Newport Beach Harbor/Back Bay
Bivalve Restoration Project
• Computational modeling approaches to ecosystems
• Rationalize interactions
• Predictive ?
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Concepts
Variables
Parameter estimates
Models
• Bath tub (simple)
• Cyclical (dynamic)
• Spatial (non-uniform, complex)
Back Bay
Newport Harbor
Newport Back Bay Salt Marsh
Back Bay
Newport Harbor
Newport Beach Harbor
Harbor
Shoreline = 16 km
Area = 62471 pix2 = 3,500,000 m2 = 1870 x 1870 m
Average depth = 4 m (13ft) (range 2.5 m (8ft) to 6 m (20ft)
Volume = 14,000,000 m3 (8,700,000 m3 – 21,000,000 m3)
Upper Newport Bay
Low tide channels = 18407 pix2= 1,000,000 m2 = 1015 x 1015 m
Average depth = 2.5 m
Volume = 2,500,000 m3
High tide area = +10340 pix2= 579,040 m2 = 761 x 761 m
Average depth = 0.5 m
Volume = 290,000 m3
Flood plain = +32798 pix2 = 1,800,000 m2 = 1355 x 1355 m
Average depth = 0.5 m
Volume = 900,000 m3
Average ~ 1.3 m (4.5 ft)
Tidal Flow
Area = 62471 pix2 = 3,500,000 m2 = 1870 x 1870 m
Average depth = 4 m (13ft) (range 2.5 m (8ft) to 6 m (20ft)
Volume = 14,000,000 m3 (8,700,000 m3 – 21,000,000 m3)
Tidal range ± 1.3 m
Volume = 4,500,000 m3
Harbor Entrance = 220 m
Depth = 6 m (20 ft)
Cross-sectional area = 1320 m2
Tidal cycle (high tide-low tide) ~ 6 hrs or 360 mins
Flow rate (m3/min) at entrance = 12,600 m3/min
Surface speed = 10 m/min (or 0.600 km/hr)
Bivalve Statistics
Typical oyster filtration rate = 22 - 100 L/day = 0.92 – 4.2 L/hr = 15 – 70 mL/min
Average size of oyster bivalve = 5 cm
No of of bivalves/m2 = 100 biv/m2 (range: 10 – 400 biv/m2)
Filtration rate range
@ 10 biv/m2 = 150 mL/min – 7,00 mL/min
@ 100 biv/m2 = 1,500 mL/min – 7,000 mL/min
@ 400 biv/m2 = 6,000 mL/min – 28,000 mL/min
Filtration rate per tide
@ 10 biv/m2= 0.15 L/min x 360 min = 54 L – 252 L
@ 100 biv/m2 = 540 L – 2520 L
@ 400 biv/m2 = 2160 L – 10,080 L
Filtration rate per tide
@ 10 biv/m2 = 0.054 m3 – 0.252 m3
@ 100 biv/m2 = 0.540 m3 – 2.520 m3
@ 400 biv/m2 = 2.160 m3 – 10.080 m3
% of Newport Harbor Water Filtered per tide
Area = 62471 pix2 = 3,500,000 m2 = 1870 x 1870 m
Tidal range ± 1.3 m
Volume = 4,500,000 m3
Total Number of Bivalves in bay
@ 10 biv/m2 = 35,000,000
@ 100 biv/m2 = 350,000,000
@ 400 biv/m2 = 1,400,000,000
Filtration rate per tide
@ 10 biv/m2 = 0.054 m3 – 0.252 m3
@ 100 biv/m2 = 0.540 m3 – 2.520 m3
@ 400 biv/m2 = 2.160 m3 – 10.080 m3
Volume filtered per tide
@ 10 biv/m2 = 0.0540 x 3,500,000 = 190,000 m3 to 880,000 m3 (4 –
20 %)
@ 100 biv/m2 = 1,900,000 m3 to 8,800,000 m3 (40 - 200 %)
@ 400 biv/m2 = 7,500,000 m3 to 29,000,000 m3 (166 – 640 %)
Spatial Gradients of Variable Factors
• Nutrient distribution
• Bivalve habitat
San Diego Creek
and Springs
flowin = m3/min
[Nutrient] = #/m3
Newport Harbor
Entrance
flowout = m3/min
bivalve density (#/m2)
Bivalve habitat
(2D  #/m2)
Spatial Gradients of Factors
• Tidal changes in volume (Dm3) & surface area (Dm2)
• Relevance to habitat (#/m2)
San Diego
Creek
Newport Harbor
Entrance
Bivalve Density: Low, Medium, High ?
Cyclical Changes
San Diego
Creek
growth = D#/min
turbidity = #/m3
filtration = m3/min
tidal flow = ± m3/min
Newport Harbor
Entrance
Stochastic Events
• Weather
• Surge run-off
San Diego
Creek
Newport Harbor
Entrance
To simplify let’s make some assumptions ….
i)
ii)
iii)
iv)
Conservation of components (in = out)
Well mixed system
Volume and surface area = constant
1 principal factor determines phytoplankton growth  bivalve population
San Diego
Creek
Input = [In] x Flowin
= #/m3 x m3/min
i.e. #/min
Newport Harbor
Entrance
Output = [Bay] x Flowout
= #/m3 x m3/min
i.e. #/min
Bivalve Ecosystem
Fresh water flow
Sunlight
• Nutrients (N, P, Fe)
turbidity
% dieoff
PP carrying capacity
(max population size)
salinity
Phytoplankton
turbidity
Biv carrying capacity
(max population size)
Salt water (tidal)
food chain
Bivalves
% dieoff
Pollutants
toxicity
Population Growth
• Exponential growth
– xt = xo(1+r)t or P(t) = Po(1+ growth rate)time interval
– Solving over time (dx/dt) for changes in population size ….
x = aekt or P(t) = Pini . e(growth constant.time)
Population
grows rapidly
for k>0
Logistic growth (Verhulst-Pearl equation)
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•
– Initial stage of growth is approximately exponential; then, as saturation begins, growth
slows, and, at maturity, net growth stops
– P(t) = 1/(1+e-t)
Solving over time …. dP(t)/dt = P(t) . (1-P(t))
For biological systems where rate of reproduction is proportional to both the existing
population and the amount of available resources  self-limiting growth of population
– dP/dt = rP(1-P/K) where r = growth rate and K is the carrying capacity
– note early exponential growth depends on +rP; later, competition for food/space etc. is
due to larger term –rP2/K
carrying capacity (K)
resource limits
(feedback)
P(t) = (K.Po.ert)/(K+Po(ert-1))
where lim P(t) = K
t→∞
Exponential
growth
(r = frac. change/time)
What is limiting for phytoplankton (PP) growth ?
• Nutrient sources (N, P, Fe) or sunlight
– Are these constant, variable or variable + periodic (seasonal)
• Will these variables change the growth rate (r), carrying
capacity (K) or both ?
• How is increasing [PP] related to turbidity  reduces sunlight
 reduces growth ?
Nutrient Level Change in Bay
d(V.Cbay(t))/dt = Cin.Q – Cbay(t).Q – KconsP(t).V
⇒ dCbay(t)/dt = Q/V(Cin-Cbay(t)) – kcons.P(t) ……. Eq. 1
where ….
C = nutrient conc. (moles/m3); Q = flow rate (m3/min)
Kcons = consumption rate (moles of nutrients/moles of PP.min)
Phytoplankton Growth
Growth of Phytoplankton
dP(t)/dt = kgrowthCbay(t)P(t)(1-P(t)/Pmax) – kdeg(V/min)Pbiv …. Eq. 2
kgrowthCbay(t) is growth rate term (r)
Pmax is PP carrying capacity (K)
– kdeg(V/min)Pbiv is clearance rate of PP by bivalve population
Turbidity
Turb(t) = kopt.P(t) ….. Eq. 3
• Turb(t) is interdependent with self-limiting growth from equation 2
• and efficiency/size of bivalve population (clearance rate)
• kopt is a conversion constant
Bivalve Population Growth
Can write similar equations for bivalve population changes…..
– Dependent on [PP] (measured as ∞ turbidity)
– Bivalve Kbiv (carrying capacity) is dependent on [PP] and timevarying variables (e.g. seasons)
– Bivalve growth rate (rbiv) is dependent on filtration rate
(efficiency) and [PP] (resource)
What factors might affect efficiency ?
– Habitat (spatial differences: tidal flats v. channels)
– Pollution (impaired growth)
Parameter Exploration