1. Flushing Times 1) Time required to replace the Volume of the basin V by the Volume Influx V in RV out V in x z t = V / V in t is obtained in seconds [ m 3 / m 3 /s] V out = V in + R V out S out = V in S in Water Budget: Salt Budget: Knudsen’s Relations

2. 2) Time required to replace the fresh water volume in the estuary by the river flow Flushing Times Volume of fresh water in the system (m 3 ) River flow (m 3 /s) 3) Same as 2) but using the concept of freshwater fraction to determine V f Define oceanic salinity as σ and salinity at any part of the estuary as S The freshwater fraction f is given by: If f = 0, all salty water; if f = 1, all fresh water average freshwater fraction Could use salinity between head and mouth to get

3. 4) Flushing by Tides (Tidal Prism Method) Tides bring oceanic water into the estuary during flood. The volume of this oceanic water V p is equal to the difference between high h w and low h l water multiplied times the surface area A of the estuary; V p = (h w – h l ) A Assume: - no variations of depth along the estuary  short estuary - over a full tidal cycle, V p is entirely mixed with V R - entire volume of mixed water is removed from estuary during ebb - on the next flood the process is repeated with seawater of S = σ entering the estuary Water going in has oceanic salinity; water going out has mixed S = Š z VRVR VpVp x hwhw hlhl Volume of fresh water Volume of tidal prism S = 0 S = σ

4. Flushing by Tides (Cont.) VRVR VpVp x hwhw hlhl Volume of fresh water Volume of tidal prism S = 0 S = σ z The average Š of the mixed water at high tide is given by: If V p >> V R, then Š  σ If V R >> V p, then Š  0 The mean fresh water fraction is: which includes River and Tidal effects

5. Flushing by Tides (Cont.) Flushing time by the tidal prism Taking our definition 3): T is the tidal period, i.e., the characteristic period of tidal exchange It would take a lot of T scales to flush the system if V >> V p + V R Drawbacks: -complete mixing from head to mouth of waters entering estuary; this shortens t T relative to real t T -no atmospheric forcing -water coming in is of oceanic salinity, which is usually not the case t T should be < t [t as derived from (1), (2) or (3)]

6. Flushing Rates Flushing rate F - rate at which the total volume of the estuary is exchanged F T should be > F In the case of a dye, if we release a dye of concentration C (in mass percentage) at a constant rate D (in kg/s): and the Flushing rate due to tidal prism F T

7. Flushing Rates in Sections (or segments) Modify tidal prism method by dividing the estuary into segments over which mixing takes place, rather than assume that there is complete mixing over the length of the estuary during each tidal cycle. The length of each segment is determined by the tidal excursion (U o T / π). Let, P i = intertidal volume for segment i (or tidal prism + V R ) V i = low water volume ViVi PiPi At the landward end: V i = V 0 -- low tide volume P i = P 0 = V R -- over a tidal cycle; provided by the river discharge

8. For the succeeding segments, assume that the high tide volume of the landward section is the low tide volume of the seaward section. This implies that the tidal excursion decreases landward or that the channel gets narrower. VnVn V n -1 P n -1 Flushing Rates in Sections (or segments) Therefore,

9. Flushing Rates in Sections (or segments) If the water within each segment is completely mixed at high tide, the proportion of water removed on ebb tide will be given by the ratio between intertidal volume and the high tide volume of the segment, or exchange ratio of segment ‘n’ r n : Modified Tidal Prism High Tide Volume VnVn V n -1 P n -1 Using: Volume of basin / (tidal prism + fresh water volume) or High Tide Volume / Modified Tidal Prism If V n = 0 (as in a tidal flat) r n = 1

10. Flushing Rates in Sections (or segments) Accumulated freshwater in each volume segment: Finally, Reference on Residence Time: Sheldon, J.E. and M. Alber (2002), A comparison of residence time calculations using simple compartment models of the Altamaha River Estuary, Georgia. Estuaries, 25:1304-1317.

11. Refer to to Tomczac’s page for more information on Flushing TimesRefer to to Tomczac’s page for more information on Flushing Times. Tejo Estuary, Portugal Residence Times (days) (following particles with a numerical model) Anabela Pacheco de Oliveira 5) Flushing times from particle tracking in numerical models

12. Flushing time in Mururoa Atoll Lagoon a coral island in Polynesia previously used for nuclear tests, determined from a numerical model The model takes into account tides and wind-driven water movement and includes flow over the coral reef as well as through the access channel. The figure on the left shows the circulation in the form of streamlines along which the water circulates. The zero streamline separates anti-clockwise circulation near the channel from clockwise circulation in the lagoon. Notice that most of the lagoon circulation is closed, so exchange with the ocean can only occur through turbulent diffusion across streamlines. The figure on the right shows the water residence time or flushing time in days. Most of the lagoon is flushed within less than 100 days, but there is a less well flushed region in the east where the flushing time exceeds 140 days. bathymetry © 2000 M. Tomczak