FAU Institutional Repository http://purl.fcla.edu/fau/fauir This paper was submitted by the faculty of FAU’s Harbor Branch Oceanographic Institute. Notice: ©1996 American Geophysical Union. An edited version of this paper was published by AGU. This publication may be cited as: Smith, N. P. (1996). Tidal and Low Frequency Flushing of a Coastal Lagoon Using a Flexible Grid Model. In Pattiaratchi, C. (Ed.), Mixing in Estuaries and Coastal Seas, Coastal Estuarine Studies, 50(171‐183), doi:10.1029/CE050 11 Tidal and Low Frequency Flushing of a Coastal Lagoon Using a Flexible Grid Model N. P. Smith Abstract Tidal and low frequency nontidal exchanges of water between a coastal lagoon and adjacent continental shelf are investigated within the context of flushing, using a computer model based on the continuity equation. Flushing is quantified by the 50% renewal time. The arrival of new ocean water occurs as a result of longitudinal diffusion and a degree of advective transport governed by the flexibility of segment boundaries to move with the ebb and Oood of Ule tide. The model is applied to the Indian River lagoon system, lying along the Atlantic coast of Florida, USA. Flushing rates are quantified for three sub-basins of Indian River lagoon, and for Banana River lagoon, connected to the northern sub-basin uf Indian River lagoon. The lagoons are microtidal and depend upon low frequency exchanges to maintain water quality. One-year simulations for the Indian River lagoon system as a whole show Olat the 50% renewal time is approximately 140 days when transport by advection. When the renewal of lagoon water is by longitudinal diffusion alone, Ole 50% renewal level is not reached after 365 days. A second series of simulations compares flushing rates for the Olree sub-basins of Indian River lagoon and for Banana River lagoon, assuming a completely flexible grid. The soulliern and central sub-basins of Indian River lagoon receive a 50% renewal of new ocean water in about 5 and 12 days, respectively; Ole northern sub-basin of Indian River lagoon and Banana River lagoon reach approximately 30% renewal by Ole end of Ole one-year simulation. MiXing in Estuaries and Coastal Seas Coastal and Estuarine Studies Volume 50, Pages 171-183 Copyright 1996 by the American Geophysical Union 171 172 Flexible Grid Model Introduction Mixing processes in estuaries dictate the rates at which salt water and fresh water enter and leave, respectively, and thus are of crucial importance in determining temporal and spatial variations of salinity, and the flushing characteristics of the estuary in general. Energetic mixing within an estuary, in combination with active estuarine-shelf exchanges, reduces the residence time of fresh water, and at the same time encourages the incursion of salt water. Thus, whether flushing is quantified by the flushing time (Officer, 1976) or, for example, the 50% renewal time of new ocean water (Pritchard, 1960), mixing within an estuary determines the estuary's natural ability to maintain or reestablish water quality. Early flushing models (Ketchum, 1951; Stommel and Arons, 1951) used time steps of one semidiurnal tidal cycle and assumed complete mixing within segments partitioned according to the local intertidal volume. While simple flushing models continue to be used (Dyer and Taylor, 1973; Robinson, 1983; Merino et al., 1990; Miller and McPherson, 1991) and serve a useful purpose ~ quicklook tools (Wood, 1979), three basic features compromise their ability to provide realistic results. First is the assumption of complete mixing, which was challenged at an early date (Austin, 1954), although Wood (1979) has suggested a modification to deal with this issue. Second is the need to work with a single tidal constituent, which eliminates the opportunity to investigate variations in flushing rates over a synodic month, for example. Third, although freshwater outflow can be incorporated into tidal prism models, low frequency nontidal exchanges between estuarine and continental shelf waters cannot. Nontidal exchanges often provide an important supplement to tidal flushing. This paper constitutes one of a series of studies that has been designed to quantify flushing rates for Indian River lagoon, lying along the Atlantic coast of Florida (Figure 1). The lagoon is, 196 km long and generally 2-4 km wide. Water depths are characteristically between 1 and 3 m, though the Atlantic Intracoastal Waterway, forming the longitudinal axis of the lagoon, has a depth of 3.5 m. The lagoon is divided into three sub-basins, defined by three inlets, all of which are in the southern half of the lagoon. Banana River lagoon is connected to the northern sub-basin. The northern end of Indian River is connected to the southern end of Mosquito Lagoon by Haulover Canal (Smith, 1993a). Indian River lagoon is microtidal, with the semidiurnal M2 tide serving as the principal constituent (Smith, 1987). M2 amplitudes in the northern sub-basin are generally 0-5 cm. Amplitudes in the central and southern sub-basins are 5-10 cm and 10-15 cm, respectively. Banana River lagoon is virtually tideless, with amplitudes of all tidal constituents less than 0.5 em. The first paper in the series (Smith, 1993b) quantified the intertidal volume by using harmonic constants of the principal semidiurnal and diurnal tidal constituents recorded at 28 study sites. Amplitudes were multiplied by the surface areas they represent, and phase angles were incorporated to account for the movement of tidal waves through the lagoon. A precise measure of the intertidal volume was obtained Smith 173 for spring and neap conditions, including effects of diurnal inequalities. The second paper (Smith, 1993c) applied these results to a flushing model that incorporated both advective and diffusive transport of fresh and salt water, and that compared flushing rates with and without ancillary nontidal exchanges. An important distinction between this approach and hydrodynamic models is that the rise and fall of the tide is specified within the model, using the predicted tide (Schureman, 1958), rather than simulated by adjusting friction within the model. As a result, tidal exchanges are modeled more precisely. Mixing within the lagoon must be specified, however, just as with a hydrodynamic model, and model verification will involve matching hydrographic measurements. ATLANTIC OCEAN Inlet Ft. Pierce Inlet o 50Km St. Lucie Inlet Figure 1. The Indian River lagoon system on Florida's Atlantic coast, including Indian River lagoon and Banana River lagoon. Dots show locations of water level recorders; lateral lines define segments 1-16 in Indian River lagoon and segments Ib-3b in Banana River lagoon. 174 Flexible Grid Model Neither of the above studies incorporated Banana River due to a lack of information on tidal conditions. Also, the flushing model assumed a complete mixing of water moving from one segment to the next, as have most of the earlier tidal prism models. This third study expands the geographic scope of earlier work on Indian River lagoon by incorporating the exchange of water between the northern sub-basin and Banana River lagoon. Also, the model used here has a flexible grid that controls the extent to which segment boundaries move along the longitudinal axis of the lagoon with the ebb and flood of the tide. When the grid flexes freely with the longitudinal flow, no advective transport from one segment to the next results, and transport is by diffusion only. When the grid is fixed and inflexible, advective transport between adjacent segments is similar to that specified in the tidal prism models. In that case, diffusion is not considered. Indian River lagoon is well understood in terms of tidal dynamics (Smith, 1987, 1990), but a dearth of hydrographic data has prevented the verification of results of flushing studies (Sheng and others, 1990, Smith, 1993c). Models can be useful in the diagnostic mode for gaining insight, however, even while the data base necessary for verification is being assembled. The model used in this study is intended to quantify flushing rates, not elucidate the dynamics of the lagoon. For that, one must tum to hydrodynamic models. The scope of this study is intentionally restricted to flushing in response to two-way lagoon-shelf exchanges. Fresh water effects are considered in other studies (see Smith, 1993c). The specific aims of the study are to obtain flushing estimates of flushing rates for the three sub-basins of Indian River "lagoon and Banana River lagoon, and to compare the assumption of complete mixing. with the assumption that mixing occurs by diffusion only. Observations Water level records from the 31 locations shown in Figure 1 were obtained between, 1969 and 1992 using Stevens Model A and Model F analog recorders, and a Stevens Model 7031 digital recorder. Water levels were read to the nearest 0.1 cm or 0.01 foot (0.3 cm). Time series varied in length, but most were between two and three months long. All records provided information on the nontidal rise and fall in lagoon water level (Smith, 1986); longer time series, in excess of one year, were used to characterize seasonal cycles. The surface areas of Indian River and Banana River lagoons represented by each of the 31 study sites were determined using a compensating polar planimeter and navigational charts. Study sites were not distributed uniformly, and individual water level time series represented surface areas of from 1.4 to 98.0 km2. Some of the smaller segments were combined, especially near the inlets, where small volumes could be completely flushed within the one-hour time steps used in the simulations. In its final form, the model included three segments in Banana River lagoon and 16 Smith 175 segments in Indian River lagoon, as shown in Figure 1. The model does not require data from a dense network of tide gauges.