estuaries november 10. flushing time (or residence time): time required to replace water with...

EstuariesEstuaries

November 10November 10

Flushing time (or residence time): time required Flushing time (or residence time): time required to replace water with “new” water. Several ways to replace water with “new” water. Several ways to compute:to compute:

Tidal Prism method:Tidal Prism method:

p

pf V

VVt

p

pf V

VVt

Where tf is number of tidal cycles required to “flush”; V is low tide volume of estuary V = (ave depth at MLLW) x (surface area)

Assumes complete mixing of tidal prism volume with low tide volume – not very realistic: Can assume some mixing parameter α

0<α≤1: fraction of intertidal volume (tidal prism)mixed with low tide volume. But how do we determine α?

In reality, water from head of estuary doesn’t get to mouth in 1 cycle; water that leaves on one cycle may return on next.One solution: Break estuary into segments each size of 1 tidal excursion

For Tampa Bay:

Bay Volume = 3.8147 x 10 9 m3 = 1.008 x 1012 gal. = 1008 billion gal.Bay Area = 1,031 km2 = 1.031 x 10 9 m2 Ave. Bay Depth = 3.7 m = 12.4 ftDeepest part of the bay is approx. 20 m = 67 ft Bay Length = 53 kmShoreline length: over 1,450 km Tidal Range = 0.7 m = 2.34 ft (difference between high and low tide)Tidal Prism = Tidal Range x Bay Area = 7.217 x 108 m3 = 191 billion gal = 19% of Bay Volume (amount of water flowing in/out of the bay on one tidal cycle)Volume of fresh water entering bay: approx. 60 m3 s-1 = 1369.4 MGD

Fraction Fresh water method: Fraction Fresh water method:

o

eofw

fw

o

eof

S

SSVV

R

V

S

SS

R

Vt

)( where

)(

V: Volume of Estuary

R: River inflowSo: Salinity at the mouthSe: Average salinity of estuaryVfw: volume of fresh water in

estuary

Time for all the fresh water in an estuary to be replaced by river inflow – Assumes that river inflow mixed evenly throughout estuary.

In reality, much more complicated – Tampa Bay modelFor Tampa Bay: tidal prism method gives 3-7 days fraction fresh water method gives 40-120 days Other definitions:

Bay Volume/Residual Circulation ~ 45 daysBay length/mean tidal excursion ~ 7 days

Residence Time varies with where you are in the bay and when you look

Estuarine CirculationEstuarine Circulation

Pressure gradient force = friction forcePressure gradient force = friction force

sityeddy visco vertical: 1

or

drag bottom : 1

2

2

z

uA

x

p

Jux

p

zo

o

Separate pressure gradient into external Separate pressure gradient into external (barotropic) and internal (baroclinic):(barotropic) and internal (baroclinic):

2

2

or z

uAJu

x

zg

xg

xgz

xg

x

p

zo

o

Pressure as a function of depth (z) at two locations along the axis of the bay. Pressure difference drives residual flow and is due both to variation in elevation of the sea surface (external) and to variation in density of the water (internal). Tidal mixing stirs fresher water from the head of the bay with saltier water from the mouth, keeping density more or less constant with depth but increasing from head to mouth.

Total flow is driven by the sum of the external and internal pressure gradient forces and is into the bay at depth and out of the bay near the surface

In rectangular estuary, get 2 layer In rectangular estuary, get 2 layer flow: flow:

0looking up “classic” picture

out

in

headmouth

mixing

Strength of mean circulation depends on Az (or J) which is parameterization of all time-Dependent processes, i.e. tidal mixing

In V-shaped estuary, get lateral gradients:In V-shaped estuary, get lateral gradients:

00

0

in

out

In deeper part of estuary, baroclinic (internal) pressure gradient is stronger – dominates balance because z is larger

In shallow flanks, barotropic pressure gradient dominates balance

+Modeled (black) and Observed (red) current components (northward and eastward) averaged for December 1997 from the Port Manatee ADCP site. Red/black dotted lines are +/- ¼ standard deviation of the ADCP data

Tampa Bay observed Residual Circulation from ADCP moorings

Average Bottom Salinity for August 31, 1991

Average salinity shows tongue of saltier water moving up ship channel …

Average Surface Salinity for August 31, 1991

… with fresher water moving out near the surface

Internal pressure gradient force drives flow into the bay in the deeper channels

External pressure gradient force drives flow out of the bay at shallower depths

Residence time is determined by the residual circulation and tidal mixing, and is shortest in the channels where circulation and mixing are strongest

Knudsen RelationsKnudsen Relations

VVii: Residual circulation inflow w/ salinity S: Residual circulation inflow w/ salinity Sii

VVoo: Residual circulation outflow w/ salinity S: Residual circulation outflow w/ salinity Soo

VViiSSii=V=VooSSoo

VVoo - V - Vii = X = R+P-E (net fresh water input) = X = R+P-E (net fresh water input)

VVii=(X S=(X Soo)/(S)/(Sii - S - Soo))

VVoo =(X S =(X Sii)/(S)/(Sii - S - Soo))

If you know X, SIf you know X, Sii, S, Soo, can estimate V, can estimate Vii, V, Voo

Fresh Water

Salt Water

Surfacez=h(x)

Mean Sea Level

Mouth

Head

z

z=0

Total Flow

VoSo

Vi

Si

X=50 m3s-1

So = 34Si = 35Vi=(X So)/(Si - So) = 1700 m3s-1

Vo =(X Si)/(Si - So) = 1750 m3s-1

X

Residual Circulation Residence Residual Circulation Residence TimeTime

RT=strength of residual circulation across a RT=strength of residual circulation across a section vs. volume bounded by that section section vs. volume bounded by that section

RT = Volume/VRT = Volume/Vii

For Tampa Bay, Volume = 3.8147 x 10 For Tampa Bay, Volume = 3.8147 x 10 99 m3 m3 RT= 2.244 x 10 6 sec = 26 daysRT= 2.244 x 10 6 sec = 26 days Compare with Volume-weighted average from Compare with Volume-weighted average from

Burwell (2000)Burwell (2000)

In larger estuaries, Coriolis is not In larger estuaries, Coriolis is not negligible – flow is concentrated to negligible – flow is concentrated to the right – in 2-layer flow:the right – in 2-layer flow:

Secondary transverse circulation

General Land UseGeneral Land Use

Urban

Ag & rural

Wetlands & water

Mining

Gaged and Ungaged Basins of

the Tampa Bay

Watershed

1930 1940 1950 1960 1970 1980 1990 2000YEAR

2 0

4 0

6 0

1 0

3 0

5 0

7 0

FL

OW

- M

GD

2 0

4 0

6 0

8 0

1 0 0

3 0

5 0

7 0

9 0

FL

OW

- C

FS

CRYSTAL SPRINGS NEAR ZEPHYRHILLS

J.W . PARK ER 16O C T2003D ATA TH R U 31M AY2003

Permitted Surface Water Permitted Surface Water UseUse

Real-time observations are combined with a model of currents and water level to provide a predictive capability for storm surge prediction and mitigation, search and rescue, environmental management/permitting, and hazardous material spills

Sewage Spill Trajectory

Desal Plant

+

+ Piney Point Phosphate Plant

Phosphate Discharge Trajectory

Big Bend Discharge

EPC Station 2