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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?