Estuarine Dynamics.

Summary of previous lessons.Estuarine Dynamics

Equations format for Env. Modelling

)( kkjj

k SiSoxc

xdtdc

)( kkk SiSodtdc

Isolated System:

Material System Moving with the flow (lagrangian formulation):

Fixe point (Eulerian formulation):

)( kkjjj

kjk SiSoxc

xxcu

tc

)( kkj

kjj

k SiSoxccu

xtc

Lotka Volterra

This model describes the dynamics, but it is quantitatively incorrect.

http://home.comcast.net/~sharov/PopEcol/

http://home.comcast.net/~sharov/PopEcol/lec10/lotka.html

Results: no interannual variability

Source and Sink terms. The Phyto Eq.

1.2 ZGPmerdtdP

Zpppp

Why to study an estuary in the course?

• Estuaries are among the richest ecosystems,• Estuarine ecosystems require knowledge of a

large number of disciplines,• They are a adequate to introduce a general

ecosystem approach that can be simplified for particular ecosystems.

Estuaries vs Coastal Lagoons

Fine (organic rich sediments settle in the upper estuary due to flocculation induced by salinity

Estuary Definition

• http://en.wikipedia.org/wiki/Estuary– An estuary is a partly enclosed coastal body of

water with one or more rivers or streams flowing into it, and with a free connection to the open sea.[1]

• In the Water Framework Directive:– An estuary is a “Transition Water” ) from a fresh

water body into a coastal water body.

Estuarine LifeEstuaries are home to an astonishing variety of plants and animals and important in the lifecycles of many more.

Salt Marshes importanceSalt marshes form in shallow, quiet water, where the water is salty and still enough for the suspended particles to settle to the bottom. These marshes are some of the most productive lands in the world and produce so many organic nutrients that their influence can be seen far out into the coastal ocean waters. Marshes are based on one plant, the Saltmarsh Cordgrass, which helps stabilize the environment so that many other plants and animals to move in.

Why are Estuaries so much demanded by people?

• Because they generate opportunities:– Goods,– Navigation,– Recreation,– ……..

• The estuarine ecosystem is biologically rich because estuaries are rich in nutrients/primary producers. They provide food and protection to many species of juveniles (they are nursery zones).

• What about eutrophication?

Classification of Estuaries

• http://www.onr.navy.mil/focus/ocean/habitats/estuaries1.htm

• Coastal Plain Estuaries or Drowned river valleys,• Tectonic Estuaries,• Bar-built Estuaries or Lagoon type,• Fjords.

Coastal Plain Estuaries

1. Coastal Plain Estuaries are formed by the sea level rising and filling an existing river valley. Examples of this are the Chesapeake Bay in Maryland and the harbor in Charleston, South Carolina

Tectonic Estuaries

2. Tectonic Estuaries are caused by the folding or faulting of land surfaces. These estuaries are found along major fault lines, like the San Francisco Bay area in California.

Bar-built Estuaries (Rias/Lagoas em Português)

Bar-built Estuaries form when a shallow lagoon or bay is protected from the ocean by a sand bar or barrier island. Examples of these are found along the Eastern Seaboard and the Gulf Coast of North America.

Fjords

Fjords are U-shaped valleys formed by glacial action. Fjords are found in areas with long histories of glacier activity, like northern Europe, Alaska and Canada.

Are this the only types of estuaries?

• Most of today's estuaries formed because the sea level has slowly risen during the last 18,000 years, drowning river valleys and filling in glacial troughs.

• This classification is relevant yes because it helps us describing estuaries. It is not because many estuaries do not fit in any of these types….

Estuarine Hydrodynamics: Tides

• http://www.onr.navy.mil/focus/ocean/motion/tides1.htm

• Tides are the periodic rise and fall of the ocean waters. They are caused by the gravitational pulls of the Moon and (to a lesser extent) Sun, as well as the rotation of the Earth.

http://www.onr.navy.mil/focus/ocean/motion/tides1.htm

Classification based on water circulation

http://en.wikipedia.org/wiki/Estuary

Salt wedgeIn this type of estuary, river output greatly exceeds marine input and tidal effects have a minor importance. Fresh water floats on top of the seawater in a layer that gradually thins as it moves seaward. The denser seawater moves landward along the bottom of the estuary, forming a wedge-shaped layer that is thinner as it approaches land. As a velocity difference develops between the two layers, shear forces generate internal waves at the interface, mixing the seawater upward with the freshwater. An example of a salt wedge estuary is the Mississippi River.[5]

Partially mixed estuary

As tidal forcing increases, river output becomes less than the marine input. Here, current induced turbulence causes mixing of the whole water column such that salinity varies more longitudinally rather than vertically, leading to a moderately stratified condition. Examples include the Chesapeake Bay and Narragansett Bay.[5]

Vertically homogenous

Tidal mixing forces exceed river output, resulting in a well mixed water column and the disappearance of the vertical salinity gradient. The freshwater-seawater boundary is eliminated due to the intense turbulent mixing and eddy effects. The lower reaches of the Delaware Bay and the Raritan River in New Jersey are examples of vertically homogenous estuaries.[5]

Fjord

Inverse estuaryInverse estuaries occur in dry climates where evaporation greatly exceeds the inflow of fresh water. A salinity maximum zone is formed, and both riverine and oceanic water flow close to the surface towards this zone.[6] This water is pushed downward and spreads along the bottom in both the seaward and landward direction.[3] An example of an inverse estuary is Spencer Gulf, South Australia

Estuary Flow properties

• Residual velocity• Residence Time• Tidal prism• Cohesive sediment dynamics

Intermittent Estuary

Estuary type varies dramatically depending on freshwater input, and is capable of changing from a wholly marine embayment to any of the other estuary types.[7][8]

(See also Estuarine water circulation)

Estuarine hydrodynamics

• Shallow water equations:• Hydrostatic pressure,• Vertical velocity is much smaller than

horizontal velocity (coriolis),• Boussinesq approximation (density)

2D Depth Integrated Hydrodynamic Model

02

2

1

1

2

21

2

22

1

212

1

12

2

12

1

111

22

11

xHu

xHu

t

xuH

xxgHfu

xuHu

xuHu

tHu

xuH

xxgHfu

xuHu

xuHu

tHu

fsjj

fsjj

MOHID Bathymetry Module• Bathymetry

– Defines the horizontal grid– The grid can be uniform or variable– The number of grid points is typically 200x200

Vertical grid (3D models)• Sigma coordinate

• Cartesian coordinate

Boundary Conditions

• Open boundary• Closed boundary• Moving boundary

MOHID main Modules• Hydrodynamic

– Propriedades de escoamento (niveís, velocidades, fluxos)• Waterproperties (Eulerian)

– Propriedades de águas (temperaturua, salinidade, phytoplankton, etc)– Abordagem euleriana

• Lagrangian– Propriedades de águas (temperatura, salinidade, phytoplankton, etc)– Abordagem lagrangiana

• WaterQuality (Sources – Sinks)– Processos de qualidade de água (fontes e poços)– Funciona como um modelo 0D

Mohid – Input Data File

• Ficheiros ASCII• Palavras Chaves• Organização por

blocos

2D Hydrodynamic model parameters

• Physical parameters:– Bottom and surface friction coefficients,– Horizontal diffusivity (viscosity).

Bottom shear stress

α

025.0

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.

23/4

22

n

mulaManningForURngUc

zutg

hfb

b

Velocity Definition

• The figure represents molecules of two fluids. The velocity across the dashed line measures the volume of molecules crossing the surface per unit of area.

• If the velocity is null the volume crossing in one sense is equal to the volume crossing on the opposite sense.

Cx Cx+∆x

Diffusion• However even if there is no velocity, there is molecules exchange

and consequently there is mixing. This is called diffusion.• If the molecules on one side of the surface are statistically different

from the molecules on the other side (different concentration) there will be a mass fluxes of individual constituents.

• If molecules move due to Brownian movement diffusion is called molecular diffusion.

• If they move due to turbulence (eddies) it will be called turbulent diffusion.

• Turbulence is defined as the movements with space and time scales to short to be described directly.

Difusive flux per unit of area

bllld ucc

lclcc lll

lcul bd

.

xc

dx

Along direction “x”:

Cx

Cx+∆x

Horizontal diffusivity in a hydrodynamic model

• Hydrodynamic models consider velocity as being uniform along the all grid cell. In fact it is not and consequently there is a velocity part not resolved by the advective transport. That part has to be accounted by diffusion. Diffusivity is proportional to the grid size and to the non-resolved velocity.

Initial and Boundary conditions • The system exchanges material with the neighbouring

areas and consequently after some time interior values do not depend on the initial conditions.

• Initial conditions can be any. The warming time decreases with its realism.

• In case of momentum there is dissipation and thus the warming time is even shorter.

• Boundary conditions have to be known, unless transformation processes have the time to modify the properties between the boundary and the region we want to study.

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