Seasonal salinity balance in the Gulf of California

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. C8, 3100, /2000JC000769, 2002 Seasonal salinity balance in the Gulf of California F. J. Beron-Vera 1 and P. Ripa 2 Departamento de Oceanografía Física, Centro de Investigación Científica y de Educación Superior de Ensenada, Ensenada, Baja California, Mexico Received 20 December 2000; revised 9 January 2002; accepted 18 January 2002; published 7 August [1] Historical data in various domains within the Gulf of California are used to describe the seasonal balance of the average salinity, hsi. The difference of evaporation minus precipitation, E P, is positive along the course of a year. This produces a positive salinity anomaly, S 0, which is exported to the Pacific Ocean through the mouth of the gulf. Even though E P has strong annual and semiannual cycles, it is not enough to explain the seasonal variation of the transport of S 0. A linear one-dimensional nondiffusive inhomogeneous two-layer model suggests that the seasonal balance of hsi is largely controlled by the Pacific Ocean, which excites a baroclinic wave at the mouth of the gulf. Advection due to this wave is the main carrier of S 0 within the gulf, and the associated water rearrangement produces a considerable change in hsi. The Pacific Ocean has been previously shown to maintain the seasonal heat balance through a similar mechanism. This paper thus adds importance to the Pacific Ocean influence on the determination of the gulf s seasonal dynamics and thermodynamics. INDEX TERMS: 4227 Oceanography: General: Diurnal, seasonal, and annual cycles; 4243 Oceanography: General: Marginal and semienclosed seas; 4203 Oceanography: General: Analytical modeling; KEYWORDS: Gulf of California, salinity balance, surface fluxes, seasonal scale, two-layer model, baroclinic motion 1. Introduction 1.1. Background Literature [2] Considerable effort has been devoted to describing the seasonal heat balance in the Gulf of California (GC) (see Figure 1) [Bray, 1988; Ripa and Marinone, 1989; Castro et al., 1994; Beron-Vera and Ripa, 2000]. In particular, Castro et al. [1994] pointed out the importance of the horizontal heat transport in the annual balance. A physical explanation for this process was proposed by Ripa [1997], who conjectured, using a one-dimensional two-layer model, that the Pacific Ocean (PO) is the main agent responsible for the along-gulf heat transport at the annual scale, by exciting a baroclinic Kelvin wave at the mouth of the GC. The Kelvin wave scenario was confirmed and extended by Beier [1997] using a horizontally two-dimensional model. These works demonstrated that a great deal of the heat balance of the GC can be explained by an adiabatic process. The simple baroclinic Kelvin wave in a shoe box basin [Ripa and avala-garay, 1999] is distorted in the GC by the strong topography and irregular coast, generating, in particular, an important barotropic component [Beier and Ripa, 1999]. The time averaged part of the heat balance cannot be explained by the Kelvin wave scenario [Beier, 1999]. [3] Less work has been done on the seasonal mass balance. Bray [1988] estimated seasonal salt transports 1 Now at Division of Applied Marine Physics, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA. 2 Deceased 3 October Copyright 2002 by the American Geophysical Union /02/2000JC across a transverse section within the Guaymas Basin (central part of the GC) using the vertical distribution of geostrophic currents. Bray s description of the seasonal cycle of these transports was largely qualitative, based on the visual inspection of observations from different months. Using data from the same basin and employing statistical tools, Ripa and Marinone [1989] computed the salt storage within the upper 50 m of the water column, and estimated the vertical salt flux assuming a virtual salt flux at the ocean surface, i.e., a flux proportional to the difference of evaporation minus precipitation [e.g., Beron-Vera et al., 1999]. These authors concluded that the horizontal salt flux divergence is at least as large as the vertical one in the seasonal salt balance. [4] Salinity is generally less tied than temperature to density in the GC; for this reason a model without salinity variations was able to reproduce the seasonal circulation [Beier, 1997]. Never the less, salinity changes can have localized dynamical or biological connotations. For instance, in the process of water mass formation in the northern gulf, small salinity variations can be essential to favoring water sinking through changes in the water column buoyancy [López-Mariscal, 1997]. On the other hand, small salinity changes can substantially alter the habitat of certain biological species, particularly in the northern and central gulf where there is a very high productivity [Álvarez- Borrego, 1983] Choice of a Balance Problem [5] It is common to study the salt and freshwater balances in a given body of seawater, particularly the time-averaged balance. Alternatively, one could study the changes of total volume (or mass) or of salinity. We prefer the second approach for the following reasons. The salt mass of the 15-1

2 15-2 BERON-VERA AND RIPA: GULF OF CALIFORNIA SALINITY BALANCE Figure 1. Map of the Gulf of California. Locations of hydrographic casts and stations where meteorological and precipitation data were obtained are indicated by small dots, big dots, and open circles, repectively. Dashed lines delimit the horizontal domains into which the data are simplified for the study of the seasonal salinity balance. Isobaths are in meters. whole GC varies due to the salt flux through its mouth, one component of which is the advection of the mouth salinity S m.ifs m were equal to the average salinity for the whole body of seawater, hsi, then the salt mass would vary just because water with the same salinity is being added or subtracted, i.e., because the total volume is changing. On the other hand, as we show below, the boundary flux in the equation for the rate of change of hsi involves the advection of S m hsi, which is typically much smaller than S m. Sea surface processes have quite different roles in the two cases. In the salt balance equation there is no surface contribution, whereas in the average salinity equation there is a flux term proportional to the difference of evaporation minus precipitation, which should not be confused with the virtual salinity flux. [6] The prognostic equation for hsi for the whole GC has the surface term mentioned in the previous paragraph, and a mouth term, which involves the advection of S m hsiand salt diffusion through that boundary. This equation is then quite similar to that for the rate of change of the average temperature (roughly proportional to the heat content). In the temperature equation the mouth term has been shown to be the most important forcing term, and is related to the excitation of a baroclinic wave by the PO [Ripa, 1997; Beier, 1997]. One of the purposes of this work is to asses the relative importance of the surface and mouth forcings in the salinity changes, something which makes no sense in the salt balance equation Goal of the Paper [7] The goal of the present paper is thus twofold. First, we seek to describe the seasonal average salinity balance in the entire GC. To this end we use the available historical data of the GC. Unlike observations from a sophisticated process-oriented experiment, the information contained in the historical data set is by no means comprehensive in either time or space, although it is sufficient to reveal the complexity of the salinity field variations. Second, we seek to determine whether the same dynamics that were shown to govern the seasonal heat balance of the GC at the annual scale by Ripa [1997] and Beier [1997] can also be invoked to model the seasonal average salinity balance. Figure 2. Hydrographic data availability classified per year and month in each horizontal domain of Figure 1 indicated by middle numbers. White bins correspond to data excluded from the seasonal analysis.

3 BERON-VERA AND RIPA: GULF OF CALIFORNIA SALINITY BALANCE Outline of the Paper [8] In section 2 we describe the data sets employed in this work. The data are reduced to 5 domains defined within the gulf. The monthly means of the data are then fitted to a seasonal signal with an annual mean plus annual and semiannual harmonics with the intention of extracting robust patterns of temporal variability. In section 3 the problem for the average salinity balance is formally posed. In section 4 the salinity exchanges between the gulf domains and the PO are estimated so as to attain a balance. In section 5 we obtain an analytical solution from a linear non-diffusive inhomogeneous two-layer model in a simplified shoe box model in order to see whether the signal we detect is reasonable for the whole GC, given the surface and mouth forcings. This allows us to assess the underlying physics of the average salinity balance. A summary and concluding remarks are finally presented in section 6. Two appendices describe some mathematical details. 2. Data and Their Treatment 2.1. Data Sets and Sources [9] The data sets considered in this paper are the following: 1. Temperature and salinity data taken from 41 cruises (about 2600 casts) made in the GC within the period Monthly mean precipitation time series recorded in the period Monthly mean time series of other meteorological variables recorded in the period , which include air temperature, relative humidity, atmospheric pressure, cloud cover, and wind speed. Data set 1 belongs to CICESE s historical data bank of the GC, which has a large gap of data in the period and a lack of data in January of all years. Data sets 2 and 3 were collected in coastal stations which belong to the Servicio Meteorológico Mexicano [Reyes et al., 1990]. In Figure 1 we depict the positions of the hydrographic casts and the onshore meteorological stations. Figure 2 shows, as a function of the year and the month, the number hydrographic cruises and casts selected for the present study. Not all of the available data are considered for reasons explained below. [10] The above data set is complemented with indirect estimations of evaporation rate, which are computed according to Q e /(r w L n ) [e.g., Gill, 1982]. Here Q e is the latent heat flux, which is estimated with the TOGA COARE bulk formulae [Fairall et al., 1996] using data set 3 and sea surface temperature values taken from the mean hydrographic profiles; L n is latent heat of vaporization; and r w is the density of freshwater at the sea surface temperature. The offshore humidity may be higher than the daily coastal averages because of the arid surroundings. Hence the offshore values of Q e could be overestimated, but not so much as to fundamentally modify the results [Lavín and Organista, 1988] Spatial Treatment of the Data [11] The GC has an important hydrographic variability in across-gulf scales smaller than its width as well as in timescales smaller than a year [Robles and Marinone, 1987]. These mesoscale signals conspire against any class of seasonal analysis. In order to smooth out this variability, we define a set of domains along the GC where the salinity profiles and data from meteorological stations are horizontally averaged. [12] The domains must be long enough to produce a monthly composite of salinity data with a good enough annual coverage, which allows for a quantification of their seasonal variability. Here we define them by dividing the GC into 5 horizontal domains by transverse lines, about 200 km apart (see Figure 1). Other configurations are possible. For instance, Castro et al. [1994] considered 11 along-gulf domains, while Ripa [1997] used 7 overlapping domains, in their respective analyses of the seasonal heat balance. However, with the present data set, the complexity of the seasonal salinity variation does not allow for a finer resolution than the one we consider here. Ripa and Marinone [1989] had already observed such complexity in the central part of the gulf.) [13] In addition to the horizontal length of the domains, we must define the vertical range. From earlier experience [Ripa, 1997a; Beron-Vera and Ripa, 2000] we have learned that we cannot mix information from deep casts with that shallow casts. We have to take only those casts that reach, at least, a certain depth h i in the ith domain. If h i is chosen too small, we have more casts but then the results will be less representative of the whole GC. Consequently, we face a tight choice for h i : given the data available today, there is a competition between h i being large enough to be representative of the whole GC, versus h i being small enough for the analysis to have (1) a good horizontal and seasonal coverage, as well as (2) reasonable uncertainties. In this study, we consider h i = 150 m for the northernmost domain (i = 1), where the average depth does not exceed 200 m, and h i = 400 m for the remaining domains (i =2,..., 5), where the average depth is about 1000 m. The choice h 1 = 150 m corresponds to the shallowness of that region. The choice h i 6¼ 1 = 400 m is more difficult to justify. In the following we present two arguments that can be used in its favor. [14] Let x be the horizontal position in the gulf, z the depth, and t the time. The vertical profile of any oceanographic variable d, corresponding to the nth cast, is represented as d n ðþ:¼ z dðx n ; z n ; t n Þ: ð1þ Consider now the average profile of this variable over all N casts and its variance, d z ðþ:¼ 1 N X d n ; n s 2 d ðþ:¼ z 1 N X d n d 2; ð2þ respectively. Consider further the vertical average from depth z to the surface, namely, ~d n ðþ:¼ z d nð0þ at the surface; R 0 z d ð3þ nðþdx x below the surface: [15] Inspection of the standard deviation of the salinity profile, s ~ S (z), shows that h i 6¼ 1 = 400 m is a reasonable choice (perhaps somewhat shallow) for domains 3, 4 and 5 in the sense that most of the variability is concentrated above such depth (see Figure 3a). (A similar analysis for the n

4 15-4 BERON-VERA AND RIPA: GULF OF CALIFORNIA SALINITY BALANCE Figure 3. (a) Standard deviation profile of salinity averaged from depth z to the surface for all casts reaching 800 m in domains 2 5. (b) Transport of salinity anomaly from the average due to the gravest baroclinic mode, normalized by the maximum transport, estimated using mean values in the same domains. temperature field led Castro et al. [1994] to the same conclusion.) This depth seems to be too shallow in domain 2, but this is a result of a crude horizontal resolution [Beron- Vera and Ripa, 2000]. A better horizontal partition should have the Ballenas Channel (between the Baja California Peninsula and the Ángel de la Guarda Island, and a tongue south of it) as an isolated domain because of its remarkably distinct hydrographic features. On average the water is a bit saltier (about 2.5 C colder) than the surrounding water at the surface, whereas about 0.5 psu saltier (10 C warmer) than the adjacent water at z = 800 m, which is a signature of mixing processes. This is actually what produces the enhancement of salinity (and temperature) variability toward deeper levels in domain 2. However, as mentioned above, higher horizontal resolution (e.g., across the gulf in the region of the big islands) would require much more salinity data than that available in order to study the seasonal variability. [16] A significant fraction of the seasonal heat balance of the GC was shown to be dominated by baroclinic processes [Ripa, 1997; Beier, 1997]. It is thus tempting to think that similar processes may drive the salinity balance. The second argument that we offer in favor of the choice h i 6¼ 1 = 400 m is its ability to represent a baroclinic signal. Let G(z) satisfy [e.g., Gill, 1982] c 2 G 00 þ N 2 r G ¼ 0; ggð0þ ¼ c 2 G 0 ð0þ; ð4aþ ð4bþ Gð H r Þ ¼ 0; ð4cþ where c is the phase speed of the gravest baroclinic mode, N r (z) the is Brunt-Väisälä frequency, g is gravity, and H r is the reference depth of the fluid. The vertical structure function of the horizontal velocity is G 0. The quantity F b ðþ:¼ z 0 z S r ðþ ~S x r ð H r Þ G 0 ðþdx; x ð5þ where S r is the reference salinity profile, is proportional to the transport by the gravest baroclinic mode, between the surface and depth z, of the salinity anomaly. In Figure 3b we plot F b (z) normalized by F b ( H r ), using time mean values in domains 2 through 5, and assuming H r = 800 m, a value not too far from the average depth of these regions. The estimated baroclinic transport through the upper 400 m represents about 70% of that one through the whole water column in each region. Consequently, the choice h i 6¼ 1 = 400 m appears as reasonable for capturing quite fairly a baroclinic signal in the GC Temporal Treatment of the Data [17] Some qualitative evidence of seasonality, based on the signature of the monthly variability, has been provided in earlier work [e.g., Bray, 1988]. Evidence of this type is generally strong for variables such as temperature, which presents two well defined extreme values per year. The interpretation of salinity data is more difficult, however, given the sparseness of the temporal sampling, and the fact that salinity has an important semiannual variability, i.e., salinity presents four extremes along the year (see Figure 4). Similar variability is also evident in evaporation and precipitation records (see Figure 5). In order to get deeper insight into the physics of this variable, a more quantitative analysis is required. [18] Thus in the present work we performed least squares fits to the monthly mean data, D(t), with the 5-parameter model D A 0 þ A 1 cosðwt j 1 ÞþA 2 cosð2wt j 2 Þ; ð6þ where here t is month of the year, and 2p/w equals one year. We do not consider the long term (interannual) variability in this present work. However, both interannual and high frequency variability contaminate the seasonal fit because not all months are equally sampled. The goodness of the seasonal fit in equation (6) is represented

5 BERON-VERA AND RIPA: GULF OF CALIFORNIA SALINITY BALANCE 15-5 Figure 4. Seasonal fits (solid curves) of average salinity in each along-gulf domain (top numbers). Circles denote monthly data; shaded bands around the prediction curves represent an uncertainty of 1 standard deviation, exclusively related to the goodness of the seasonal fit. throughout this paper by uncertainty bars drawn at 1 standard deviation; these do not include errors from measurements or other sources (see Appendix A). The relevance of the fit is also assessed by comparing the explained variance with that corresponding to random data through a Monte Carlo simulation [e.g., Ripa and Marinone, 1989]. [19] In order to get a significant seasonal fit of salinity, some data, which represent extreme anomalies, had to be excluded from the analysis (see Figure 2). Excluded Figure 5. As in previous figure, but the evaporation minus precipitation rate.

6 15-6 BERON-VERA AND RIPA: GULF OF CALIFORNIA SALINITY BALANCE data correspond to hydrographic casts satisfying the condition 0 h i 2dz 0 S n2ii S > r s 2 S dz; h i where I i is the set of casts belonging to the ith domain. If r is chosen too large, all data are included and the seasonal fits derived from this data set are not significant. If r is too small, on the other hand, there is not enough data to estimate the seasonal signal. The ad hoc choices of r =2in domain 3, r = 1.5 in domains 1, 2, and 4, and r =2in domain 3, were found to reduce substantially the uncertainties of the estimated annual and semiannual components in all domains, except in domain 2. A higher value of r in this domain does not leave enough monthly mean data to capture the semiannual component. However, the exclusion of data from the cruise made in 1984 considerably improves the quality of the seasonal fit. The data in this domain describe a quite clear sinusoidal signal, with maximum near June, except for the data of March which correspond to the above mentioned cruise. Probably, these anomalies could be associated to the persistence of the very strong El-Niño signal of [Lavín et al., 1997]. However, the exclusion of data collected during well documented El Niño event years does not produce an improvement in the quality of the seasonal fits in any domain. To the contrary, it produces a large gap of data from July through September in regions 4 and 5 which conspires against the goodness of the determination of semiannual component. Additional random reductions of the data set do not change significantly the estimated amplitudes and phases, which gives certain degree of confidence to the present analysis. [20] More months sampled with better horizontal coverage and vertical resolution would be required in order to reduce significantly the uncertainties of our results. The analysis would benefit from data for January in all domains, as well as more observations in the trimester July August September in all domains. In particular, a better annual coverage in domain 2 would help us to determine the nature of the anomalies presented in the 1984 cruise data, which have been excluded from the analysis. 3. Average Salinity Balance Equation [21] Consider the common incompressibility approximation ru ¼ 0; and write the salinity conservation law as ð7þ t S þ u rs rðk S rsþ ¼ 0; ð9þ where r and u are the three-dimensional gradient and velocity, respectively, and k S stands for salt diffusivity. Consider further an arbitrary volume V(t) of seawater surrounded by the From equations (8) and (9) it follows that the average salinity within the volume, hsi :¼ V 1 SdV; V ð10þ changes according to V ds h i I ¼ ½S 0 ðu Þ k S rsš^n da; ð11þ where S 0 :=S hsi, and is any velocity following the boundary, whose normal unit vector and area differential are ^n and da, respectively. [22] The boundary is comprised of two + U@V, + (t) denotes the ocean surface is a fixed surface ^n = 0). Let E and P represent freshwater volume transports (per unit horizontal area) due to evaporation and precipitation, respectively. An adequate boundary condition + is given by [e.g., Beron-Vera et al., 1999] ½S 0 ðu þþ k S rsš^n þ ¼ hsiðp EÞ: ð12þ it is assumed u ^n =0=k S rs ^n the coastline and the bottom of the ocean; fluxes of any kind throughout it are allowed only represents the mouth or any boundary between two consecutive domains in the GC. [23] Combining equation (12) with (11) yields the (advective plus diffusive) transport of the salinity anomaly S 0 necessary to attain a balance within a seawater volume subject to a freshwater transport through the sea surface, ðs 0 u k S rsþ^n da ¼ hsi ðe PÞda þ V ds h i dt þ ð13þ The non-zero-flux boundary condition (equation (12)) is based on the assumption that no salt crosses the air sea interface during evaporation and precipitation, which implies that the sea surface is a material surface of the salt continuum [e.g., Beron-Vera et al., 1999]. This condition must not be confused with the so-called virtual salt flux, which is an unphysical surface boundary condition frequently used in numerical models. Such a virtual salt flux implies salt and freshwater volume changes such that there is no change in the seawater volume! In contrast, equation (12) prevents spurious volume changes since it implies ½Sðu þþ k S rsš ^n þ ¼ 0 ð14þ +, which in a closed basin guarantees salt conservation. [24] If the time mean part of the surface transport term in the right hand side of equation (13) does not vanish, then there must exist a transport of S 0 across the to compensate it. Yet this is not the case for the salt balance, which reads r ½su k S rsš^n da ¼ dt V rs dv; ð15þ where s 10 3 S is the salt fraction and r is seawater density, which can be taken as constant to Boussinesq order. Since there is no salt transport crossing the air sea interface, the time mean part of the salt transport must vanish.

7 BERON-VERA AND RIPA: GULF OF CALIFORNIA SALINITY BALANCE 15-7 [25] Balance equation (13) is in complete analogy with the average temperature balance equation that has been used to study the heat balance in the GC [Beron-Vera and Ripa, 2000]. ðt 0 u k T rt ^n Þda þ Q T 0 ðe PÞ da þ rc p V dt h i ; ð16þ dt where T 0 : = T ht i is the temperature anomaly; Q represents the total heat input ( per unit horizontal area), k T is the thermal diffusivity; and C p is some specific heat reference value. This fact facilitates the comparison of the physical processes that determine the average temperature and salinity balances as mentioned earlier. 4. Observed Seasonal Balance [26] The exchanges of S 0 among the 5 domains in Figure 1 are estimated here by applying (salbal1) to each of these regions. Notice that freshwater transports associated with river run-off are not included in equation (13); this is well justified in the GC due to the damming of the Colorado River [Lavín and Sánchez, 1999]. Identifying, from head to mouth, the transversal boundaries of the domains by the numbers m 1 2 (m =1,..., 6), denoting F m 1 the respective 2 transports of S 0, and assuming zero transport through the bottom boundaries, for the ith domain equation (13) takes the form ds h i F iþ 1 2 F i 1 2 ¼ hsi i A i ðe PÞ i V i i dt ði ¼ 1; ; 5Þ; ð17þ with the condition F1 2 = 0 (no flow at the head). Here A i, V i, (E P) i, and hsi i h i 1~S i ( h i ) are the surface area, volume, evaporation minus precipitation rate, and average salinity of the ith domain, respectively. Equation (16) is an algebraic system, closed in the 5 unknown transports F iþ 1 2, which are computed separately for each component of the seasonal decomposition (equation (6)). [27] The variables hsi i,(e P) i, and F i þ 1 will be shown 2 at positions x i of the middle point of each domain, with the origin of the along-gulf coordinate, x, at the head of the gulf. We will also consider the balance for the entire gulf, which is given by F 5þ 1 2 ¼ X i hsi i A i ðe PÞ i X i ds h i V i i : ð18þ dt 4.1. Along-Gulf Structure of the Balance Evaporation minus precipitation [28] In the annual mean, E always exceeds P along the GC, reaching the maximum excess of 0.8 ± 0.1 m y 1 in region 2 (see Figures 4 and 5). The annual amplitude of E P has a maximum of 1.1 ± 0.1 m y 1 also in domain 2; this value is about 25 times that reached at the mouth of the GC. The maximum value of the annual cycle occurs around November from the head to the mouth except in domain 4, where it occurs about 4 months earlier. The semiannual amplitude, which is smaller than the annual one except near the mouth, remains close to 0.25 m y 1 throughout the GC. The extreme values of the semiannual cycle occur around March/September everywhere except in domain 2 where they occur in May/November. [29] The large excess of E over P reported in the domain of the big islands suggests an important atmosphere-ocean interaction in the region, where convective processes are presumably intense [e.g., Beron-Vera and Ripa, 2000]. We do not have an explanation for the pronounced shift of the annual phase in domain 4; however, the annual harmonic alone in this domain represents only a very small fraction of the seasonal variance (see Table 1) Average salinity [30] The annual mean of hsi estimated in each along-gulf domain decreases from ± 0.01 psu at the head to ± 0.01 psu at the mouth (see Figures 4, 6, and 7). The annual amplitude has a maximum of 0.08 ± 0.02 psu in domain 2. The along-gulf average amplitude represents about one tenth of the longitudinal variation of the annual mean value. The largest uncertainties are found in domains 1 and 2, but are much smaller than the expected values. The maximum value of the annual cycle occurs between June and September in domains 2 through 5, and around December in the northernmost region. The average salinity also exhibits an important semiannual component, with the corresponding amplitudes of the same order of the annual ones except in domains 2 and 3. The semiannual maxima occur between January/July and April/October. As for the annual component, the semiannual amplitude uncertainties are large near the head of the GC; in domain 3 the uncertainty is as large as the expected amplitude. The annual fit alone is significant at the 90% confidence level (CL) in domains 3 and 4 (see Table 1). The semiannual component increases the explained variance making the annual plus semiannual fit significant at the 90% CL in domains 1, 2, and 4. The inclusion of a component with a 4 month harmonic does not improve the significance of the fit in domains 1, 2, and 3. In all domains, the annual fit and the annual plus semiannual fit are statistically significant at the 80% CL. [31] The shallowness of domain 1 with respect to domain 2 explains why even though the annual mean value of E P is greatest in domain 2, that of hsi is largest in domain 1. The lack of correlation between the along-gulf structure of the average salinity and E P at the annual and semiannual frequencies is indicative of the main conclusion of our paper, namely, that advective processes dominate the seasonal balance. A better correlation between hsi and E P might be expected if a shallower depth were used in the calculation of hsi; however, there is not a good correlation, even between S at the surface and E P [Ripa and Marinone, 1989] Salinity anomaly transport [32] The along-gulf structure of the estimated transport of S 0 is depicted in Figure 8. In the annual average, the transport increases from zero at the head to (9.8 ± 0.4) 10 2 psu Sv (1 Sv = 10 6 m 3 s 1 ) at the mouth in a quite linear fashion. This transport has an important annual variation with an amplitude which also increases toward the mouth. The annual amplitude acquires a maximum value there which is three times as large as the annual

8 15-8 BERON-VERA AND RIPA: GULF OF CALIFORNIA SALINITY BALANCE Table 1. Percentage of Variance Explained by the Annual (A) and Annual Plus Semiannual (AS) Fits of the Evaporation Minus Precipitation Rate E P and the Average Salinity hsi Within Each Horizontal Domain of Figure 1 a E P A 80 a 85 a 53 a AS 96 a 90 a 82 a 72 a 79 a hsi A a 70 a 41 a 50 AS 72 a 83 a a 73 a Fits significant at the 90% confidence level, determined by Monte Carlo simulations (at the 80% level all fits are significant). mean. The annual cycle reaches its maximum value around November all along the GC, except at the head where it occurs about 3 months later. The semiannual component of the residual salinity transport is also very important. The semiannual amplitude increases toward the mouth, where it is twice as large as the annual mean; the uncertainties, however, are rather large. The semiannual maxima occur around March/September all along the GC Global Balance [33] The results of the balance in the whole GC are summarized in Figure 9 and Table 2. In the annual mean, there is a net excess of E over P of 0.61 ± 0.03 m y 1. This produces a net excess of S over hsi, which is exported into the PO through the mouth in order to attain a balance. But this transport through the mouth has an even more important seasonal variation. More precisely, the estimated amplitudes of the annual (semiannual) component is three (two) as large as the estimated annual mean value. On the other hand, the corresponding changes in hsi due to the imbalance E P represent only a small fraction of the total variation. This evidences the important role of the PO in determining the seasonal balance of hsi in the GC. The PO was shown to play a similar role in the seasonal heat balance [Castro et al., 1994], for which case the semiannual cycle is not too important [Beron-Vera and Ripa, 2000]. Notice, however, that the uncertainties of the present global results are rather large; more data are needed in order to produce more robust results. [34] According to the present data, hsi within the whole GC experiences a maximum variation of nearly 0.2 psu y 1 over the course of a year. The profile of salinity, averaged over all casts, varies from about 35.2 psu at the surface to roughly 34.7 psu at 400 m (see Figure 10). Note that the reported temporal variation represents a significant fraction, about 40%, of this vertical change. 5. Modeled Seasonal Balance [35] Ripa [1997] showed that a linear one-dimensional non-diffusive two-layer model, with an inhomogeneous slab-like upper layer, is able to reproduce the essential features of observations of the transversely averaged seasonal variations of the sea surface elevation, heat content, surface velocity, and heat transport. Most of the dynamics and thermodynamics were shown to be controlled by the PO through the excitation of a baroclinic wave at the mouth of the GC. Wind drag and heat input through the surface, which produce a slight slope in the sea surface elevation and a local heating of the upper Figure 6. Evaporation minus precipitation rate in each domain of Figure 1. Here and in the subsequent figures, x is the along-gulf coordinate with x = 0 at the gulf s head. Error bars, in this and the following figures, are 1 standard deviation uncertainties exclusively related to the goodness of the seasonal fit.

9 BERON-VERA AND RIPA: GULF OF CALIFORNIA SALINITY BALANCE S annual mean [psu] [psu] [psu] annual amplitude semiannual amplitude x [Mm] annual phase semiannual phase x [Mm] M A F J O ND S A M JJ O N S A J J M M A D JF [month] [month] Figure 7. Average salinity as a function of the along-gulf position. Circles are estimations in each of the domains of Figure 1. Curves correspond to the local prediction of this quantity (i.e., a depth average) by the one-dimensional model at the annual and semiannual frequencies. Solid, dashed, and dot-dashed lines correspond to mouth, mouth plus wind, and mouth plus wind plus surface fluxes forced solutions, respectively). Figure 8. Along-gulf salinity anomaly transport (1 Sv = 10 6 m 3 s 1 ). Circles are estimations of the transports between the domains in Figure 1 and the Pacific Ocean. Curves correspond to the onedimensional model predictions at the annual and semiannual frequencies. The line style convention is the same as in Figure 7.

10 15-10 BERON-VERA AND RIPA: GULF OF CALIFORNIA SALINITY BALANCE Figure 9. Seasonal balance of the average salinity in the whole Gulf of California. The solid line represents the total average salinity change, whereas the dashed line indicates that part due to the imbalance of evaporation and precipitation. The difference between both curves represents the salinity anomaly transport (divided by the total gulf s volume) through the mouth required to attain a balance. The shaded bands represent an uncertainty of 1 standard deviation exclusively related to the goodness of the seasonal fit. layer, respectively, were shown to have a small effect on the surface velocity and the horizontal heat transport. With this in mind, the goal of this section to investigate whether this simple model can also be used to explain the seasonal average salinity balance not only at the annual scale but also at the semiannual one, which we showed erlier to be very important. This requires us to account for salinity variations in the upper layer and include freshwater fluxes through the surface, which were not considered by Ripa [1997]. Here we will neglect the GC s topography, as by Ripa [1990], which allows us to obtain an analytical solution Model Equations [36] Consider a two-layer narrow channel, with uniform width W, a flat bottom, and length L, aligned in the x direction (see Figure 11). Let u j (x, t) and H j be the alongchannel velocity and the unperturbed depth in the upper ( j = 1) and lower ( j = 2) layer. The linearized volume conservation equations in each layer are [e.g., Gill, 1982] along-gulf diffusion, the linearized temperature and salinity conservation equations t T 1 ¼ Q= rc p H 1 ; t S 1 ¼ S1 r ðe PÞ=H 1; ð20bþ where Q is the surface heat flux ( per unit horizontal area). The buoyancy inhomogeneity in the upper layer produces a depth-dependent pressure gradient. Vertically averaging the pressure force in each layer yields the momentum equations of the model [e.g., Ripa, 1993], whose linearized form can be written t u 1 x p 1 ¼ t=h 1 ; ð21aþ t u 2 x p 2 ¼ lu 2 ; ð21bþ p 1 ¼ gh þ 1 2 H 1J; p 2 ¼ gh þ g 0 z þ H 1 J: t ðh zþþh x u 1 ¼ P E; t z þ H x u 2 ¼ 0; ð19bþ where h(x, t) and z(x, t) denote the sea surface and interface elevations, respectively. The lower layer is assumed homogeneous and the temperature and salinity are denoted by T r 2 and S r 2, respectively. Let T r 1 + T 1 (x, t) and S r 1 + S 1 (x, t) be the temperature and salinity in the slab upper layer, with r r T 1 and S 1 their corresponding constant values in the formulation of a homogeneous layer model. Neglecting Table 2. Rate of Change of the Average Salinity in the Whole Gulf of California Due to the Surface and Mouth Fluxes a A 0 A 1 j 1 /w A 2 j 2 /(2w) Surface 2.8 ± ± /11 ± ± /5 ± 4 Mouth 2.8 ± ± 2 5/5 ± ± /5 ± 11 a Amplitudes are in 10 2 rm psu rm y 1, and Phases are in Days. Quoted uncertainties are of 1 standard deviation, related exclusively to the goodness of the seasonal fit (they do not include errors of measurement or other sources).

11 BERON-VERA AND RIPA: GULF OF CALIFORNIA SALINITY BALANCE where S 0 j :=S j r hsi r, is given x F ¼ hsi r ðe PÞW ðh 1 þ H 2 t hsi x : ð25þ This equation is the average salinity balance (equation (13)), without diffusion, now expressed in the variables of the one-dimensional dynamical model, which we will be evaluated and compared with the observations Forcing and Parameter Choices Mouth forcing [39] The system (18) (20b) is solved by requiring zero flow at the head (x = 0), and forcing at the mouth (x = L) by a baroclinic signal p 1 ðl; tþ p 2 ðl; tþ H 2 ¼ ghðl; tþþ 1 H 1 2 H 1JðL; tþ: ð26þ Figure 10. Average profile of salinity over all casts reaching 400 m. The curves indicate the average in each domain (excluding the shallowest one) or the average of all domains. Here t is the wind stress (divided by r); l is a bottom friction coefficient; g 0 := g[a(t 1 r T 2 r ) b(s 1 r S 2 r )] is the buoyancy jump across the interface; and is J :=g(at 1 bs 1 ) is the buoyancy change of the upper layer, where a and b are the thermal expansion and salt contraction coefficients, respectively. [37] According to this model, the average salinity is given locally by hsi x ¼ hsi r þ Sr 1 Sr 2 H 2 H 1 h z þ S 1 ; H 1 þ H 2 H 1 þ H 2 H 1 þ H 2 ð23þ Here h(l, t) is the observed average sea level between both coasts at the mouth, whose amplitudes (extreme values) equal 11 cm (on November 9) and 1.75 cm (on February/ August 11) at the annual and semiannual frequencies, respectively Wind stress [40] As by Ripa [1997], t is considered as uniform along the gulf with an annual amplitude of m 2 s 2 and phase corresponding to a maximum on February 13. These values were estimated by Ripa [1990] from the geostrophic wind calculated from the difference of atmospheric pressure at sea level in each coast, approximately in the middle of the gulf. The wind thus changes direction with the season blowing toward the head (mouth) in summer (winter). No information on the semiannual cycle of the wind stress is available Surface forcing [41] The surface flux forcing is set as polynomial fits of the annual and semiannual components of the along-gulf distribution of E P and Q (see Figure 12). The latter is given by the sum of the net solar (short wave) radiation Q s, where hsi r := (S 1 r H 1 + S 2 r H 2 )/(H 1 + H 2 ) is the reference average salinity. Neglect for the moment salinity variations in the upper layer, i.e., set S 1 = 0. For a barotropic signal z H 2 h/(h 1 + H 2 ) which implies that changes in hsi x are negligible. For a baroclinic signal, on the other hand, z h and t hsi x (S 2 r S 1 r )@ t z/(h 1 + H 2 ); namely, hsi x varies because of the water rearrangement produced by this signal. In the more general situation with S 1 6¼ 0, we have that changes in S 1 are responsible for the variations of hsi x in the presence of a barotropic signal. For a baroclinic signal, both contributions are present; the dominant contribution depends on the relative magnitude of z/h 1 and S 1 /(S 1 r S 2 r ). In the GC the vertical displacement is more important than the salinity variations in the upper layer, as we shall see below. [38] Finally, using equations (18) and (21), it follows that the divergence of the residual salinity flux, F :¼ S1 0 H 1u 1 þ S2 0 H 2u 2 W; ð24þ Figure 11. model. Sketch of the one-dimensional two-layer

12 15-12 BERON-VERA AND RIPA: GULF OF CALIFORNIA SALINITY BALANCE Figure 12. Observed surface heat flux Q and evaporation minus precipitation rate E P (circles and triangles denote the annual and semiannual components, respectively, with error bars of 1 standard deviation exclusively related to the goodness of the fit), and their polynomial fits (solid and dashed lines correspond to the annual and semiannual components, respectively). the net long wave radiation Q b, the evaporative (or latent) heat flux Q e, and the sensible heat flux (or turbulent heat conduction) Q h. We estimate these terms indirectly from the historical meteorological data employing the TOGA COARE bulk formulae [Fairall et al., 1996b] Parameters [42] Reference temperatures in each layer are set as T 1 r = 20.1 C and T 2 r =9.3 C, respectively, and reference salinities as S 1 r = 35.1 psu and S 2 r = 34.6 psu, respectively. The reference total density is chosen as r = 1028 kg m 3,the specific heat as C p = 3997 J kg 1 K 1, and the heat expansion and salt contraction coefficients as a = K 1 and b = psu 1, respectively. In addition, we consider H 1 = 70 m for the upper layer reference depth as found from the along-gulf sea level slope and an estimate of the geostrophic wind [Ripa, 1990]. The total depth is chosen as the average depth of the GC, i.e., H 1 + H 2 = 730 m. For the bottom friction we use l = s 1, a value that gives the best fit to the M 2 tide observations in the GC [Ripa and Velázquez, 1993]. These parameter choices cannot be strongly justified and are only considered as typical; no attempt was made to optimize them in order to improve the likeness of the model and the observations. The same parameter values were used by Ripa [1997] to explain the heat balance. Finally, we define our shoe box gulf dimensions by W = 150 km and L =1.1 Mm, which are the average width and length of the GC, respectively Analytic Solution [43] The baroclinic mode solution to the system (equations (18) (20b)) (see Appendix B) is considered here by switching on and off the surface forcing agents in order to evaluate their relative contributions. Thus, we consider the baroclinic responses to the 1. mouth forcing alone; 2. mouth and wind-forcing; and 3. mouth, wind, and surface flux forcing Average salinity [44] The mouth-forced solution describes about 80% of the observed annual amplitude of hsi in the whole GC (see Figure 7). Wind and surface fluxes (to a lesser extent) contribute to the headward enhancement of hsi. All solutions predict an annual phase in August which is close to the observations except at the head. At the semiannual scale, for which there are no estimates of wind stress, the mouthforced solution gives only about 50% of the observed hsi for the entire GC; no differences with the solution which includes surface fluxes are seen. The largest discrepancies between modeled and observed semiannual amplitudes of hsi along the gulf, are found toward the head. The best agreement between modeled and observed phases is found near the head, however. In a more realistic, and sophisticated, model [Ripa, 1995] we expect the changes of the upper layer salinity, due to E P concentration/dilution, to be distributed nonuniformily within the layer, putting the model predictions in better agreement with the observations Salinity anomaly transport [45] At the annual frequency, the transports of S 0 predicted by the three model solutions are very close to each other and in very good agreement with observations (see Figure 8). This shows that the forcing at the mouth is the main driving agent of the transport at this scale, i.e., longitudinal advection being the main carrier of S 0. The

13 BERON-VERA AND RIPA: GULF OF CALIFORNIA SALINITY BALANCE annual phase predicted by the three solutions coincide and are in very good agreement with the observations except at the head. At the semiannual frequency, there is good agreement between model predictions and observations, within their uncertainties, in both amplitude and phase. Again, the mouth-forced solution dominates the horizontal transport, which is thus mainly advective. 6. Summary and Concluding Remarks [46] In this paper we have studied the seasonal balance of the average salinity, hsi, in the Gulf of California using equation (13). This relation shows that the rate of change of hsi is given by evaporation minus precipitation, E P, concentration/dilution and by along-gulf (advective plus diffusive) transport of the salinity anomaly, S 0. [47] To this end we reduced the available historical data into 5 domains defined along the gulf. The monthly means of these data, fitted to a temporal signal with an annual mean value plus annual and semiannual harmonics, were then employed to determine the rate of change of hsi within each domain as well as E P. The exchanges of S 0 among the various along-gulf domains and with the Pacific Ocean were finally estimated, for each component of the harmonic decomposition. [48] The net excess of E over P over the course of a year was shown to produce a net excess of S over hsi, which has to be exported into the Pacific Ocean through the mouth of the gulf in order to attain a balance. Even though E P has strong annual and semiannual cycles, it is not enough to explain the seasonal variation of the transport of S 0. The annual mean, and annual and semiannual amplitudes of the transport of S 0 were shown to reach their maximum values toward the mouth, and decrease to zero at the head, while the phases remain practically uniform in along-gulf position. The uncertainties of these results are rather large, however. More data would be required in order to refine the analysis and conclusions. [49] A linear one-dimensional nondiffusive inhomogeneous two-layer model was used to gain some understanding on underlying physics of the seasonal balance of hsi. The model was forced at the mouth with a baroclinic wave, and at the surface by the wind, heat and freshwater fluxes. No optimization of any kind were performed, except reproducing the observed annual and semiannual components of the sea level at the mouth (estimated as the average of both coastal observations). Despite the simplicity of the model, a quite good agreement was observed between model predictions and the observed longitudinal transport of S 0,at both annual and semiannual scales. The agreement with the observed along-gulf variation of hsi at the annual and semiannual frequencies was not so good, however. For both variables the mouth-forced solution was shown to dominate. [50] We conclude that a large fraction of the seasonal balance of hsi is controlled by the Pacific Ocean, through the excitation of a baroclinic wave at the mouth of the gulf. Advection due to this wave is the main carrier of S 0, and the associated water rearrangement produces a considerable change in hsi. A more complete modeling effort would be desirable to reinforce this result, which adds importance to the Pacific Ocean influence on the seasonal dynamics and thermodynamics of the Gulf of California. Appendix A: Error Estimates [51] With respect to the error analysis applied to the fit (equation (6)), the m (= 5) coefficients a =(a 1,..., a m ) T are calculated from the n (12) monthly mean data D =(D 1,..., D n ) T by minimization of krk 2 :=r T Wr, for some positive definite metric W, where r :¼ D Fa ða1þ are the residuals of the fit, and F the (sine and cosine) fitting functions matrix. This results in a ¼ MFWD; r ¼ PD; ða2þ where M: =(F T WF) 1 and P: =I FMF T W with I an n n identity matrix. Quoted uncertainties of a correspond to 1 standard deviation s and are only a function of the misfit krk; they do not reflect, therefore, any other source of error. More precisely, the uncertainties, da, are estimated as 1; C a :¼bdada T e¼s 2 diag F T ^WF ða3þ where W^ is a diagonal matrix with elements which are the data per month involved in the monthly averages, and be denotes an ensemble average, which is meant as a statistical average over a hypothetical set of identical realizations. Result (equation (A3)) involve the following assumptions [e.g., Draper and Smith, 1981]: 1. The D are equal to some expected values of the form bde = F bae (i.e., with vanishing least residuals) plus some random errors, dd, with zero mean, and which are uncorrelated and have the same mean square root, namely, bdde = 0 and C D :=bdddd T e s 2 W^, respectively. 2. The standard deviation of the data errors s can be estimated by equating krk 2 to the number of degrees of freedom, n m, using the fact that the optimum value of W, i.e., that one that minimizes C a, is proportional to C D 1. [52] Finally, let us review the propagation of errors technique, which has been extensively used in the present study. Consider a function f (a) =f (bae ± da) which satisfies b f e = f (bae) +O(da 2 ) since bdae = 0. (Functions of this type appear in this paper in the resolution of the salinity exchanges.) Then ðdf Þ 2 :¼bðf bfeþ 2 T e¼ r bae f diagca r bae f ; ða4þ where r bae ½ a1 Š; ;@ ½ am Appendix B: Š T. This result is presented as f ðaþ ¼ f ðbaeþdf : ða5þ Modal Solution [53] Equations (18) and (20a) (20b) can be split into two normal modes, i.e., an external or barotropic mode and an internal or baroclinic mode. The contribution of the latter to (u j, p j ) is given by ðu 1 ; p 1 Þ ¼ m þ m þ m 1 ðu; pþ; ðu 2 ; p 2 Þ ¼ ðu; pþ; ðb1þ m m þ