

":

•"

."

\~.

.".

•

•

(hi Fig. 2 Contours of surface temperature (in °C) with selected station values for autumn (upper panel) and winter (lower panel). Autumn observations made 23 November to 10 December, 1965. Winter observations made 8 February to 19 February, 1966.

vertical mixing was virtually complete by late winter, zX% over the column being typically less than 0.2 and often half an order of magnitude smaller. These stations had shown noticeable stratification in autumn, A~, over the column being typically of order 0.5 (compare Figs. 5 and 6). Near the Italian (and to a much lesser extent the Istrian) coast, river outflow depressed surface

The winter circulation of the Adriatic Sea 12"

.@:

12"

16"

14"

355 14i

16"

, /;~/N

.

.

.

.

• .i....i ,+

.....

+,

,

43 °

(a) 12"

14 °

(a) 16"

12"

14 •

16 °

)

45'

i-

43'

(h) Fig. 3.

Same as Fig. 2 but for surface salinity (in ~o). (Upper panel, autumn; lower, winter.)

T and S and, for example, maintained A% at 2.0 or 3.0 over 50-m depth in the Po plume. Excluding these regions, as well as the deepest water in the Jabuka Pit, wintertime AO"t top to bottom are smaller than 0"2. 2. W I N T E R METEOROLOGY The striking increase in density of northern Adriatic water between autumn 1965 and winter 1966 suggests intense evaporation• We have

.

..

(b) Fig. 4.

Same as Fig. 3 but for surface density (in ¢~tunits).

examined meteorological data with the ultimate aim of quantitatively relating the hydrographic meteorological fields. Jerome Namias first brought to our attention a large anomalous deviation in the January 1966 monthly mean surface pressure field from the 20-year monthly mean for the region surrounding the northern Adriatic Sea. During November and December 1965 and February 1966 the flow of air over the Adriatic Sea was dominated by Atlantic

356

M Y R L C . HENDERSHOTT a n d PAOLA R I Z Z O L I

marine air coming almost directly from the west, while during January 1966 the mean flow was from the northeast. Surface pressure for January 3, 1966, showed an almost normal flow of Atlantic marine air over Italy, but 24 h later, a high pressure ridge extended from Gibraltar to the British Isles and completely disrupted the flow of Atlantic marine air into western Europe. The surface pressure map (Fig. 6) for January 6 shows the anomalous pattern in full development. Although the subsequent pressure field was by no means steady, blockage of the normal flow of Atlantic marine air into western Europe persisted for 15 days. Relative humidity at Venice, Trieste (Annali Idrologiei, 1965, 1966), and Pula (supplied by the Federal Hydrometeorological Institute of Jugoslavia) shows that around the northern Adriatic Sea, this period of blocking was characterized by exceptionally dry air, the dryest between 5 and 7 January. Thereafter, the relative humidity climbed slowly and irregularly towards its normal range (Fig. 7).

3. E S T I M A T I O N OF AIR-SEA FLUXES To estimate the effect of the atmosphere on the sea, we need the wind stress • (dyn cm-=), the areal rate of evaporation E ( g c m -z s-l), and the conductive heat flux Qc (cal cm -2 s-1) from ocean to atmosphere or vice versa. However, we had only coastal surface meteorological observations beginning 1 January, 1966, and thus had to extrapolate over the sea. To estimate sea surface wind stress, daily mean surface pressures at Brindisi, Bad, Amendola, Pescara, Ancora, Marina di Ravenna, Venice, Trieste, Pula, Zara, Split, and Dubrovnik were least square (LSQ) fitted to a quadratic polynomial in two orthogonal horizontal coordinates with each station weighted proportionally to its inverse square distance from the point at which an estimate was to be obtained. The pressure gradient and corresponding geostrophic wind were obtained by differentiating the LSQ polynomial. The geostrophic wind was attenuated by 50% to estimate anemometer height winds and the direction of the attenuated wind was adjusted as

STATION

STATION .,

,.

•

. , . .

"

5o

28.3, , , , / , ,

73 t

74 )

° r : / Y I" ~" ~'~ :

:

k7

/ r~ "

= ~-

\ )oo

"

~ "

• "

. ' : 28,8

68 69 70 71 72 i I i ~ Or-~) • ,~29,2 ,-

29.o~4

29,1>'0

•

"/'3 I

75 i

:

~29.0

~,

" {29,11)~

~ 2 8 , , \ "f :

•

:

:

2 9 2 " ~ 2O0 200

74 i

STATION

72 I

),2/

•

/,

STATION 68 69 70 71 r-- i i I

t

292

29,0"~....~ 25

Fig. 5. Variation of density (in c) units) during autumn (left panels) and winter (right panels) across sections B (upper panels) and I (lower panels).

The winter circulation of the Adriatic Sea

Fig. 6.

A t m o s p h e r i c pressure ( m b a r ) r e d u c e d

to sea level for the N o r t h J a n u a r y 6, 1966.

80'

_

40

~I00 -

~

E

"=r

Venice

t

i

i

,

~ov '

t

1

I

l

t

I

~

t

I

i

,

1

~

I

I

I

I

t

~EcJ

I

IjA. '

t

'I~Ee

a¢ 6C

. ~ 4C

"61oc 6C 4c z0

Pula

Fig. 7. Variation o f relative h u m i d i t y ( % ) at three n o r t h e r n Adriatic coastal cities f r o m N o v e m b e r 1965 to F e b r u a r y 1966.

in BLACKADAR (1962) to obtain a surface wind speed, IV, and direction. The daily mean wind stress in the axial or cross-basin direction was then computed from the bulk formula

= o.,r I w lw.i cross

l cross

(3.1)

357

Atlantic a n d E u r o p e at 00:00 G M T

at seven standard locations (Fig. 1). A 5-day running mean of stress components was averaged over the seven standard locations (Fig. 8). This procedure was used successfully by ROBINSON, TOMASIN and ARTEGIANI (1972) to forecast storm surges in the northern Adriatic Sea. They found it superior to LSQ interpolation of coastal anemometer records and we adopted it for the present, less demanding task. The most striking features of coastal anemometer records (three or four peaks 1 or 2 days long and 15-20 knots* in amplitude spaced irregularly through January, followed by a significantly quieter February) were generally reproduced in the attenuated geostrophic wind records at nearby standard locations with errors of a few knots. To estimate E and Qc, we used JACOBS' (1951) bulk formulae E -- 0-249 (ew - - ea) IV (3.2) Qc = 0"01 (Ts~a -- Tdry ) E L / ( e w - - ea), *1 k n o t = 0.51 m s -1.

358

MYra. C. I-l~NoEasnorrand PAOLARIZZOLI

A

E o

"o

LU

l0

20

3

iC~ Z ~

a

~t

Fig. 8. Five-day running mean of axial (solid line) and cross-basin (dashed line) wind stresses (dyn cm-2) averaged over the seven standard locations of Fig. 1. where L is the latent heat of evaporation of seawater (cal g-0, W is the wind speed (knots). T ~ is the water temperature (°F), Tdry is the dry bulb air temperature (°F), and ew and ea are the pressures (inches of mercury) of saturated aqueous vapor in the atmosphere for given wet and dry bulb temperatures, Tw,t and Tdry. MANABE (1957) has shown that Jacobs' formulae are capable of better than order-of-magnitude accuracy when good estimates of the independent variables are available. Our estimation of these at sea from coastal surface meteorological data was necessarily ad hoc. We made LSQ fits of a quadratic polynomial in two orthogonal space directions to daily means of Tdry and of ea(Tdry, Twet) at coastal cities from records of wet and dry bulb temperatures there. Because Q¢ is small relative to LE, the extrapolation of ea is the most crucial one; the qualitative similarity of ea from both sides of the basin suggests that it is not in order of magnitude error. Initially, we intended to fix T~,~ at its autumn value or at a mean between winter and autumn values, but we soon found that the effect of sea surface temperature changes upon the rate of evaporation is so great that this is not satisfactory when computing E. Instead we must predict Ts~~ on the basis of past evaporation and sensible heat flux in order to estimate the current evaporation rate E.

In principle we must construct a model whose heat budget is sufficiently realistic that, starting from a given sea surface temperature and accepting estimates of W, ca, and Tdry, the model can predict simultaneously T,~ and E. We constructed such a model, discussed below (Section 4) in detail, but it combines the budget of heat and salt into a single mass budget and so is not directly suitable for the computation of T ~ . However, in the case of water vapor and heat fluxes having time but no space variation, model solutions (Section 5) show that in the interior the density of water columns is determined well from only the history of evaporation at their surface. Thus, had the model been extended to include a separate heat budget, the temperature T,,,~ of a water column would be largely determined by the history of the heat flux at its surface, i.e. D ~Ts,~/~t = -- ( L E + Qc)/OoCp,

(3.3)

where D is the depth of the column, L is the latent heat of evaporation of seawater, P0 the mean density of seawater, and cr the specific heat of seawater at constant pressure. Evaporation of seawater leaves behind denser water so that an additional term proportional to E and to the salinity must be included in a similar expression for the approximate rate of change of density of a mid-basin fluid column. PmLLIPS (1966) showed that the equivalent mass flux across the sea surface due to cooling and evaporative salinization of seawater is E ~ ~ (LE + Qc)~/c r, where (~7 is the decimal salinity (mass salt/mass brine)and zv is the volumetric coefficient of thermal expansion p-l~p-I/t~T. The approximate expression governing the history of the density of a mid-basin fluid column is therefore

D~t ~- 10 ~ [E ,Sf + ( L E -~ Qc) ~v/cp], (3.4)

where we have introduced 9 = O0 +

103 ~.

(3.5)

359

The winter circulation of the Adriatic Sea

In the shallow northern Adriatic Sea, ~ is virtually the usual *tWe used (3.3) in conjunction with LSQ estimates of ea, W, and Tory at sea to predict T,o, and E simultaneously at seven mid-basin standard locations whose depths range from 33 to 200 m (Fig. 1). The total equivalent mass flux E ~f// + ( L E + Q~)oc,,/cp was then computed at each location (Fig. 9). The evolution of ocean temperature and of density at two of these locations (depths 33 and 200 m) according to (3.3) and (3.4) is shown in Fig. 10. The contrast between the evolution of the density field *(T0), when ocean temperature is held constant at its autumn value, and the evolution , ( T ~ ) occurring when ocean temperature T ~ is predicted by (3.3), is noteworthy. Evaporation is strongly self limiting; the initial evaporative episode rapidly cools the water to where ew -- ea becomes small and evaporation virtually ceases. These predictions cannot be perfect, in part because the coastal meteorological data did not include November and December 1965, and in part because the initial state was not entirely vertically homogeneous. In view of the strong outbreak of continental air that began 4 January, 1966, we believe we have introduced no major

//\ o

JAN 3o FEB TIME (doys)

n,.

6o

Fig. lO. Ocean temperature (left scale, °C) predicted by (3.3) at locations 33 m deep (solid line) and 200 m deep (dashed line) plus the corresponding increments of (h (right scale) predicted by (3.4) using either the prediction of (3.3) or the autumn surface temperature To. Comparison of the two density curves at one location shows the inhibiting effect of evaporative cooling of the sea on further evaporation.

error by ignoring evaporative effects before 1 January, 1966. 4.

A MODEL OF THE WINTER CIRCULATION

We have studied the relative importance of some of the physical processes (such as river inflow, evaporation, horizontal advection and diffusion, exchange with the southern Adriatic Sea) that determine the winter fields of density and 2O0 mass transport with the aid of a numerical model. This section formulates the model. The necessary assumptions are discussed in Section 6. Our primary idealization, suggested by the winter data of 1966, is that vertical mixing of heat ~ 17'0 and salt is complete over the entire water column and that this mixing occurs so rapidly relative to ~ 8o horizontal diffusion and advection that the vertical distribution of these quantities, and hence of the density, is always virtually uniform. We therefore integrate the mass conservation equation vertically to obtain an equation in uJ o JAN 30 FEB 6o which the local rate of change of the density of a TIME (doys) homogeneous column depends upon horizontal advection and diffusion and upon evaporative Fig. 9. Daily values of total equivalent mass flux E ~ (LE + Q~)cL,~/Cp ( g c m 2 yr-1) averaged over the seven fluxes at the sea surface. We also vertically standard locations of Fig. 1. integrate approximate horizontal equations of

360

MYRLC. HENDESSHOTTand PAOLARIZZOLI

momentum conservation as in KOZLOV (1969) to obtain an equation in the mass transport stream function in which the (vertically homogeneous) density and the depth appear both in non-constant coefficients and in driving terms. In deriving this equation, we allow for bottom drag stresses in Ekman layer approximation. KozLov (1969) integrates the full equation of horizontal momentum conservation for a rotating, stratified, hydrostatic, Boussinesq fluid to obtain a single equation for the mass transport stream function +. Bottom stresses are incorporated by the Ekman approximation; Kozlov also includes horizontal advection and horizontal eddy diffusion in the dimensionless form of the transport equation [his equation (2)]. The sizes of the nonlinear advective terms, of the lateral diffusion terms, and of the bottom stress terms relative to terms of order one are measured by the parameters

Table 1. Scaling parameters and dimensionless numbers. _$ymbpJ

quantity Scaled

Numer,lca,1, ,Va!ue

X

Horizontal length

pO

Mean depth, vertlcal distance

]00 km lO0 m

fo

Mean Corlolls parameter

lO"4 s"l

~'10 ) ~o

Observedhorizontal density variation

T

Wind stress

1 dy 04"z

U

Horizontal speed given by thermal wind 10-3 g(~/p)Do/(fo X}

5 on s "1.

T

Ttme scale given by X/U

2xlO6 s

Av

Vertical coefficient of eddy viscosity

102 cm2 S"1

KV

Vertical coefficient of eddy dif£ualvity

102 ~t2 s"l

KH

Horizontal coefficient of eddy dlffuslvlty

lO6 cm2 s"l

Ds

Depth of thermal penetration given by

140 m

0.5 9m cm"3

(Kv XIU)~Ig

LI/2

1/~/~-ttn!es the ratio of Ek~mn layer e-folding

depth to n~san depth, given

0.1

by (Av/foOe2}I/2

r

Dimensionless horizontal diffuslvity given by KHDs2/KvX2

O.OZ

¢~

Scale factor for dimensionless wind stress

0.2

¢~*Oo/oo AvU

U

~H --L~o, eL = AL/XZf2o,

e v 1t2 =

(AJ2Do~£2o) 1J2, *Also the value scaling the barotropic flow that emerges from the numerical computations.

where A, and A c are vertical and horizontal eddy viscosities, U is a scale current speed, X and Do are horizontal and vertical length scales, and f20 is the magnitude of the Coriolis parameter. For values appropriate to the northern Adriatic Sea (Table 1), these parameters are approximately

lateral diffusion, and, momentarily, time dependence and so derive our stream function equation starting from

- - i v = -- Px/Po + A,U~z eft ~ 5 X 10-z,

eL

~

10--4'

e V 1/2 ~

fu

Had Kozlov allowed for time dependence in his calculations, he would have had to add a term in 8 V " d~/Ot to his equation (2), and it would have been scaled by er

=

(4.1)

0"07.

1/(~2oT),

where T is the time scale of the motion. For e r -----0.1 ev 1/$, T - 20 days. If we restrict ourselves to motions having this or a larger time scale for order-of-magnitude variation of the transport stream function (see Section 6), then ev 1/2 > e r by one order of magnitude while ev ~/2 >> et. and

=

- ey/po + A vv=,

in which z is the vertical coordinate, positive upwards, and x, y are coordinates transverse and axial to the computational basin with corresponding velocity components u, v; P is the fluid pressure and P0 the mean density. Here, as subsequently, differentiation with respect to x, y, z, t is denoted by subscripting. At the sea surface (z ----- 0) the wind stress zx, Ty (whose superscripts x, y denote direction) forces surface velocity gradients uz : Tx/p0Av, vz = TY/poAv at z = 0,

(4.2)

eV 1"2 >~ ff-'H"

We therefore neglect momentum advection,

while at the sea floor [z = -- D(x, y)], a bottom

361

The winter circulation of the Adriatic Sea

___.

Ekman layer brings to zero the geostrophic flow u8, v8 prevailing above that Ekman layer. That geostrophic flow satisfies - f v* = - P,,p,,

f us = - P,,P,,

and we subsequently denote vertical integration by the overbar. Solution of each of (4.7) for A, and x,, followed by elimination of R by cross-differentiation yields

(4.3)

while the bottom Ekman layer stress becomes l/2 1

~A,uz=&

-

V&P

p. O*(dD,D,)

-

g,(2po)J(D2,4, P) (4.9)

(4.4)

P Avvz = (v, + U,)P

@“2U7 KW4

- Wpo)

at z = - D(x, y). We explicitly let the density p(x, y) be independent of z and so, by the hydrostatic equation, 0 = - P, - gp,

(4.5)

we express the pressure field in terms of a surface pressure X(X, y) and a density depth-dependent part P = n - gpz. (4.6) Now (4.1) can be integrated vertically from the sea floor z = - D(x, y) to the sea surface z = 0 and the surface and bottom stresses expressed in terms of (4.2) and (4.4). The geostrophic flow is then expressed in terms of the pressure (4.6) by (4.3) to obtain -S

Jrx = - DG/P,

+ C4,/2fY’2~/~o(-

- g D’P,/~ ~0 + t”l~o

71, + g DP,

+ 5

+ g DP,) (4.7)

- f 4~, = - Drr,l~o - g D2~,./2~o + NP~ + WV91’2~/~o(nx - g DP, + 5 - g DP,), where the transport stream function 4 is defined by 0

fix

s

udz = - &,, V =

-D

J(D/D,, P)

+ g/p,

(

$

)

[-

VWWJVP

s

vdz = $X,

(4.8)

+

J(DINh, ~11,

where D, = D - (A,/2f)l12, D, = D2 -(A,/2f)/D,, and J(a, b) = - a,,b, + a,b,,. We now suppose (A,/2fDo2)1’2 < 1, whence D, and D1 are replaced by D and (4.9) becomes

J(+,f/D)

+ ($)“2Y7*(

i2 v +) = do curl (/to)

V2p.

(4.10)

The equation of mass conservation is Pf + UPX + VPy+ WPZ= KP,Z + K,,(P,,

i- p,),

(4.11) where K, and KH are vertical and horizontal eddy coefficients of diffusion. A scale depth D, of vertical change of the density profile with depth is defined by supposing horizontal advection and vertical diffusion to be of the same order,

0

-D

- D2/(D,D,)1V~~

-u

x

K I=---

D?’

362

MYa,L C. H~rot~aSnoTrand PAOLARIZZOLI

where U and X are horizontal velocity and length scales. We shall require

wind relationship U = gDo × lO-aA~r/(foXpo)

D, >> Do,

where Do is the mean depth of the basin, as an expression of our assumption that vertical mixing of heat or salt is rapid relative to horizontal transfer processes. In our solution, the flow tends to be along lines of constant depth; the vertical velocity therefore has the size ev ~/~ U Do/X set by Ekman pumping and the term wp~ appearing in (4.11) is of order evat2Do/D, ,~ 1 relative to up~ + vpy. We therefore neglect this term and integrate (4.11) from z = -- D(x, y) to z = 0, supposing no vertical diffusive flux through the bottom, to obtain Dpt + Ugx 4:- fPy = [E . _ ~ + (Qc q- LE)o~/c~,] q- D K u V n u p ,

(4.15)

The wind stress is scaled by z' (z% rY) = r'(T% Ty),

D -- D O5 and f = fo 9.

+ ~ curl (T/~) -- 2

V~S'

(4.20)

while (4.13) becomes

5St + J(~, S) --= LUDoAa j [E ~ +

(Qc +

LE)o~,,Icp]

+ 8FVtj2S.

(4.21)

In the variation of 9/8, the depth variation dominates because the basin is small so that 9 = 1 was always assumed, i.e. the beta effect was neglected. Two dimensionless numbers appear:

(4.16) = A,./(foDo2),

F ~- KnDs~/K,X 2 ~- KI_I/(UX).

(4.22)

and it is convenient to define .= "r ' Do/(poAvU),

(4.19)

Although negligible in the stream function equation (4.10), time dependence is important in the density equation (4.13) if the time scale T is the advective one X / U or smaller; we scale time in (4.13) accordingly. With this nondimensionalization, (4.10) becomes

(4.14)

so that ~ris nearly the usual %. N o w , is scaled by its observed spatial variation A~ ~ 0.5 to obtain the dimensionless density S given by ---- S A~.

as about 5 cm s -1 appears. Do and X are vertical and horizontal scales of depth and length, of order 100 m and 100 kin, and f0 is the scale of the Coriolis parameter, of order 10-4 s-L The dimensionless depth 8 and dimensionless Coriolis parameter 9 are defined by

(4.13)

in which the term in brackets is the equivalent mass flux of Section 3. For computational convenience, we cast equations (4.10) and (4.13) into dimensionless form; all of the scaling parameters are summarized in Table 1. First introduce P : 90 + 10-s ~r,

(4.18)

(4.12)

(4.17)

in which the velocity scale U, given by the thermal

They measure the Ekman bottom drag and the horizontal diffusion of density and are both of order 10-3 (Table 1).

The winter circulation of the Adriatic Sea The value of Kv = l0 s cm 2 s -1 of vertical eddy diffusivity used in most of the computations accords with both of our simultaneous assumptions that • ~ 1 (there are well-defined Ekman layers) while D, = (KvX/U) xjz >> Do (vertical mixing of heat and salt is almost complete), and it falls in the middle of the range of values quoted by, for example, HUANG(1969) for Lake Michigan. The value Kn = 106 cm 2 s-~ of lateral eddy diffusivity used in most of the computations emerges from application of TAYLOR'S (1953) discussion of the dispersion of solute in pipe shear flow to the estimated vertical shear (4.18) implied by the thermal wind equation and to the observed horizontal variation of density. STOMM~L and LEETI~,A (1973) previously employed Taylor's approximation in their study of wintertime, weakly (vertically) stratified flow over continental shelves. They point out that, in this approximation, the effective lateral diffusivity is a function both of Ekman transports and of the vertical thermal wind shear. We could accordingly let Kn vary as the solutions for mass transport and density evolve but, for simplicity, we have only used these considerations to arrive at an order of magnitude estimate of K n. The coupled equations (4.20) and (4.21) specify the transport stream function and the density. Once they have been solved, the surface pressure n can be recovered via (4.7) if required. If along coasts, we specify the mass flux and the density of the river water, we must require our model to describe explicitly the subsequent mixing of river water and seawater. But the assumption of complete vertical mixing (demonstrably not valid at the mouths of major rivers) and the need for resolution at horizontal scales sufficiently small to describe the boundary mixing make the present model ill-suited to this task, even though it may describe the larger scale behavior with reasonable accuracy. We therefore specify the river influx of fresh water as a diffusive flux of salt across the coasts. This enables us to incorporate the effect of river inflow on the density without an unrealistically large coefficient of horizontal diffusion. If V is the rate of river inflow (g cm -~ s-x) and ~ is the decimal salinity of

363

the seawater with which it mixes, then V y is the equivalent flux of salt out of the sea. This salt flux is modeled diffusively so that

-- D K n VP" h = V y p

(4.23)

specifies the coastal normal gradient of density. In dimensionless variables

_rVnS.h=

[

Kn

×

Xp0 I V (j¢,(4.24) 10-3 DoA~r

where ~ is outward normal to the coastline. In our calculations it is this change of density of near coastal water that is of primary importance for the flow; the actual augmentation by river input of the amount of water circulating is entirely negligible. The coastal boundary conditions are thus that ~ is constant and S satisfies (4.24), with V as tabulated in Table 2. Across the open mouth we must specifiy d~ and either S or V S " h. Several computations with differing boundary conditions there have been made (Section 5). Equations (4.20) and (4.21) with the boundary conditions discussed above constitute our model. In general we must solve them numerically, especially when 5(x, y) is based upon observed

Table 2. Monthly mean estimates of the fresh water runoff into the Adriatic Sea from November 1965 to February 1966 (GALAVERNI, 1972). (All transports in m e s-1.) River or Oralnege Basin (DB) Jugoslavla south of Istr|a Istria Isonzo River D8 TagIIamento River DB Piave River DB Brenta River DB Adtge River Llenure River Po River Reno River Lamore R|ver to Sarlo Narecch1~ River to Tr~to River

November I%5 1368. 254 354 86 ]o8 183 34 145 75 9B 146 90 130ff 6g 87 gO

December1965 January I§66 2576 196 163 62 44 Ili 5 84 G4 42 125 29 1150 67 64 85

1754 49 4Z 46 8 7g - +

70 45 35 106 2g 865 46 48 166

February1966 1891 13B IbO 56 4R l~Z 44 90 77 55 11g 35 1530 70 64 78

364

MvrtL C. HENDEIL~HOTTand PAOLARIZZOLI

bottom relief. For convenience, we work in a rectangular computational basin. The bottom relief is derived from the actual relief of the Adriatic (supplied for us in the 5-km means by G. Poretti) by left justifying each cross-basin traverse so that the western (Italian) coastline is made straight. This procedure conveniently produces a relief that preserves the tendency of isobaths near the Italian coast to run parallel to the coast and changes the interior relief only slightly (Fig. 11): For actual computations, this relief was smoothed by repeated application of a nearest neighbor mean a n d the northernmost boundary was taken at approximately the 30-m isobath. The computation basin is 145 by 395 km, corresponding to a 20 x 80 finite difference mesh with mesh spacing Ax of 5 km. The numerical treatment was straightforward. At any instant, the density was stepped forward in time using (4.21) and a new stream function was then obtained by sequential over-relaxation of (4.20). All nonlinear terms were approximated by the ARAKAWA (1966) second order scheme with slight modifications at the boundaries. The time step At ---- 6 X 104 s was determined empirically and was in general accord with the (comparable) results obtained by requiring

Fig. 11. Computational bottom relief (isobaths in m at irregular intervals). For clarity, basin width is exaggerated by 3/2 in this figure and in Figs. 13 and 14.

UAt
I" At/AX 2 < 1/4. The actual time-step used was At :- 6 x lift s. 5.

MODEL

SOLUTIONS

AND

OBSERVATIONS

The model equations (4.20) and (4.21) have a simple solution in the case that ~ ---- 1" -----r ---- 0 and when Q ~ (IOaX/UDoAo) [E y + (LE + Qc)~t/Cp] is a function of time only. In that case, (4.20) (with 9 = 1) becomes J(6 -~, t~) = 0.5 J(~, S), while (4.21) becomes

6S, + J(t~, S) : Q(t). A solution of these equations is t

S=5-1

I

Q(t')dt',

~ = ~(5).

(5.1)

0

The density is altered only by evaporation; advection vanishes because fluid columns flow parallel to isobaths that are also isopycnals. Even if horizontal diffusion and bottom friction are not zero, we expect a similar dependence of density on depth whenever Q(t) increases over a time significantly shorter than advective or diffusive time scales, but streamlines need not follow isobaths. A plot (Fig. 12) of ~rI versus 8 -1 for winter stations without obvious river-induced stratification falls rather well on a straight line except for the stations of section A, which are evidently diluted with runoff water. The slope of the straight line leads to an average for Q of about 25 g c m -~yr -1 [about half of the mean (46 g cm -~ yr -1) obtained by averaging the results of Fig. 9] when allowance for the inhomogeneity of the initial state is made, but the value is uncertain because of the autumn stratification. The result suggests that our meteorological

The winter circulation of the Adriatic Sea I

I i

B

29.4~

r J

o-t

I 29,2

29.0

~ .L

0 1 2 3 INVERSE DEPTH (lOOm/depth) Fig. 12. nt plotted against inverse depth (100 m/depth) for winter interior stations. The total range of nt values at each station is shown by the vertical bars.

estimate of Q is too large, although not by an order of magnitude. Although (5.1) thus provides a reasonably accurate description of the winter density field away from coasts, the associated flow bears little resemblance to that found by numerical solution of the model equations (4.20) and (4.21). For that solution, we averaged Q and ~ over the seven standard locations to obtain Q(t) (Fig. 9) and ~'(t) (Fig. 8), and then solved with no space dependence or with at most idealized space dependence. For the coastal boundary condition on ~ S • h, GALAVERNI'S(1972) values (Table 2) of river flux V for January 1966 were incorporated into (4.24). Her tabulation is partly as runoff between major rivers plus the fluxes of those rivers themselves. All of the latter were distributed over artificially enlarged river mouths to avoid sharp peaks in V S • h while still conserving mass. Thus, for example, the total etttux of the Po river, which in reality is distributed over perhaps 50 to 75 km of delta coastline, was spread over

365

150 km. This reduces coastal gradients of S and may cause the model to underestimate coastal advection. There is no objective way to specify the open boundary conditions on d/and S. We experimented with them and sought features of the interior flow not strongly dependent upon them. Most experiments were run with the (dimensionless) condition ---- -- 0.5 sin(rex), which forces transport of 0.5 x l0 s m 3 s-1 northward across the eastern open boundary and southward along the western open boundary. Doubling this value or setting it equal to zero had little effect on the interior flow. The density across the open boundary was variously held constant, made to have no normal gradient, or allowed to vary as St = 8 -1 Q(t) in response to local evaporation only. All experiments were run forward for 70 steps (49 days) or until instability terminated them. When this occurred, it was usually late in the computation, when density gradients near the open boundary or near the Po River delta locally became very large. In the solutions of Table 3 these computational difficulties occurred only after the strongest evaporation was finished and the major features of density and transport fields were already well established. Table 3 summarizes the numerical experiments carried out over the 'actual' relief. To facilitate intercomparison, Table 3 lists maximum values of density and of gyral transport (most negative value of the stream function at the gyre center) for various time steps. Cases el through e3 summarize the sensitivity of the solutions to variations of the parameters e and r. The solutions were not qualitatively altered by these variations in e. Case e, for which streamlines and isopycnals are shown at 38.10 days in Fig. 13, is typical of all other cases in the formation of a pool of dense water in the shallow northern region of the basin with a counterclockwise gyre partly or entirely closed at its southern end just north of the Jabuka Pit. Initially, evaporation increases rapidly

366

MYRL C. HENDERSHOTT a n d PAOLA RIZZOLI

Table 3. Summary of numerical experiments. Experiment

Evaporation

Wind stress

Open mouth condition on stream function, density

a

Based on Venice meteorology

zero

b

Based'on LSQ mld-basln meteorology

Zero

a

Order One, irregularly variable

zero

~ = -O.5sin(~x

parameters c r

extreme values of stream function density

at step

0.52

0.99

55

a

-0.38

3.12

55

55 20

O.Ol, 0.02

c

b

zero

a

Set by local evaporati on

a

-0.40 -0.22

3.12 1.88

d

b

zero

a

No normal gradient

a

-0.38

3.00

58

a

-o.3g -0.34

3.22 2.91

88 45

e

b

axial LSQ

a

c

el

b

e

a

c

e = .05

-0.16

1.84

20

e2

b

•

a

c

e = .005

-0.21

1.83

20

e3

b

e

a

C

F=

.l

-0.4* -0.5 -0.6 -0.6

1.34 1/6" 1.6 , 1.4

20 30 45 55

As in b but multiplied

•

a

c

a

-0.30

1.48

55

f

by 0.5

*To one decimal point because output was graphical rather than printed. -10

/

Fig. 13. Dimensionless mass transport stream function ¥ and density S, both with contour labels × 100, for case e of Table 3 at step 55 (38.10 days). Stream function contour may be interpreted as dimensional transports in units of 10-a m 2 s-* while density contours are increments of 2at in units of 10-2. Note horizontal exaggeration of basin width as in Fig. 11. and the early density distribution has a strong tendency for isopycnals to parallel isobaths everywhere except very near the coast, where fresh water inflow depresses the density. Continuing evaporation forms a pool of dense water centered in the northern part of the basin with a 'tail' extruding southward along the shallow relief off the western coast. Once the 'tail' has

formed, advection along the western coast intensifies it relative to the purely diffusive case. Ultimately this dense water begins to leave the coast and flow out along the north side of the Jabuka Pit as part of a counterclockwise gyre having a total transport of about 0.3 × l0 s m 3 s -1. This flow is well developed within 15 or 20 days, but 30 or 40 days are necessary before its effects on the density field are obvious. The flow is, as noted above, not simply a northward extension of the flow forced across the southern (open) boundary. Consequently, the evolution of density and mass transport away from the open boundary tends to be independent of the conditions imposed there. The final density field is qualitatively realistic in its spatial variation. The autumn and winter fields of salinity (Fig. 3) and the autumn temperature field (Fig. 2) show a configuration near the Jabuka Pit similar to that of the computed isopycnals after 40 or 50 days, but this feature is barely suggested in the winter temperatures. Inclusion of a spatially constant wind stress had little qualitative effect on the flow. Initially, the wind blows strongly southward and tends to intensify the counterclockwise flow. When the outbreak of continental air ends, the wind reverses and tends to blow northward for the remainder of the computation, thus slowing the

367

The winter circulation of the Adriatic Sea

flow, but the principal features of the computed fields are not altered significantly. In the stream function equation (4.20), before appreciable density gradients have developed, the wind stress curl is the dominant driving term but thermohaline driving through the third and fifth terms rapidly takes over. This occurs in spite of the fact that the wind field is initially fully developed whereas the density field evolves relatively slowly. The terms S t and Q [defined for (5.1)] of the density equation (4.21) are initially in almost complete balance except very near coastlines, where lateral diffusion overpowers Q. This primary balance is preserved in the interior of the basin throughout the entire computation although advection continuously erodes it, especially near the boundaries. In every case, gyral flow was evident by the 15th or 20th time step, but full closure, with separation of the interior flow from that forced across the open mouth, did not occur until later in the computation. Full closure was found in the later stages of every case except cases a, f, e3, and h. Case e3 is far more diffusive (P = 0.1) than the others (F = 0-02). Cases a, f, and h are all distinguished by substantially lower evaporation rates than the other cases. Even though complete separation did not occur in these cases, the closed component of circulation remained appreciable (see Fig. 14). To explore the separation mechanism, two additional cases (e4 and e5) were computed. The parameters of Table 3 were as in case e, but the computations supposed idealized bottom relief, either uniformly shoaling from 200 m across the open mouth to 25 m at the northern coast (e4), or first deepening from 110 m across the open mouth to 200 m one-quarter of the way up the basin and thereafter shoaling uniformly to 25 m at the northern coast (e5). The fields of mass transport and density after 25 steps are shown in Fig. 14 for case e5; the fields of e4 are qualitatively identical with those of e5 north of the trough in relief. The regular relief, with no cross-basin variation, results in solutions simpler than those obtained using the 'actual' relief, yet

-1o

-20

eo_..~-. Fig. 14.

Same as Fig. 13 but for case e5 (see text) at step 25 (17.38 days).

e5 shows substantial separation. With relief having only y dependence, (4.20) becomes (~)1/2V. (h2V~b) -}-hyqbx= --hySx/(2h 2)

where h = 5 -1 and curl (Th) vanishes identically for our choice T = Ty(t). Numerical solution of this equation with a right-hand side everywhere negative and having only gentle space variation yields flows entirely analogous to the beta plane wind driven circulation of STOMMEL(1948). The term of (5.2) equivalent to beta is by, positive if the relief shoals northward. In that case, the solutions are intensified to the west with a boundary layer of thickness 0(e/2) xt2. The solutions of e4 and e5 with river inflow are, if anything, intensified to the east. This is because the density field, S, forced by interior evaporation and coastal runoff, makes the righthand side of (5.2) strongly positive at both east and west coasts. Thus, a Sverdrup-like solution of (5.2), i.e. a solution satisfying (2~)xl~hy~y -~- hy~x = -- hySx/(2h ~) -

(5.3)

368

MYRL C. HENDERSHOTTand P^OLA RIZZOLI

would have +~ > 0 near both coasts when hy > 0. This implies intensification of northward flow along the eastern boundary and spreading of southward flow along the western boundary. In this sense, the tendency of the equivalent beta effect to intensify the flow westward is offset by the combined effect of relief and density variations. The ultimate result is a counterclockwise circulation in the north. In case e4 (uniform northward shoaling) this circulation smoothly joins the flow forced across the open boundary, although (,/2)t/2V. (h~V+) becomes large near the east coast as well as near the west on account of the rapid variation of the right-hand side of (5.2) induced by the diffusive coastal boundary layer in the density field. But in case eS, the density field has a local minimum spanning the entire basin over the trough in relief because evaporation is least effective at increasing density where fluid columns are deepest. Thus, both S and + are almost independent of x and the balance of terms in (5.2) is ( ~ ) ' " ~ V . (h~-V~b)= --(~)1"V~-S/2

(5.4)

to within about 20%. To the north and the south of this region, + < 0 while within the region VaS > 0. Consequently V 2 d / < 0, and d?attains a local maximum extending the width of the basin, in coincidence with the trough in relief, and isolating the flow in the northern part of the basin from that to the south. T o the south, the flow imposed at the boundaries is so large that the balance of terms in (5.2) tends towards

( ~ ) ~ " v . (h~V+) + h,+~ = O,

(5.5)

i.e. the principal mechanism allowing for crossisobath flow at the rapid rate forced across the open boundary is Ekman bottom drag. For convenience, neglect the y variation of h in the first term, put [3 = hy and T = h~(~/2)1In so that ~'V'+ + 13+x -- O.

(5.5a)

By setting + = ~e -(o/2~)x, we find

V ' n - (~/4~f)n = o, so that (5.5a) has elementary solutions of the form sin n z x exp [--([~/2~/)x] exp [--(n21tI + [32/47~)tt2 y] away (y > 0) from a boundary at y ----0 where ~b is specified. Solutions of (5.5) are thus characterized by a depth of greatest penetration ( ~ + ~2/4~,s)-1'~ that is small when ~, is small for either sign of [3, i.e. for either slope of the relief. In case e5, where relief deepens just north of the open boundary, 13 ~ 0.5 while 7 ~ 0.04 so that the (dimensionless) penetration depth is roughly 1/7, appreciably smaller than the distance (unity) from the open boundary to the deepest part of the trough. This argument is, however, only approximate because the density field near the inflow region is strongly advected so that (5.5) does not remain a good approximation as time passes. Over 'actual' relief, solutions of (4.20) no longer are characterized by regions having such markedly different balances of terms, especially in the later stages of the computation. Nevertheless, the mechanisms discussed above appear to be important. In the northern gyre, the right-hand side of (4.20) is strongly positive near the west and east coasts, and a counterclockwise gyre forms. Early in the computations, before advective effects have become significant, a density minimum forms over the pit. The two Jacobian terms of (4.20) take on small values relative to the remaining terms and the balance is locally approximately (5.4). The streamfunction shows a local maximum and the northern gyral flow begins to separate from the flow forced across the open boundary. As the flow evolves, the balance (5.4) is gradually eroded, although it tends to persist longest in the tongue-like minimum of density extending out from the east coast over the pit. The later evolution of the flow is more difficult to understand because advective effects strongly distort the density field. The early density minimum and later tongue

The winter circulationof the Adriatic Sea of high density water are conspicuously absent in those cases (a, f, e3, h) showing the greatest communication of interior and boundary forced flow. Cases e3 and h especially show instead strong east-west density gradients penetrating into the interior well over the pit. In case e3, they are due to the unusually strong lateral diffusion chosen, while in case h they occur because the evaporation is artificially concentrated along the axis of the basin. The observed autumn and winter fields of T, S, and density show more resemblance near the pit to the cases with northern basin flow isolation than to cases with free communication between open boundary and northern basin, but we have no other synoptic data with which to test the computations. 6.

CRITIQUE AND SUMMARY

Several aspects of the model require discussion. We stepped the density equation (4.21) forward in time but the stream function equation (4.20) was taken as steady. This restricts us to a time scale of order 20 days or longer (Section 4). The only forcing of (4.21) is the evaporative increase of tit

t

density ~ Q(t')dt', which rises smoothly over the it/

0

period of the simulation (Fig. 10) with a time scale of 20 days for unit variation of density and consequently of mean transport. The scale condition is thus just fulfilled. The accuracy of this assumption has been checked by reprogramming the model to include time dependence in (4.20) and re-running case e. Even though the forcing includes the much more rapidly varying wind stress as well as the evaporation, the computed fields differ overall only by about 10% and are qualitatively unchanged. Topographic planetary waves with frequencies the order of f (bottom slope)/D0, i.e. with periods of a few days, might have been expected in the dissipationless case, but the bottom drag over-damps them with a time scale (fo~i,/l/2) -1, the order of a few days. They were not evident in the time-dependent calculations.

369

The ARAKAWA(1966) finite difference Jacobian used in the nonlinear terms of the model differs from the continuous Jacobian by terms of order Axe/6, i.e. by about 4 × 10-3 for our mesh. These terms may lead to appreciable numerical smoothing in some applications, but in the present case they do not appear significant, being two orders of magnitude smaller than either the Ekman bottom drag term of (4.20) or the diffusive term of (4.21) for our choice of ~ and F. A numerical check of their importance in (4.21) was made by running case e with 1-' = 0. The results after 20 steps were very different from those obtained with the usual F = 0.02, having density and a very weak circulation tightly constrained by relief. The model equations (4.20), (4.21), with their assumption of complete vertical mixing, cannot completely describe the flow near the coasts where the river runoff induces noticeable stratification. Their solutions are thus interior solutions in that further analysis is required to elucidate the equations governing the flow in the region of runoff-induced stratification. In principle, this analysis must be done to determine the boundary conditions to be satisfied at the coast by the present interior variables, but because of the difficulty of this analysis (comparable to that required for the three-dimensional Gulf Stream problem) and because of the complete lack of vertical structure of our interior variables, we have preferred to proceed as in Section 4 by making the coast a streamline and specifying the equivalent mass flux due to river runoff as a diffusive flux of density at the coasts. Our procedure is likely to overestimate the dynamical significance of nearshore density gradients (although this will be compensated for by their tendency to be normal to coastal isobaths) and will not include the spinup as rivers eject fluid columns with sufficient speed to force them across isobaths [in our model, this can be estimated by estimating the size of the second term of (5.3); for a river flow of 0.001 x 10e m 3 s-1 over I00 km that term is of order 10-3 at most and hence two orders of magnitude smaller than the other terms in (5.3) for the coasts of case e].

370

MYRL C. HENDERSHOTT and PAOLA RIZZOLI

Even granting our boundary conditions, our isobaths run straight into the east coast so that the dynamical significance of offshore density gradients there is probably overemphasized. Unfortunately the Jugoslav coast is so rugged and the relief rises so abruptly toward it that any numerical study on the present (5 km) or a comparable mesh will experience similar difficulties. In summary, we conclude (i) the interior wintertime augmentation of density in the northern Adriatic Sea is determined with better than order-of-magnitude accuracy by the depth of the water and the overhead sensible and latent heat fluxes; (ii) the horizontal density gradients induced by these heat fluxes plus coastal river inflow of fresh water are capable of driving a horizontal flow in the northern Adriatic Sea with mass transport of order l0 s m a s-X; (iii) this flow may be isolated from flow in more southern parts of the basin by the combined effect of bottom relief and of the density field induced by that relief and overhead evaporation; and (iv) in winter, this flow may exceed the strength of the wind driven flow. The conclusions are listed in decreasing order of certainty. We are most confident of the first two. The third might well hold during some years and not others, especially if air-sea fluxes show wide spatial variation. The fourth is heavily dependent upon the applicability of our model equations and boundary conditions to the total flow.

in Venice. In La Jolla, Mr. R. SALMONcapably assisted in the last stages of our numerical work. Meteorological data for Jugoslav cities were supplied by the Federal Hydrometeorological Office of Jugoslavia. G. PORETTI made available a digitization of Adriatic bottom relief. JUDY MORLEYexpertly drafted numerous figures. Myrl Hendershott was an Alfred P. Sloan Fellow while this study was in progress. REFERENCES

Annali Idrologici (1965, 1966) Ufficio Idrografico del Magistrato alle Acque, Venezia, Direttore: Dott. Ing. L. Dorigo. Ministero dei Lavori Pubblici, Roma, 1968. ARAKAWAA. (1966) Computational design for long term numerical integration of the equations of motion: two dimensional incompressible flow, part 1. Journal of Computational Physics, 1, 119-143. BLACKADAR A. (1962) The vertical distribution of wind and turbulent exchange in a neutral atmosphere. Journal of Geophysical Research, 67, 30953102. GALAVERNI S. (1972) Distribuzione costiera delle acque dolci continentali nel Mare Adriatico. Technical Report no. 44, CNR Publications, Venezia. HtJANO J. (1969) The thermal current structure in Lake Michigan. Ph.D. Thesis, University of Michigan. JAcons C. (1951) The energy exchange between sea and atmosphere and some of its consequences.

Bulletin c)~Scripps Institution of Oceanography, 6, 27-122. KOZLOV V. (1969) Effect of bottom topography on geostrophic currents in the Pacific Ocean. Oceanology, 9, 796-802. MANAnE S. (1957) On the modification of air-mass over the Japan Sea when the outburst of cold air predominates. Journal of the Meteorological Society of Japan, 35, 1-16. PHILLIPSO. M. (1966) On turbulent convection currents and the circulation of the Red Sea. Deep-Sea Research, 13, 1149-1160. ROBINSONA., A. TOMASINand A. ARTEGIANI(1972) Flooding of Venice; phenomenology and prediction of the Adriatic storm surge. Quarterly Journal of

the Royal Meteorological Society, London, 99, 686-692.

Acknowledgements--We wish to thank Dr. ROBERTO STOMUEL H. (1948) The westward intensification of FRASSETTO,Director of the Laboratorioper 1o Studio della ocean current. Transactions. American Geophysical Dinamica delle Grandi Masse, Venice, Italy, for his conUnion, 29, 202-206.

tinued support and encouragement. STO~EL H. and A.LEETMAA(1973) The circulation JEROME NAMIASfirst pointed out to us the unusual on the continental shelf. Proceedings of the National nature of the 1965 to 1966 winter. Ing. RENZO DAZZl Academy of Science, U.S.A., 69, 3380-3384. forwarded essential data and reports to us in the United TAYLORG. I. (1953) Dispersion of soluble matter in a States. Professor L. TROTTI consented to our use of solvent flowing slowly through a tube. Proceedings Bannock data in advance of his forthcoming study of the of the Royal Society, London, A, 219, 446--468. Adriatic Sea. Dr. S. GALAVERNIkindly allowed us to make TROTh L. (1970) Crociere Mare Adriatico. Consiglio use of her study of river runoff in advance of publication. Nazionale delle Ricerche, Raccolta dati oeeanoDr. A. TOMASINmade available to us his programs for grafici, Serie A, no. 29. estimating wind stresses over the Adriatic Sea and ZORE-ARMANDAM. (1963) Les masses d'eau de lamer generously helped with many aspects of our computations Adriatique. Acta Adriatica, 10(3), 5-88.