2. creating your coastal model - island wakeswakes.uma.pt/cimar/partiii_lecture2.pdf · { {several...

$: 2. Creating your coastal model - Island Wakeswakes.uma.pt/cimar/PartIII_lecture2.pdf · { {Several courses: z2006, Lisbon; z2007, Lisbon; z2008, Sarigerme (Turkey); {Free code. Coastal$
2. Creating your coastal model

Ângela Canas (MARETEC, IST)

Coastal ModellingDoctoral School in Marine & Environmental

Sciences - 2009

Contents

2.1. Definition of scope2.2. Definition of processes2.3. Definition of space/time scale2.4. Choice of modelling tool2.5. Modelling techniques2.6. Data requirements2.7. Model calibration2.8. Model validation2.9. Data assimilation


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2.1. Definition of scope

Your model is what you make of it!

Model application

Model application


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Clearly state the objective:Which is the modelling area?What are the problems to be investigated?What is the desired outcome of model?

Justified recommendations;Quantitative relationships between variables;Schemes/charts;Etc.;

What are the intended results of model?Interest properties;Maximum/ minimum/ average, distribution.

Model application


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Objectives should not be changed in research… unless resources are exhausted:

Time;Computers;Data loss.


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Example:Calculate the average time needed for sediment aggregates of size 400 μm to be transported in Nazare Canyon from 50m shelf depth to 5000m abyssal plain.

D83 Hermes Project, 2007


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2.2. Definition of processes

Elements of model:

Equations

Numerical algorithm

Computer code

Defined according to processes to be modeled!


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Important physical processes in Portuguese Coast:

Tide;Internal tides;Wind;Storms; Rivers;


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Tide:Tidal wave progresses around amphidromic points:

South to North in Portuguese Coast;

Important South to North residual current (0.02m/s) is created;

Nível normalizado (0-1)

N

Módulo velocidade (m/s)

NEstremadura Plateau

Tide only simulation


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Shallow water tides:High-frequency (6h or less) tides in shallow waters:

Shelf;Estuaries;

Caused by non linear terms in motion equations:

Bottom friction;Advection; Bathymetry: dark blue = 20m, bright red = 5000m


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Tide changes from South to North:

Semi diurnal amplitude increases;

Center

North

South

semi diurnal diurnal

quatradiurnal


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Tide changes within estuaries:

Tagus Estuary case;

measurements

Ocean Tagus river


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Internal tides:Tide flux interacts with bathymetry (e.g. canyons) in presence of stratification causing tide energy trapping:

Isotherms oscillate;Local turbulence and mixing is enhanced;

Affects sediment transport along shelf and shelf slope.


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Wind:Blowing persistently from North/NorthWest (Summer) in presence of stratification causes upwelling events;Characteristic of oriental margin of Atlantic/Pacific;Very relevant for biologic productivity;


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Storms:Extratropical storms (Lozano et al., 2004):

From southwest NorthAtlantic;Winter;Last for some days (4-5);3 storms per year;Extreme storm every 7 years (Andrade et al., 2008).

North Atlantic Oscillation (NAO) Sea level pressure gradient (Keim et al., 2004)


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Storm surge:Significant elevation of water level relative to tide (Gill, 1982);Can be produced in storms by:

Wind;Atmospheric pressure (Portuguese Coast, Fanjul et al., 1998);

Expressed by inverted barometer formulation:p refζ =-0.000101*(P-P )

Level change (m) due to atmospheric pressure

Reference pressure (101330Pa)


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Detided level changes in Tagus Estuary:


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Storm surge affects estuaries (Andrade et al., 2004; Valdemoro et al., 2007):

Hydrodynamics:Severe circulation change;

Water quality:Increased turbidity;Sediment transport;

Biology:Exposure of wetlands to coastal processes.

Tagus Estuary case:Main limiting factor for biologic productivity is turbidity (INAG, 2002).


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Rivers:Very important in estuaries and Regions of Fresh Water Influence (ROFI);Flow influences flushing time:

Time for measurable volume of water to be replaced by river water, ocean water or precipitation;


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Mondego Estuary case:

Influence of river flow (winter/summer situation) in residence time: Winter

Summer

Average estuary volume = 3.0x107 m3

WinterDaily volume change by tide (neap) =

7.5x106 m3;Daily volume change by river = 4.8x106 m3;

Residence time = 1 day.

SummerDaily volume change by tide (neap) =

7.5x106 m3;Daily volume change by river = 2592 m3;

Residence time = 10 days.

Average estuary volume = 2.9x107 m3


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Different relative importance (Martins, 1999):

Coast:Horizontal density gradients;Coriolis effect;Wind (surface);Tide (shelf);

Estuaries:Tide;Rivers;Wind (small).


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2.3. Definition of space/time scale

Space:Extension of domain:

All relevant processes should be modelled or íntroduced through boundary;

Resolution:Should be smaller than scale of processes.

Tagus Estuary case:


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2.3. Definition of space/time scale

Time:Resolution:

Should be smaller or equal than half the dominant period of signal to be simulated (Nyquist rule);Connected to spatial resolution in numerical discretizations according with the Courant number:

If Cr too high models with explicit discretizations become unstable.

UΔt/Δx = Courant number (<1 if 1D)

2. Creating your coastal model

Ângela Canas (MARETEC, IST)


Sciences - 2009

Contents

2.1. Definition of scope2.2. Definition of processes2.3. Definition of space/time scale2.4. Choice of modelling tool2.5. Modelling techniques2.6. Data requirements2.7. Model calibration2.8. Model validation2.9. Data assimilation


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2.4. Choice of modelling tool

No need to invent the wheel!

“If I have seen further it is only by standing on the shoulders of Giants.”Isaac Newton


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Equations

Numerical algorithm

Computer code


Able to meet modelling objective;Able to be used as Decision Support Tool;


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Decision Support Tool model:Able to produce results that describe a reference situation:

e.g. characterization of ecosystem in a reference year prior to instalation of water sewage system;

Able to produce results that describe hypothetical scenarios:

e.g. several locations and configurations for sewage system and wide range of natural conditions and ecological stress;sensitivity analysis;comparison between each scenario and reference situation.

illustrates solution’s impact on environment


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Decision Support Tool model:

One or more models;Results must be available in time for decisions;Typically used by non-specialists in numerical methods:

Pre and post process with GUI (Graphical User Interface).

GUI

Equations

Numerical algorithm

Computer code

Mod

el

GUI


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Help on using model:Documentation:

Websites;Wiki websites;

Support software:Pre/post processing;Format conversion;

From others: Forums;Courses;

Your own: free codes!

MOHID Water case:www.mohid.com;www.mohid.com/wiki;www.mohid.com/forum;Several courses:

2006, Lisbon;2007, Lisbon;2008, Sarigerme (Turkey);

Free code.


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Why freely available code is useful?Possible to identify model running error sources;Possible to compile model executables:

Latest model version in volatile codes;Adequate memory amount reserved;

Introduce changes in the code through programming.


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2.5. Modelling techniques

Downscalling;Nesting;Boundary conditions;Vertical resolution;Initialization;Lagrangean tracers.


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Downscalling:Transpose a model result to a smaller scale using another model (e.g. global to regional);

Scale connected with:Spatial horizontal resolution:

• Coarse solution considered in open boundary;• Detailed model with higher resolution;

Processes.


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Operational Model for the Portuguese Coast case:

TemperatureSalinityVelocity

Tide

Mer

cato

r Oce

an(w

ww

.mer

cato

r-oc

ean.

fr)

8km 6km


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Nesting:Same rationale as downscalling;Connection between scales is processed within same model;High resolution only where needed;Imposed constraints:

Boundary bathymetry should be concurrent;Spatial resolution increased maximum by factor of 3.

Tagus Estuary case:2km

300m


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Mondego Estuary case:

2D model too strong sensibility to wind forcing;Nest in Portuguese Coast Model domain!


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Boundary conditions:Open;Moving.


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Open boundary conditions:

Arise because of need to confine domain to study area;Variables values introduced so that:

Info of what happens outside is guaranteed to enter domain;Waves (process or noise) generated inside the domain should be allowed to go out.

Nível normalizado (0-1)

N


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Open boundary conditions types:Dirichelet:

Variable values are imposed in boundary;Newmann:

Gradient of variables is imposed in boundary;E.g. null gradient;

Radiation:Boundary values depend on internal model variability.

axP=

∂∂

aP =


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Open boundary condition:Perfect condition does not exist;Most suitable condition depends on:

Domain;Processes.


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Open boundary condition:

Hydrodynamic (water level):

Blumberg and Kantha (1985):

Flather (1976):

Water properties:Dirichelet (nested domain);Null gradient.

( ) ( )ηηηη−=∇+

∂∂

extd

E Tnc

t1.rr

( )( )ncqq Eextextrr .ηη −=−

Tide

Nes

ted

dom

ain

flow levelcelerity of waves


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Moving boundaries:

Immersion/ submersion areas in estuaries;Reproduction of intertidal areas.

Tagus Estuary case:

Velocity modulus (m/s)

Leitão (2003)


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Vertical resolution:Sigma coordinates:

Where bathymetry is important (e.g. estuaries);

Cartesian coordinates:Where density gradients are important;

Important rule:Layers should be oriented according with dominant flow.

sigma

cartesian


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Vertical resolution:If inadequate model simulations may break;

Attention to density gradients between layers!


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Initialization:Initial conditions are probably not best system representation:

First guesses which need to be evolved to best model solution;May be unstable and cause model disruption;

Approaches:Gradual connection of forces:

• Tide (slowstart e.g. for some days);• Baroclinic forces;

Spin up: time for model to recover from initial conditions.


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Lagrangean tracers:Model follows moving elements;Useful to simulate localized processes with sharp gradients:

Submarine outfalls pollution;Sediment transport and erosion; Oil dispersion.

Garcia (2008)


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Lagrangean tracers:Tracer:

Most important property is position (x, y, z);Other properties:

• Volume;• Others (each with a

concentration, e.g. Water properties, coliform bacteria).

Representation of:

( ),tt t

dx u x tdt

=

Water massSediment particle / Group of

particlesMolecule / Group of

moleculesPhytoplankton cell

Shark


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Lagrangean tracers:Adquate for flushing time calculation;Mondego Estuary case:

Winter


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Lagrangean tracers:Mondego Estuary case:

Winter: 1 day Summer: 10 days

Braunschweig et al. (2003)


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2.6. Data requirements

Initial conditions;Boundary conditions;Bathymetry.

Model


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Initial conditions:Schematic:

Null velocities;Constant value (water level, properties);

Solution from measurement interpolation;Past solution from model;Solution from other models (e.g. from a coarser scale);Solution of data assimilation (objective analysis) of measurements in a first guess solution.


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Boundary conditions:Open:

Larger scale models: e.g. FES 95, MERCATOR, HYCOM (http://hycom.rsmas.miami.edu/hycom-model/index.html);Climatologies: e.g. Levitus (1982) Climatological atlas for the World Ocean (new version http://ingrid.ldeo.columbia.edu/SOURCES/.LEVITUS94/);Schematic;

Surface:Meteorological models;Reanalysis: ERA40 (http://www.ecmwf.int/research/era/do/get/era-40), NCEP (http://www.ncep.noaa.gov/);Climatologies: e.g. Hellerman and Rosenstein (1983);Schematic.


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Mondego Estuary case:Model provided currents not strong enough so that nutrients are reallistically expelled from domain;Schematic land-sea breeze provided the adequate current magnitude for the nutrients not artificially accumulate in domain.


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Boundary conditions:

Rivers:Measurements: case of Operational System for Tagus Estuary;River basin model results.


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Boundary conditions:Bathymetry:

Bathymetric surveys;International sources:

• ETOPO (http://www.ngdc.noaa.gov/mgg/fliers/01mgg04.html);

• GEBCO (http://www.bodc.ac.uk/data/online_delivery/gebco/).


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2.7. Model calibration

Objective:Tune the model so that differences between model solution and measurements are reduced;Parameters:

Wind friction factor;Bottom friction factor;Boundary conditions;Bathymetry.


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2.8. Model validation

Quantitative:Statistical techniques:

Descriptive statistics:

• Average;• Standard

deviation (variability);

• Extremes: maximum, minimum;

Error statistics.


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2.8. Model validation

Qualitative:Literature review;Known physics;Statistical techniques:

Harmonic analysis;Spectral analysis;EOF analysis:

• Decomposition of variability in modes.


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2.9. Data assimilation

Models are not perfect nor measurement networks: why not take only the best from each one?


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2.9. Data assimilation

Basic concepts;Approximations;Methods for coastal areas:

Variational assimilation;Sequential assimilation;

Implementation constraints/costs.


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ReferencesAndrade, C., M. Freitas, J. Moreno and S. Craveiro, 2004, “Stratigraphical evidence of Late Holocene barrier breaching and extreme storms in lagoonal sediments of Ria Formosa, Algarve, Portugal”, Marine Geology, 210, pp. 339-362.Andrade, C., R. Trigo, M. Freitas, M. Gallego, P. Borges and A. Ramos, 2008, “Comparing historic records of storm frequency and theNorth Atlantic Oscillation (NAO) chronology for the Azores region”, Holocene, 18 (5), pp. 745-754.Braunschweig, F., F. Martins, P. Chambel and R. Neves, 2003, “A methodology to estimate renewal time scales in estuaries: the TagusEstuary case”, Ocean Dynamics, 53, pp. 137-145.Canas, A., 2008, Modelling and Data Assimilation Techniques for Operational Hydrodynamic Forecast in Tagus Estuary, Tese de doutoramento provisória, Instituto Superior Técnico, Universidade Técnica de Lisboa.Fanjul, E., B. Gomez, J. Carretero and I. Arevalo, 1998, “Tide and surge dynamics along the Iberian Atlantic coast”, Oceanologica Acta,21(2), pp. 131-143.Garcia, A., 2008, Tese de doutoramento, Instituto Superior Técnico, Universidade Técnica de Lisboa.Gill, A., 1982, Atmosphere-Ocean Dynamics, San Diego, California: Academic Press, International Geophysics Series, 662 p.Hellerman, S. and M. Rosenstein, 1983, “Normal monthly wind stress over the world ocean with error estimates”, Journal of Physical Oceanography, 13, pp. 1093-1104.INAG (Instituto da Água) / MARETEC, 2002, Water Quality in Portuguese Estuaries: Tejo, Sado and Mondego, Lisbon.Keim, B.; Muller, R., and Stone, G., 2004, “Spatial and temporal variability of coastal storms in the North Atlantic Basin”, Marine Geology,210, pp. 7-15.Leitão, P., 2003, Integração de Escalas e de processos na Modelação do Ambiente Marinho, Ph.D. thesis, Instituto Superior Técnico,Universidade Técnica de Lisboa, Lisboa.Levitus B., 1982, Climatological atlas for the World Ocean, NOAA Prog. Papers 13, US Government Printing Office, Washington DC.Lozano, I.; Devoy, R.; May, W., and Andersen, U., 2004, “Storminess and vulnerability along the Atlantic coastlines of Europe: analysis ofstorm records and of a greenhouse gases induced climate scenario”, Marine Geology, 210, 205-225.Martins, F., 1999. Modelação Matemática Tridimensional de Escoamentos Costeiros e Estuarinos usando uma Abordagem deCoordenada Vertical Genérica. Ph.D. Thesis, Instituto Superior Técnico, Universidade Técnica de Lisboa, Lisboa.Valdemoro, H.; Sánchez-Arcilla, A., and Jiménez, J., 2007, “Coastal dynamics and wetland stability. The Ebro delta case”, Hydrobiologia,577, pp. 17-29.

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