Education supported
by the NDSEG
Fellowship
Quantification of Residence Time in a Process-Based Model of an Ideal Inlet
Patrick Rynne1, Ad Reniers1, Jacobus van de Kreeke1, Jamie MacMahan2
1 University of Miami Rosenstiel School of Marine & Atmospheric Science, Miami FL , USA
Funded by ONR
2 Naval Postgraduate School, Monterey CA, USA
4.) How to measure it
t0
Cons
7
10
Photo by Gordan Farquharson
Surface Drifters
Pros Easy to deploy & track.
Cons Only capture 2d flow, requires many drifters, tedious
Destin Pass
t 0 + 3Δt
squares approach are presented in Figures 1 and 2. The final form of equations (11),
Channel Volume (m3)
t 0 + nΔt = Tr (x0 , y0 , z0 ,t 0 )
6
10
(12) and (13) for Florida Inlets are,
5
10
Inlet
Pass
Channel
Cut
Creek
Entrance
Inlet Data Fit
All Data Fit
4
10
10
t 0 + 2 Δt
Natural Tracers
already there!
Pros They’re
fluorescence etc... )
t 0 + 5 Δt
Cons
Residence time (Tr) is the total time a water parcel stays
entrained within a given boundary, like an estuary, bay or harbor.
2.) Why is it useful?
They might not be there, not always conservative.
7
10
Nuemann Boundary
8
9
10
(14b)
10
(14c)
An ideal inlet
model (right) is constructed
based on observations
L = 1.74P
from 15 inlets in the State of Florida (left, blue dots).
( 0.4 )
c
Mean Tidal Prism,
P (m3)
Flow Area,
Ac (m2)
Channel Volume,
vc (m3)
Channel Length,
lc (m)
Mean Depth,
hc (m)
Channel Width,
hc (m)
1.5 × 10 7
865
1.12 × 10 6
1.3 × 10 3
4.6
188
8.) Results
M = total mass of dye in system
Table 2: Ideal Florida Inlet dimensional parameters.
}
Q
6
10
Tidal Prism (m3)
5.) Virtual Tracer Technique
Release
Location (x0 , y0 , z0 )
Vc = 2.57 × 10 −6 P1.62
2
10 5
10
(salinity, temperature, ultraviolet
(14a)
Ac = 1.48 × 10 −6 P1.22
3
t 0 + 4 Δt
Nuemann Boundary
8
10
Water Level Boundary
New River Inlet
t 0 + 6 Δt
67 Florida Entrances
9
10
and entrance classifications. To ensure the most accurate empirical relationships, both
Expensive, requires lots of dye, need many sensors, dye can
equation (11) and (12) are applied to Florida inlets only. The best fit results from a least
disappear
1
Velocity in Channel
Water Level Inside
Water Level Outside
The inlet hydraulics suggest that
the system is flood dominated
midway through inlet channel and
that the estuarine tidal range is
nearly the same as the ocean. The
flood dominance is attributed to
modulation by overtides.
Equilibrium Dye
Distribution
Ebb Tide
Jet
Tidal Exchange
0
−0.5
−1
Runoff
3.) Tidal Exchange
0
- Virtual tracer is continuously released from a single point at a
flux rate ( Q ).
- The system runs until a tidally-averaged equilibrium is
reached (the tracer entering the system is balanced by the
tracer exiting the system on each tidal cycle).
- The tidally-averaged residence time for (x0 , y0 , z0 )
is defined as T = M
r
}
}
Cumulative Flux of tracer [kg]
6.) Population Model
Comparison
Time [hr]
10
15
r
Q
Tidal exchange is the process of replacing estuarine water with
seawater on each tidal cycle. The fraction of the tidal prism that is
renewed depends on the inlet geometry, the tidal range, and
physical processes that influence the ebb/flood flows.
Average Age
Population Model
Hydrodynamic Model
Birth Rate
# of people living
of Death
In a model, the flux of ( B )
High exchange
(N )
(D)
Q
B
Low exchange
tracer into and out of
N
M
estuary through the
Tracer
leaving
B
D
Tr
inlet channel can be
system
N
during ebb
D=
C
measured. Here, the
B
Tracer returning
exchange fraction is 1.) Imagine the birth rate of a closed population is one
during flood
individual per year
expressed as,
A
2.) Assume each individual dies after 80 years.
⎛ B−C⎞
ε = 1− ⎜
3.) How big is the population after 100 years assuming the
⎟
6
12
18
⎝ B − A⎠
Time [hr]
population started from zero?
5
The tidally-averaged residence time
distribution in the idealized basin is
presented to the right. Here the model
Figure 5: Model bathymetry and grid based on Florida inlet dimensions from
is run in 2D mode with tidal forcing only Table 2.
(M2). Although the spatial mean (T ) is
6.2 days, the residence time varies from
as little as 3 days near the inlet channel
to over 13 days on the opposite shore.
6.3
Tr ≈ aε b + c
a = 0.1794
6.2
6.1
Mean Residence Time [days]
40% of the global population lives
within 100km of the coast. Harbors, bays and
estuaries provide us access to the sea and are
renewed by rivers, runoff from the surrounding watershed and
through tidal exchange. Residence time calculations allow us to
precisely quantify the spatial variability of this renewal.
Depth (m)
Flood Tide
Withdrawal Zone
Water Level [m] & U [m/s]
0.5
River Discharge
Depth (m)
Release Location (x0 , y0 , z0 )
t 0 + Δt
7.) Idealized Model Domain
Conservative Tracers
Pros Capture 3d flows, controlled source, measurable with optical sensors.
6
Tidal exchange (ε) is varied using longshore
currents that are introduced to the model
by imposing a pressure gradient between
the two cross-shore Nuemann boundaries.
The strength of the gradient directly
influences the tidal exchange percentage
and the residence time distribution.
b = −6.2779
c = 5.1305
5.9
5.8
5.7
5.6
5.5
5.4
0.75
0.8
0.85
0.9
Tidal Exchange Fraction
0.95
1
9.) Future Work
Our ultimate goal is to apply this method to a validated model of
New River Inlet and examine the correlation between residence
time and water quality parameters through salinity and CDOM
observations. Our hypothesis is that water quality in a tidal inlet
system is controlled by residence time.
Residence Time [days]
1.) What is Residence Time?