The Summer Buoyancy Dynamics of a Shallow Mediterranean Estuary and Some Effects of Changing Bathymetry: Tomales Bay, California

Estuarine, Coastal and Shelf Science (1997) 45, 497–506

The Summer Buoyancy Dynamics of a Shallow Mediterranean Estuary and Some Effects of Changing Bathymetry: Tomales Bay, California C. J. Hearna and J. L. Largierb a b

Oceanography, Adfa Campus of University of New South Wales, Canberra 2600, Australia Scripps Institution of Oceanography, University of California at San Diego, La Jolla, CA 92093, U.S.A.

Received 20 November 1995 and accepted in revised form 24 September 1996 A numerical study is presented of the summer buoyancy dynamics of Tomales Bay (California, U.S.A.) which is an example of a shallow mediterranean estuary. Tomales Bay lies along the line of the San Andreas fault, and the resultant unidirectionality of the estuary greatly simplifies its hydrodynamics. The numerical model hindcasts the temperature and salinity of Tomales Bay from 1987 to 1993 using detailed hydrological and meteorological data, and the results are compared with field observations made during that 7-year period. A second simulation is made over the same 7-year period but using the bathymetry for 1861 when the estuary was longer and deeper. This allows an analysis to be made of the effects on the summer buoyancy dynamics of anthropogenic bathymetry changes. The model predicts that the historical estuary experienced greater negative buoyancy inputs during the late summer periods, and became more inverse with faster dispersion near the head of the basin. ? 1997 Academic Press Limited Keywords: estuaries; models; flushing time; salinity variations; buoyancy; bathymetry; historical; California coast

Introduction This paper considers the summer buoyancy dynamics of Tomales Bay in California, U.S.A. (Smith et al., 1991a,b) with both its modern and historical bathymetries. Tomales Bay is a shallow mediterranean estuary, i.e. one lying in a mediterranean climate with wet winters and very dry summers (having little cloud cover, strong solar radiation and high net evaporation). During normally wet winters, such estuaries are efficiently flushed by storm river flow. However, in summer, their water exchange with the ocean is driven primarily by surface buoyancy fluxes and is often very slow. Consequently, estuaries of this class typically become hypersaline in later summer (under the influence of net evaporation) and may also develop seasonal inverse horizontal density gradients. During droughts, these late summer conditions, with their weak exchange, extend partially, or wholly, into winter. There are many examples of human damage to the ecologies of shallow mediterranean estuaries (such as the Peel Harvey in South-west Australia; McComb et al., 1981) which have their origins in this very weak ocean exchange. The strength of the surface buoyancy flux depends on the meteorological conditions but is also very sensitive to the baroclinic, or buoyancy, dynamics of the basin. This paper is presented as part 0272–7714/97/040497+10 $25.00/0/ec960197

of a series of investigations of these summer dynamics designed to assist understanding of the effects of human influences on this class of estuary. Tomales Bay was chosen for the present study because of the availability of long-term time series of physical data which span the major interannual variations in weather conditions (particularly winter rainfall). These were collected from 1987 to 1993 (Smith et al., 1991a) as part of the Land Margin Ecosystem Research program (LMER Coordinating Committee, 1992). A factor influencing the choice of Tomales Bay as a study site was its geometry which should constrain the hydrodynamics to be essentially unidirectional and so reduced the number of stations needed in the observational programme. To first order, the lateral effects in the basin are probably minor, and the present paper takes advantage of this simplification by implementing a two-dimensional model in the vertical longitudinal plane of the estuary. It is driven by longitudinal density gradients along the basin, and all lateral effects including wind-forced circulation are ignored. The model is used to hindcast temperature and salinity during the 7 year study period, using meteorological and hydrological data which were also collected during that programme, and a comparison is made with the field observations. The aim of the paper is to use the model to investigate ? 1997 Academic Press Limited

498 C. J. Hearn & J. L. Largier

Tomales Bay California 0

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Tomales Bay (Figures 1 and 2) lies in the mediterranean climate of the Californian-west coast of North America, just to the north of San Francisco Bay (Smith et al., 1991a,b). It is a highly unidirectional drowned rift valley, lying directly on the San Andreas Fault, about 25 km long and 1·4 km wide. Most of the (dominantly winter) freshwater runoff enters either at its head (Lagunitas Creek), or at the seaward end of the inner basin (Walker Creek), with some relatively minor groundwater flow. The estuary has steeply sloping terrain to its east over which is spread the

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possible changes to the summer estuarine state produced by human modifications of the basin. Any such change could affect the summer flushing and dispersion within the basin, which would be important to a variety of environmental balances in the estuary. Three types of physical modification to the estuary are particularly evident and may have significantly altered the summer buoyancy forcing. The first is the contraction in the size of the estuarine basin resulting from both the increased deposition of riverine sediment (due to changes in land usage) and the reclamation of bordering wetlands. Comparisons of a series of bathymetric surveys of Tomales Bay made from 1861 to 1994 show progressive reductions in both the length and depth of the estuarine basin. These bathymetric changes are discussed in more detail later in this paper and are displayed in Figure 4. The effects of this contraction on the summer buoyancy dynamics is the major theme of this paper. The analysis is based on a comparison of model simulations of the estuary using the modern and historical bathymetries. The second type of physical change to the estuary involves modifications to the tidal channel at its mouth and the Tomales Bay surveys do show major sediment deposition in this region (Figure 4). However, these changes are excluded from the present study since they have been discussed more generally by Hearn (1995); in some estuaries of this class, engineering changes have also been made to these channels. The third type of physical change, which will also be considered elsewhere (using the present model), involves the human control of freshwater runoff into the basin and, of particular relevance, the release of reservoir water during the summer dry season. Longer term climatological variations may also alter the buoyancy dynamics but these effects are outside the scope of the present studies. Accordingly, all the present simulations use meteorological and river flow data collected during the study period 1987–93.

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F 1. Tomales Bay; its location and catchment area.

catchment area (shown by the boundary line in Figure 1) with two reservoirs. Figure 3 shows the cumulative (impeded) freshwater flows from the two creeks during the study period. The total freshwater flow during those 7 years was about five times the volume of the inner basin, with the annual flows ranging from 20 to 200% of the basin volume. The maximum daily flow over this period (in early 1993) was 18% of the inner bay volume but winter values rarely exceed 1%. Typical summer daily flows are two orders of magnitude smaller (or 0·3 mm day "1 averaged over the area of the inner bay). The summer period is dominated by

Summer buoyancy dynamics 499 Outer Bay

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F 2. Tomales Bay, showing the monitoring stations and identifying the inner and outer bays. Shallows of less than 2 m are stippled. The lower part of the figure shows the longitudinal variation of the laterally averaged depth.

Flow (106 m3)

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limited) river flow. The maximum tidal currents reach 0·2 ms "1 in the Tomales Bay channel (which is consistent with its stability) but are very small elsewhere in the estuary: tides are mixed, with mean range of about 1 m; attenuation of the tidal elevation along the Bay is small. The channel, therefore tends to create an inner basin which has very limited barotropic tidal dispersion, so that its summer dynamics are forced by the surface buoyancy flux. The channel itself usually has comparatively small horizontal gradients in summer, and the flushing of Tomales Bay is largely controlled by horizontal transport through the inner basin. Sediment from Lagunitas Creek has shoaled the head of the basin, and that from Walker Creek has helped form the long shallow bank (Figure 1) through which cuts the tidal entry channel (this region is referred to as the outer bay in the figure). Figure 4 shows comparative depth contours (in feet) for the southern section of Tomales Bay (i.e. the inner basin) for 1861 and 1990. The datum for this chart is mean lower low water which is about 2·8 feet below mean sea level. The modern estuary is shorter than the historical estuary because shallows have been removed at the head by drainage and land reclamation programmes; these were of less than 1 foot depth. Infilling by sediments from Lagunitas Creek has created extensive modern shoals in regions containing historical contours down to 12 feet; the 6, 12 and 18 foot contours have migrated about 2 km along the estuary since 1861.

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Salinities and density gradient in Tomales Bay 100

0 1987

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F 3. Cumulative river flows into Tomales Bay from 1987 to 1993. ——, flow to inner bay (Lagunitas Creek); – – –, flow to outer bay (Walker Creek).

net evaporation, and the annual evaporation is of order 5% of the volume of the inner bay or about 1 mm day "1. This would produce a salinity increase of order 0·01 for each day that a vertically mixed water parcel was resident in the basin. Figure 2 shows the tidal channel at the mouth of Tomales Bay. Such channels are typical of estuaries of this class, and their bar-built geomorphology (Kjerfve, 1994) arises from the seasonal (and usually rather

Observed salinities in Tomales Bay over the 7-year study period are presented in Figure 5. For clarity, the model bottom salinity of the inner bay is shown twice to allow easier comparison with the observed salinity at the mouth (lower part of the figure) and the average observed bottom salinity (upper part of the figure). The time series for the salinity at the mouth has been interpolated from the approximately 3-weekly observations but the inner bay salinity is represented by the original data points. Regional shelf surface salinities range from 33·1 to 33·8 (Denver & Lentz, 1994), and salinities at the mouth of Tomales Bay are close to 34 in summer but decrease by several parts per thousand in winter. Mean winter salinities of the inner bay typically reach 25. At the end of the winter river flows, the salinity of the inner basin starts a seasonal increase and reaches marine values by early summer. By late summer, it may be 1 to 2 units greater than the salinity at the mouth, i.e. the inner basin becomes hypersaline. The

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F 4. Comparative depth contours (in feet) for Tomales Bay in 1861 and 1990.

extent of this hypersalinity clearly depends on the river flow during the preceding winter. Since the mean summer evaporation is only a few millimetres per day, the magnitude of the hypersalinity suggests that flushing times in late summer must be of order 100 days. The mean flushing time of the inner basin can be deduced directly from the observed salinities using a salt balance, provided that the rates of freshwater inflow and evaporation are known. Smith et al. (1991a) constructed a box model of this type in which

evaporation was calculated from meteorological data and observed water temperature. This showed that (as expected) the flushing time is of order a few days in winter and confirmed that later summer values are typically 100 days. Figure 6 presents time series for density (ót) at the mouth, and head, of the estuary (and also total river flow), and shows that during the later summer hypersaline period, the value of ót for the inner bay is very close to that at the mouth. Figure 6 verifies that the

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F 6. Observed density (ót) at the mouth and head of Tomales Bay over the study period (Stations 0 and 14 in Figure 2). Other lines show äót (the density stratification at Station 14) and river flow.

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density gradient during this season is smaller than at any time of the year, so that baroclinic processes would be expected to be small, which is consistent with the observed variation of flushing time. In the absence of a density gradient, the estuary will be flushed solely by the weak tidal, and wind-driven, barotropic processes and so the salt balance indirectly demonstrates that this barotropic flushing time must be in excess of 100 days. The longitudinal density difference Äót, defined as:

is positive for the winter classical estuary and returns to zero (neutral estuary) by early summer. Äót is negative for an inverse estuary (Pritchard, 1967), but Figure 6 shows that Äót in Tomales Bay is, at most, only slightly inverse in late Summer. Figure 7 allows a more detailed view of an annual cycle of salinity and river flow (for the dry year 1990). Prior to the middle of the year, the salinity depression due to individual storms in Figure 7 can be seen to recover with a time

River flow

30 Salinity

F 5. Salinities in Tomales Bay over the study period 1987 to 1993. · · · ·, modelled mean bottom salinity for the inner bay; ——, salinity at the mouth (Station 0 in Figure 2); +, observed bottom salinity of the inner bay.

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15 1990

0 1991 Year

F 7. Salinities in Tomales Bay during the dry year 1990, showing mean salinities for the inner bay, from observations and the model, together with the salinity at the mouth. The figure also shows relative river flow. ——, modelled bottom salinity of inner bay; +, observed bottom salinity of inner bay; · · · ·, salinity at mouth; – – –, river flow (arbitrary units).

constant of order 10 days (winter/spring values of Äót range from 2 to 5). Hypersalinity occurs from 90·5 to 90·9 (on the time axis of Figure 7), and notice that during this summer/autumn period, ót, at the head of the basin in Figure 5 exceeds that at the mouth so the estuary becomes marginally inverse (during that dry year). Figure 6 also shows the vertical density stratification of the water column at Station 14 (see

502 C. J. Hearn & J. L. Largier

Numerical model

F 8. Scatter diagram of the modelled and observed values of áÄT and âÄS which are the temperature and salinity of the inner bay (respectively), relative to values at the mouth, multiplied by the coefficients defined in Equation 3. Model output is based on the present bathymetry. The figure illustrates the compensation of the density increase due to hypersalinity by the decrease due to heating. +, model 1994; X, observations.

Figure 2), defined by:

and it is evident that äót is only significant during strong winter river flow; otherwise, the water column is well mixed (to within the resolution of the present data). The weakly inverse summer values of Äót do not exceed "0·5, which is small in relation to the summer hypersalinity differences of up to 2. This indicates some temperature compensation, and Figure 8 shows a scatter diagram of áÄT against âÄS in which ÄT is the temperature difference between the inner bay and mouth, and ÄS is the corresponding salinity difference. Only positive values of âÄS and áÄT are shown and the coefficients are defined as:

where the angular brackets represent averages over the temperature and salinity ranges found in the hypersaline summer estuary. The points in Figure 8 are mostly in the classical estuarine regime áÄT>âÄS i.e. the density difference in Equation 1 is positive, with some points just entering the inverse regime áÄT<âÄS in late summer.

A model is required which is driven by the hydrological and meteorological data, and predicts the seasonal and annual variation of the temperature and salinity of the inner basin of Tomales Bay. A simple model which allows the baroclinic dynamics to be derived directly from basic physical processes involves a vertical plane along the longitudinal axis of Tomales Bay. The unidirectional form of the estuary simplifies such a model because lateral variations are of only minor significance. This approach is used here, with lateral averaging, and is similar to that adopted by Perrels and Karelse (1981), but with the inclusion of runoff and evaporation/precipitation (see also Hearn et al., 1994, for a discussion of such models for shallow estuaries). The model cells are 185 m long with 10 equally spaced levels giving a vertical resolution of about 0·5 m. The time step is limited by the CourantFriedrichs-Lewy (CFL) criterion and is chosen as about 10 s. The model is probably adequate for the purpose of this study which is to consider seasonal variability of differences between the inner basin and mouth of Tomales Bay. Due to the small aspect ratio of width to length, depth-averaged wind-driven circulation would not be expected to be of importance in the basin. This does not preclude wind-induced vertical shear, which can be important to circulation in such basins (Hunter & Hearn, 1987), but Tomales Bay data show little correlation between currents and wind speed (or direction) so that wind forcing is entirely neglected in the model. Vertical mixing is assumed to be due to the turbulence created by bottom stress, and is incorporated via a vertical diffusivity (Heaps & Jones, 1987) which is independent of position within the water column (wind mixing is not included) and has the form:

where h is the depth and u* is the bottom stress velocity (due primarily to tidal flow) given by:

with Cd denoting the bottom drag coefficient (0·0025) and u("h) being the bottom velocity. The bottom boundary condition is:

and since the wind stress is neglected, the stress vanishes at the surface. A Richardson number

Summer buoyancy dynamics 503

dependence (Munk & Anderson, 1948; Leendertse & Liu, 1975) is used to multiply the otherwise constant vertical mixing coefficients for momentum, heat and salt. The Richardson number involves velocity shear (which is basically just tidal) and the vertical density gradient. The water column is essentially vertically mixed in summer so the Richardson number dependence has little effect apart from convective adjustment necessary to stabilize the water column when the surface buoyancy flux becomes negative. The model boundary was chosen as the mouth of Tomales Bay which is representative of conditions in Bodega Bay (Figure 1), rather than the open shelf, since (as discussed above) it is itself affected by freshwater runoff in winter. At the boundary, the model uses predicted tidal elevations. The boundary salinity and temperature, at all depths, are given the surface values interpolated from the data collected at 3-week intervals at Station 0 in Figure 2. In a shallow (almost vertically mixed) basin, baroclinic processes (Officer, 1976; Bowden, 1983) are forced by the horizontal density gradient associated with Äót (horizontal transport is further dependent on the vertical variation within the water column). Baroclinic processes act to reduce Äót but may leave compensating temperature and salinity differences ÄT and ÄS as observed in Tomales Bay. The extent of the density gradient is dependent on the surface buoyancy flux defined as "g)ñ/)t, where ñ(T,S) is density, g is the acceleration due to gravity, and the derivative refers to the (depth-averaged) rate of change of density due to surface fluxes of mass and heat; it can be written as:

The first term in Equation 7 represents net evaporation (E is an evaporative velocity from which is subtracted the effects of precipitation and river flow), and the second corresponds to heating/cooling, with á defined in Equation 3. Writing the total heat input (from net surface heating and freshwater inflow) as Ù, with Cp as the specific heat at constant pressure:

Finally, the mean buoyancy flux per unit mass into the inner bay, denoted by B, is defined as an average over Equation 7:

The model was run over the 7-year period from January 1987 to December 1993 using meteorological input files assembled from weather data collected with Sierra Misco ALERT stations, and a simple runoff algorithm, based on hydrological data, as described by Smith et al. (1991a). The evaporative rate (and latent heat loss) together with sensible, and radiative, heat losses were determined from model surface temperature, air temperature, humidity and wind data (Smith et al., 1991a), using the expressions given by Fischer et al. (1979); where meteorological records were missing, data from other years were repeated periodically. Q involves vertical irradiance determined by the position of the sun as a function of latitude, day of year and time; the amount of light penetrating the surface is then determined (from the angle of the sun). The cloud cover was assumed to be constant in the present model which is fairly representative of the summer mediterranean climate of interest here. The heat input Q contains small contributions from runoff and precipitation but both of these were ignored, and inflowing freshwater was assumed to have the temperature of the estuarine surface. The mean modelled salinity time series is shown in Figure 5. Detailed agreement with the winter data is not obtained, probably because the observations were made only every few weeks (much of the data are restricted to the surface) and the model is limited by the algorithms used for river flow. However, the model agrees reasonably with the observations during the dry season, and the spring/summer increase of salinity to marine values is reproduced as is the summer hypersaline regime. Figure 7 shows the salinities in more detail for 1990. There is a period of about 4 months in which the freshwater flow (shown in the figure) is less than 1% of the peak flow. During this drought period, the difference between the model and observed hyper-salinities is less than 10% of the observed values. Figure 9 presents the time series for the model buoyancy flux B which shows large positive peaks due to winter runoff. The small negative excursions of B in late summer are due to the positive net evaporative term exceeding that representing net heating in Equation 7. The model measures horizontal dispersion in the estuary through the time evolution of a pulse of tracer released at a selected model cell. The quantity of tracer remaining in the cell is determined at subsequent time steps for 1 day (which is a sufficient time to average over the astronomical tides for that day) and the reduction is used to define a dispersion time. The tracer is released uniformly through the water column but is differentially dispersed by the action of velocity shear. Vertical mixing of the tracer uses the same algorithm as for salt and heat given in Equation 4

504 C. J. Hearn & J. L. Largier

–3

Buoyancy flux × 10 per mass (m )

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F 9. Time series over the study period of the average buoyancy flux (per unit mass) B into the inner bay based on modern bathymetry.

Dispersion rate (inverse weeks)

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(which is affected by the state of the spring-neaps tidal cycle). Figure 10 shows the model distribution of dispersion rates for the present and historical estuary (for two late summer days). The spatial structure, with scales of a few kms, in these curves is related to variations in the bathymetry and cross-sectional area of the bay, and may be merely an artefact of the twodimensional nature of the model. The model historical estuary has faster dispersion near the head, and inspection of the predicted longitudinal variation of density confirms that this increase is associated with a greater (inverse) local density gradient. The dispersion rates closer to the mouth show less difference. Very close to the mouth the rates shown in the figure are less than the real rates associated with the tidal channel (because of the combined effects of tidal advection and mixing in Bodega Bay). The model is not intended to reproduce dispersion in this region. Discussion The purpose of this study is to understand the summer buoyancy dynamics of Tomales Bay and to consider how those dynamics may have been altered by anthropogenic changes to the bathymetry of the inner basin. The study has stressed the importance of baroclinic (density-driven) processes to the flushing to Tomales Bay. These processes are generally dominant over tidal dispersion and other mechanisms which transport salt along the estuary (Jay, 1991; Lewis & Lewis, 1983). The occurrence of hypersalinity in late summer is indicative of weak ocean exchange during that season, and this is a consequence of the longitudinal density gradients being at an annual minimum.

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F 10. Modelled late summer dispersion rates in present Tomales Bay for (a) the dry year 1990 (4 September), and (b) the wet year 1991 (30 September), based on present (——) and historical (– – –) bathymetries.

During this hypersaline season, the estuary becomes only weakly inverse (or remains classical or neutral) due to compensatory temperature increases. Analysis of the buoyancy flux, which is necessary to drive baroclinic processes, shows that the evaporative and heating terms tend to balance so that whilst there is appreciable net evaporation, and heating, the buoyance flux remains comparatively small. The model runs based on the historical bathymetry show greater inversion of the density gradient and faster dispersion near the head of the estuary. This change involves increased summer negative buoyancy flux. It is illustrated by Figure 11 which shows two cycles of buoyancy flux for the dry year 1990 based on the modern and historical bathymetries; salinity and river flow for that year are shown in Figure 7. Although the dispersion times within the historical estuary are shorter at the head of the estuary, this does not seem to compensate for the increased length in terms of total flushing time of the estuary since the estuary is more hypersaline. This flushing time is

Summer buoyancy dynamics 505

temperature compensation of the density change due to hypersalinity. Define the ratio of compensation of salinity by temperature as:

Buoyancy flux × 108 per mass (m s–3)

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F 11. A comparison of the model buoyancy fluxes for the dry year 1990 based on the modern and historical bathymetries. ——, 1994; – – –, 1861.

understood to represent the time for particles introduced into the basin to exit to the ocean. The concept has limited meaning in a seasonal situation in which the flushing time would exceed the seasonal time scales. The major consequences of the change in bathymetry is the modification of local dispersion rate close to the head so that the modern, more neutral, basin does show less horizontal dispersion. Table 1 shows the number of weeks per year that the model modern and historical estuaries (in pathentheses) are hypersaline and inverse. The modern estuary is nearly neutral during the hypersaline period which lasts for an average of some 18 weeks. The historical estuary is hypersaline for only a marginally longer period but is considerably more hypersaline and inverse. The historical estuary is ‘ negative ’ in the sense of the average buoyancy flux being negative, whilst in this sense, the modern estuary remains positive. It is of interest to enquire as to the effect of the modified bathymetry on the efficiency of the

where ÄT and ÄS are the temperature and salinity differences, and á, â are defined in Equation 3. The compensation ratio can be expected to decrease as the estuary becomes more inverse. This is confirmed by the mean salinity and temperature differences in Table 1 which show that the present hypersaline estuary has a compensation ratio c of 0·90, whilst in the historical hypersaline estuary, c is lower at 0·66. A major conclusion of this paper is the importance of the surface buoyancy flux to the summer flushing of shallow mediterranean estuaries, and the study has emphasized the extreme sensitivity of the estuarine state to the geometry of the basin. It is evident that there are a number of ways in which the increase in size of the inner basin can change the buoyancy dynamics and flux. In the present case, the most important effect seems to come from the increase in length. The historical basin also has a greater mean depth, which tends to reduce the mean buoyancy flux B (per unit mass) defined in Equation 9; it has also shallows near the head which would increase B. Vertical overturning in the water column due to a negative buoyancy flux tends to reduce horizontal transport in a flat-bottomed basin. The present model uses a convective adjustment algorithm based on the Richardson number which increases the vertical mixing coefficient to achieve rapid overturning, and thereby reduces horizontal dispersion. The study suggests the need for a systematic classification and modelling study of the effects of various types of bathymetric change on the state of a shallow mediterranean estuary. The present model has neglected wind forcing and all lateral effects within the estuarine

T 1. Average salinity, temperature and density differences (ÄS, ÄT and "Äót) between the inner basin and mouth of Tomales Bay for the present and historical (entries in parentheses) estuaries Estuarine state

Weeks per year

ÄS

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Äót

Average B

Hypersaline Inverse

18·0 (21·9) 3·9 (9·9)

0·65 (1·26) 0·22 (0·82)

1·75 (2·48) 0·27 (1·02)

0·28 (0·08) "0·28 ("0·41)

4·72 ("6·35) 4·23 ("6·96)

Averages are calculated for conditions in which the estuary is hypersaline, or inverse, and the table shows the average number of weeks per year for which these conditions occur. Average buoyancy fluxes per unit mass B#1010 (m s "3) are also shown.

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basin. This makes the model restrictive. There is clearly a need for a fully three-dimensional model (with tidal and wind forcing) to be applied to a range of shallow mediterranean estuaries including those with strong wind forcing (e.g. Harvey Estuary in Western Australia; Hearn et al., 1994), and higher aspect ratio of width to length. There is also a need for field observations with greater spatial and temporal resolution which could definitively identify inverse gravitational circulation and verify the model in more detail. Acknowledgements The model used here was developed under a grant from the Australian Research Council. The authors are indebted to Stephen V. Smith who made available data collected under the Land Margin Ecosystem Research, and Biological Reactions in Estuaries, programmes funded by National Science Foundation Grants OCE-8613647, OCE-8816709, OCE8914833, OCE-8616469, and OCE-8914921. One of the authors (CJH) is grateful to the Department of Oceanography, University of Hawaii (UH), for hospitality during much of this research. The U.S. Geological Survey and Marin Municipal Water District provided hydrological data, and John Rooney (UH) prepared the bathymetric data. The authors are very grateful to the anonymous referees for a series of important suggestions which greatly improved this paper. References Bowden, K. F. 1983 Physical Oceanography of Coastal Waters. John Wiley and Sons, New York, 302 pp. Denver, E. P. & Lentz, S. J. 1994 Heat and salt balances over the northern California shelf in winter and spring. Journal of Geophysical Research 99, 16001–16017. Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic Press, New York, 483 pp.

Heaps, N. S. & Jones, J. E. 1987 Estimation of storm generated currents. In Three Dimensional Models of Marine and Estuarine Dynamics (Nihoul, J. C. J. & Jamart, B. M. eds). Elsevier, Amsterdam, pp. 505–538. Hearn, C. J. 1995 Water exchange between shallow estuaries and the ocean. In Eutrophic Shallow Estuaries and Lagoons (McComb, A. J. ed.). CRC Press, Boca Raton, pp. 151–172. Hearn, C. J., McComb, A. J. & Lukatelich, R. J. 1994 Coastal lagoon ecosystem modelling. In Coastal Lagoon Processes (Kjerfve, B. ed.) Elsevier, Amsterdam, pp. 449–484. Hunter, J. R. & Hearn, C. J. Lateral and vertical wind-driven circulation in long shallow lakes. Journal of Geophysical Research 92, 13106–13114. Jay, D. A. 1991 Estuarine salt conservation: a Lagrangian approach. Estuarine, Coastal and Shelf Science 32, 547–565. Kjerfve, B. 1994 Coastal lagoon ecosystem modelling. In Coastal Lagoon processes (Kjerfve, B. ed.). Elsevier, Amsterdam, pp. 1–80. LMER Coordinating Committee. 1992 Understanding Changes in Coastal Environments: The LMER Program. Eos Trans. AGU 73, 481–485. Leendertse, J. J. & Liu, S-K. 1975 A Three-dimensional Model for Estuaries and Coastal Seas. Vol. II. The RAND Corporation, R-1764-OWRT. Lewis, R. E. & Lewis, J. O. 1983 The principal factors contributing to the flux of salt in a narrow, partially stratified estuary. Estuarine, Coastal and Shelf Science 16, 599–626. McComb, A. J., Atkins, R. P., Birch, P. B., Gordon, D. M. & Lukatelich, R. J. 1981 Eutrophication in the Peel-Harvey estuarine system, Western Australia. In Nutrient Enrichment in Estuaries (Neilsen, B. J. & Cronin, L. E. eds). Humana Press, New Jersey, pp. 332–342. Munk, W. H. & Anderson, E. R. 1948 Notes on the formation of the thermocline. Journal of Marine Research 7, 276–295. Officer, C. B. 1976 Physical Oceanography of Estuaries (and Associated Coastal Waters) John Wiley and sons, New York, 446 pp. Perrels, P. A. J. & Karelse, M. 1981 A two dimensional laterally averaged model for salt intrusion in estuaries. In Transport Models for Inland and Coastal Waters (Fischer, H. B. ed.). Academic Press, New York, pp. 483–535. Pritchard, D. W. 1967 Observations of circulation in coastal plain estuaries. In Estuaries (Lauff, G. H. ed.). AAAS Publ. #83, Washington, pp. 37–44. Smith, S. V., Hollibaugh, J. T., Dollar, S. J. & Vink, S. Tomales Bay metabolism: C-N-P stoichiometry and ecosystem heterotrophy at the land-sea interface. Estuarine, Coastal and Shelf Science 33, 223–257. Smith, S. V., Hollibaugh, J. T., Dollar, S. J. & Vink, S. 1991b Tomales Bay, California: A case for carbon controlled nitrogen cycling. Limnology and Oceanography 34, 37–52.