The e�ect of coastal upwelling on the sea-breeze circulationat Cabo Frio, Brazil: a numerical experiment

S. H. Franchito, V. B. Rao, J. L. Stech, J. A. Lorenzzetti

Instituto National de Pesquisas Espaciais, INPE, CP 515, 12201-970, SaÄ o Jose dos Campos, SP, Brazil

Received: 20 June 1997 /Revised: 21 January 1998 /Accepted: 12 February 1998

Abstract. The e�ect of coastal upwelling on sea-breezecirculation in Cabo Frio (Brazil) and the feedback ofsea-breeze on the upwelling signal in this region areinvestigated. In order to study the e�ect of coastalupwelling on sea-breeze a non-linear, three-dimensional,primitive equation atmospheric model is employed. Themodel considers only dry air and employs boundarylayer formulation. The surface temperature is deter-mined by a forcing function applied to the Earth'ssurface. In order to investigate the seasonal variations ofthe circulation, numerical experiments consideringthree-month means are conducted: January-February-March (JFM), April-May-June (AMJ), July-August-September (JAS) and October-November-December(OND). The model results show that the sea-breeze ismost intense near the coast at all the seasons. The sea-breeze is stronger in OND and JFM, when the upwellingoccurs, and weaker in AMJ and JAS, when there is noupwelling. Numerical simulations also show that whenthe upwelling occurs the sea-breeze develops and attainsmaximum intensity earlier than when it does not occur.Observations show a similar behavior. In order to verifythe e�ect of the sea-breeze surface wind on the upwel-ling, a two-layer ®nite element ocean model is alsoimplemented. The results of simulations using thismodel, forced by the wind generated in the sea-breezemodel, show that the sea-breeze e�ectively enhances theupwelling signal.

Key words. Meteorology and atmospheric dynamics(mesoscale meteorology; ocean-atmosphereinteractions) á Oceanography (numerical modeling)

1 Introduction

The best known regions of coastal upwelling are locatedin the eastern margins of the world oceans, e.g. in Peru,Ecuador, California and Oregon on the Paci®c Oceancoast, and northwest Africa and southern Benguelacurrent on the Atlantic Ocean coast. This oceanographicphenomenon is of fundamental importance for themaintenance of the high biological productivity of theseregions. Although less intense, coastal upwelling is alsopresent at some coastal regions located at the westernmargins of the oceans. For example, during the summerperiod a coastal upwelling is observed at Cape Canav-eral in the southeastern continental shelf of the UnitedStates (Lorenzzetti et al., 1987).

Along part of the Brazilian southeast continentalshelf, and particularly near Cabo Frio (22�590S,42�020W) (Fig. 1), a seasonal upwelling is present duringthe spring and summer months. During the fall andwinter seasons, there is a relaxation of the upwelling(Stech et al., 1995). The upwelling at Cabo Frio isanother example of this phenomenon occurring on thewest coast of oceans. Considering that the surface layersof this region are dominated by warm waters of tropicalorigin, with low levels of productivity, the observedcoastal upwelling is of great importance for the biolog-ical enrichment of the water and sustaining of the ®sheryactivities of this region. Studies using ship, coastalstations data and infrared satellite images have shownthat strong negative sea surface temperature (SST)anomalies are present during most of the year in thisregion (Lorenzzetti et al., 1988; Valentin, 1984; Miran-da, 1982). In particular, the infrared images from theNOAA satellites have shown that coastal upwellingoccurs from the coast of Espirito Santo state, north ofCabo Frio, to the region near Guanabara Bay, with thelargest negative SST anomalies occurring along thecoast near the Capes of SaÄ o Tome , Bu zios and Frio(Humi and Lorenzzetti, 1991). Figure 2 shows a NOAA-Correspondence to: S. H. Franchito

Ann. Geophysicae 16, 866±881 (1998) Ó EGS ± Springer-Verlag 1998

12 AVHRR satellite image that illustrates the presenceof negative SST anomalies in this region.

It has been speculated that the seasonality of theCabo Frio upwelling is associated with the onshore/o�shore seasonal migration of the South Atlantic

Central Water (SACW) at the continental slope. Recentstudies have shown that the SACW is the source of thecold waters that crop up near the coast in this region(Gaeta et al., 1994; Valentin, 1984). Sometimes whenstrong NE winds persist for several days, strong

Fig. 1. Region of Cabo Frio.The coastline considered in themodel is indicated by a thickline. The smaller rectangle rep-resents the model domain. Thedashed lines represent the iso-baths in m. The line AB indi-cates grid-points along aparallel line 10 km northwardfrom the EW coast; the line CDcorresponds to grid-pointsalong a parallel line 10 kmwestward from the NS coast;the point E represents a grid-point situated 10 km inlandfrom both the EW and NScoastlines; F indicates the inter-ception of the EW and NScoastlines. These lines andpoints are useful for analyzingthe model results

Fig. 2. Sea surface temperature satelliteimage showing the coastal upwelling in theCabo Frio region. The yellow square repre-sents the model domain

S. H. Franchito et al.: The e�ect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil 867

upwelling can develop with surface temperatures drop-ping to 13±14�C near the coast, close to Cabo Frio.These temperatures are about 10�C cooler than the mid-and outer shelf waters. On the synoptic time scale of 6±11 days, as cold fronts pass over the region, the surfacewinds rotate counterclockwise and blow for a few daysfrom the southern quadrant, inhibiting the upwelling.

The large-scale atmospheric high pressure centerlocated over the South Atlantic ocean makes theprevailing surface wind blow from the northeast alongthe Brazilian coast near Cabo Frio (Stech and Loren-zzetti, 1992). The southwest-northeast and east-westorientation of the coastline in this region (Fig. 1), favorsthe development of a strong alongshore wind stresscomponent, which is the main forcing of this upwelling.

Most of the Brazilian coastal regions are in¯uencedby the sea-breeze circulation which occurs due to thehorizontal temperature di�erence between the land andthe ocean. Since the land is warmer than the oceanduring the day, the local surface wind blows from sea toland (sea-breeze); at higher altitude, there is a weakerreturn ¯ow, which blows from land to sea. Thecirculation is opposite during the night because the landis colder than the ocean (land breeze). These local windsmay have an important role in determining the climatein coastal regions because they in¯uence the character-istic air ¯ow, the precipitation and the humidity andpollutant transports (Lu and Turco, 1994; Kousky,1980; Anthes, 1978; Ramos, 1975).

The sea-breeze circulation may be stronger whencoastal upwelling is present because the negative SSTanomalies increase the horizontal temperature di�erencebetween the ocean and land. The sea-breeze circulationin turn modulates the coastal ocean circulation. Prelim-inary analysis of coastal wind time series clearly shows astrong sea-breeze near Cabo Frio, as noted in Fig. 3.Thus, the coastal upwelling should intensify the ocean-atmosphere interaction processes in this region whoseconsequences are not yet known.

The objective of the present work is to study thein¯uence of the coastal upwelling on the local atmo-spheric circulation in the region of Cabo Frio and toverify the feedback of the sea-breeze on the upwellingsignal. Basically, we propose to conduct a numericalsimulation of the sea-breeze circulation forced by thecharacteristic SST of this region. The upwelling occurs

mainly in austral summer and it is practically absent inwinter. Numerical experiments using the atmosphericmodel will be carried out separately for three-monthmean conditions: January-February-March (JFM),April-May-June (AMJ), July-August-September (JAS)and October-November-December (OND), in order tostudy the seasonal variations in the sea-breeze circula-tion of this region. The in¯uence of the breeze on theupwelling is investigated using a numerical ocean model.These two models are described in Sect. 2; the modelresults and comparisons with observations are discussedin Sect. 3; and the summary and conclusions arepresented in Sect. 4.

2 The numerical models

2.1 The sea-breeze model

The atmospheric model developed for this study is athree-dimensional, non-linear, primitive equation modelfor dry air. This model is a three-dimensional version ofthe two-dimensional model developed by Franchito andKousky (1982).

The hydrodynamical equations, the structure of thehorizontal and vertical grids and the temporal integra-tion scheme are based on the mesoscale model devel-oped by Anthes and Warner (1978). However,simpli®cations are made in the parametrizations of thesurface diurnal heating and the planetary boundarylayer. Since the model of Franchito and Kousky (1982)was published in a journal of limited circulation, adetailed description is given below.

2.1.1 Basic equations. The equations are written in a�x; y; r; t� system, where x and y are the west-east andsouth-north directions, respectively, and r is the verticalcoordinate given by:

r � �p ÿ pt�=p� �1�where p� � ps ÿ pt; ps is the surface pressure; pt thepressure at the top of the model (500 hPa); and p, thepressure at some level of the model.

The momentum, continuity, hydrostatic and thermo-dynamic equations are given, respectively, by:

Fig. 3. Diurnal variations of the horizontal surface wind-vector near the coast in Cabo Frio (22�590S, 42�020W). Data are from Operation CaboFrio 8 conducted by the Brazilian Navy in 16±22 January 1986. Units are m sÿ1

868 S. H. Franchito et al.: The e�ect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil

@�p�u�=@t � ÿ@�p�uu�=@xÿ @�p�vu�=@y ÿ @�p�u _r�=@r� p�fvÿ p���RT �=�p� � pt=r�@p�=@x

� @/=@x� � FU ; �2�@�p�v�=@t � ÿ@�p�uv�=@xÿ @�p�vv�=@y ÿ @p�v _r�=@r

ÿ p�fuÿ p���RT �=�p� � pt=r�@p�=@y

� @/=@y� � FV ; �3�@p�=@t � ÿ�@�p�u�=@x� @�p�v�=@y� ÿ @�p� _r�=@r; �4�@/=@ ln�r� pt=p�� � ÿRT ; �5�@�p�T �=@t� ÿ@�up�T �=@xÿ @�vp�T �=@y� ÿ @�p�T _r�=@r

� RT x=�cp�r� pt=p��� � FT : �6�The equation of the tendency of pressure is obtained

through the integration of the continuity equation fromthe surface to the top of the model. So,

@p�=@t � ÿZ�@�p�u�=@x� @�p�v�=@y� dr �7�

where

x � dp=dt �8�and �FU; FV� are the frictional accelerations in �x; y�direction and FT is the temporal rate of change of �p�T �due to lateral and vertical di�usion of heat. The symbolshave their usual meanings and are de®ned in Ap-pendix A.

2.1.2 Structures of the horizontal and vertical grids. Thehorizontal and vertical grid structures are similar tothose used by Anthes and Warner (1978). The horizon-tal grid is staggered, with the horizontal velocitycomponents de®ned at the grid points xi � �iÿ 1�Dxand yj � �jÿ 1�Dy, and all the other variables arede®ned at the grid points xi�1=2 � �iÿ 1=2�Dx andyj�1=2 � �jÿ 1=2�Dy.

The vertical grid for our three-dimensional version ofthe model is also staggered, with the values of thehorizontal velocity components, geopotential and tem-perature de®ned at the levels which are adjacent to thelevels where _r is de®ned (1015, 1000, 980, 960, 940, 900,850, 700, 500 hPa). Figure 4 illustrates the structures ofhorizontal and vertical model grids. The grid intervalsDx and Dy are 10 km.

The ®rst level of the model where Eqs. (2), (3) and (6)are applied in order to obtain the ®elds of velocitycomponents (u, v) and the temperature �T � is 990 hPa(which is around 200 m). The values of these variables atthe lowest level above surface (1007.5 hPa) are calcu-lated using a logarithmic interpolation.

2.1.3 Initial conditions. The SST is almost constantduring the day compared to the land surface tempera-ture (LST) because the heat capacity of sea water is largeand the thermal mixing is very intense in the sea. Hence,the SST is assumed constant during the model integra-tion. The diurnal change of LST is given by:

f �t� � 5 sin�2pt=s� � 1:7 sin�4p�t ÿ 2�=s� : �9�Expression (9) has a general form of the diurnal

variation of temperature: a maxima around 14:00 LTand a minima around 06:00 LT. The LST is assumedequal to SST at the beginning of the model integration�t � t0�. Since the values of LST are di�erent from thoseof SST (Table 1) it is necessary to obtain the value of twhich represents the di�erence between LST and SST�DT �. The value of t which corresponds to f �t� � 0 isassumed as the initial time of integration. If thisdi�erence is negative (positive) the value of LST islower (higher) than SST by the DT , so that the abscissain Fig. 5 must be moved up (down) by jDT j to makef �t� � 0. The value of t whose value of f �t� � 0 is t0.Because of the values of LST and SST (and consequent-ly jDT j and t0) depend on season, the diurnal variationof temperature has a seasonal component.

Since LST = SST at t � t0, the sea-breeze circulationhas not set in yet. Thus, as an initial state theatmosphere is assumed to be at rest (u = v = 0) andin a stable equilibrium. The initial pro®le of temperature

Fig. 4a,b. Structure of the model grid: a horizontal: the horizontalvelocity components are de®ned at the cross-points, and all the othervariables are de®ned at the dot points; b vertical: the vertical velocityis de®ned at the levels of the model (solid lines), and all the othervariables are de®ned at the intermediate levels (broken lines)

S. H. Franchito et al.: The e�ect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil 869

is the same over both land and sea, and it is obtainedfrom climatological values.

2.1.4 Boundary conditions. The boundary conditions aresimilar to those used by Ookouchi et al. (1978).

V � 0; _r � 0 �10�at the surface and top of the model because the e�ect ofthe prevailing wind is not considered. Laterally, it isassumed:

@�p�; T ;V�=@x � @�p�; T ;V�=@y � 0 : �11�The boundary conditions should not cause serious

errors in the model results if the area of the domain ofintegration is su�ciently large.

2.1.5 Boundary layer parametrization. The model plan-etary boundary layer parametrization is similar to thatproposed by Ookouchi et al. (1978). The heat andmomentum di�usion processes are taken into accountby using di�erent coe�cients for unstable and stablestrati®cations.

In the case of unstable strati®cation, after KEYPS(Yamamoto, 1959), the eddy coe�cient for momentumKm is given by:

Km � l2��@u=@z�2 � ag=haj@h=@zj�1=2 �12�

where 1 is the mixing-length; ha, a constant representingpotential temperature (290 K); and a � Kh=Km. Al-though a is generally considered to be a function of theRichardson number and others, it does not deviate verymuch from 1 in the terrestrial atmosphere. Therefore, ais assumed to be equal to 1 and Km � Kh. Since the e�ectof the general wind is not considered, the ®rst term ofEq. (12) (vertical wind shear) is small. Thus, Eq. (12)becomes:

Km � Kh � l2�g=haj@h=@zj�1=2 : �13�

The mixing-length 1 is assumed to be constant in themodel because its value is almost constant above 100 m(Blackadar, 1962). The value of 1 is determined from thecriterion of convective instability. The critical Rayleigh(Ra) number is about 660 under free boundary condi-tions (Chandrasekhar, 1961). Thus,

Ra � g=haj@h=@zjH4=KmKh

� g=haj@h=@zjH4=�g=haj@h=@zjl4� � 660 : �14�The depth of the unstable layer H is about

200 � 300 m. If a mean value �H � 250m� is considered,the corresponding value of l is 50 m, which is used in themodel.

In the case of stable strati®cation, Eq. (12) is not agood approximation. Then, it is assumed that Km �Kh � 5 m2sÿ1.

2.1.6 Temporal integration scheme. The temporal inte-gration scheme is that developed by Shuman (1971) andgeneralized by Brown and Campana (1978). In thisscheme the values of p� and / are calculated beforecomputing u and v values. Then, the weighted average ofp� and / at the time steps (n ± 1), (n) and (n+1) are usedin the pressure gradient terms of the momentumequations. These averages are made as following:

g�n� � n�g�nÿ1� � g�n�1�� � �1ÿ 2n�g�n� �15�where g refers to p� and /.

This scheme allows for a time step 1.6 to 2 timeslarger than that allowed by the conventional leap-frogscheme and it is stable for n � 0:25. The value ofn � 0:2495 is used in the present model, as in Anthesand Warner (1978).

Although this scheme is stable for n � 0:25 thecomputational mode may become noticeable for longintegrations. In order to avoid the growth of theseerrors, a temporal smoothing operator is applied at each100 time steps:

g�n� � �g�n�1� � g�nÿ1� � 2g�n��=4 �16�

Table 1. Values of LST, SST, DT = LST ) SST, t0 (initial time ofintegration), and the local time which corresponds to t0 for three-month-averages: JFM, AMJ, JAS and OND in the region of CaboFrio. The SST and LST data are obtained from DHN andINMET, respectively

LST(°C)

SST(°C)

DT(°C)

t0(h)

Local time(h)

JFM 25.1 23.6 +1.5 )0.02 9:00 amAMJ 22.5 22.9 )0.4 1.0 10:00 amJAS 20.9 20.5 +0.4 )1.0 8:00 amOND 23.0 18.9 +4.1 )4.8 4:12 am

Fig. 5. Diurnal change of land surface temperature f �t�. The valuet � 0 corresponds to 9:00 LT. Units are �C

870 S. H. Franchito et al.: The e�ect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil

where g refers to the model prognostic variables. Thistemporal smoothing operator is also applied to the timestep (nÿ 1).

2.1.7 Source of data. SST data were obtained from theNational Center of Oceanographic Data at the Hydrog-raphy and Navigation Directory (Centro Nacional deDados Oceanogra ®cos, Directoria de Hidrogra®a eNavegacË aÄ o ± DHN) of the Brazilian Navy. These SSTdata correspond to three-month mean values (JFM,AMJ, JAS and OND) from 1957 to 1982. The LST datawere obtained from the Center for Climate Analysis atthe National Institute of Meteorology of Brazil (Insti-tuto Nacional de Meteorologia ± INEMET) andrepresent monthly means for the period from 1931 to1960. These data were used to obtain the LST meanvalues for JFM, AMJ, JAS, and OND. The mean SSTand LST values are given in Table 1. As can be noted,the thermal contrast between land and ocean is larger inOND and JFM (when there is upwelling) and smaller inthe winter months (when there is no upwelling).

The initial vertical air temperature pro®le used in themodel refers to climatological values for JFM, AMJ,JAS and OND (averages for the period 1969±1976) forGaleaÄ o (22�490S, 43�150W) obtained from the MonthlyClimatic Data for the World. These vertical pro®les oftemperature correspond to stable equilibrium states ofthe atmosphere.

2.2 The ocean model

The ocean model used for the study of the upwellingderives from a ®nite element formulation by Wang andConnor (1975) and consists of two layers with constantbut di�erent densities. The advective terms are ignoredbased mostly on the small velocities present. The modelformulation does not allow for interface outcropping orthe collapse of the lower layer. When this happens thecomputations must be terminated. Arbitrary bottomtopography can be included by specifying depths atelement nodes. Vertically integrated equations of mo-tion are derived for each layer which are solved in aCartesian coordinate system with positive z upwards.The following equations of continuity and momentumare used:

@Hi=@t � @qix=@x� @qiy=@y � 0 ; �17�@qix=@t ÿ fqiy � ÿ@�Fip ÿ Fixx�=@x� @Fiyx=@y

� 1

qifsix ÿ s�iÿ1�x � pi@ni=@x

ÿ p�iÿ1�@n�iÿ1�=@xg ; �18�@qiy=@t � fqix � ÿ@�Fip ÿ Fiyy�=@y � @Fixy=@x

� 1

qifsiy ÿ s�iÿ1�y � pi@ni=@y

ÿ p�iÿ1�@n�iÿ1�=@yg : �19�

Subscript i is 1 or 2 for lower or upper layers,respectively; H is layer thickness; u and v are ¯uidvelocities; qx and qy are layer-integrated volume trans-ports; f is the Coriolis parameter; q is the layer density;n0 is bottom elevation, n1 is the interface elevation andn2 is the surface elevation; p0 is the bottom pressure; p1 isthe interface pressure, p2 is the atmospheric pressure(here assumed equal to zero), s is the bottom, interface,or surface shear stress; Fxx; Fyx; Fyy , are internal momen-tum exchanges; and Fip � 1

2 gH2i � qÿ1i piHi.

The density di�erence re¯ects a temperature changebetween the two layers. This density di�erence admits abaroclinic mode in the model and to some extentcontrols the internal wave characteristics. Mixing be-tween layers is ignored and thus the densities remainconstant at values typical of hydrographic data. Thebottom and interface stresses are parametrized, respec-tively, as

s0x � q1CB��u21 � �v21�1=2�u1 ; �20�s1x � q1C1���u1 ÿ �u2�2 � ��v1 ÿ �v2�2�1=2��u2 ÿ �u1� �21�with analogous expressions for the y-direction. Theoverbar variable represent the average layer velocity,CB � 2:3� 10ÿ3 is the bottom friction coe�cient, andC1 � 0:4� 10ÿ3 is the interfacial shear stress coe�cient.The value chosen for CB is typical for bottoms withroughness heights of 20±30 cm and layer thickness of30±40 m; similar values have been suggested by Thomp-son and O'Brien (1973) and Hickey and Hamilton(1980). Much less is known about the interfacial stresscoe�cient in oceanic ¯ows. Average values range from4� 10ÿ4 to 15� 10ÿ4, Karelse (1974). Previously,O'Brien and Hurlburt (1972) have used the same�0:4� 10ÿ3� to study upwelling. The wind stress isparametrized in the usual way as

s2 � qairCDjU10jU10 �22�where qair is the air density, U10 is the wind speed,measured at a height of 10 m MSL, and CD is the windstress drag coe�cient, given by

CD � �1:1� 0:0536U10� � 10ÿ3;U10 in msÿ1 �23�as proposed by Wang and Connor (1975). This formu-lation is slightly di�erent but in general agreement withthat proposed by Wu (1980).The integrated internal stresses are parametrized as

Fixkxm � Ekm@qik@xm� @qim@xk

� �; i � 1; 2 �24�

where x1 � x, x2 � y, and qik is the transport in layer i inthe direction k, and Ekm is an eddy viscosity tensor. Theprimary function of including the internal momentumtransfer terms is to allow some dissipation of shortperiod waves when these arise from the numericalcalculations.

The system of equations is solved numerically using a®nite element formulation with linear triangular ele-ments for the spatial derivatives and a ``split-time'' ®nitedi�erence scheme in time to advance the solution to the

S. H. Franchito et al.: The e�ect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil 871

next time step. A detailed description of these proce-dures can be found in Wang and Connor (1975).

3 Results and discussion

3.1 Atmospheric model

3.1.1 Results. The model was run using three-monthmean conditions (JFM, AMJ, JAS and OND) in orderto investigate the seasonal variations of the sea-breezecirculation. The results refer to the second day ofintegration. In analyzing the model results, it is impor-tant to consider the behavior of the circulation in bothnorth-south (NS) and east-west (EW) directions dueto the con®guration of the coastline near Cabo Frio(Fig. 1).

The model results show that the winds associatedwith the sea-breeze reach their maximum intensity about15:00±16:00 LT in all the periods. Tables 2 and 3 showthe seasonal variations of the u and v-components of thehorizontal wind (at the level of 990 hPa), respectively, at15:00 LT. It can be seen that the sea-breeze is moreintense in both the EW and SN directions in OND andJFM (where there is upwelling) and weaker in AMJ andJAS (where there is no upwelling), with the maximaoccurring near the coast. The seasonal variations of thesea-breeze are in agreement with the seasonal land-ocean thermal contrast (Table 1), showing that thecoastal upwelling plays an important role in regulatingthe intensity of the local circulation in this region. Thestrongest sea-breeze occurs in OND, when the coastalupwelling is most intense; in AMJ and JAS, when thereis no coastal upwelling, the circulation is weaker.

In order to study the dynamical and thermal e�ectsof coastal upwelling on the sea-breeze circulation in theregion of Cabo Frio, OND and AMJ are chosen as thecharacteristic periods of upwelling and no upwelling,respectively.

Figure 6 shows the development of the horizontalextension of the sea-breeze circulation as a function oftime for OND and AMJ. As the LST becomes higherthan SST, the sea-breeze starts near the seashore in boththe cases. There is a lag between the time of thebeginning of the circulation for the two periods. Thesea-breeze begins to develop around 1 h earlier in ONDthan in AMJ.

With the continued heating of the land, the circula-tion increases in horizontal extension and progresseslandward and seaward, as shown in Fig. 6. The strongestwinds occur around 14:00±16:00 LT. Figure 7 shows thecross section of the u and v-components of the horizon-tal wind at 15:00 LT. At this time, in AMJ the sea-breezepenetrates 100 km inland in the EW direction and 20 kmin the SN direction, and reaches a depth of 1250 m and900 m in the EW and SN directions, respectively. Thehighest values of u (ÿ5:8 msÿ1) and v (5:1 m sÿ1) occurnear the coast. For OND, the easterlies reach 100 kminland in the EW direction and the southerlies penetrate30 km inland in the SN direction. The depth of thecirculation is about 1500 m and 1200 m in the EW andSN directions, respectively. The strongest winds alsooccur near the coast: ÿ7:5 msÿ1 (u) and 6:5 m sÿ1 (v).The corresponding cross sections of the vertical velocityare shown in Fig. 8. The maxima in the ascendingmotions inland in the EW direction are 18:1 cm sÿ1 and16:2 cm sÿ1 in OND and AMJ, respectively, while in theSN direction the highest values of the vertical velocityare 21:4 cm sÿ1 and 18:4 cm sÿ1 in OND and AMJ,respectively. These results show that the circulation isstronger in OND than in AMJ.

The horizontal distribution of the wind-vector, at thelevel of 990 hPa, at 15:00 LT is shown in Fig. 9. Thesea-breeze comes from SE in the areas nearest to thejunction of the two coastlines, showing the simulta-neous e�ect of both the u and v-components of thehorizontal wind. For the inland region far from the SNcoastline, the e�ect of the v-component overcomes thatof the u-component. The opposite occurs in the inlandregions far from the EW coastline. The intensi®cationof the circulation in OND compared to AMJ is alsoevident.

As the sea-breeze penetrates inland a frontal zone isgenerated separating the sea-air from the air over land.Figure 10 shows that this frontal zone is more pro-nounced when there is upwelling (OND).

After the occurrence of its maximum, the sea-breezecontinues gradually to increase in horizontal extensionin both the periods, although the circulation is moreintense in OND (Fig. 6). With the decreased heating ofthe land surface during the night, the sea-breeze isweakened. Even when the temperatures over landbecome lower than those over the sea, the overall ¯owis still directed from sea to land, although the windspeed weakens with the passing of time, as shown in Fig.6. The circulation is reversed and a weak land-breezesets during the early hours of the next day.

These results indicate that the sea-breeze circulationin the Cabo Frio region is intensi®ed during the periodsof coastal upwelling. This intensi®cation of the circula-

Table 2. Seasonal EW variations of the u-component of thehorizontal wind (at the level of 990 hPa), at 15:00 LT, along lineAB (Fig. 1). Units are m s)1

50 km 40 km 30 km 20 km 10 km Coast

JFM )1.0 )1.1 )1.3 )1.9 )3.8 )6.6AMJ )0.8 )0.9 )1.1 )1.6 )3.3 )5.8JAS )0.9 )1.0 )1.2 )1.7 )3.4 )6.0OND )1.2 )1.3 )1.7 )2.7 )4.7 )7.5

Table 3. Seasonal SN variations of the v-component of thehorizontal wind (at the level of 990 hPa), at 15:00 LT, along lineCD (Fig. 1). Units are m s)1

40 km 30 km 20 km 10 km Coast

JFM 0.1 0.2 0.9 3.0 5.6AMJ 0.1 0.1 0.7 2.6 5.1JAS 0.1 0.1 0.7 2.7 5.2OND 0.4 0.8 1.6 4.0 6.5

872 S. H. Franchito et al.: The e�ect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil

tion can be seen in its onset, horizontal and verticalextension, and in the magnitudes of the wind.

3.1.2 Comparison with observations. Limited observa-tional data were available for the region of Cabo Frio.In this section the results of the model simulations arecompared with the observations. Figure 11 shows themonthly mean surface wind for 10 years (1971±1980)obtained from the Meteorological Station in Cabo Frio.These observations correspond to two hourly meanvalues of the surface horizontal wind (10 m abovesurface) near the coastal region. As can be noted, thedominant northeasterlies at night tilt towards the zonaldirection in the afternoon in all months due to thepresence of sea-breeze. Because of the coastline orien-tation in the region of Cabo Frio (Fig. 1), the sea-breezeblows from east to west along the SN coast and south tonorth along the EW coast. Also, the larger the magni-tude of inclination in the zonal direction of observedhorizontal vector wind, the stronger the sea-breeze.

Thus, as noted in Fig. 11, this circulation in general ismore intense during the summer months, when thecoastal upwelling occurs.

To compare the observations with the model results,means of 3 months (JFM, AMJ, JAS, and OND) wereobtained. It should be kept in mind that the modelresults refer only to the sea-breeze circulation, while theobserved wind gives the total wind, i.e. the prevailingwind plus sea-breeze.

Figure 12 shows the seasonal variation of simulated(at 990 hPa) and observed horizontal wind (10 m abovesurface) near the coast at 15:00 LT and 21:00 LT. It canbe noted that the simulated sea-breeze is stronger duringJFM and OND, which seems to agree with observations.In the observations for these two periods, the horizontalwind-vectors are more inclined in the zonal directionindicating stronger sea-breezes. During the night thesea-breeze circulation weakens and the observed windblows from northeast.

Regarding the seasonal variation of temperature, themodel results are compared with observational data for

Fig. 6a±d. Simulated temporalvariation of the horizontal ex-tension of the sea-breeze at the990 hPa level: a EW variation ofthe u-component along line AB(Fig. 1) simulated for OND.The easterlies are indicated bybroken lines; and the westerliesare represented by solid lines; bas a, except for AMJ; c SNvariation of the v-componentalong line CD simulated forOND. The southerlies are indi-cated by solid lines and thenortherlies are represented by abroken line; and d as c, exceptfor AMJ. Units are m sÿ1

S. H. Franchito et al.: The e�ect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil 873

1972 obtained from DHN. Figure 13 shows that theseasonal variation of temperature simulated by themodel(at 990 hPa level) is similar to the observed variation nearthe surface at 15:00 LT and 21:00 LT. In both, amaximum in JFM and a minimum in JAS can be noted.

Next, model results are compared with the observa-tions, considering the two situations: with upwelling(OND) and without upwelling (AMJ). Table 4 showsthe simulated values for u and v at 990 hPa level andsurface observations (10 m above surface) near the coastin these two cases. During the periods OND and AMJ inthe observations at 15:00 LT, the easterlies are intensi-®ed and northerlies are weakened with respect to theobservations at 21:00 LT, showing the presence of thesea-breeze circulation. The sea-breeze is more intense inOND. This feature seems to be well simulated by themodel. As Table 4 clearly shows the magnitude of thesimulated horizontal winds is larger than the observedvalues. This is related to the fact that the model resultsrefer to values at 990 hPa and the observationscorrespond to values at 10 m above the surface.

Figure 14 and 15 show the simulated (at 990 hPa) andobserved diurnal variation of wind (10 m above surface)

for OND and AMJ. For a better comparison betweenthe model results and observations, an attempt to isolatethe sea-breeze from the observed wind is made. This isdone assuming that the observed wind is a combinationof a mean wind and a perturbation (sea-breeze).Twenty-four hour means of u and v for each periodare taken as the mean wind. This mean is subtractedfrom the observed wind for each hour giving the u and vvalues of the sea-breeze. These ®gures show that themodel results are in good agreement with the observa-tions. The sea-breeze intensi®es in the afternoon andevening, and weakens during the night. It ®nally blowsin the opposite direction, forming the land-breeze,during the morning of the next day. It can also benoted that the sea-breeze is much stronger than the sea-breeze in OND. Comparing Figs. 14b and 15b, it can benoted that the sea-breeze is intensi®ed when upwellingoccurs. The simulations show good agreement withobservations (Fig. 14a, 15a). A comparison of Figs. 14band 15b shows that the sea-breeze onset and the mostintense sea-breeze with upwelling occurs earlier thanwhen there is no upwelling. Model results also showsimilar features, as commented on in Sect. 3a.

Fig. 7a±d. Cross section of the simulated horizontal wind at 15:00 LT: aEWvariation of the u-component along line AB (Fig. 1) for OND; b sameas a, except for AMJ; c SN variation of the v-component along line CD (Fig. 1) for OND; and d same as c, except for AMJ. Units are m sÿ1

874 S. H. Franchito et al.: The e�ect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil

Fig. 8a±d. Cross section of the simulated vertical velocity at 15:00 LT:a EW variation of w along a line parallel to AB (Fig. 1) situated 5 kmnorthward from the EW coastline for OND; b same as a, except for

AMJ; c SN variation of w along a line parallel to CD (Fig. 1) situated5 km west ward from the SN coastline for OND; and d same as c,except for AMJ. Units are cm sÿ1

Fig. 9a,b. Simulated horizontalwind-vector (at level of 990 hPa)at 15:00 LT for: a OND and bAMJ. Units are m sÿ1

S. H. Franchito et al.: The e�ect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil 875

As shown there is good agreement between the modelresults and the available observations (Figs. 11±15).However, it should be mentioned that the modelequations and parametrizations are made for an ideali-zed situation of land and sea-breezes. Also, the interac-tions between sea-breeze circulation and the mean windand the topography are not included. Thus, somedi�erences between observations and model results areexpected. Further, the model results and observationsare for di�erent levels: 990 hPa for the model and 10 mabove surface for the observed data. Even with these

limitations there is good agreement between observa-tions and model simulations, which is encouraging. Itshould be emphasized that we ran the model usingobserved seasonal values of SST. Thus, the simulatedsea-breeze circulation responds to an enhanced temper-ature forcing which is due to cold water upwelling nearthe coastal region of Cabo Frio. In the next section, thee�ect of the enhanced sea-breeze on the upwellingstrength is investigated.

3.2 Ocean model

In order to estimate the sea-breeze signal over the oceancirculation in the Cabo Frio upwelling region, a simpletwo-layer coastal numerical model was implemented.Details of this model can be found in Lorenzzetti et al.(1987). The intensity of the upwelling in this oceanicmodel is determined by the values of the interfaceanomaly elevations. In a two-layer model, the upwellingis characterized by a decrease of the upper layerthickness which is associated with positive interfaceanomalies.

The ocean model was run using the surface sea-breezeobtained from the atmospheric model superimposedover a constant wind of 6 msÿ1 blowing from NE,representing the prevailing wind without the sea-breeze.This NE prevailing wind is favorable for upwellingthroughout the region. For both the N-S and E-Wcoastline regions, the component of the wind parallel to

Fig. 10a±d. Horizontal variation of the simulated potential tempera-ture (at level of 990 hPa) for three time stages: a EW variation along aline parallel to AB (Fig. 1) situated 5 km northward from the EW

coastline forOND; bSNvariation of potential temperature along a lineparallel to CD (Fig. 1) situated 5 km westward from the NS coastlineforOND; c same as a, except forAMJ; and d same as b, except forAMJ

Fig. 11. Monthly mean of the surface horizontal wind-vector (10 mabove surface) observed near the coast in the Cabo Frio region for15:00 LT and 21:00 LT. The data are obtained from theMeteorological Station in Cabo Frio (point F in Fig. 1) for ten-yearmeans (1971±1980)

876 S. H. Franchito et al.: The e�ect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil

the coast is favorable for upwelling, since the Ekmantransport is to the left of the wind direction. The ®rst 24h of integration was made using only the constant6 m sÿ1 NE winds and starting from rest. A two hourramp was used at the beginning of the integration tobring the wind from zero to 6 m sÿ1 normal intensity.Two other experiments were completed separately toverify the e�ects of sea-breeze on the intensi®cation andchange of direction of the prevailing wind. The ®rst oneused a constant direction wind with its magnitudemodulated by the sea-breeze. The second one used aconstant intensity 6 m sÿ1 wind but with a directionvarying according with the sea-breeze e�ect.

The ocean model is implemented for this region usinga linear triangular grid composed of 740 elements and432 nodes. At each node, the local mean depth wasdetermined through an interpolation of a NauticalChart of the Brazilian Navy. The following parameters

were used in all experiments: time step of integrationDt � 60 s; q1 � 1025:5 kg mÿ3; q2 � 1022:5 kg mÿ3;f � ÿ0:533� 10ÿ4 sÿ1, corresponding to the latitudeof 21.5 S. At time zero the upper layer thickness isconstant and equal to 20 m. At the coastal boundary,normal ¯ow is set to zero for both layers and a slipcondition is applied to the alongshore ¯ow. For thespeci®cation of boundary conditions along the openboundaries, extensive testing showed that the bestresults were obtained by implementation of a spongelayer at the north and south extremes of the domain.These two layers e�ectively absorbed most of the waveenergy near these boundaries. The rationale of thesponge layer implementation is explained in Lorenzzettiand Wang (1986). Adiabatic boundary conditions, i.e.,®xed surface and interface elevations, were used alongthe o�shore boundary, represented in the model by the150 m isobath, corresponding to the continental shelfbreak in the region. A time ramp of 2 h was used on thewind stress forcing in the beginning of all experiments inorder to avoid shocking the model. The numericalmodel was integrated for 72 h in all experiments.

In order to serve as a comparison, a ®rst model runwas made using a constant wind of 6 m sÿ1 from NE,representing the prevailing wind of this region. A secondexperiment was carried out using a constant 6 m sÿ1 NEwind for the ®rst 24 h followed by a vector compositionof this wind with the summertime sea-breeze wind signalobtained from the atmospheric model for 200 m heightand reduced to surface through a logarithmic interpol-ation. Two auxiliary experiments were also carried outin a similar manner as the second experiment: the ®rstone keeping the direction of the summertime sea-breezesignal constant and NE, and the second one keeping theintensity of the wind equal to 6 m sÿ1 but varying itsdirection in accordance with the sea-breeze. These twolast experiments were carried out to verify the separatee�ects of direction and intensity modi®cation intro-duced by the sea-breeze on the prevailing wind, andconsequently on the upwelling strength. No simulationsof the e�ect of the sea-breeze wind on the upwellingwere carried out for wintertime conditions since there isno upwelling during this season.

Fig. 12a,b. Simulated and observed three-month averages of thehorizontal wind-vector for: a 15:00 LT and b 21:00 LT. The modelvalues refer to the simulated sea-breeze (at level of 990 hPa) at agridpoint situated inland 10 km from both the SN and EW coastlines

(point E in Fig. 1); and the data correspond to surface windobservations (10 m above surface) near coast for ten-year means(1971±1980) obtained from the Meteorological Station in Cabo Frio(point F in Fig. 1). Units are m sÿ1

Fig. 13. Simulated and observed three-month averages of the tem-perature at 15:00 LT and 21:00 LT. The model values refer to thesimulation at the level of 990 hPa at a gridpoint situated 5 km inlandfrom both the SN and EW coastlines; and the data correspond to airsurface values near coast for 1972 (DHN). Units are �C

S. H. Franchito et al.: The e�ect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil 877

Figure 16 shows the time series of interface anomaliesfor summertime conditions and for the four di�erentexperiments described before. Cases a and b correspondto two points located near the coast and in the vicinityof Cabo Frio and Cabo de SaÄ o Tome , respectively.These two points were chosen in areas known asmaximum intensity cores of the upwelling signal in theregion. For both locations, Fig. 16 shows growingpositive interface anomaly values characteristic ofupwelling. With the inclusion of the sea-breeze signalafter 24 h of integration, it is possible to see a substan-tial enhancement of the upwelling, corresponding toincreases of approximately 6 m for Cabo Frio and 4 m

for Cabo de SaÄ o Tome of additional elevation of theinterface (broken line).

For both places, the increase of the upwelling causedby the sea-breeze seems to be associated mostly with anincrease in intensity of the wind. This point can beobserved by the short dashed-dot lines representing thecase in which the forcing contains the NE basic wind plusthe sea-breeze signal, but keeping the NE direction ®xedand allowing only the modulation of the wind strength.

The case in which we make the sea-breeze e�ectiveonly in the direction of the basic wind but keeping itsoriginal strength unaltered can be observed in Fig. 16a,b by the long dashed-dot lines. For Cabo Frio, the

Table 4. Values of u and v-components of the horizontal wind at15:00 LT and 21:00 LT for OND and AMJ: a simulated at agridpoint inland situated 10 km from both the SN and EWcoastlines (point E in Fig. 1) at the level of 990 hPa; b observed

10 m above surface. The data are obtained from the Meteorolo-gical Station in Cabo Frio (point F in Fig. 1) for 10-y means, 1971±1980. Units are m s)1

a Model b Data

OND AMJ OND AMJ

15:00 21:00 15:00 21:00 15:00 21:00 15:00 21:00

u )4.7 )3.5 )3.3 )2.2 )3.0 )1.8 )1.6 )0.8v 4.0 0.9 2.6 0.3 )1.4 )2.1 )0.4 )1.2

Fig. 14a,b. Simulated and observed diurnal variation of the sea-breeze for an upwelling case: a simulated values for OND, at 990 hPa,at a grid point situated inland 10 km from both the SN and EWcoastlines (point E in Fig. 1); and b observed values (10 m above

surface) near coast for OND (10 y means, 1971±1980) obtained fromthe Meteorological Station in Cabo Frio (point F in Fig. 1). Units arem sÿ1

Fig. 15a,b. The same as Fig. 14, except for a non upwelling case. The simulations and observations correspond to AMJ

878 S. H. Franchito et al.: The e�ect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil

change of wind direction clearly results in a smallincrease in the upwelling, resulting from a betteralignment of the wind with the coastline. Notice inFig. 9a that near Cabo Frio, the sea-breeze wind vectorscontain a favorable component for upwelling. This iscaused by the abrupt change of coastline orientation,making the sea-breeze wind not perfectly normal to thecoast. On the other hand, the change of wind directionproduced by the sea-breeze at Cabo de SaÄ o Tome isveri®ed as having a negative e�ect on the upwelling.This could be associated with the fact that the coastlineorientation in this region is mostly parallel to the basicNE wind. The change of direction produced by the sea-breeze tends to make the wind less parallel to the coast,resulting in a weakening of the upwelling.

4 Summary and conclusions

This work investigates the role of the coastal upwellingin modulating the sea-breeze circulation and the feed-back of the sea-breeze on the upwelling signal at CaboFrio (Brazil).

A three-dimensional numerical model of primitiveequations is utilized in a study of the e�ect of coastalupwelling on sea-breeze circulation. Seasonal variationof atmospheric circulation is investigated by conductingnumerical experiments forced by three-month means ofobserved SST in this region: JFM, AMJ, JAS and OND.In all cases the sea-breeze is most intense o�shore butnear the coast. Model results show that the sea-breeze isstronger in OND and JFM, when upwelling occurs, andweaker in AMJ and JAS, when there is no upwelling.Observations show a similar behavior.

The intensi®cation of the simulated sea-breeze withthe occurrence of upwelling can be noted in the highervalues of the horizontal wind, larger horizontal andvertical extensions and stronger vertical motion over thecontinent.

Numerical simulations and observations also showthat there is a di�erence in the initiation of the sea-breeze and the maxima values in the situations with andwithout upwelling. In the case with upwelling, the sea-breeze develops and attains its maximum intensityearlier than the case without upwelling.

A general agreement is observed between the atmo-spheric model results and observations, which show anintensi®cation of sea-breeze circulation in the afternoonand evening when the upwelling occurs. This intensi®-cation of the sea-breeze makes the direction of the wind,which is mostly northeast, become more zonal. Whereno upwelling occurs, the sea-breeze is weak.

The results of the oceanic model forced with the sea-breeze wind ®eld generated by the atmospheric modelshow that the upwelling is enhanced by the sea-breeze.The main reason for this enhancement is associated withthe intensi®cation of the prevailing wind caused by thesea-breeze. At Cabo Frio, a secondary reason is relatedto the change of orientation of the prevailing windforced by the sea-breeze. In Cabo de SaÄ o Tome , thise�ect is negative, that is, the change of wind directionproduced by the sea-breeze causes a decrease in theupwelling strength.

In summary, the atmospheric model results andobservations show that upwelling has an important rolein regulating the sea-breeze circulation in Cabo Frio(Brazil). The sea-breeze is intensi®ed by an enhancedtemperature forcing which is due to cold water upwel-ling near coast. The ocean model results show that thiscoastal upwelling is enhanced by the sea-breeze circula-tion. Thus, it is suggested that there is a positivefeedback between sea-breeze and coastal upwelling inthis region. Although these results are obtained by usingtwo separate models (one atmospheric and the otheroceanic), they constitute a pioneering attempt in mod-eling the feedback e�ect between sea-breeze and coastalupwelling in this region.

Fig. 16a,b. Time series of interface anomaly elevations obtained fromthe ocean model. a and b refer to summertime conditions and to gridpoints located near the coast in the vicinity of Cabo Frio and Cabo deSaÄ o Tome , respectively. Solid line: constant NE wind; broken line: full

sea-breeze signal after 24 h of integration; short dashed-dot line: sea-breeze signal with NE constant direction after 24 h of integration;long dashed-dot line: sea-breeze signal with constant magnitude after24 h of integration

S. H. Franchito et al.: The e�ect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil 879

Appendix: List of symbols

Atmospheric model

Cp speci®c heat of dry air at constant pressuref Coriolis parameterf �t� forcing function at land surfaceFT temporal rate of �p�T � due to lateral and

vertical di�usionFU frictional acceleration in x directionFV frictional acceleration in y directiong acceleration due to gravityH depth of the unstable layerKh eddy di�usion coe�cient of heatKm eddy di�usion coe�cient of momentuml mixing-lengthp pressure at some level of modelps surface pressurept pressure at the top of the modelp� ps ÿ ptR gas constant for dry airt timet0 initial time of integrationT temperatureu component of the horizontal velocity

in x directionv component of the horizontal velocity

in y directionV horizontal wind-vectorx horizontal coordinate oriented from west to easty horizontal coordinate oriented from south

to northz vertical coordinatew vertical velocity, dz=dta Kh=Km/ geopotentialg p� or / in Eq. (15), and the prognostic variables

in equation 16h potential temperatureha a constant representing potential temperature

(290 K)r vertical coordinate de®ned by �p ÿ pt=�ps ÿ pt�_r vertical velocity: dr=dts period of one dayx vertical velocity: dp=dtn constant equal 0.2495�n� time stepDx grid interval in x directionDy grid interval in y direction

Ocean model

f Coriolis parameterg acceleration due to gravityq1; q2 lower and upper layer density, respectivelyH layer thicknessEkm eddy viscosity coe�cientp0 pressure at the bottomp1 pressure at the interfacep2 pressure at the surfacet time

u average layer velocity in x directionv average layer velocity in y directionqx layer integrated volume transport in

the x directionqy layer integrated volume transport in

the y directionx horizontal coordinate oriented from west to easty horizontal coordinate oriented from south

to northn0 bottom elevationn1 interface elevationn2 surface elevations0 bottom stresss1 interface stresss2 surface wind stressFxx; Fyx;Fyy internal momentum exchange coe�cientsFip pressure stressC1 interface stress coe�cientCB bottom friction coe�cientqair average air densityCD wind stress drag coe�cient

Acknowledgements. The authors wish to thank the FAPESP(Foundation for the Support of Research of SaÄ o Paulo State),for the ®nancial support of COINT project; Dr Merritt R.Stevenson, of INPE, for discussing and improving the manuscript,Carlos L. da Silva Jr for processing the satellite infrared imagepresented in this paper, and to Regina R. Rodrigues for helpingwith the oceanic model runs.

Topical Editor D. Y. Webb thanks R. P. Pearce and anotherreferee for their help in evaluating this paper.

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