This document outlines the course for Ocean Modelling. It begins with definitions of models, including physical, schematic, and mathematical models. It discusses how mathematical models work by representing real-world phenomena using equations and allowing analysis, predictions, and insights. Examples are provided of common mathematical models. Ocean models are introduced as representations of physical ocean processes using equations. The importance of ocean models is that they allow studying the ocean at higher resolutions than observations alone. Components of ocean models can include physical, chemical, biological, atmospheric and other factors. Different types of ocean models are distinguished by their scales, dimensions, topics modeled, and whether they are coupled or not. Observation data is also emphasized as important for validating and improving ocean models.

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Dr. Subrata Sarker
Department of Oceanography
Shahjalal University of Science and
Technology
Email: subratasrk-ocg@sust.edu
Ocean Modelling
General Concept of Modelling

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Course Outline
 General concept of modelling
 Introduction to ocean modelling
 Ocean modelling techniques
 Examples of ocean models
 Development of statistical and
ecological models
 Case studies
 Introduction to R, MATLAB and Delf3D
 Group research project on ocean model,
statistical model and ecological model

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What is a Model?
 Building representations of things in the ‘real world’ and allowing ideas to be
investigated
Models are:
a means of understanding the problems involved in building something
an aid to communication between those involved in the project, especially
between the requirements analyst and the user, as part of some deliverable
a component of the methods used in development activities
A model is an abstraction, which allows people to concentrate on the
essentials of a (complex) problem by keeping out non-essential details.

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What is a Model?
 Physical models
 It is a constructed copy of the modeled object
 Example: Model airplane, model solar system,
humanoid robot, building, bridge
 Application in thermodynamics, fluid dynamics,
aeronautics, architecture

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What is a Model?
 Schematic models
 Schematic model provide means of
visualizing system structure
 Organization charts
 Process charts
 Graphs
 Geographical map
 Diagram
 The visual information provided by GPS

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What is a Model?
 Mathematical models
 Mathematical model is a representation of the behaviour of real objects and
phenomena in mathematical language
 Algebraic equations
 Differential equations
 Integral equaitons
 Algorithms
 Formulas
 Theorems
https://www.ndtv.com/

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Why Mathematical Model is Important?
 Technical, ecological, economic and other systems investigated by modern
science cannot be studied adequately using regular theoretical methods
 Direct experiment is:
 Time-consuming
 Expensive
 Often even dangerous
 Sometimes impossible
Think of a real situation where it is dangerous
to perform direct experiment without prior
testing (through computer
Simulations/mathematical model)
Think about launching a satellite without prior
mathematical computations!!
https://weatherboy.com/

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How Does Mathematical Model Work?
 Mathematical modelling is a process that
uses the language of mathematics to:
 Analyze
 Make prediction
 Provide insight of real-world phenomena
 Find optimal solutions to real-world
challenges
https://courses.lumenlearning.com/

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How Does Mathematical Model Work?
 Mathematics on its own will not solve any
practical problem!!
 The main requirement of mathematics is
that it should be:
 Self consistent with its axioms, and
 It should lead by rigorous arguments, to
amazing theorems e.g. Pythagoras
Theorem which represent eternal truths
a
c
b

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How Does Mathematical Model Work?
To apply mathematics to the real world, mathematicians must work with scientist/engineers,
to run real life problems into mathematics, and to then use mathematics, to solve the
resulting equations

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Examples of Mathematical Model
We know three measurements:
l (length),
w (width), and
h (height), l
w
h
The formula for the volume of the cuboid is:
Volume = l × w × h

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The cardboard is "t" thick, and all measurements are outside the box
... …….
How much space is inside?
The inside measurements need to be reduced
by the thickness of each side:
The inside length is l-2t
The inside width is w-2t,
The inside height is h-2t
and now the formula is:
Inside Volume = (l-2t) × (w-2t) × (h-2t)
Examples of Mathematical Model

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Examples of Mathematical Model
An ice cream company keeps track of how many ice creams get sold on different days
 By comparing this to the weather on each day
they can make a mathematical model of sales
versus weather
 They can then predict future sales based on
the weather forecast, and decide how many
ice creams they need to make ... ahead of
time!

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Examples of Mathematical Model
A better example: A simple climate model
T = average Earth temperature
S(t) = Solar radiation
A = Earth’s albedo
E = Average atmospheric
emissivity
Balance energy from the sun with energy lost from the Earth to give:
Allows simple predictions of the change of temperature with Carbon Dioxide and ice
melt
https://earthscience.stackexchange.com/

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Remember Before Performing Mathematical Models!!!!
Model: A simplification to a small system equations which capture its essential essence
and are simple enough to make analytical calculations
Everthing should be as simple as possible, And no SIMPLER!
A. Einstein
https://energywavetheory.com/

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Remember Before Performing Mathematical Models!!!!
One shoe does not fit all !!!
https://en.wikiversity.org/

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Pitfalls of Mathematical Model
All Models are Wrong, But Some of Them are Useful
George Box, 1976

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Pitfalls of Mathematical Model
Don’t eat the menu

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Pitfalls of Mathematical Model
The Mathematical Drunkard
https://www.scottdmiller.com/

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Pitfalls of Mathematical Model
The Ivory Tower
Nature will throw out mighty
problems, but they will never
reach the mathematician.
He may sit in his ivory tower
waiting for the enemy with an
arsenal of guns, but the enemy will
never come to him. Nature does
not offer her problems ready
formulated. They must be dug up
with pick and shovel, and he who
will not soil his hand will never see
them.

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What is Ocean Model?

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What is Ocean Model?
It is a representation, in the form of equations/computer code, describing physical
processes of our understanding of how the ocean works
https://stephengriffies.github.io/

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What is Ocean Model?
 Ocean movement/dynamics, including
horizontal and vertical advection
 Exchange of energy between the ocean
and external sources (radiation,
precipitation, evaporation, river-runoff,
wind, etc.)
 3D mixing and dissipation processes
https://ceoas.oregonstate.edu/

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What is Ocean Model?
 Zoo of the physical ocean process
McMohn et al., 2021
Sommer et al., 2018

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What is Ocean Model?
 Zoo of the physical ocean process
McMohn et al., 2021
Horn et al., 2021

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Why Model the Ocean?
 Making full ocean observations cost
money
 1 day cruise of RV Polarstern costs
about 100000 EUROS
 Satellite launching is also expensive

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 Ocean Models are comparatively less expensive
 Higher spatial/temporal resolution compared to other methods:
 Satellites provide only surface data, and
 In-situ measurement are limited in spatial coverage
 Ability to forecast (e.g. SST, SSH, SSS, etc.)
Why Model the Ocean?
 Understanding the 3D
dynamics of the ocean on a
GLOBAL scale
MacKinnon et al, 2017

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Why Model the Ocean?

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Why Model the Ocean?

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Why Model the Ocean?

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Why Model the Ocean?

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Observation is Important for Ocean Modelling
Observational data is important for Ocean Model Validation

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Observation is Important for Ocean Modelling
Observational data helps to reduce the error and improve the model outputs
Liblik and Lips, 2019
Jakacki and Meler, 2019

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Components of Ocean Model
Ocean is an essential part of our climate system
https://www.globalchange.gov/
Christodoulaki et al., 2016

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Components of Ocean Model
Scanu et al, 2013
 Physical components
 Chemical components
 Biological components
 Geological components
 Atmospheric components
 Anthropogenic components

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Types of Model in Oceanography
https://medium.com/
Models can be simple to complex
Simple statistical
model
Complex fluid
model

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Types of Model in Oceanography
Models can be small scale to large scale
 Global Ocean Model
 Regional Ocean Model

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Types of Model in Oceanography
Models can be Two Dimensional to Three Dimensional
https://tos.org/

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Types of Model in Oceanography
Models can be physical, chemical, biological, atmospheric, geological and coupled
https://incois.gov.in/documents/Wave_forecasting_system_Sandhya.pdf

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https://onlinelibrary.wiley.com/doi/full/10.1111/j.1365-2486.2010.02364.x
Types of Model in Oceanography
Models can be physical, chemical, biological, atmospheric, geological and coupled

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Types of Model in Oceanography
Models can be physical, chemical, biological, atmospheric, geological and coupled
Sarker et al., 2018

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Types of Model in Oceanography
Models can be physical, chemical, biological, atmospheric, geological and coupled
https://www.frontiersin.org/articles/10.3389/fmars.2021.567266/full

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 Definition of model
 Types of model
 Mathematical model
 Working process of mathematical models
 Examples of mathematical models
 Keep in mind before Modelling
 Pitfall of mathematical modelling
 Ocean model
 Importance of ocean model
 Importance of observation in ocean modelling
 Components of ocean models
 Types of model in oceanography
What Have We Learnt?

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Thank You
Department of Oceanography
Shahjalal University of Science and
Technology