Newport Beach Harbor/Back BayBivalve Restoration Project

• Computational modeling approaches to ecosystems• Rationalize interactions• Predictive ?

• Concepts• Variables• Parameter estimates• Models

• Bath tub (simple)• Cyclical (dynamic)• Spatial (non-uniform, complex)

Newport Harbor

Back Bay

Newport Back Bay Salt Marsh

Newport Harbor

Back Bay

HarborShoreline = 16 kmArea = 62471 pix2 = 3,500,000 m2 = 1870 x 1870 mAverage 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 mAverage depth = 2.5 mVolume = 2,500,000 m3

High tide area = +10340 pix2= 579,040 m2 = 761 x 761 mAverage depth = 0.5 mVolume = 290,000 m3

Flood plain = +32798 pix2 = 1,800,000 m2 = 1355 x 1355 mAverage depth = 0.5 mVolume = 900,000 m3

Newport Beach Harbor

Average ~ 1.3 m (4.5 ft)

Area = 62471 pix2 = 3,500,000 m2 = 1870 x 1870 mAverage 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 mDepth = 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/minSurface speed = 10 m/min (or 0.600 km/hr)

Tidal Flow

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

Area = 62471 pix2 = 3,500,000 m2 = 1870 x 1870 mTidal 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 %)

% of Newport Harbor Water Filtered per tide

San Diego Creek and Springs

Newport HarborEntrance

Spatial Gradients of Variable Factors

• Nutrient distribution• Bivalve habitat

flowout = m3/min

[Nutrient] = #/m3

bivalve density (#/m2)

flowin = m3/min

Bivalve habitat (2D #/m2)

San Diego Creek

Newport HarborEntrance

Spatial Gradients of Factors

• Tidal changes in volume (Dm3) & surface area (Dm2)• Relevance to habitat (#/m2)

Bivalve Density: Low, Medium, High ?

San Diego Creek

Cyclical Changes

Newport HarborEntrance

filtration = m3/min

growth = D#/min tidal flow = ± m3/min

turbidity = #/m3

San Diego Creek

Newport HarborEntrance

Stochastic Events

• Weather• Surge run-off

San Diego Creek

Newport HarborEntrance

To simplify let’s make some assumptions ….

i) Conservation of components (in = out)ii) Well mixed systemiii) Volume and surface area = constantiv) 1 principal factor determines phytoplankton growth bivalve population

Input = [In] x Flowin

= #/m3 x m3/min i.e. #/min

Output = [Bay] x Flowout

= #/m3 x m3/min i.e. #/min

Bivalve Ecosystem

• Nutrients (N, P, Fe)Fresh water flow Sunlight

Salt water (tidal)

Phytoplankton

% dieoff

PP carrying capacity (max population size)

Biv carrying capacity (max population size)

% dieoff

food chain

Bivalves

turbidity

salinity

turbidity

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 rapidlyfor k>0

Logistic growth (Verhulst-Pearl equation)– 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)

Exponential growth

resource limits (feedback)

P(t) = (K.Po.ert)/(K+Po(ert-1))

where lim P(t) = K t→∞

(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 PhytoplanktondP(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

TurbidityTurb(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 time-

varying 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