The circulation pattern in the northern Gulf of California, based on drifting buoys and hydrographic observations, can be explained using the results of a linear two-layer primitive equations model forced, at the annual frequency, by the Pacific Ocean, wind stress, and heat flux through the surface. The modeled surface circulation consists of a cyclonic gyre from June to October and an anticyclonic gyre from December to April, both located in the central region of the northern Gulf of California, which includes Ángel de la Guarda Island. The maximum intensities of the gyres occur in August and February, respectively, with values of surface velocities of 65 cm s−1 (in agreement with the observations) and very low opposite velocities in the bottom layers. May and November are transition months in which both gyres can be observed. Finally, in June/July or December/January the growing gyre is still connected with the rest of the Gulf of California, through the narrows between Tiburón Island, San Esteban Island, and the Baja California coast, whereas from August through October and from February through April the respective gyre is isolated. The vertical structure of the model results indicates a mainly baroclinic signal both in the southern and central regions of the Gulf of California. In the northern gulf, however, the velocities in the annual signal are a combination of barotropic and baroclinic movements, with similar intensities, coupled by topography effects. Thus, only part of the dynamics is associated to great movements of the interface, which shows maximum values of 40 m.
The annual variability in the Gulf of California has recently been studied by Ripa (1997) and Beier (1997), hereafter R97 and B97 respectively. Based on a conjecture formulated by Ripa (1990), R97 and B97 use numerical models whose results compare favorably with the analysis of the main oceanographic variables at the annual frequency. These models indicate that the seasonal variability of the gulf is mainly forced by the Pacific Ocean with the wind stress and surface heating acting as secondary factors. In B97, the effect of the Pacific Ocean is introduced specifying at the mouth of the Gulf of California the transverse structure of an incoming baroclinic Kelvin wave trapped against the continental coast. After traveling around the gulf, the wave leaves, trapped against the coast of Baja California. This wave is greatly influenced and distorted by topography, dissipation, and, to a lesser extent, the variation of the Coriolis parameter with latitude. All of the dynamics is strongly influenced by a small internal deformation radius of the order of 30 km. The response of the gulf to the wind stress, on the other hand, can be explained as a forced wave that, trapped against the coast, propagates along the whole Gulf of California with its amplitude growing from a null value at the mouth to a maximum value at the head on the continental side and then decreasing toward the mouth on the Baja California side due to the opposing effect of the wind. This wind-forced wave can be seen as a superposition of a baroclinic Kelvin wave and a barotropic topographic Rossby wave although topography, coastline variations, and bottom friction couple all vertical and transversal modes. The relative importance of the Pacific Ocean and wind stress forcing can be appreciated in Fig. 1, which shows results from R97’s model in a run made without friction. Most of the potential energy is internal, indicating a preponderance of baroclinic motion, except in the shallow region near the head. In the northern Gulf of California (NGC) the accumulated effect of the wind is two to three times smaller than that due to the Pacific Ocean, although both are important for the total signal.
Using Argos drifters, Lavín et al. (1997, hereafter L97) observed velocities in the NGC from 13 September to 9 October 1995 and from 19 February to 18 April 1996. Their observations indicate that during the September–October period there is a well-defined cyclonic gyre that occupies all the central and southern area of the NGC. For the February–April period, they found an anticyclonic gyre, slightly displaced toward the northwest, but with the same characteristics as the September–October cyclonic gyre, that is, average velocities of 30 cm s−1, 7-day rotation time, and maximum velocities of 50 cm s−1. The observations made by L97 are the first direct measurements to test the prediction of B97’s numerical model, namely, that the pattern of circulation in the NGC is a seasonally reversing gyre. Using CTD data simultaneous to the observation of currents, L97 speculated about the vertical structure and concluded that the summer gyre is of baroclinic character, while the winter one results from a combination of both baroclinic and barotropic movements. Argote et al. (1998) simulated the circulation in the Gulf of California induced by a typical winter wind using a vertically integrated nonlinear model. The numerical results were compared to observations made by an array of current meters at different depths from 1 December 1994 through 6 February 1996. Argote et al. found an anticyclonic circulation both in the model and the observations, though the magnitudes of the observed velocities are five to six times higher than those obtained with the model. Furthermore, the anticyclonic gyre is not closed. They concluded that the effects of stratification have to be considered (the NGC is not homogeneous in winter) if more realistic velocities are sought. In B97’s model, the contrasts of density between both layers change solely due to the local surface heat flux. This is not enough to reproduce the changes in stratification reported by Carrillo-Bribiezca (1996). A more realistic model should also incorporate winter mixing.
Sea level observations around the gulf and the heat balance estimated by Castro et al. (1994) from the hydrographic data compared agreeably with the results of the model in B97. Due to lack of velocity observations, B97 could not verify and study in detail the prognosticated current. In the light of the recent observations mentioned above, the purpose of this work is to analyze the velocity fields obtained with B97’s model and to determine the degree of correspondence with the observations.
2. The northern Gulf of California
a. Results of the model
A description of the model and the parameters used in the simulation can be found in B97. The model is forced in the annual frequency with a wind stress τ with a maximum value of τ/ρ of 3.8 × 10−5 m2 s−2 (corresponding to a wind speed of 5.3 m s−1) in February, toward the mouth of the gulf. The surface heat flux has a maximum amplitude in the region of the archipelago and phase in June.
Figure 2 shows the sea level elevation and surface velocities for July and August. The circulation pattern consists of an intense cyclonic gyre that occupies all of the central and southern region of the NGC, with maximum speeds of the order of 63 cm s−1 occurring in August. In the deep water region, sea level elevations are associated to the gyre and reach values of 15 cm, which decrease toward the center within the internal deformation radius. Velocities are very low in the shallow area, of the order of 5 cm s−1. As summer advances, the gyre contracts and moves toward Delfín Basin, near the coast of Baja California, as shown in Fig. 3a, which corresponds to September. The maximum velocities in the summer months occur on the side of Baja California. During August, September, and October, the velocities in the region between Tiburón and San Esteban Islands and between the latter and the Baja California coast (henceforth “the narrows”) are practically null and the circulation in the NGC is isolated from the adjacent gulf.
Figures 3b and 4a correspond to the transition period from cyclonic to anticyclonic circulation. In October, an anticyclonic jet starts to grow near the continent while the cyclonic gyre starts contracting and weakening, with maximum velocities of 30 cm s−1. The anticyclonic gyre continues to develop through November, although there is still a weak cyclonic gyre. In November, the three forcing agents produce a horizontal heat flux of 14 TW through the narrows. This flux corresponds with a transversely integrated surface velocity of 3 cm s−1 toward the central gulf (see R97). In December the anticyclonic gyre covers the whole NGC, as shown in Fig. 4b.
Since the model is linear and forced with a single frequency, the winter circulation pattern and the summer–winter transition are the same as those shown in Figs. 2, 3, and 4, with opposite sign for elevations and velocities, that is, a well-defined anticyclonic gyre in the central region during February, with practically null interchange with the central region of the Gulf of California, and a period of transition from anticyclonic to cyclonic circulation in April and May, with very intense outgoing and incoming fluxes through the narrows. The comparison of the model’s pattern of circulation with observations is hindered by the fact that in the few current measurements available there are several other scales involved besides the annual one. For instance, L97’s observations cover periods of 1½ or 2 months. Synoptic events with wind intensities of twice the value used here may occur during that time span. Nevertheless, one purpose of this note is to see to what extent the observations of L97 can be explained by a simple model forced at the annual frequency.
Figure 3c of L97 shows the cyclonic gyre observed during September and the beginning of October of 1995, which coincides with the circulation pattern predicted in Figs. 3a and 3b of this paper. The intensities of the observed velocities agree with those predicted. L97 shows that during October of 1995 the buoys abandoned the NGC traveling along the continental coast, in accordance with Fig. 3b of this work. Moreover, the model predicts that during the month of October, surface water moves toward the head through the Ballenas Channel. It is then reasonable that no buoy was observed to leave the deployment area on the Baja California side. During 12–20 September 1995, the geostrophic surface velocities relative to 100 m reported by L97 in Fig. 3b are also very similar to those of the model in Fig. 3a of this work. In October, the velocities of the model show an anticyclonic gyre that starts to develop on the continental side. Although the Lagrangians velocities cover a period of only one month, the summer gyre has been well documented by Bray (1988a) and Carrillo-Bribiezca (1996) for all summers in which the hydrographic data were available.
Figure 5c of L97 shows an intense anticyclonic gyre, observed between the second half of February through the first half of April 1996, with speeds close to those of the model. An anticyclonic geostrophic gyre was also detected by Bray (1988b) in March 1985. We can find this pattern in the opposite of Figs. 3a,b, and part of Fig. 4a of this paper, that is, by lagging the results of the model 20 days. During the transition period, the gyre moves to the northwest, both in the model and in the observations. In April, the surface water flows mouthward through the Ballenas Channel, but this flux is weak, which might be the reason why no buoys were observed in this area. The trajectories of the buoys do not detect the cyclonic gyre that starts to develop in April. If we imagine the circulation pattern of April as opposite to that in Fig. 3b, it can be seen that no buoy could detect that incipient cyclonic gyre unless its initial position were on the side of the continent and toward the archipelago region, which was not the case with this deployment (M. F. Lavín 1996, personal communication).
b. Barotropic and baroclinic circulation
Figure 5a shows the temporal mean values of the potential and kinetic energy per unit length transversely integrated as a function of the distance to the head of the Gulf of California obtained in the simulation. The energy is mainly potential except near the mouth, where the kinetic and potential energies have similar values. The energies grow from the mouth to the head because of the wind-forced wave, which has a maximum amplitude in the NGC. A run made with the same three forcing agents but in a uniform semienclosed channel with dimensions similar to those of the Gulf of California (100-km length, 150-km width, and 730-m depth) shows an equal partition between kinetic and potential energy in the whole gulf except near the head, where the potential energy is greater than the kinetic one, because of the evanescent Poincaré modes required to satisfy the no-flux condition. In our main run, with a more realistic gulf, the irregularities along the coast and the changes of topography excite evanescent modes in the whole gulf. To the south, in an area between 800 and 1100 km from the head, the mean kinetic energy corresponds to 32% of the total mean energy, but in the NGC this fraction is reduced to only 19%. Notice that in the narrows, the kinetic energy has a minimum that is in agreement with the scarce interchange of water between the NGC and the central gulf. Figure 5a also shows the barotropic and baroclinic components of the kinetic energy. In the southern gulf the barotropic energy is a small fraction of the total energy. Similar results are found in the central gulf. The barotropic circulation is important only in the shallow areas or where the changes in topography are significant. These are the conditions that characterize the NGC, which, except for the Delfin Basin, is shallow and has a wide shelf on the continental side. The barotropic potential energy (not shown) is very small in comparison to the total potential energy. Figure 5b shows the differences between energies when the friction parameter has been reduced by a factor of 10. With this drastic change of the bottom friction, the total energy increases 17% in all of the gulf, 12% in the NGC, 17% in the central gulf, and 23% in the southern gulf. This increase occurs mainly in potential energy: 21% for all the gulf versus 9% of kinetic energy. Although the friction has been reduced one order of magnitude, the percentages of both barotropic and baroclinic energy are very similar. Consequently, barotropic and baroclinic modes are then coupled mainly by the topography effects and to a lesser extent by the effects of bottom friction. One may then speculate that in the area far from the mouth, this coupling has been enough to produce a significant barotropic circulation. Figure 5a shows that in the NGC the mean barotropic kinetic energy is 44% of the total kinetic energy. As a consequence, the velocities in the NGC are a mixture of barotropic and baroclinic movements of almost the same intensity. This is an important result since the barotropic movements are not associated with large isopycnal displacements and cannot be detected by geostrophic diagnosis from hydrographic observations alone. The barotropic velocities occur on shallow areas. During summer or winter the displacement of the interface is of the same order as H1(x, y) or H2(x, y) (the mean upper and bottom layers, respectively); thus it is possible to think that the baroclinic movement cannot be sustained in a two-layer model and causes the energy to be transferred to the barotropic mode.
Figures 6a and 7a show sea level elevations and the barotropic contribution to the upper-layer current during April and May, respectively. The barotropic velocity is given by v = (H1v1 + H2v2)/HT, where v1 and v2 are velocities in the upper and bottom layers, respectively, and HT is the total depth. In both cases the barotropic velocities are high on the continental side, over the shelf, and in shallow areas where there is only one layer. In April, maximum barotropic velocities are of the order of 16 cm s−1, more than half the value of surface velocities, which are of the order of 30 cm s−1. In May, the contribution of the barotropic mode to surface velocities is even larger.
Figures 6b and 7b show the interface displacement and the baroclinic velocities in April and May, respectively. This velocity is defined by v = H2(v1 − v2)/HT, so that the sum of the barotropic and baroclinic contributions give surface velocity v1. The baroclinic circulation is important in April on the Baja California side and on the Delfín Basin, where the anticyclonic gyre is located. In May the baroclinic velocities are high in the whole anticyclonic gyre zone, including the Ballenas Channel.
L97 made observations of temperature and salinity fields during 12–20 September 1995 and 30 March through 9 April 1996, simultaneously with the observations of Lagrangian currents. Figures 3b and 5b in L97 show the geostrophic velocities at 10 m relative to a 100-m level of no motion. Figures 4c and 6c show the transverse structure of densities and Figs. 4d and 6d the geostrophic velocities relative to the bottom for both periods. Figure 8a of this work shows the interface displacements obtained with the model for the same transverse section and for the same period shown by L97. Negative velocities are toward the head. In September, the interface displacement, of the order of 35 m, shows the cyclonic gyre in the central region. The contribution of the baroclinic and barotropic velocities of the model to the surface layer are shown in Fig. 8b. Maximum baroclinic velocities of 37 cm s−1 were obtained on the Baja California side and of 19 cm s−1 on the continental side. A high fraction of the gyre is over the shelf on the continental side. These velocities can be compared to the geostrophic velocities relative to the bottom show in Fig. 4d of L97 for this transversal section. L97 obtained maximum surface velocities of the order of 40 cm s−1 on the Baja California side and 25 cm s−1 on the continental side. Almost half of the gyre is located over the shelf, as in the model. The interface displacement is very similar in form and magnitude to the isopycnal displacements shown by L97. Figure 8a shows that in April the interface has two concavities associated with the two gyres. Maximum displacements of the order of 25 m are obtained in this period. The contribution of the baroclinic velocities to the surface layer shows maximum values of 21 cm s−1 on the Baja California, 18 cm s−1 in the central region, and 6 cm s−1 on the shelf. If these are compared to the geostrophic velocities relative to the bottom in Fig. 6d of L97, the distribution is similar, though with maxima values of 12 cm s−1 on the Baja California side, 8 cm s−1 in the central region, and 4 cm s−1 on the shelf. Notice that the barotropic velocities in September and April are higher than the baroclinic velocities on the continental side and over the shelf. The form and magnitude of the interface are very similar to those shown by L97 for the isopycnals.
Using results of a two-layer model, the annual circulation in the northern Gulf of California is predicted to consist of a surface cyclonic gyre from June to October and an anticyclonic gyre from December to April. The response of the model is mainly due to the action of the Pacific Ocean at the mouth and, to a lesser extent, to the cumulative effect of the wind from that region to the head. Though traditional, it would be clearly incorrect in this case to try to model the low-frequency circulation only with the wind stress. A numerical experiment carried out with the wind in isolation shows in the NGC the same relation between barotropic kinetic energy and baroclinic kinetic energy and does not change the pattern of circulation, but the velocities, sea level elevation around the coast, and horizontal heat flux decrease by 60%, failing to reproduce the observations. The seasonally reversing gyre prognosticated by the model is caused by the interaction of the propagating internal wave with the varied topography and coastline. A run using a uniform semienclosed channel shows that the gyres are not formed. Although there are a few Eulerian observations of currents available to support the numerical results, observations of Lagrangian currents by Lavín et al. (1997) confirm the existence of the two gyres not only in their intensity but also in their size and location. The pattern of circulation obtained with the model is a mixture of barotropic and baroclinic movements of similar intensity. To reinforce the fact that the barotropic movement is originated by the propagation of the internal wave in shallow areas we have made a new run using a coastline corresponding to the position of the 70-m isobath and a constant total depth of 730 m (two layers everywhere). The run shows that the gyres are formed but the barotropic kinetic energy component decreases considerably. Thus, only part of the obtained dynamics is associated to great interface displacements or to pure baroclinic movements. The isopycnal displacement and the surface geostrophic velocities obtained simultaneously with the measurements of currents are similar to the surface baroclinic velocities and the interface displacements predicted by the model. The large winter/summer asymmetry in the stratification reported by Carrillo-Bibriezca (1996) and L97 cannot be reproduced by the present setup of the model (linear and monochromatic), which might need the addition of the winter convection analyzed by Lavín and Organista (1988).
Critical reading of the manuscript and access to L97’s manuscript prior to publication by Dr. M.F. Lavín is sincerely appreciated. Adriana Usabiaga (UABC) was very helpful with language corrections. This work has been funded by CICESE and CONACyT (México) under Grants 2667OT and 1890PT. Scholarships were awarded to Emilio Beier by CICESE and CONACyT.
Corresponding author address: Dr. Emilio Beier, CICESE, Oceanografia Fisica, P.O. Box 434844, San Diego, CA 92143-4844.